%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP213_3 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:24:10 EDT 2024

% Result   : Theorem 25.65s 7.70s
% Output   : Refutation 26.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1515
% Syntax   : Number of formulae    : 2022 ( 495 unt;1010 typ;   0 def)
%            Number of atoms       : 2248 ( 865 equ;   0 cnn)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives : 14053 ( 245   ~;  22   |; 324   &;12505   @)
%                                         ( 109 <=>; 848  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Number of types       :  931 ( 930 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   83 (  80 usr;  36 con; 0-4 aty)
%            Number of variables   : 2549 (   0   ^2481   !;  68   ?;2549   :)

% Comments : 
%------------------------------------------------------------------------------
thf(fun_Pr3358449090565925198_nat_o_type,type,
    fun_Pr3358449090565925198_nat_o: $tType ).

thf(fun_fu4927615759029954091_nat_o_type,type,
    fun_fu4927615759029954091_nat_o: $tType ).

thf(fun_fu3932451362284101085et_nat_type,type,
    fun_fu3932451362284101085et_nat: $tType ).

thf(fun_Pr3978243888342905947et_nat_type,type,
    fun_Pr3978243888342905947et_nat: $tType ).

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

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

thf(fun_fu4695829907076200203_int_o_type,type,
    fun_fu4695829907076200203_int_o: $tType ).

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

thf(fun_fu9160953773549289085nt_int_type,type,
    fun_fu9160953773549289085nt_int: $tType ).

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

thf(fun_fu7582738562687708775_nat_o_type,type,
    fun_fu7582738562687708775_nat_o: $tType ).

thf(fun_fu2265384587115734689et_nat_type,type,
    fun_fu2265384587115734689et_nat: $tType ).

thf(fun_op4346303324771211497at_nat_type,type,
    fun_op4346303324771211497at_nat: $tType ).

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

thf(fun_fu1754067819247394666at_nat_type,type,
    fun_fu1754067819247394666at_nat: $tType ).

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

thf(fun_se8464659365716347869at_nat_type,type,
    fun_se8464659365716347869at_nat: $tType ).

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

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

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

thf(fun_Pr6341106346053136302_nat_o_type,type,
    fun_Pr6341106346053136302_nat_o: $tType ).

thf(option5899113203645146382et_nat_type,type,
    option5899113203645146382et_nat: $tType ).

thf(set_Pr4040394263813967220et_nat_type,type,
    set_Pr4040394263813967220et_nat: $tType ).

thf(fun_Pr1227177680593602867_nat_o_type,type,
    fun_Pr1227177680593602867_nat_o: $tType ).

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

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

thf(fun_Pr886604116968709228_int_o_type,type,
    fun_Pr886604116968709228_int_o: $tType ).

thf(produc4193628355235574503at_nat_type,type,
    produc4193628355235574503at_nat: $tType ).

thf(fun_fu6286765928754279603_int_o_type,type,
    fun_fu6286765928754279603_int_o: $tType ).

thf(fun_se5750412846314922030_nat_o_type,type,
    fun_se5750412846314922030_nat_o: $tType ).

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

thf(fun_fu1905361174868762994et_nat_type,type,
    fun_fu1905361174868762994et_nat: $tType ).

thf(produc3112576180687729086et_nat_type,type,
    produc3112576180687729086et_nat: $tType ).

thf(fun_fu2611741329380808165_nat_o_type,type,
    fun_fu2611741329380808165_nat_o: $tType ).

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

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

thf(fun_se3981709065971081742_nat_o_type,type,
    fun_se3981709065971081742_nat_o: $tType ).

thf(fun_Pr782666833218042862_nat_o_type,type,
    fun_Pr782666833218042862_nat_o: $tType ).

thf(fun_fu714798943701216869_nat_o_type,type,
    fun_fu714798943701216869_nat_o: $tType ).

thf(fun_fu465145433024125141nt_int_type,type,
    fun_fu465145433024125141nt_int: $tType ).

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

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

thf(fun_Pr4885567672785483807et_nat_type,type,
    fun_Pr4885567672785483807et_nat: $tType ).

thf(fun_se5672428230568430382_nat_o_type,type,
    fun_se5672428230568430382_nat_o: $tType ).

thf(fun_Pr8463018485500633518_nat_o_type,type,
    fun_Pr8463018485500633518_nat_o: $tType ).

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

thf(fun_se5282722391638144526_nat_o_type,type,
    fun_se5282722391638144526_nat_o: $tType ).

thf(fun_fu1322491050725084261_nat_o_type,type,
    fun_fu1322491050725084261_nat_o: $tType ).

thf(fun_op1633239139951409690_nat_o_type,type,
    fun_op1633239139951409690_nat_o: $tType ).

thf(fun_Pr4781553364444837327nt_int_type,type,
    fun_Pr4781553364444837327nt_int: $tType ).

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

thf(fun_op636363337204153321_nat_o_type,type,
    fun_op636363337204153321_nat_o: $tType ).

thf(fun_op2843162390950497001_nat_o_type,type,
    fun_op2843162390950497001_nat_o: $tType ).

thf(produc9140211490168418807atural_type,type,
    produc9140211490168418807atural: $tType ).

thf(produc2453742332425399446nteger_type,type,
    produc2453742332425399446nteger: $tType ).

thf(fun_se8505878878902388681at_nat_type,type,
    fun_se8505878878902388681at_nat: $tType ).

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

thf(fun_op5061235789045561272_nat_o_type,type,
    fun_op5061235789045561272_nat_o: $tType ).

thf(fun_fu1046317085317675843at_nat_type,type,
    fun_fu1046317085317675843at_nat: $tType ).

thf(fun_se2896342228535362350_nat_o_type,type,
    fun_se2896342228535362350_nat_o: $tType ).

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

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

thf(option1544258867535432659nt_int_type,type,
    option1544258867535432659nt_int: $tType ).

thf(fun_Pr8346683996641107384_nat_o_type,type,
    fun_Pr8346683996641107384_nat_o: $tType ).

thf(fun_se6131316820643522691at_nat_type,type,
    fun_se6131316820643522691at_nat: $tType ).

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

thf(fun_se2369204539228100110_nat_o_type,type,
    fun_se2369204539228100110_nat_o: $tType ).

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

thf(fun_fu2988548197490738277_nat_o_type,type,
    fun_fu2988548197490738277_nat_o: $tType ).

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

thf(set_Pr6700895561065273913nt_int_type,type,
    set_Pr6700895561065273913nt_int: $tType ).

thf(fun_Pr3540825087398332590_int_o_type,type,
    fun_Pr3540825087398332590_int_o: $tType ).

thf(fun_fu4253467608928286509nt_int_type,type,
    fun_fu4253467608928286509nt_int: $tType ).

thf(produc3043004577601930755nt_int_type,type,
    produc3043004577601930755nt_int: $tType ).

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

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

thf(fun_fu6865642474282033866_int_o_type,type,
    fun_fu6865642474282033866_int_o: $tType ).

thf(option4955102875562834416et_nat_type,type,
    option4955102875562834416et_nat: $tType ).

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

thf(fun_fu4836394952439539509_nat_o_type,type,
    fun_fu4836394952439539509_nat_o: $tType ).

thf(set_Pr1312406793078187350et_nat_type,type,
    set_Pr1312406793078187350et_nat: $tType ).

thf(fun_Pr2620521676128474833_nat_o_type,type,
    fun_Pr2620521676128474833_nat_o: $tType ).

thf(fun_fu4934440599869564003_set_o_type,type,
    fun_fu4934440599869564003_set_o: $tType ).

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

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

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

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

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

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

thf(fun_fu2352890940381120596et_nat_type,type,
    fun_fu2352890940381120596et_nat: $tType ).

thf(fun_Pr8696298990344678139nt_int_type,type,
    fun_Pr8696298990344678139nt_int: $tType ).

thf(produc8799533983703829792et_nat_type,type,
    produc8799533983703829792et_nat: $tType ).

thf(fun_fu8419763957888848259_nat_o_type,type,
    fun_fu8419763957888848259_nat_o: $tType ).

thf(fun_fu3373238862511017284_nat_o_type,type,
    fun_fu3373238862511017284_nat_o: $tType ).

thf(fun_fu5323616038969315652_int_o_type,type,
    fun_fu5323616038969315652_int_o: $tType ).

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

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

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

thf(fun_fu2847332191311216467_nat_o_type,type,
    fun_fu2847332191311216467_nat_o: $tType ).

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

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

thf(fun_fu6048389457699795770at_nat_type,type,
    fun_fu6048389457699795770at_nat: $tType ).

thf(fun_fu7573985428940033010nt_nat_type,type,
    fun_fu7573985428940033010nt_nat: $tType ).

thf(produc7476732711998919211atural_type,type,
    produc7476732711998919211atural: $tType ).

thf(produc7509114972854644512nteger_type,type,
    produc7509114972854644512nteger: $tType ).

thf(fun_Pr7920380315054183110_nat_o_type,type,
    fun_Pr7920380315054183110_nat_o: $tType ).

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

thf(fun_fu5458086908000294626et_nat_type,type,
    fun_fu5458086908000294626et_nat: $tType ).

thf(fun_fu6384561554008368101_nat_o_type,type,
    fun_fu6384561554008368101_nat_o: $tType ).

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

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

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

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

thf(fun_op6018817604785332104_num_o_type,type,
    fun_op6018817604785332104_num_o: $tType ).

thf(fun_op298641349230941576_nat_o_type,type,
    fun_op298641349230941576_nat_o: $tType ).

thf(fun_Pr285225112257423215e_term_type,type,
    fun_Pr285225112257423215e_term: $tType ).

thf(fun_Pr5098669352780829690e_term_type,type,
    fun_Pr5098669352780829690e_term: $tType ).

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

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

thf(produc6576344331059438605e_term_type,type,
    produc6576344331059438605e_term: $tType ).

thf(option6186025235080601855nt_int_type,type,
    option6186025235080601855nt_int: $tType ).

thf(fun_fu9079770784915425324et_nat_type,type,
    fun_fu9079770784915425324et_nat: $tType ).

thf(fun_fu4266222366127506568et_int_type,type,
    fun_fu4266222366127506568et_int: $tType ).

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

thf(fun_fu2790023284655001759nteger_type,type,
    fun_fu2790023284655001759nteger: $tType ).

thf(set_Pr4166680992137330533nt_int_type,type,
    set_Pr4166680992137330533nt_int: $tType ).

thf(fun_Pr1196100989263358594_int_o_type,type,
    fun_Pr1196100989263358594_int_o: $tType ).

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

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

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

thf(fun_fu4618385802829667198_set_o_type,type,
    fun_fu4618385802829667198_set_o: $tType ).

thf(fun_se2185695799324892244_nat_o_type,type,
    fun_se2185695799324892244_nat_o: $tType ).

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

thf(fun_Pr7763680713840462443e_term_type,type,
    fun_Pr7763680713840462443e_term: $tType ).

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

thf(fun_fu792289584686185660er_nat_type,type,
    fun_fu792289584686185660er_nat: $tType ).

thf(fun_fu4176442768802536380er_nat_type,type,
    fun_fu4176442768802536380er_nat: $tType ).

thf(fun_fu202463024092729020er_int_type,type,
    fun_fu202463024092729020er_int: $tType ).

thf(fun_fu8759299743271765508er_int_type,type,
    fun_fu8759299743271765508er_int: $tType ).

thf(fun_op8016730479996091735_num_o_type,type,
    fun_op8016730479996091735_num_o: $tType ).

thf(fun_op7041624247167716439_nat_o_type,type,
    fun_op7041624247167716439_nat_o: $tType ).

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

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

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

thf(fun_na8407688532849143408at_nat_type,type,
    fun_na8407688532849143408at_nat: $tType ).

thf(fun_fu5631754973857388633nt_int_type,type,
    fun_fu5631754973857388633nt_int: $tType ).

thf(produc4788131091073775919nt_int_type,type,
    produc4788131091073775919nt_int: $tType ).

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

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

thf(fun_fu2978539155105838238_int_o_type,type,
    fun_fu2978539155105838238_int_o: $tType ).

thf(fun_Pr1099658227000185396_nat_o_type,type,
    fun_Pr1099658227000185396_nat_o: $tType ).

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

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

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

thf(fun_se7788542033685991124_nat_o_type,type,
    fun_se7788542033685991124_nat_o: $tType ).

thf(fun_fu8336550301028287791at_nat_type,type,
    fun_fu8336550301028287791at_nat: $tType ).

thf(fun_fu1095011443884336175at_nat_type,type,
    fun_fu1095011443884336175at_nat: $tType ).

thf(fun_fu4854240044958656303at_int_type,type,
    fun_fu4854240044958656303at_int: $tType ).

thf(fun_fu1493779525457017043nt_int_type,type,
    fun_fu1493779525457017043nt_int: $tType ).

thf(fun_fu4083202260958266008eger_o_type,type,
    fun_fu4083202260958266008eger_o: $tType ).

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

thf(fun_Pr3592279944642289454ural_o_type,type,
    fun_Pr3592279944642289454ural_o: $tType ).

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

thf(fun_a_8304141829328133171at_nat_type,type,
    fun_a_8304141829328133171at_nat: $tType ).

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

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

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

thf(set_op239864471688321678it_nat_type,type,
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thf(fun_op479301348043730329_nat_o_type,type,
    fun_op479301348043730329_nat_o: $tType ).

thf(produc4166570645942440679at_nat_type,type,
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thf(fun_Pr2477239776880934807at_nat_type,type,
    fun_Pr2477239776880934807at_nat: $tType ).

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

thf(fun_mu7838234450475261998_nat_o_type,type,
    fun_mu7838234450475261998_nat_o: $tType ).

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

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

thf(fun_Pr3059359313727237556_nat_o_type,type,
    fun_Pr3059359313727237556_nat_o: $tType ).

thf(fun_fu4735791719682850818eger_o_type,type,
    fun_fu4735791719682850818eger_o: $tType ).

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

thf(fun_fu9217243180581622273at_nat_type,type,
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thf(fun_Pr5876161306168176259nteger_type,type,
    fun_Pr5876161306168176259nteger: $tType ).

thf(fun_fu4638078822479986034_int_o_type,type,
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thf(fun_fu4306744791715064858_rat_o_type,type,
    fun_fu4306744791715064858_rat_o: $tType ).

thf(fun_fu6699046866436802030_int_o_type,type,
    fun_fu6699046866436802030_int_o: $tType ).

thf(fun_Pr4340503698666692462at_nat_type,type,
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thf(fun_na5926011011515597590it_nat_type,type,
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thf(fun_fu3253069483457113587at_nat_type,type,
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thf(fun_fu108291945127110899et_nat_type,type,
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thf(fun_fu6327154928193479288nteger_type,type,
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thf(fun_fu3890538715107687308nteger_type,type,
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thf(fun_fu8767785434844327952er_rat_type,type,
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thf(fun_fu2498091903632033272er_nat_type,type,
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thf(fun_fu1007793439646807308er_int_type,type,
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thf(fun_Pr367382672041210069at_nat_type,type,
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thf(option2158460348403737357at_nat_type,type,
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thf(fun_fu8958601512183576259eger_o_type,type,
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thf(option8956607266484857688it_nat_type,type,
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thf(fun_se5244420045238757833at_nat_type,type,
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thf(fun_fu717549361983437348nt_int_type,type,
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thf(fun_fu918106826131887214nt_int_type,type,
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thf(fun_mu2328110650637990531at_nat_type,type,
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thf(set_op4617111635268443007it_nat_type,type,
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thf(fun_a_5925824989894720534et_nat_type,type,
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thf(fun_op9133723461703387112_nat_o_type,type,
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thf(produc3843707927480180839at_nat_type,type,
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thf(fun_se5908002238701803220_nat_o_type,type,
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thf(set_Pr1354866905816374718it_nat_type,type,
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thf(fun_fu4073184632390761289at_nat_type,type,
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thf(fun_fu9148247276982919825at_nat_type,type,
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thf(fun_fu3143578834292514029nt_nat_type,type,
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thf(fun_fu4584101141160326545at_int_type,type,
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thf(fun_fu7802804735324696557nt_int_type,type,
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thf(fun_fu3180206027003385489at_nat_type,type,
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thf(fun_fu6398909621167755501nt_nat_type,type,
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thf(fun_fu7141499545569947298eger_o_type,type,
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thf(fun_Pr8032424337255632745_nat_o_type,type,
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thf(set_Pr457366540195662369at_nat_type,type,
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thf(fun_fu3064074204415222357nt_int_type,type,
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thf(fun_fu7732904369943091395at_nat_type,type,
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thf(fun_fu1098312133097393581at_rat_type,type,
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thf(fun_fu8843022549979047619nt_nat_type,type,
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thf(fun_Pr557098546508347797at_nat_type,type,
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thf(fun_na1668100129766719005at_nat_type,type,
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thf(fun_se5639961202347202350_nat_o_type,type,
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thf(fun_fu9045186299510176150at_o_o_type,type,
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thf(fun_Co2470855966376689427nteger_type,type,
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thf(fun_fu4592178885959468770_int_o_type,type,
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thf(fun_fu8427683764667544036nt_int_type,type,
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thf(fun_Pr8586684092290301266at_rat_type,type,
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thf(fun_Pr2871540613828922186at_nat_type,type,
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thf(fun_Pr7917061631174501286at_int_type,type,
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thf(fun_na3202795955365919216at_nat_type,type,
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thf(fun_in5957238474111007380at_nat_type,type,
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thf(fun_fu2612476005019691883er_nat_type,type,
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thf(fun_fu6248970101513325091er_int_type,type,
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thf(fun_fu2840411409734105307er_int_type,type,
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thf(fun_fu4917398172150038123at_nat_type,type,
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thf(fun_fu3117156669030583587at_int_type,type,
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thf(fun_fu548297510352026403at_int_type,type,
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thf(fun_fu6780308020184860635nt_int_type,type,
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thf(fun_as3747249873083764768_nat_o_type,type,
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thf(fun_fu7237799034916548881_nat_o_type,type,
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thf(fun_fu7601549123499533073_int_o_type,type,
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thf(fun_Pr4403862266400233414at_nat_type,type,
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thf(option3562590408128118217it_nat_type,type,
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thf(fun_a_8173838432492502368et_nat_type,type,
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thf(fun_a_3360290013704583612et_int_type,type,
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thf(set_Pr8693737435421807431at_nat_type,type,
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thf(fun_fu3959123160307459545t_assn_type,type,
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thf(fun_fu5832215286117076717t_assn_type,type,
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thf(fun_Pr363642936170290612_nat_o_type,type,
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thf(fun_Pr435983442313151109et_nat_type,type,
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thf(produc8664842809031399944it_nat_type,type,
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thf(fun_fu8532066432991188095_nat_o_type,type,
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thf(fun_fu63825462011493995_int_o_type,type,
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thf(produc732395585841259969at_nat_type,type,
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thf(fun_se320340636488258563at_nat_type,type,
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thf(list_P6935614879863011209it_nat_type,type,
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thf(fun_fu4640364191220304065at_nat_type,type,
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thf(fun_fu4422690180167752641at_nat_type,type,
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thf(fun_fu1432006813369012345at_int_type,type,
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thf(fun_fu8188496484073410517nt_int_type,type,
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thf(fun_se374060482380105870_nat_o_type,type,
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thf(fun_se4767462807232413326_int_o_type,type,
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thf(set_Pr1932065953672099015od_o_o_type,type,
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thf(fun_fu3275390434952296369_nat_o_type,type,
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thf(fun_fu3068557634114553409_int_o_type,type,
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thf(fun_op386870758422531628et_nat_type,type,
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thf(set_Pr7098220151150636591it_nat_type,type,
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thf(fun_fu5207212825597307859nt_int_type,type,
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thf(fun_Pr5746006151868627512_nat_o_type,type,
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thf(produc6197004810343482825et_nat_type,type,
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thf(fun_a_6228866161775505738_set_o_type,type,
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thf(fun_fu5510336631606277565nteger_type,type,
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thf(fun_fu1763652423599918571nteger_type,type,
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thf(fun_fu6385016345819965645er_nat_type,type,
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thf(fun_fu8693872822272901183eger_o_type,type,
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thf(fun_Pr5633121574208248783_set_o_type,type,
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thf(fun_fu7601192970096278275eger_o_type,type,
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thf(fun_fu165634461008800387_nat_o_type,type,
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thf(fun_fu5813846785102284803eger_o_type,type,
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thf(fun_fu7864316720324808067_int_o_type,type,
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thf(fun_fu6309186030181755779eger_o_type,type,
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thf(fun_fu8096999557949053699_nat_o_type,type,
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thf(fun_fu7527167023631164035eger_o_type,type,
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thf(fun_fu354264921998911491_int_o_type,type,
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thf(fun_na8713714802964096592at_nat_type,type,
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thf(produc5835291356934675326atural_type,type,
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thf(fun_fu4618758991028193283_o_nat_type,type,
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thf(fun_fu5572043292636673283_o_nat_type,type,
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thf(fun_fu731591423980087811_o_int_type,type,
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thf(fun_fu5188028542856013059_o_int_type,type,
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thf(fun_fu7677565902479959693_rat_o_type,type,
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thf(fun_Co6386927884524458043e_term_type,type,
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thf(fun_Co3544761417380347684eger_o_type,type,
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thf(fun_Co3460408610320954864e_term_type,type,
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thf(fun_a_5416464254913058730at_nat_type,type,
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thf(produc859450856879609959at_nat_type,type,
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thf(fun_Pr4335030045194121423et_nat_type,type,
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thf(fun_Pr1844946900262394667et_int_type,type,
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thf(fun_a_1313742400928293293it_nat_type,type,
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thf(fun_fu3109912920687205353_nat_o_type,type,
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thf(fun_fu607692679349591509_int_o_type,type,
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thf(option936205604648967762et_nat_type,type,
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thf(fun_fu8391177546919232046_nat_o_type,type,
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thf(fun_fu7503566767892366382_int_o_type,type,
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thf(fun_Pr4799464687642144302_num_o_type,type,
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thf(fun_Pr2028404973800837934_nat_o_type,type,
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thf(fun_Pr9018117161326028078_int_o_type,type,
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thf(produc2934264451710624999od_o_o_type,type,
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thf(produc3260487557148687353it_nat_type,type,
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thf(set_Pr7577011563204128103nteger_type,type,
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thf(fun_se4014881416909572940_nat_o_type,type,
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thf(fun_se5614109888078709212_int_o_type,type,
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thf(fun_Pr494705684233454228eger_o_type,type,
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thf(fun_Co1741750543637222241nteger_type,type,
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thf(fun_Co968421022063998397nteger_type,type,
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thf(fun_fu7409062071265970153_int_o_type,type,
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thf(fun_fu1345883967705819239_int_o_type,type,
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thf(fun_se7651465595257595690_nat_o_type,type,
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thf(fun_a_2467521563176467050_nat_o_type,type,
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thf(fun_fu6579618355643354601at_rat_type,type,
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thf(fun_fu5935951186182374353at_nat_type,type,
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thf(fun_fu2944589659160432777nt_nat_type,type,
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thf(fun_fu7170425908843507849at_int_type,type,
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thf(fun_fu5979305884941020809nt_nat_type,type,
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thf(fun_fu960360787657196261at_int_type,type,
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thf(fun_fu4179064381821566273nt_int_type,type,
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thf(fun_fu6092417073193843705nt_int_type,type,
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thf(fun_fu1617438229336688381nt_rat_type,type,
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thf(fun_fu973771059875708133nt_nat_type,type,
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thf(fun_fu8212914225227247425at_int_type,type,
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thf(fun_fu5221552698205305849nt_int_type,type,
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thf(fun_fu5082522747898945281r_assn_type,type,
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thf(fun_fu1095064002760310426er_nat_type,type,
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thf(fun_fu8277437853836697484_nat_o_type,type,
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thf(fun_fu8854380836519874772_int_o_type,type,
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thf(fun_fu513762604956806682er_nat_type,type,
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thf(fun_fu3779984648686517950er_nat_type,type,
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thf(fun_fu1289901503754791194er_int_type,type,
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thf(fun_fu5459709170960931212eger_o_type,type,
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thf(fun_fu1028834580611891924eger_o_type,type,
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thf(fun_Pr6460944699146269935_nat_o_type,type,
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thf(fun_Pr8691148245588442629_set_o_type,type,
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thf(fun_fu2987389051837124479on_num_type,type,
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thf(fun_fu1574286537503582443on_num_type,type,
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thf(fun_fu5285309056923805367un_o_o_type,type,
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thf(fun_fu5848294987682527897eger_o_type,type,
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thf(fun_fu5257111247350578329un_o_o_type,type,
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thf(fun_fu5820097178109300859eger_o_type,type,
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thf(fun_fu8716660765737269145un_o_o_type,type,
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thf(fun_fu7460908759652350970nt_rat_type,type,
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thf(fun_na4143055713577223196at_nat_type,type,
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thf(fun_Co6597186368970283863nteger_type,type,
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thf(fun_in5730379987311621695e_term_type,type,
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thf(fun_Co2498591179490635159nteger_type,type,
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thf(fun_fu9090758901314268781nt_o_o_type,type,
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thf(fun_fu2454420574033104442at_nat_type,type,
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thf(fun_fu3739269683040691718nt_int_type,type,
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thf(fun_se5087743179055239239nteger_type,type,
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thf(fun_Pr4343998633453697049at_nat_type,type,
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thf(fun_fu1806770557662746761_nat_o_type,type,
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thf(fun_fu6075382464776002713_nat_o_type,type,
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thf(fun_fu1481857817119020493_int_o_type,type,
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thf(fun_fu6453395667394816515nt_int_type,type,
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thf(fun_fu7714913403879666293_int_o_type,type,
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thf(fun_fu855086506144988854eger_o_type,type,
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thf(fun_fu2729256655946442782nteger_type,type,
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thf(fun_fu2439999276549649860er_nat_type,type,
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thf(fun_Pr2118491707810114563at_nat_type,type,
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thf(fun_Pr2478283820680522243nt_int_type,type,
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thf(option233860712434008220it_nat_type,type,
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thf(produc6491284506569428743nteger_type,type,
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thf(fun_na5914473681949881652_nat_o_type,type,
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thf(list_P131111800688179804it_nat_type,type,
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thf(fun_fu1590586450949517859at_nat_type,type,
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thf(fun_fu945287533868614691et_nat_type,type,
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thf(fun_fu2499394402704830801nteger_type,type,
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thf(fun_fu3628599891403802633nteger_type,type,
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thf(fun_fu722387130092441185er_rat_type,type,
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thf(fun_na8856381646659805649nteger_type,type,
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thf(fun_Co5080488584548667985nteger_type,type,
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thf(produc3658429121746597890et_nat_type,type,
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thf(fun_fu1076126395241477261at_nat_type,type,
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thf(fun_fu1730513324920958169_nat_o_type,type,
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thf(fun_fu716243638958221197nt_nat_type,type,
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thf(fun_fu1985264055766458053_int_o_type,type,
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thf(fun_fu6473686551640679437at_nat_type,type,
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thf(fun_fu3983603406708952681at_int_type,type,
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thf(fun_fu5979819066169710441nt_int_type,type,
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thf(fun_fu4844139638962010283eger_o_type,type,
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thf(fun_fu1898041513128675305r_assn_type,type,
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thf(fun_se5529282185252607396eger_o_type,type,
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thf(fun_Pr7971309923680890661_nat_o_type,type,
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thf(fun_fu6436183194761443139_nat_o_type,type,
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thf(fun_fu5646853623633916995_int_o_type,type,
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thf(fun_fu8304507701009772099_nat_o_type,type,
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thf(fun_fu7493154764834273859_int_o_type,type,
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thf(fun_fu927436805355353155_nat_o_type,type,
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thf(fun_fu138107234227827011_int_o_type,type,
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thf(fun_fu167450956818022195at_nat_type,type,
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thf(fun_fu7590581490553343467at_int_type,type,
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thf(fun_fu4065359935906217011at_int_type,type,
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thf(fun_fu1073998408884275435nt_int_type,type,
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thf(fun_fu5861359551626625881un_o_o_type,type,
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thf(fun_fu4472246792138249213_nat_o_type,type,
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thf(fun_Pr27309308411849096et_nat_type,type,
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thf(fun_na4518284863240432007_nat_o_type,type,
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thf(fun_fu7075445697382584196_int_o_type,type,
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thf(fun_fu923337204662071120nt_int_type,type,
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thf(fun_se1909708154429037836et_nat_type,type,
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thf(fun_se6573205548028396576et_int_type,type,
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thf(fun_se6140325459843756218er_nat_type,type,
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thf(fun_ra8505079968215247908at_rat_type,type,
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thf(fun_Co8514937155073724839atural_type,type,
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thf(fun_Co1981900195452921617nteger_type,type,
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thf(fun_fu1237770272497958833_nat_o_type,type,
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thf(fun_fu4523568072766896123eger_o_type,type,
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thf(fun_fu2182969643484777475eger_o_type,type,
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thf(fun_fu1992263728252513447eger_o_type,type,
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thf(fun_fu991479512444375705er_rat_type,type,
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thf(fun_fu7371465849922053265er_nat_type,type,
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thf(fun_fu4881382704990326509er_int_type,type,
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thf(fun_fu152868422178311599um_num_type,type,
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thf(fun_fu1947565687807238081um_int_type,type,
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thf(fun_fu4719417816141531311on_num_type,type,
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thf(fun_fu7964671872712412353on_num_type,type,
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thf(fun_fu1502755112258691281at_nat_type,type,
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thf(fun_fu5130958774822480081on_num_type,type,
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thf(fun_se8285385046356996962_nat_o_type,type,
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thf(fun_se6300720826873464854un_o_o_type,type,
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thf(fun_se2032030289318007650_nat_o_type,type,
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thf(fun_se2103980781540968966_int_o_type,type,
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thf(fun_se7515062963244431458_int_o_type,type,
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thf(fun_op3323321805596408808on_num_type,type,
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thf(fun_op7680796716376270858on_nat_type,type,
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thf(fun_se1865396762483378772_nat_o_type,type,
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thf(fun_na4138050610385705875at_nat_type,type,
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thf(fun_in1696471567231710611nt_int_type,type,
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thf(set_Pr5488025237498180813et_nat_type,type,
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thf(set_Pr2522554150109002629et_int_type,type,
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thf(fun_fu1994797156054922755_nat_o_type,type,
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thf(fun_ra1107035566227760819at_rat_type,type,
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thf(fun_Pr3947133745332865710_nat_o_type,type,
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thf(fun_Pr4126283446944868854_int_o_type,type,
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thf(fun_na6244580715232974919at_nat_type,type,
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thf(fun_na34515594046663331at_nat_type,type,
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thf(fun_in2640216123419753727at_int_type,type,
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thf(fun_in5653523039088217947at_int_type,type,
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thf(fun_Co1766037875893669450eger_o_type,type,
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thf(option6357759511663192854e_term_type,type,
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thf(fun_fu4367955990186087364er_nat_type,type,
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thf(fun_fu2995346897264222311t_assn_type,type,
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thf(fun_fu6568868615275847455t_assn_type,type,
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thf(fun_fu9042756939175893756at_int_type,type,
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thf(fun_fu2006306477014139736nt_int_type,type,
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thf(fun_fu7066070072329265113un_o_o_type,type,
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thf(fun_fu2641566564518291801un_o_o_type,type,
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thf(fun_fu5915781709770235737un_o_o_type,type,
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thf(fun_he4135464443191253079_nat_o_type,type,
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thf(fun_Pr3513738403344720850et_nat_type,type,
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thf(fun_op493924057549976310_num_o_type,type,
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thf(fun_fu3819205551299168222un_o_o_type,type,
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thf(fun_fu7181763470137098718nteger_type,type,
    fun_fu7181763470137098718nteger: $tType ).

thf(list_P6011104703257516679at_nat_type,type,
    list_P6011104703257516679at_nat: $tType ).

thf(list_P3521021558325789923at_int_type,type,
    list_P3521021558325789923at_int: $tType ).

thf(list_P8198026277950538467nt_nat_type,type,
    list_P8198026277950538467nt_nat: $tType ).

thf(list_P5707943133018811711nt_int_type,type,
    list_P5707943133018811711nt_int: $tType ).

thf(fun_fu4625457934454704336_o_nat_type,type,
    fun_fu4625457934454704336_o_nat: $tType ).

thf(fun_fu7138923643431704310un_o_o_type,type,
    fun_fu7138923643431704310un_o_o: $tType ).

thf(fun_fu1426755399112167834un_o_o_type,type,
    fun_fu1426755399112167834un_o_o: $tType ).

thf(fun_he8413527710729349838unit_o_type,type,
    fun_he8413527710729349838unit_o: $tType ).

thf(set_Pr1261947904930325089at_nat_type,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(set_Pr958786334691620121nt_int_type,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(fun_Pr6331313853612757382_num_o_type,type,
    fun_Pr6331313853612757382_num_o: $tType ).

thf(fun_Pr4796943543331071514_nat_o_type,type,
    fun_Pr4796943543331071514_nat_o: $tType ).

thf(fun_Pr3238374608701176162_int_o_type,type,
    fun_Pr3238374608701176162_int_o: $tType ).

thf(fun_o_8988054265482332260nt_int_type,type,
    fun_o_8988054265482332260nt_int: $tType ).

thf(fun_na7234455742697417626_nat_o_type,type,
    fun_na7234455742697417626_nat_o: $tType ).

thf(fun_li105789395169216470at_rat_type,type,
    fun_li105789395169216470at_rat: $tType ).

thf(fun_set_nat_set_nat_type,type,
    fun_set_nat_set_nat: $tType ).

thf(fun_se7586849273513198688nteger_type,type,
    fun_se7586849273513198688nteger: $tType ).

thf(fun_set_int_set_int_type,type,
    fun_set_int_set_int: $tType ).

thf(fun_Co3734316457315071362atural_type,type,
    fun_Co3734316457315071362atural: $tType ).

thf(fun_Co8499238673658658103nteger_type,type,
    fun_Co8499238673658658103nteger: $tType ).

thf(fun_se382663106265794036_nat_o_type,type,
    fun_se382663106265794036_nat_o: $tType ).

thf(fun_se867122708194164540_int_o_type,type,
    fun_se867122708194164540_int_o: $tType ).

thf(fun_na8563630686737515764_nat_o_type,type,
    fun_na8563630686737515764_nat_o: $tType ).

thf(fun_na8635581178960477080_int_o_type,type,
    fun_na8635581178960477080_int_o: $tType ).

thf(fun_na6318815019539281885eger_o_type,type,
    fun_na6318815019539281885eger_o: $tType ).

thf(fun_in4891666191172872833eger_o_type,type,
    fun_in4891666191172872833eger_o: $tType ).

thf(fun_Co196715998180962002_nat_o_type,type,
    fun_Co196715998180962002_nat_o: $tType ).

thf(fun_Co7174943067365291894_int_o_type,type,
    fun_Co7174943067365291894_int_o: $tType ).

thf(fun_Co1375048237525739357_nat_o_type,type,
    fun_Co1375048237525739357_nat_o: $tType ).

thf(fun_Co8353275306710069249_int_o_type,type,
    fun_Co8353275306710069249_int_o: $tType ).

thf(fun_assn_fun_assn_o_type,type,
    fun_assn_fun_assn_o: $tType ).

thf(fun_fu4001317426178549763_nat_o_type,type,
    fun_fu4001317426178549763_nat_o: $tType ).

thf(fun_fu1756172458508103847_int_o_type,type,
    fun_fu1756172458508103847_int_o: $tType ).

thf(fun_fu6128684156180612191_nat_o_type,type,
    fun_fu6128684156180612191_nat_o: $tType ).

thf(fun_fu3883539188510166275_int_o_type,type,
    fun_fu3883539188510166275_int_o: $tType ).

thf(fun_fu1989461620956114563_o_rat_type,type,
    fun_fu1989461620956114563_o_rat: $tType ).

thf(fun_fu6701067901881939075_o_nat_type,type,
    fun_fu6701067901881939075_o_nat: $tType ).

thf(fun_fu6940589326549028739_o_int_type,type,
    fun_fu6940589326549028739_o_int: $tType ).

thf(fun_set_o_fun_o_assn_type,type,
    fun_set_o_fun_o_assn: $tType ).

thf(fun_fu3143923321121214633un_o_o_type,type,
    fun_fu3143923321121214633un_o_o: $tType ).

thf(fun_fu7714003655882793385o_assn_type,type,
    fun_fu7714003655882793385o_assn: $tType ).

thf(fun_se5038631536132265326et_o_o_type,type,
    fun_se5038631536132265326et_o_o: $tType ).

thf(list_P7333126701944960589_nat_o_type,type,
    list_P7333126701944960589_nat_o: $tType ).

thf(list_P5087981734274514673_int_o_type,type,
    list_P5087981734274514673_int_o: $tType ).

thf(list_P6285523579766656935_o_nat_type,type,
    list_P6285523579766656935_o_nat: $tType ).

thf(list_P3795440434834930179_o_int_type,type,
    list_P3795440434834930179_o_int: $tType ).

thf(fun_Pr2191293291710260995t_unit_type,type,
    fun_Pr2191293291710260995t_unit: $tType ).

thf(set_set_list_nat_type,type,
    set_set_list_nat: $tType ).

thf(produc6271795597528267376eger_o_type,type,
    produc6271795597528267376eger_o: $tType ).

thf(fun_set_list_nat_o_type,type,
    fun_set_list_nat_o: $tType ).

thf(fun_rat_fun_rat_rat_type,type,
    fun_rat_fun_rat_rat: $tType ).

thf(fun_rat_fun_nat_rat_type,type,
    fun_rat_fun_nat_rat: $tType ).

thf(fun_num_fun_num_num_type,type,
    fun_num_fun_num_num: $tType ).

thf(fun_num_fun_num_int_type,type,
    fun_num_fun_num_int: $tType ).

thf(fun_nat_fun_rat_rat_type,type,
    fun_nat_fun_rat_rat: $tType ).

thf(fun_nat_fun_nat_rat_type,type,
    fun_nat_fun_nat_rat: $tType ).

thf(fun_nat_fun_nat_nat_type,type,
    fun_nat_fun_nat_nat: $tType ).

thf(fun_nat_fun_nat_int_type,type,
    fun_nat_fun_nat_int: $tType ).

thf(fun_nat_fun_int_nat_type,type,
    fun_nat_fun_int_nat: $tType ).

thf(fun_nat_fun_int_int_type,type,
    fun_nat_fun_int_int: $tType ).

thf(fun_int_fun_nat_nat_type,type,
    fun_int_fun_nat_nat: $tType ).

thf(fun_int_fun_nat_int_type,type,
    fun_int_fun_nat_int: $tType ).

thf(fun_int_fun_int_rat_type,type,
    fun_int_fun_int_rat: $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(set_set_set_nat_type,type,
    set_set_set_nat: $tType ).

thf(set_set_Code_integer_type,type,
    set_set_Code_integer: $tType ).

thf(heap_T5738788834812785303t_unit_type,type,
    heap_T5738788834812785303t_unit: $tType ).

thf(fun_set_set_nat_o_type,type,
    fun_set_set_nat_o: $tType ).

thf(fun_se7289222521248229150eger_o_type,type,
    fun_se7289222521248229150eger_o: $tType ).

thf(fun_set_o_fun_o_rat_type,type,
    fun_set_o_fun_o_rat: $tType ).

thf(fun_set_o_fun_o_nat_type,type,
    fun_set_o_fun_o_nat: $tType ).

thf(fun_set_o_fun_o_int_type,type,
    fun_set_o_fun_o_int: $tType ).

thf(fun_option_num_num_type,type,
    fun_option_num_num: $tType ).

thf(fun_option_num_nat_type,type,
    fun_option_num_nat: $tType ).

thf(fun_option_num_int_type,type,
    fun_option_num_int: $tType ).

thf(fun_num_option_num_type,type,
    fun_num_option_num: $tType ).

thf(fun_nat_option_num_type,type,
    fun_nat_option_num: $tType ).

thf(fun_nat_option_nat_type,type,
    fun_nat_option_nat: $tType ).

thf(fun_int_option_num_type,type,
    fun_int_option_num: $tType ).

thf(fun_int_option_int_type,type,
    fun_int_option_int: $tType ).

thf(fun_Co480733329897759773un_o_o_type,type,
    fun_Co480733329897759773un_o_o: $tType ).

thf(fun_o_4021313873839786239eger_o_type,type,
    fun_o_4021313873839786239eger_o: $tType ).

thf(fun_a_6093291656547882009Heap_a_type,type,
    fun_a_6093291656547882009Heap_a: $tType ).

thf(fun_fu1330587012114714103un_o_o_type,type,
    fun_fu1330587012114714103un_o_o: $tType ).

thf(fun_fu7670380996171670171un_o_o_type,type,
    fun_fu7670380996171670171un_o_o: $tType ).

thf(fun_fu6337961365400742745un_o_o_type,type,
    fun_fu6337961365400742745un_o_o: $tType ).

thf(fun_fu6781074197733401937un_o_o_type,type,
    fun_fu6781074197733401937un_o_o: $tType ).

thf(fun_fu7756609662939579309un_o_o_type,type,
    fun_fu7756609662939579309un_o_o: $tType ).

thf(fun_fu8257668495121851639_nat_o_type,type,
    fun_fu8257668495121851639_nat_o: $tType ).

thf(fun_fu6012523527451405723_int_o_type,type,
    fun_fu6012523527451405723_int_o: $tType ).

thf(fun_fu830079035465870425_o_rat_type,type,
    fun_fu830079035465870425_o_rat: $tType ).

thf(fun_fu7210065372943547985_o_nat_type,type,
    fun_fu7210065372943547985_o_nat: $tType ).

thf(fun_Pr6626665806141890376t_assn_type,type,
    fun_Pr6626665806141890376t_assn: $tType ).

thf(heap_e7401611519738050253t_unit_type,type,
    heap_e7401611519738050253t_unit: $tType ).

thf(product_prod_num_num_type,type,
    product_prod_num_num: $tType ).

thf(product_prod_nat_num_type,type,
    product_prod_nat_num: $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(list_P4002435161011370285od_o_o_type,type,
    list_P4002435161011370285od_o_o: $tType ).

thf(fun_nat_list_nat_type,type,
    fun_nat_list_nat: $tType ).

thf(fun_list_nat_rat_type,type,
    fun_list_nat_rat: $tType ).

thf(fun_list_nat_nat_type,type,
    fun_list_nat_nat: $tType ).

thf(fun_list_nat_int_type,type,
    fun_list_nat_int: $tType ).

thf(set_Product_prod_o_o_type,type,
    set_Product_prod_o_o: $tType ).

thf(fun_set_nat_rat_type,type,
    fun_set_nat_rat: $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_num_Code_natural_type,type,
    fun_num_Code_natural: $tType ).

thf(fun_num_Code_integer_type,type,
    fun_num_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_Code_natural_type,type,
    fun_int_Code_natural: $tType ).

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

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

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

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

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

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

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

thf(fun_fun_rat_rat_o_type,type,
    fun_fun_rat_rat_o: $tType ).

thf(fun_fun_int_int_o_type,type,
    fun_fun_int_int_o: $tType ).

thf(fun_rat_fun_rat_o_type,type,
    fun_rat_fun_rat_o: $tType ).

thf(fun_num_fun_num_o_type,type,
    fun_num_fun_num_o: $tType ).

thf(fun_nat_fun_nat_o_type,type,
    fun_nat_fun_nat_o: $tType ).

thf(fun_nat_fun_int_o_type,type,
    fun_nat_fun_int_o: $tType ).

thf(fun_nat_fun_o_nat_type,type,
    fun_nat_fun_o_nat: $tType ).

thf(fun_nat_fun_o_int_type,type,
    fun_nat_fun_o_int: $tType ).

thf(fun_int_fun_nat_o_type,type,
    fun_int_fun_nat_o: $tType ).

thf(fun_int_fun_int_o_type,type,
    fun_int_fun_int_o: $tType ).

thf(fun_int_fun_o_int_type,type,
    fun_int_fun_o_int: $tType ).

thf(fun_o_fun_nat_nat_type,type,
    fun_o_fun_nat_nat: $tType ).

thf(fun_o_fun_nat_int_type,type,
    fun_o_fun_nat_int: $tType ).

thf(fun_o_fun_int_int_type,type,
    fun_o_fun_int_int: $tType ).

thf(fun_set_o_set_o_type,type,
    fun_set_o_set_o: $tType ).

thf(set_option_num_type,type,
    set_option_num: $tType ).

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

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

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

thf(fun_set_o_fun_o_o_type,type,
    fun_set_o_fun_o_o: $tType ).

thf(fun_option_num_o_type,type,
    fun_option_num_o: $tType ).

thf(fun_o_option_num_type,type,
    fun_o_option_num: $tType ).

thf(fun_fun_o_o_fun_o_o_type,type,
    fun_fun_o_o_fun_o_o: $tType ).

thf(option_Product_unit_type,type,
    option_Product_unit: $tType ).

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

thf(product_prod_nat_o_type,type,
    product_prod_nat_o: $tType ).

thf(product_prod_int_o_type,type,
    product_prod_int_o: $tType ).

thf(product_prod_o_nat_type,type,
    product_prod_o_nat: $tType ).

thf(product_prod_o_int_type,type,
    product_prod_o_int: $tType ).

thf(fun_list_nat_o_type,type,
    fun_list_nat_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

thf(fun_set_nat_o_type,type,
    fun_set_nat_o: $tType ).

thf(fun_set_int_o_type,type,
    fun_set_int_o: $tType ).

thf(fun_Code_natural_o_type,type,
    fun_Code_natural_o: $tType ).

thf(fun_Code_integer_o_type,type,
    fun_Code_integer_o: $tType ).

thf(fun_o_set_nat_type,type,
    fun_o_set_nat: $tType ).

thf(fun_o_Code_integer_type,type,
    fun_o_Code_integer: $tType ).

thf(fun_nat_fun_o_o_type,type,
    fun_nat_fun_o_o: $tType ).

thf(fun_int_fun_o_o_type,type,
    fun_int_fun_o_o: $tType ).

thf(fun_o_fun_nat_o_type,type,
    fun_o_fun_nat_o: $tType ).

thf(fun_o_fun_int_o_type,type,
    fun_o_fun_int_o: $tType ).

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

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

thf(option_set_o_type,type,
    option_set_o: $tType ).

thf(fun_Product_unit_o_type,type,
    fun_Product_unit_o: $tType ).

thf(fun_o_Product_unit_type,type,
    fun_o_Product_unit: $tType ).

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

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

thf(set_list_o_type,type,
    set_list_o: $tType ).

thf(product_prod_o_o_type,type,
    product_prod_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(fun_list_o_o_type,type,
    fun_list_o_o: $tType ).

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

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

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

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

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

thf(fun_assn_o_type,type,
    fun_assn_o: $tType ).

thf(fun_o_assn_type,type,
    fun_o_assn: $tType ).

thf(fun_set_o_o_type,type,
    fun_set_o_o: $tType ).

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

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

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

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

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

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

thf(fun_o_fun_o_o_type,type,
    fun_o_fun_o_o: $tType ).

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

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

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

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

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

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

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

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

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

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

thf(fun_rat_o_type,type,
    fun_rat_o: $tType ).

thf(fun_num_o_type,type,
    fun_num_o: $tType ).

thf(fun_nat_o_type,type,
    fun_nat_o: $tType ).

thf(fun_int_o_type,type,
    fun_int_o: $tType ).

thf(fun_o_rat_type,type,
    fun_o_rat: $tType ).

thf(fun_o_nat_type,type,
    fun_o_nat: $tType ).

thf(fun_o_int_type,type,
    fun_o_int: $tType ).

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

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

thf(list_o_type,type,
    list_o: $tType ).

thf(fun_a_o_type,type,
    fun_a_o: $tType ).

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

thf(set_o_type,type,
    set_o: $tType ).

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

thf(aTP_Lamm_cz_type,type,
    aTP_Lamm_cz: fun_se2170385732985038782_nat_o ).

thf(aTP_Lamm_eg_type,type,
    aTP_Lamm_eg: assn > fun_assn_option_assn ).

thf(aTP_Lamm_eo_type,type,
    aTP_Lamm_eo: fun_Pr6460944699146269935_nat_o ).

thf(aTP_Lamm_ep_type,type,
    aTP_Lamm_ep: assn > fun_as3747249873083764768_nat_o ).

thf(aTP_Lamm_eq_type,type,
    aTP_Lamm_eq: assn > fun_as3747249873083764768_nat_o ).

thf(aTP_Lamm_fs_type,type,
    aTP_Lamm_fs: fun_assn_assn ).

thf(aTP_Lamm_gz_type,type,
    aTP_Lamm_gz: assn > fun_Pr6460944699146269935_nat_o ).

thf(aTP_Lamm_of_type,type,
    aTP_Lamm_of: fun_nat_assn > fun_na2454419004871237530n_assn ).

thf(abs_assn_type,type,
    abs_assn: fun_Pr6460944699146269935_nat_o > assn ).

thf(rep_assn_type,type,
    rep_assn: assn > fun_Pr6460944699146269935_nat_o ).

thf(in_range_type,type,
    in_range: fun_Pr6460944699146269935_nat_o ).

thf(one_assn_raw_type,type,
    one_assn_raw: fun_Pr6460944699146269935_nat_o ).

thf(one_assn_raw_rel_type,type,
    one_assn_raw_rel: fun_Pr7920380315054183110_nat_o ).

thf(pure_assn_type,type,
    pure_assn: fun_o_assn ).

thf(pure_a825153325127701367it_nat_type,type,
    pure_a825153325127701367it_nat: $o > fun_Pr6460944699146269935_nat_o ).

thf(relH_type,type,
    relH: set_nat > heap_e7401611519738050253t_unit > fun_he8413527710729349838unit_o ).

thf(times_assn_raw_type,type,
    times_assn_raw: fun_Pr6460944699146269935_nat_o > fun_fu8419763957888848259_nat_o ).

thf(wand_assn_type,type,
    wand_assn: fun_as3983628580203722482n_assn ).

thf(wand_raw_type,type,
    wand_raw: fun_Pr6460944699146269935_nat_o > fun_fu8419763957888848259_nat_o ).

thf(finite_finite_nat_type,type,
    finite_finite_nat: fun_set_nat_o ).

thf(minus_minus_assn_type,type,
    minus_minus_assn: fun_as3983628580203722482n_assn ).

thf(minus_minus_set_nat_type,type,
    minus_minus_set_nat: fun_se1909708154429037836et_nat ).

thf(one_one_assn_type,type,
    one_one_assn: assn ).

thf(times_times_assn_type,type,
    times_times_assn: fun_as3983628580203722482n_assn ).

thf(uminus_uminus_assn_type,type,
    uminus_uminus_assn: fun_assn_assn ).

thf(uminus5710092332889474511et_nat_type,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(groups6906906614972039071t_assn_type,type,
    groups6906906614972039071t_assn: fun_nat_assn > set_nat > assn ).

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

thf(heap_Time_success_a_type,type,
    heap_Time_success_a: heap_Time_Heap_a > fun_he8413527710729349838unit_o ).

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

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

thf(inf_inf_assn_type,type,
    inf_inf_assn: fun_as3983628580203722482n_assn ).

thf(inf_inf_option_assn_type,type,
    inf_inf_option_assn: option_assn > option_assn > option_assn ).

thf(inf_inf_set_nat_type,type,
    inf_inf_set_nat: fun_se1909708154429037836et_nat ).

thf(sup_sup_assn_type,type,
    sup_sup_assn: fun_as3983628580203722482n_assn ).

thf(sup_sup_set_nat_type,type,
    sup_sup_set_nat: fun_se1909708154429037836et_nat ).

thf(some_assn_type,type,
    some_assn: assn > option_assn ).

thf(bot_bot_assn_type,type,
    bot_bot_assn: assn ).

thf(bot_bot_set_nat_type,type,
    bot_bot_set_nat: set_nat ).

thf(ord_less_set_nat_type,type,
    ord_less_set_nat: fun_se2170385732985038782_nat_o ).

thf(ord_less_eq_set_nat_type,type,
    ord_less_eq_set_nat: fun_se2170385732985038782_nat_o ).

thf(ord_le5018287362838994063_nat_o_type,type,
    ord_le5018287362838994063_nat_o: fun_Pr6460944699146269935_nat_o > fun_Pr6460944699146269935_nat_o > $o ).

thf(ord_le5132100987546516070_nat_o_type,type,
    ord_le5132100987546516070_nat_o: fun_Pr7920380315054183110_nat_o > fun_Pr7920380315054183110_nat_o > $o ).

thf(top_top_assn_type,type,
    top_top_assn: assn ).

thf(power_power_assn_type,type,
    power_power_assn: assn > fun_nat_assn ).

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

thf(produc1824681642469235216et_nat_type,type,
    produc1824681642469235216et_nat: produc3658429121746597890et_nat > heap_e7401611519738050253t_unit ).

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

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

thf(image_nat_nat_type,type,
    image_nat_nat: fun_nat_nat > set_nat > set_nat ).

thf(is_empty_nat_type,type,
    is_empty_nat: fun_set_nat_o ).

thf(accp_P5801069581201407417et_nat_type,type,
    accp_P5801069581201407417et_nat: fun_Pr7920380315054183110_nat_o > fun_Pr6460944699146269935_nat_o ).

thf(aa_o_assn_type,type,
    aa_o_assn: fun_o_assn > $o > assn ).

thf(aa_assn_assn_type,type,
    aa_assn_assn: fun_assn_assn > assn > assn ).

thf(aa_assn_option_assn_type,type,
    aa_assn_option_assn: fun_assn_option_assn > assn > option_assn ).

thf(aa_ass954072293579886259n_assn_type,type,
    aa_ass954072293579886259n_assn: fun_as3983628580203722482n_assn > assn > fun_assn_assn ).

thf(aa_ass4243947775541419017_nat_o_type,type,
    aa_ass4243947775541419017_nat_o: fun_as3747249873083764768_nat_o > assn > fun_Pr6460944699146269935_nat_o ).

thf(aa_hea7994211679605476167unit_o_type,type,
    aa_hea7994211679605476167unit_o: fun_he8413527710729349838unit_o > heap_e7401611519738050253t_unit > $o ).

thf(aa_nat_o_type,type,
    aa_nat_o: fun_nat_o > nat > $o ).

thf(aa_nat_assn_type,type,
    aa_nat_assn: fun_nat_assn > nat > assn ).

thf(aa_nat_fun_assn_assn_type,type,
    aa_nat_fun_assn_assn: fun_na2454419004871237530n_assn > nat > fun_assn_assn ).

thf(aa_Pro653082453696054616_nat_o_type,type,
    aa_Pro653082453696054616_nat_o: fun_Pr6460944699146269935_nat_o > produc3658429121746597890et_nat > $o ).

thf(aa_Pro7278237734719282863_nat_o_type,type,
    aa_Pro7278237734719282863_nat_o: fun_Pr7920380315054183110_nat_o > produc3658429121746597890et_nat > fun_Pr6460944699146269935_nat_o ).

thf(aa_set_nat_o_type,type,
    aa_set_nat_o: fun_set_nat_o > set_nat > $o ).

thf(aa_set_nat_set_nat_type,type,
    aa_set_nat_set_nat: fun_set_nat_set_nat > set_nat > set_nat ).

thf(aa_set7861427066675100071_nat_o_type,type,
    aa_set7861427066675100071_nat_o: fun_se2170385732985038782_nat_o > set_nat > fun_set_nat_o ).

thf(aa_set2309701074089104077et_nat_type,type,
    aa_set2309701074089104077et_nat: fun_se1909708154429037836et_nat > set_nat > fun_set_nat_set_nat ).

thf(aa_fun2638059832795814268_nat_o_type,type,
    aa_fun2638059832795814268_nat_o: fun_fu8419763957888848259_nat_o > fun_Pr6460944699146269935_nat_o > fun_Pr6460944699146269935_nat_o ).

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

thf(member_nat_type,type,
    member_nat: nat > fun_set_nat_o ).

thf(p_type,type,
    p: assn ).

thf(q_type,type,
    q: fun_a_assn ).

thf(r_type,type,
    r: assn ).

thf(as1_type,type,
    as1: set_nat ).

thf(as2_type,type,
    as2: set_nat ).

thf(as_type,type,
    as: set_nat ).

thf(c_type,type,
    c: heap_Time_Heap_a ).

thf(h_type,type,
    h: heap_e7401611519738050253t_unit ).

thf(h2_type,type,
    h2: heap_e7401611519738050253t_unit ).

thf(r2_type,type,
    r2: a ).

thf(404,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_inf__left__idem) ).

thf(2163,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(470,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
        & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_mod__and__dist) ).

thf(2452,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(232,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_Un__empty__right) ).

thf(1469,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(170,axiom,
    ! [A: produc3658429121746597890et_nat,B: $o] :
      ( ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
      <=> B )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ C @ D ) )
             => ( ( B
                <=> ( D = bot_bot_set_nat ) )
               => ~ ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3462_one__assn__raw_Opelims_I1_J) ).

thf(1190,plain,
    ! [A: produc3658429121746597890et_nat,B: $o] :
      ( ( ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
         => B )
        & ( B
         => ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A ) ) )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ C @ D ) )
             => ( ( ( B
                   => ( D = bot_bot_set_nat ) )
                  & ( ( D = bot_bot_set_nat )
                   => B ) )
               => ~ ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(163,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_sup_Oright__idem) ).

thf(1168,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(390,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ B @ C ) )
             => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ B @ C ) )
               => ( C != bot_bot_set_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3461_one__assn__raw_Opelims_I2_J) ).

thf(2109,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ B @ C ) )
             => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ B @ C ) )
               => ( C != bot_bot_set_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(306,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_Int__assoc) ).

thf(1767,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(149,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_sup__inf__distrib1) ).

thf(1105,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(83,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2136_sup_Ostrict__coboundedI2) ).

thf(846,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(492,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_inf__sup__aci_I2_J) ).

thf(2559,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(66,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4793_DiffD2) ).

thf(777,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(41,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ! [D: set_nat] :
          ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
         => ( aa_set_nat_o @ C @ D ) )
    <=> ! [D: set_nat] :
          ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
         => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7802_all__subset__image) ).

thf(666,plain,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ( ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
           => ( aa_set_nat_o @ C @ D ) )
       => ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
           => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) )
      & ( ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
           => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) )
       => ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
           => ( aa_set_nat_o @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(414,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_inf__sup__aci_I3_J) ).

thf(2199,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(197,axiom,
    ! [A: assn,B: assn,C: nat] :
      ( ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
        = one_one_assn )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ ( aa_nat_assn @ ( power_power_assn @ B ) @ C ) )
        = one_one_assn ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3604_left__right__inverse__power) ).

thf(1322,plain,
    ! [A: assn,B: assn,C: nat] :
      ( ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
        = one_one_assn )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ ( aa_nat_assn @ ( power_power_assn @ B ) @ C ) )
        = one_one_assn ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(279,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_inf__commute) ).

thf(1665,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(360,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_Int__empty__right) ).

thf(1995,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(429,axiom,
    ! [A: assn,B: assn,C: nat] :
      ( ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ B )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3553_power__commuting__commutes) ).

thf(2263,plain,
    ! [A: assn,B: assn,C: nat] :
      ( ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ B )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(101,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_Un__assoc) ).

thf(909,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(30,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ? [C: nat] : ( aa_set_nat_o @ ( member_nat @ C ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4675_psubset__imp__ex__mem) ).

thf(628,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ? [C: nat] : ( aa_set_nat_o @ ( member_nat @ C ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(500,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C != bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2893_one__assn__raw_Oelims_I2_J) ).

thf(2595,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C != bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(478,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B )
     => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9251_mod__star__trueI) ).

thf(2499,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B )
     => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(382,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
    <=> ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
        | ~ ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7838_infinite__Un) ).

thf(2077,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ~ ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
          | ~ ( aa_set_nat_o @ finite_finite_nat @ B ) ) )
      & ( ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
          | ~ ( aa_set_nat_o @ finite_finite_nat @ B ) )
       => ~ ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(300,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_inf_OboundedI) ).

thf(1750,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(174,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_sup__bot_Oleft__neutral) ).

thf(1211,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(160,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_inf__right__idem) ).

thf(1158,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(416,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_ep @ A ) @ B ) @ C )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
        | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10137_ATP_Olambda__446) ).

thf(2210,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_ep @ A ) @ B ) @ C )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
       => ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_ep @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(54,axiom,
    ! [A: set_nat,B: fun_set_nat_o] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ! [C: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ C )
           => ( ! [D: set_nat] :
                  ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ D ) @ C )
                 => ( aa_set_nat_o @ B @ D ) )
             => ( aa_set_nat_o @ B @ C ) ) )
       => ( aa_set_nat_o @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7839_finite__psubset__induct) ).

thf(730,plain,
    ! [A: set_nat,B: fun_set_nat_o] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ! [C: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ C )
           => ( ! [D: set_nat] :
                  ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ D ) @ C )
                 => ( aa_set_nat_o @ B @ D ) )
             => ( aa_set_nat_o @ B @ C ) ) )
       => ( aa_set_nat_o @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(506,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_inf_Oright__idem) ).

thf(2622,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(449,axiom,
    ! [A: assn,B: assn] :
      ( ( ( rep_assn @ A )
        = ( rep_assn @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Rep__assn__inject) ).

thf(2381,plain,
    ! [A: assn,B: assn] :
      ( ( ( ( rep_assn @ A )
          = ( rep_assn @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( rep_assn @ A )
          = ( rep_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(124,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat,F: set_nat] :
          ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F ) )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ E ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ F ) ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_distrib__imp2) ).

thf(994,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat,F: set_nat] :
          ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F ) )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ E ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ F ) ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(294,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4833_boolean__algebra__class_Oboolean__algebra_Odouble__compl) ).

thf(1728,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(172,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_inf__sup__aci_I4_J) ).

thf(1205,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(156,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5315_disjoint__eq__subset__Compl) ).

thf(1142,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(39,axiom,
    ! [A: fun_nat_o] :
      ( ( ( collect_nat @ A )
        = bot_bot_set_nat )
    <=> ! [B: nat] :
          ~ ( aa_nat_o @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Collect__empty__eq) ).

thf(655,plain,
    ! [A: fun_nat_o] :
      ( ( ( ( collect_nat @ A )
          = bot_bot_set_nat )
       => ! [B: nat] :
            ~ ( aa_nat_o @ A @ B ) )
      & ( ! [B: nat] :
            ~ ( aa_nat_o @ A @ B )
       => ( ( collect_nat @ A )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(353,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2450_in__range__empty) ).

thf(1971,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(43,axiom,
    ! [A: fun_nat_o] :
      ( ( bot_bot_set_nat
        = ( collect_nat @ A ) )
    <=> ! [B: nat] :
          ~ ( aa_nat_o @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__Collect__eq) ).

thf(677,plain,
    ! [A: fun_nat_o] :
      ( ( ( bot_bot_set_nat
          = ( collect_nat @ A ) )
       => ! [B: nat] :
            ~ ( aa_nat_o @ A @ B ) )
      & ( ! [B: nat] :
            ~ ( aa_nat_o @ A @ B )
       => ( bot_bot_set_nat
          = ( collect_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(195,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
             => ( C != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_disjoint__iff__not__equal) ).

thf(1305,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ! [D: nat] :
                ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
               => ( C != D ) ) ) )
      & ( ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ! [D: nat] :
                ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
               => ( C != D ) ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(225,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5281_inf__shunt) ).

thf(1437,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(135,axiom,
    ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) ) @ as2 )
    = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_DJN) ).

thf(1041,plain,
    ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) ) @ as2 )
    = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(453,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ top_top_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9257_mod__h__bot__iff_I2_J) ).

thf(2395,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ top_top_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(378,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
        | ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Un__iff) ).

thf(2062,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          | ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          | ( aa_set_nat_o @ ( member_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(345,axiom,
    ( top_top_assn
    = ( abs_assn @ in_range ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9253_top__assn__def) ).

thf(1939,plain,
    ( top_top_assn
    = ( abs_assn @ in_range ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(427,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ A @ C )
        <=> ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
     => ( B
        = ( abs_assn @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2584_Abs__assn__eqI_I2_J) ).

thf(2248,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( ( aa_Pro653082453696054616_nat_o @ A @ C )
           => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
          & ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C )
           => ( aa_Pro653082453696054616_nat_o @ A @ C ) ) )
     => ( B
        = ( abs_assn @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(302,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2160_sup_Ostrict__boundedE) ).

thf(1756,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(469,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
          ( A
         != ( produc7507926704131184380et_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_one__assn__raw_Ocases) ).

thf(2448,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
          ( A
         != ( produc7507926704131184380et_nat @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(465,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_inf__left__idem) ).

thf(2434,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(178,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ is_empty_nat @ A )
    <=> ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2507_Set_Ois__empty__def) ).

thf(1233,plain,
    ! [A: set_nat] :
      ( ( ( aa_set_nat_o @ is_empty_nat @ A )
       => ( A = bot_bot_set_nat ) )
      & ( ( A = bot_bot_set_nat )
       => ( aa_set_nat_o @ is_empty_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(476,axiom,
    ! [A: $o,B: produc3658429121746597890et_nat,C: $o] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
      <=> C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( C
            <=> ~ ( ( E = bot_bot_set_nat )
                  & A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2642_pure__assn__raw_Oelims_I1_J) ).

thf(2476,plain,
    ! [A: $o,B: produc3658429121746597890et_nat,C: $o] :
      ( ( ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
         => C )
        & ( C
         => ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B ) ) )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( ( C
               => ~ ( ( E = bot_bot_set_nat )
                    & A ) )
              & ( ~ ( ( E = bot_bot_set_nat )
                    & A )
               => C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(338,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_IntD1) ).

thf(1919,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(58,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4771_Diff__idemp) ).

thf(747,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(273,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_sup_Oabsorb1) ).

thf(1640,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(111,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_inf_Oorder__iff) ).

thf(945,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( A
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) )
      & ( ( A
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(350,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_le__supI) ).

thf(1954,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(372,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_Int__subset__iff) ).

thf(2042,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(9,axiom,
    ! [A: fun_nat_nat] :
      ( ( image_nat_nat @ A @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5877_image__empty) ).

thf(538,plain,
    ! [A: fun_nat_nat] :
      ( ( image_nat_nat @ A @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(229,axiom,
    ! [A: fun_Pr7920380315054183110_nat_o,B: fun_Pr7920380315054183110_nat_o] :
      ( ( ord_le5132100987546516070_nat_o @ A @ B )
     => ( ord_le5018287362838994063_nat_o @ ( accp_P5801069581201407417et_nat @ B ) @ ( accp_P5801069581201407417et_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2416_accp__subset) ).

thf(1458,plain,
    ! [A: fun_Pr7920380315054183110_nat_o,B: fun_Pr7920380315054183110_nat_o] :
      ( ( ord_le5132100987546516070_nat_o @ A @ B )
     => ( ord_le5018287362838994063_nat_o @ ( accp_P5801069581201407417et_nat @ B ) @ ( accp_P5801069581201407417et_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(497,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_star__or__dist2) ).

thf(2575,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(144,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_inf_OorderI) ).

thf(1078,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(313,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_le__iff__sup) ).

thf(1788,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(222,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4959_boolean__algebra_Ode__Morgan__disj) ).

thf(1426,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(126,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ A ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4929_boolean__algebra_Oconj__cancel__right) ).

thf(1001,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ A ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(211,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_Int__left__absorb) ).

thf(1391,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(117,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2184_less__supI2) ).

thf(973,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(234,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_sup__idem) ).

thf(1475,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(317,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_inf__bot__right) ).

thf(1803,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(152,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
    <=> ( ( aa_set_nat_o @ finite_finite_nat @ A )
        & ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7747_finite__Un) ).

thf(1127,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ( aa_set_nat_o @ finite_finite_nat @ A )
          & ( aa_set_nat_o @ finite_finite_nat @ B ) ) )
      & ( ( ( aa_set_nat_o @ finite_finite_nat @ A )
          & ( aa_set_nat_o @ finite_finite_nat @ B ) )
       => ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(311,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_sup__assoc) ).

thf(1782,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(366,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_o,D: fun_nat_o] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ! [E: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ E ) @ A )
           => ( ( aa_nat_o @ C @ E )
             => ( aa_nat_o @ D @ E ) ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( collect_nat @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( collect_nat @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1207_Int__Collect__mono) ).

thf(2020,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_o,D: fun_nat_o] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ! [E: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ E ) @ A )
           => ( ( aa_nat_o @ C @ E )
             => ( aa_nat_o @ D @ E ) ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( collect_nat @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( collect_nat @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(81,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4729_Diff__Un) ).

thf(841,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(262,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_sup__inf__absorb) ).

thf(1601,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(209,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_sup_OorderI) ).

thf(1386,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(455,axiom,
    ! [A: assn,B: assn] :
      ( ( inf_inf_option_assn @ ( some_assn @ A ) @ ( some_assn @ B ) )
      = ( some_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1458_inf__Some) ).

thf(2400,plain,
    ! [A: assn,B: assn] :
      ( ( inf_inf_option_assn @ ( some_assn @ A ) @ ( some_assn @ B ) )
      = ( some_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(245,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1255_Un__Int__assoc__eq) ).

thf(1529,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ A ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ A )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(333,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_le__infE) ).

thf(1904,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(289,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
    <=> ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1409_bot_Oextremum__unique) ).

thf(1703,plain,
    ! [A: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
       => ( A = bot_bot_set_nat ) )
      & ( ( A = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(138,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_le__sup__iff) ).

thf(1055,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(371,axiom,
    ! [A: set_nat] :
      ( ! [B: nat] :
          ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2252_subset__emptyI) ).

thf(2039,plain,
    ! [A: set_nat] :
      ( ! [B: nat] :
          ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(320,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4966_boolean__algebra_Ode__Morgan__conj) ).

thf(1826,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(410,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_Un__Int__distrib2) ).

thf(2185,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(493,axiom,
    ! [A: assn] :
      ( ( abs_assn @ ( rep_assn @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2535_Rep__assn__inverse) ).

thf(2562,plain,
    ! [A: assn] :
      ( ( abs_assn @ ( rep_assn @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(108,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_inf__absorb1) ).

thf(934,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(359,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_inf__sup__distrib1) ).

thf(1992,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(394,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
     => ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1414_bot_Oextremum__uniqueI) ).

thf(2126,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
     => ( A = bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(231,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_sup_Oabsorb__iff2) ).

thf(1462,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(444,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ one_one_assn )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2922_mult_Oright__neutral) ).

thf(2356,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ one_one_assn )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(334,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1431_boolean__algebra_Odisj__conj__distrib) ).

thf(1907,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(479,axiom,
    ! [A: assn,B: $o,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_o_assn @ pure_assn @ B ) ) ) @ C )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
        & B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2451_mod__pure__star__dist) ).

thf(2501,plain,
    ! [A: assn,B: $o,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_o_assn @ pure_assn @ B ) ) ) @ C )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & B ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & B )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_o_assn @ pure_assn @ B ) ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(326,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4941_inf__compl__bot__right) ).

thf(1860,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(417,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ one_one_assn )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3062_mult_Ocomm__neutral) ).

thf(2217,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ one_one_assn )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(248,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1445_boolean__algebra_Odisj__conj__distrib2) ).

thf(1545,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(490,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_inf_Oleft__idem) ).

thf(2552,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(196,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4927_boolean__algebra_Oconj__cancel__right) ).

thf(1319,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(200,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( B
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_sup_OorderE) ).

thf(1347,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( B
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(65,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1527_subset__eq) ).

thf(770,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) )
      & ( ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(482,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_inf__left__commute) ).

thf(2520,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(308,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_inf_OboundedE) ).

thf(1773,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(148,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ? [F: set_nat,G: set_nat] :
                ( ( E
                  = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ G ) )
                & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ G )
                  = bot_bot_set_nat )
                & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ D @ F ) )
                & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ D @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_times__assn__raw_Oelims_I3_J) ).

thf(1100,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ? [F: set_nat,G: set_nat] :
                ( ( E
                  = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ G ) )
                & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ G )
                  = bot_bot_set_nat )
                & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ D @ F ) )
                & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ D @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(324,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_le__inf__iff) ).

thf(1847,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(339,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_inf_Oabsorb1) ).

thf(1922,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(74,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4656_Diff__Int__distrib) ).

thf(817,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(99,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
            = bot_bot_set_nat )
         => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7608_prod_Ounion__disjoint) ).

thf(902,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
            = bot_bot_set_nat )
         => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(406,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ one_one_assn ) @ A )
    <=> ( ( produc8586169260539613262et_nat @ A )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9386_mod__emp) ).

thf(2169,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ one_one_assn ) @ A )
       => ( ( produc8586169260539613262et_nat @ A )
          = bot_bot_set_nat ) )
      & ( ( ( produc8586169260539613262et_nat @ A )
          = bot_bot_set_nat )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ one_one_assn ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(456,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_star__or__dist1) ).

thf(2403,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(419,axiom,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_a_assn @ q @ r2 ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as1 @ h ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MDL) ).

thf(2222,plain,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_a_assn @ q @ r2 ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as1 @ h ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(105,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_inf__assoc) ).

thf(924,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(68,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4670_Un__Diff) ).

thf(789,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(270,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_Un__Int__distrib) ).

thf(1632,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(392,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_sup_Oleft__idem) ).

thf(2122,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(109,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2176_sup_Oabsorb3) ).

thf(937,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(208,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_sup__absorb2) ).

thf(1383,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(369,axiom,
    ( as
    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ as1 ) @ as2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__092_060open_062as_A_061_Aas1_A_092_060union_062_Aas2_092_060close_062) ).

thf(2034,plain,
    ( as
    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ as1 ) @ as2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(491,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
         => ( hoare_hoare_triple_a @ A @ B @ C ) )
     => ( hoare_hoare_triple_a @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_hoare__triple__preI) ).

thf(2555,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn] :
      ( ! [D: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
         => ( hoare_hoare_triple_a @ A @ B @ C ) )
     => ( hoare_hoare_triple_a @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(504,axiom,
    ! [A: assn,B: assn,C: nat] :
      ( ( aa_nat_assn @ ( power_power_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ ( aa_nat_assn @ ( power_power_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3558_power__mult__distrib) ).

thf(2616,plain,
    ! [A: assn,B: assn,C: nat] :
      ( ( aa_nat_assn @ ( power_power_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ C ) ) @ ( aa_nat_assn @ ( power_power_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(348,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_inf_Oidem) ).

thf(1946,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(219,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_inf_Oleft__idem) ).

thf(1418,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(424,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_star__false__left) ).

thf(2236,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(28,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ ( image_nat_nat @ C @ A ) )
       => ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7877_finite__surj) ).

thf(623,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ ( image_nat_nat @ C @ A ) )
       => ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(283,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5305_shunt1) ).

thf(1682,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ B ) ) @ C ) ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ B ) ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(154,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4865_Compl__disjoint) ).

thf(1136,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(256,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_inf__bot__left) ).

thf(1581,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(439,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B )
     => ~ ! [C: produc3658429121746597890et_nat] :
            ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9252_mod__star__trueE) ).

thf(2335,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B )
     => ~ ! [C: produc3658429121746597890et_nat] :
            ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(168,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D )
            = bot_bot_set_nat )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C )
            = bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1486_disjoint__mono) ).

thf(1183,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D )
            = bot_bot_set_nat )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C )
            = bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(191,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4951_inf__compl__bot__left1) ).

thf(1283,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(45,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4871_inter__compl__diff__conv) ).

thf(687,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(466,axiom,
    ! [A: assn,B: assn,C: assn,D: assn] :
      ( ( A
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ A )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1388_boolean__algebra__cancel_Oinf2) ).

thf(2437,plain,
    ! [A: assn,B: assn,C: assn,D: assn] :
      ( ( A
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ A )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(432,axiom,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( D = bot_bot_set_nat )
              & A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2640_pure__assn__raw_Oelims_I3_J) ).

thf(2281,plain,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( D = bot_bot_set_nat )
              & A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(92,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_Int__empty__left) ).

thf(877,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(227,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
    <=> ( ( B
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
        & ( B != A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2152_sup_Ostrict__order__iff) ).

thf(1447,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
       => ( ( B
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
          & ( B != A ) ) )
      & ( ( ( B
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
          & ( B != A ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(483,axiom,
    ! [A: $o,B: heap_e7401611519738050253t_unit,C: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) )
    <=> ( ( C = bot_bot_set_nat )
        & A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2643_pure__assn__raw_Osimps) ).

thf(2523,plain,
    ! [A: $o,B: heap_e7401611519738050253t_unit,C: set_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) )
       => ( ( C = bot_bot_set_nat )
          & A ) )
      & ( ( ( C = bot_bot_set_nat )
          & A )
       => ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(268,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_Int__mono) ).

thf(1622,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(212,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2077_inf_Ostrict__coboundedI2) ).

thf(1394,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(244,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1444_boolean__algebra_Oconj__disj__distrib2) ).

thf(1526,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(125,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4714_Un__Diff__Int) ).

thf(998,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(122,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ finite_finite_nat @ A )
        | ( aa_set_nat_o @ finite_finite_nat @ B ) )
     => ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7739_finite__Int) ).

thf(988,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ finite_finite_nat @ A )
        | ( aa_set_nat_o @ finite_finite_nat @ B ) )
     => ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(388,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_sup__mono) ).

thf(2103,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(451,axiom,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ one_one_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3422_mod__emp__simp) ).

thf(2392,plain,
    ! [A: heap_e7401611519738050253t_unit] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ one_one_assn ) @ ( produc7507926704131184380et_nat @ A @ bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(1,conjecture,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_a_assn @ q @ r2 ) ) @ r ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as @ h ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_a_assn @ q @ r2 ) ) @ r ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as @ h ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(507,plain,
    ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_a_assn @ q @ r2 ) ) @ r ) ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as @ h ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(287,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6062_image__Int__subset) ).

thf(1697,plain,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(180,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ C ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5181_inf__cancel__left1) ).

thf(1242,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ C ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(84,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_Int__absorb2) ).

thf(849,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(327,axiom,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          | B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2446_merge__pure__or) ).

thf(1863,plain,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          | B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(475,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_inf__assoc) ).

thf(2473,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(8,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7637_prod_Ounion__diff2) ).

thf(534,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(141,axiom,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( collect_nat @ A ) ) @ ( collect_nat @ B ) )
    <=> ! [C: nat] :
          ( ( aa_nat_o @ A @ C )
         => ( aa_nat_o @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1587_Collect__mono__iff) ).

thf(1067,plain,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( collect_nat @ A ) ) @ ( collect_nat @ B ) )
       => ! [C: nat] :
            ( ( aa_nat_o @ A @ C )
           => ( aa_nat_o @ B @ C ) ) )
      & ( ! [C: nat] :
            ( ( aa_nat_o @ A @ C )
           => ( aa_nat_o @ B @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( collect_nat @ A ) ) @ ( collect_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(70,axiom,
    ! [A: set_nat] :
      ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2260_not__psubset__empty) ).

thf(798,plain,
    ! [A: set_nat] :
      ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(142,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4648_Diff__subset) ).

thf(1074,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(263,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Un__Int__eq_I1_J) ).

thf(1604,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(189,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
    <=> ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
        & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2452_in__range__dist__union) ).

thf(1274,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat,C: set_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
       => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
          & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ C ) ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
          & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ C ) ) )
       => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(292,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_sup__inf__distrib2) ).

thf(1723,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(96,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_inf__sup__aci_I3_J) ).

thf(894,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(112,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_inf_Obounded__iff) ).

thf(952,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(75,axiom,
    ! [A: set_nat,B: fun_nat_assn,C: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( groups6906906614972039071t_assn @ B @ A )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) @ ( groups6906906614972039071t_assn @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7443_prod_OInt__Diff) ).

thf(820,plain,
    ! [A: set_nat,B: fun_nat_assn,C: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( groups6906906614972039071t_assn @ B @ A )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) @ ( groups6906906614972039071t_assn @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(238,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_inf__sup__distrib2) ).

thf(1487,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(502,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
        | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_mod__or__dist) ).

thf(2606,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(365,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1491_disjointI) ).

thf(2015,plain,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(165,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_UnCI) ).

thf(1174,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(281,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_inf__sup__aci_I5_J) ).

thf(1676,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(47,axiom,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
    <=> ? [D: set_nat] :
          ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
          & ( A
            = ( image_nat_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5999_subset__image__iff) ).

thf(693,plain,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
       => ? [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
            & ( A
              = ( image_nat_nat @ B @ D ) ) ) )
      & ( ? [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
            & ( A
              = ( image_nat_nat @ B @ D ) ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(31,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5168_diff__eq) ).

thf(630,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(267,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_inf__bot__right) ).

thf(1619,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(399,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_UnE) ).

thf(2150,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(204,axiom,
    ! [A: $o] :
      ( ( aa_o_assn @ pure_assn @ A )
      = ( abs_assn @ ( pure_a825153325127701367it_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2607_pure__assn__def) ).

thf(1370,plain,
    ! [A: $o] :
      ( ( aa_o_assn @ pure_assn @ A )
      = ( abs_assn @ ( pure_a825153325127701367it_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(396,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_inf__sup__absorb) ).

thf(2132,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(458,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_option_assn @ ( aTP_Lamm_eg @ A ) @ B )
      = ( some_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9929_ATP_Olambda__238) ).

thf(2414,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_option_assn @ ( aTP_Lamm_eg @ A ) @ B )
      = ( some_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(468,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2771_ab__semigroup__mult__class_Omult_Oleft__commute) ).

thf(2445,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(134,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ~ ? [F: set_nat,G: set_nat] :
                  ( ( E
                    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ G ) )
                  & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ G )
                    = bot_bot_set_nat )
                  & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ D @ F ) )
                  & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ D @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_times__assn__raw_Oelims_I2_J) ).

thf(1032,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ~ ? [F: set_nat,G: set_nat] :
                  ( ( E
                    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ G ) )
                  & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ G )
                    = bot_bot_set_nat )
                  & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ D @ F ) )
                  & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ D @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(494,axiom,
    ! [A: fun_nat_assn,B: nat] :
      ( ( aa_nat_fun_assn_assn @ ( aTP_Lamm_of @ A ) @ B )
      = ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9962_ATP_Olambda__271) ).

thf(2565,plain,
    ! [A: fun_nat_assn,B: nat] :
      ( ( aa_nat_fun_assn_assn @ ( aTP_Lamm_of @ A ) @ B )
      = ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(85,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_inf_OorderE) ).

thf(852,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(194,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ D @ E ) )
              & ! [F: heap_e7401611519738050253t_unit,G: set_nat] :
                  ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ G )
                      = bot_bot_set_nat )
                    & ( aa_hea7994211679605476167unit_o @ ( relH @ E @ D ) @ F )
                    & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ F @ E ) )
                    & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ F @ G ) ) )
                 => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ F @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2483_wand__raw_Oelims_I3_J) ).

thf(1296,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ D @ E ) )
              & ! [F: heap_e7401611519738050253t_unit,G: set_nat] :
                  ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ G )
                      = bot_bot_set_nat )
                    & ( aa_hea7994211679605476167unit_o @ ( relH @ E @ D ) @ F )
                    & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ F @ E ) )
                    & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ F @ G ) ) )
                 => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ F @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(323,axiom,
    ! [A: $o,B: $o] :
      ( ( ( aa_o_assn @ pure_assn @ A )
        = ( aa_o_assn @ pure_assn @ B ) )
    <=> ( A
      <=> B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2444_pure__assn__eq__conv) ).

thf(1836,plain,
    ! [A: $o,B: $o] :
      ( ( ( ( aa_o_assn @ pure_assn @ A )
          = ( aa_o_assn @ pure_assn @ B ) )
       => ( ( A
           => B )
          & ( B
           => A ) ) )
      & ( ( ( A
           => B )
          & ( B
           => A ) )
       => ( ( aa_o_assn @ pure_assn @ A )
          = ( aa_o_assn @ pure_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(277,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_IntD2) ).

thf(1656,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(215,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
     => ~ ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7831_Un__infinite) ).

thf(1407,plain,
    ! [A: set_nat,B: set_nat] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
     => ~ ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(50,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4577_Un__Diff__cancel2) ).

thf(710,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(284,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_sup_Ocobounded1) ).

thf(1687,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(228,axiom,
    aa_hea7994211679605476167unit_o @ ( relH @ as2 @ h2 ) @ h,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__092_060open_062relH_Aas2_Ah_Ah_H_092_060close_062) ).

thf(1457,plain,
    aa_hea7994211679605476167unit_o @ ( relH @ as2 @ h2 ) @ h,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(5,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4880_Compl__Diff__eq) ).

thf(522,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(78,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4569_empty__Diff) ).

thf(830,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(94,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_inf__sup__ord_I2_J) ).

thf(889,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(408,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_sup__commute) ).

thf(2179,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(298,axiom,
    ! [A: $o] :
      ( ( ( aa_o_assn @ pure_assn @ A )
        = one_one_assn )
    <=> A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2950_pure__assn__eq__emp__iff) ).

thf(1740,plain,
    ! [A: $o] :
      ( ( ( ( aa_o_assn @ pure_assn @ A )
          = one_one_assn )
       => A )
      & ( A
       => ( ( aa_o_assn @ pure_assn @ A )
          = one_one_assn ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(335,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_UnI1) ).

thf(1910,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(259,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_inf_Oright__idem) ).

thf(1592,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(356,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_inf_Oleft__commute) ).

thf(1983,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(37,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ) @ ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6071_image__diff__subset) ).

thf(650,plain,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ) @ ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(130,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ A )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1387_boolean__algebra__cancel_Oinf2) ).

thf(1017,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ A )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(140,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4947_inf__compl__bot__left2) ).

thf(1064,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(176,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4695_Diff__triv) ).

thf(1227,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(481,axiom,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ~ ( ( D = bot_bot_set_nat )
                & A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2641_pure__assn__raw_Oelims_I2_J) ).

thf(2509,plain,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( pure_a825153325127701367it_nat @ A ) @ B )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( B
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ~ ( ( D = bot_bot_set_nat )
                & A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(213,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_IntI) ).

thf(1397,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(426,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2927_mult__1) ).

thf(2245,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(201,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_o] :
      ( ? [D: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
          & ( aa_nat_o @ C @ D ) )
    <=> ( ? [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
            & ( aa_nat_o @ C @ D ) )
        | ? [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
            & ( aa_nat_o @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_bex__Un) ).

thf(1350,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_o] :
      ( ( ? [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            & ( aa_nat_o @ C @ D ) )
       => ( ? [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
              & ( aa_nat_o @ C @ D ) )
          | ? [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
              & ( aa_nat_o @ C @ D ) ) ) )
      & ( ( ? [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
              & ( aa_nat_o @ C @ D ) )
          | ? [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
              & ( aa_nat_o @ C @ D ) ) )
       => ? [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            & ( aa_nat_o @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(344,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_Int__absorb) ).

thf(1936,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(402,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_Un__commute) ).

thf(2157,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(391,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_sup_Oabsorb__iff1) ).

thf(2115,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
          = B ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
          = B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(304,axiom,
    ! [A: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ bot_bot_set_nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_empty__subsetI) ).

thf(1762,plain,
    ! [A: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ bot_bot_set_nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(387,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_boolean__algebra_Oconj__zero__right) ).

thf(2100,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ bot_bot_set_nat )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(445,axiom,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          & B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2445_merge__pure__star) ).

thf(2359,plain,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          & B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(205,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_sup_OboundedE) ).

thf(1375,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(199,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat,D: $o] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
      <=> D )
     => ~ ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ E @ F ) )
           => ( D
            <=> ~ ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ F ) )
                  & ! [G: heap_e7401611519738050253t_unit,H: set_nat] :
                      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ H )
                          = bot_bot_set_nat )
                        & ( aa_hea7994211679605476167unit_o @ ( relH @ F @ E ) @ G )
                        & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ G @ F ) )
                        & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ G @ H ) ) )
                     => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ G @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ H ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2485_wand__raw_Oelims_I1_J) ).

thf(1329,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat,D: $o] :
      ( ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
         => D )
        & ( D
         => ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C ) ) )
     => ~ ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ E @ F ) )
           => ( ( D
               => ~ ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ F ) )
                    & ! [G: heap_e7401611519738050253t_unit,H: set_nat] :
                        ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ H )
                            = bot_bot_set_nat )
                          & ( aa_hea7994211679605476167unit_o @ ( relH @ F @ E ) @ G )
                          & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ G @ F ) )
                          & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ G @ H ) ) )
                       => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ G @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ H ) ) ) ) ) )
              & ( ~ ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ F ) )
                    & ! [G: heap_e7401611519738050253t_unit,H: set_nat] :
                        ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ F ) @ H )
                            = bot_bot_set_nat )
                          & ( aa_hea7994211679605476167unit_o @ ( relH @ F @ E ) @ G )
                          & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ G @ F ) )
                          & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ G @ H ) ) )
                       => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ G @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ F ) @ H ) ) ) ) )
               => D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(60,axiom,
    ! [A: nat,B: set_nat] :
      ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5394_ComplI) ).

thf(753,plain,
    ! [A: nat,B: set_nat] :
      ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(221,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_relH__sym) ).

thf(1424,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(375,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_sup__inf__distrib1) ).

thf(2053,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(257,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5289_sup__neg__inf) ).

thf(1584,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(503,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_inf_Ocommute) ).

thf(2613,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(175,axiom,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          & B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2449_merge__pure__and) ).

thf(1214,plain,
    ! [A: $o,B: $o] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( aa_o_assn @ pure_assn @ B ) )
      = ( aa_o_assn @ pure_assn
        @ ( A
          & B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(329,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_inf__le1) ).

thf(1889,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(265,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4967_boolean__algebra_Ode__Morgan__conj) ).

thf(1612,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(159,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ D )
       => ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_relH__trans) ).

thf(1155,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ D )
       => ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(472,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: assn] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) )
      <=> ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_mod__relH) ).

thf(2460,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: assn] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) )
         => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) ) )
        & ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ C @ A ) )
         => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(240,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4691_Int__Diff__disjoint) ).

thf(1493,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(48,axiom,
    ! [A: nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( B != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2218_memb__imp__not__empty) ).

thf(701,plain,
    ! [A: nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( B != bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(484,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_inf__sup__aci_I4_J) ).

thf(2536,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(56,axiom,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
       => ? [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
            & ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( A
              = ( image_nat_nat @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7887_finite__subset__image) ).

thf(738,plain,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
       => ? [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
            & ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( A
              = ( image_nat_nat @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(187,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ D )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1382_boolean__algebra__cancel_Oinf1) ).

thf(1266,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ D )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(280,axiom,
    ! [A: fun_se1909708154429037836et_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) ) @ D )
     => ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) ) @ E )
       => ( ! [D: set_nat,E: set_nat,F: set_nat] :
              ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ E )
             => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ F )
               => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ E ) @ F ) ) ) )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C )
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_inf__unique) ).

thf(1668,plain,
    ! [A: fun_se1909708154429037836et_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) ) @ D )
     => ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) ) @ E )
       => ( ! [D: set_nat,E: set_nat,F: set_nat] :
              ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ E )
             => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ F )
               => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ E ) @ F ) ) ) )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C )
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(473,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B )
     => ~ ! [C: produc3658429121746597890et_nat] :
            ( ( ( produc1824681642469235216et_nat @ C )
              = ( produc1824681642469235216et_nat @ B ) )
           => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ C ) ) @ ( produc8586169260539613262et_nat @ B ) )
             => ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9387_mod__star__trueE_H) ).

thf(2465,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ top_top_assn ) ) @ B )
     => ~ ! [C: produc3658429121746597890et_nat] :
            ( ( ( produc1824681642469235216et_nat @ C )
              = ( produc1824681642469235216et_nat @ B ) )
           => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ C ) ) @ ( produc8586169260539613262et_nat @ B ) )
             => ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(363,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_inf__sup__ord_I4_J) ).

thf(2006,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(223,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_inf_Ocommute) ).

thf(1429,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(67,axiom,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ! [C: nat] :
          ( ( aa_nat_o @ A @ C )
        <=> ( aa_nat_o @ B @ C ) )
     => ( ( collect_nat @ A )
        = ( collect_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Collect__cong) ).

thf(779,plain,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ! [C: nat] :
          ( ( ( aa_nat_o @ A @ C )
           => ( aa_nat_o @ B @ C ) )
          & ( ( aa_nat_o @ B @ C )
           => ( aa_nat_o @ A @ C ) ) )
     => ( ( collect_nat @ A )
        = ( collect_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(303,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4678_subset__minus__empty) ).

thf(1759,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(36,axiom,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1521_subsetD) ).

thf(647,plain,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(309,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_Int__Un__distrib) ).

thf(1776,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(186,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_inf__absorb2) ).

thf(1263,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(393,axiom,
    hoare_hoare_triple_a @ p @ c @ q,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_assms) ).

thf(2125,plain,
    hoare_hoare_triple_a @ p @ c @ q,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(121,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4945_inf__compl__bot__left2) ).

thf(985,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(4,axiom,
    ! [A: fun_nat_nat,B: set_nat] :
      ( ( bot_bot_set_nat
        = ( image_nat_nat @ A @ B ) )
    <=> ( B = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5887_empty__is__image) ).

thf(515,plain,
    ! [A: fun_nat_nat,B: set_nat] :
      ( ( ( bot_bot_set_nat
          = ( image_nat_nat @ A @ B ) )
       => ( B = bot_bot_set_nat ) )
      & ( ( B = bot_bot_set_nat )
       => ( bot_bot_set_nat
          = ( image_nat_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(235,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_sup__least) ).

thf(1478,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(488,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_inf__idem) ).

thf(2546,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(3,axiom,
    ! [A: set_nat] :
      ( ( A != bot_bot_set_nat )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ bot_bot_set_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2067_bot_Onot__eq__extremum) ).

thf(508,plain,
    ! [A: set_nat] :
      ( ( ( A != bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ bot_bot_set_nat ) @ A ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ bot_bot_set_nat ) @ A )
       => ( A != bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(104,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_sup__inf__absorb) ).

thf(921,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(10,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( image_nat_nat @ C @ A ) ) @ ( image_nat_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6024_image__mono) ).

thf(541,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( image_nat_nat @ C @ A ) ) @ ( image_nat_nat @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(63,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
       => ~ ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7810_infinite__super) ).

thf(765,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
       => ~ ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(192,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_inf_Oabsorb__iff2) ).

thf(1286,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
          = A ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
          = A )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(243,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) )
    <=> ? [E: set_nat,F: set_nat] :
          ( ( D
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) )
          & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
            = bot_bot_set_nat )
          & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ C @ E ) )
          & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ C @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_times__assn__raw_Osimps) ).

thf(1515,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) )
       => ? [E: set_nat,F: set_nat] :
            ( ( D
              = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) )
            & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
              = bot_bot_set_nat )
            & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ C @ E ) )
            & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ C @ F ) ) ) )
      & ( ? [E: set_nat,F: set_nat] :
            ( ( D
              = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) )
            & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
              = bot_bot_set_nat )
            & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ C @ E ) )
            & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ C @ F ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(132,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_inf__sup__absorb) ).

thf(1026,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(440,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ top_top_assn ) @ A )
    <=> ( aa_Pro653082453696054616_nat_o @ in_range @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9235_mod__true) ).

thf(2338,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ top_top_assn ) @ A )
       => ( aa_Pro653082453696054616_nat_o @ in_range @ A ) )
      & ( ( aa_Pro653082453696054616_nat_o @ in_range @ A )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ top_top_assn ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(171,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4933_boolean__algebra_Oconj__cancel__left) ).

thf(1202,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(69,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ B )
            = ( groups6906906614972039071t_assn @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7374_prod_Omono__neutral__left) ).

thf(792,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ B )
            = ( groups6906906614972039071t_assn @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(32,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4873_Diff__Compl) ).

thf(633,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(310,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_IntE) ).

thf(1779,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(169,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2084_inf_Ostrict__coboundedI1) ).

thf(1187,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(42,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7814_rev__finite__subset) ).

thf(674,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( aa_set_nat_o @ finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(461,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_inf_Oassoc) ).

thf(2423,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(40,axiom,
    ! [A: set_nat] :
      ( ! [B: nat] :
          ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
     => ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_equals0I) ).

thf(662,plain,
    ! [A: set_nat] :
      ( ! [B: nat] :
          ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
     => ( A = bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(100,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B )
      = ( abs_assn @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_ep @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2597_sup__assn__def) ).

thf(906,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B )
      = ( abs_assn @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_ep @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(362,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ~ ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
           => ! [E: set_nat] :
                ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ C )
               => ( A
                 != ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1243_subset__UnE) ).

thf(2001,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ~ ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
           => ! [E: set_nat] :
                ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ C )
               => ( A
                 != ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(59,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ aTP_Lamm_eo @ A )
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10752_ATP_Olambda__1061) ).

thf(750,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( aa_Pro653082453696054616_nat_o @ aTP_Lamm_eo @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(407,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1422_boolean__algebra_Odisj__zero__right) ).

thf(2176,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(499,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ A @ C )
        <=> ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
     => ( ( abs_assn @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2583_Abs__assn__eqI_I1_J) ).

thf(2585,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: assn] :
      ( ! [C: produc3658429121746597890et_nat] :
          ( ( ( aa_Pro653082453696054616_nat_o @ A @ C )
           => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
          & ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C )
           => ( aa_Pro653082453696054616_nat_o @ A @ C ) ) )
     => ( ( abs_assn @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(76,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4573_Diff__empty) ).

thf(824,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(299,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1238_Un__absorb2) ).

thf(1747,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(23,axiom,
    ! [A: fun_nat_assn] :
      ( ( groups6906906614972039071t_assn @ A @ bot_bot_set_nat )
      = one_one_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6269_prod_Oempty) ).

thf(601,plain,
    ! [A: fun_nat_assn] :
      ( ( groups6906906614972039071t_assn @ A @ bot_bot_set_nat )
      = one_one_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(183,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_inf_Ocobounded1) ).

thf(1251,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(26,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( aa_set_nat_o @ finite_finite_nat @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7806_finite__subset) ).

thf(618,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( aa_set_nat_o @ finite_finite_nat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(305,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ D ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4646_Diff__mono) ).

thf(1764,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ D ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(249,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2192_less__supI1) ).

thf(1548,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(341,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2112_inf_Oabsorb3) ).

thf(1927,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(368,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7597_prod_Ounion__inter__neutral) ).

thf(2028,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
            = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(260,axiom,
    ! [A: set_nat,B: set_nat,C: heap_e7401611519738050253t_unit] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ B ) )
       => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2462_in__range__subset) ).

thf(1595,plain,
    ! [A: set_nat,B: set_nat,C: heap_e7401611519738050253t_unit] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ B ) )
       => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(322,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_inf__sup__aci_I6_J) ).

thf(1833,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(128,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_le__supI2) ).

thf(1007,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(337,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_sup_Oidem) ).

thf(1916,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(373,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ minus_minus_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5169_diff__eq) ).

thf(2048,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ minus_minus_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(411,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_Int__Un__distrib2) ).

thf(2188,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(495,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
       => ? [F: heap_e7401611519738050253t_unit,G: a,H: nat] :
            ( ( aa_nat_o @ ( heap_Time_effect_a @ B @ D @ F @ G ) @ H )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_a_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2433_hoare__triple__effect) ).

thf(2568,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
       => ? [F: heap_e7401611519738050253t_unit,G: a,H: nat] :
            ( ( aa_nat_o @ ( heap_Time_effect_a @ B @ D @ F @ G ) @ H )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_a_assn @ C @ G ) ) @ ( produc7507926704131184380et_nat @ F @ ( hoare_new_addrs @ D @ E @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(91,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1228_Un__upper2) ).

thf(875,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(113,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5173_inf__cancel__left2) ).

thf(958,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(314,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_sup_Ocommute) ).

thf(1795,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(151,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ A )
      = ( abs_assn @ ( aTP_Lamm_gz @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5339_uminus__assn__def) ).

thf(1124,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ A )
      = ( abs_assn @ ( aTP_Lamm_gz @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(185,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
       != A )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
       != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4683_disjoint__alt__simp2) ).

thf(1256,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
         != A )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
         != bot_bot_set_nat ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
         != bot_bot_set_nat )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
         != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(266,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ B )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ B ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2225_inter__eq__subsetI) ).

thf(1615,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ B )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ B ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(210,axiom,
    ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ as1 ) @ as2 )
    = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_DJ) ).

thf(1389,plain,
    ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ as1 ) @ as2 )
    = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(155,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_inf__left__commute) ).

thf(1139,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(413,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ B @ C ) )
             => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ B @ C ) )
               => ( C = bot_bot_set_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3460_one__assn__raw_Opelims_I3_J) ).

thf(2193,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ A )
       => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
              ( ( A
                = ( produc7507926704131184380et_nat @ B @ C ) )
             => ( ( aa_Pro653082453696054616_nat_o @ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel ) @ ( produc7507926704131184380et_nat @ B @ C ) )
               => ( C = bot_bot_set_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(418,axiom,
    ( aTP_Lamm_fs
    = ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3135_lambda__one) ).

thf(2220,plain,
    ( aTP_Lamm_fs
    = ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(433,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aTP_Lamm_gz @ A ) @ B )
    <=> ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
        & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9813_ATP_Olambda__122) ).

thf(2293,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aTP_Lamm_gz @ A ) @ B )
       => ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
          & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
          & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) )
       => ( aa_Pro653082453696054616_nat_o @ ( aTP_Lamm_gz @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(51,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
         => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4803_DiffE) ).

thf(713,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
         => ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(271,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_sup__bot_Oright__neutral) ).

thf(1635,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(467,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_inf__commute) ).

thf(2442,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(405,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_Un__Int__crazy) ).

thf(2166,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(332,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = A )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4687_disjoint__alt__simp1) ).

thf(1897,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = A )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(272,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
     => ( aa_hea7994211679605476167unit_o @ ( relH @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2461_relH__refl) ).

thf(1638,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
     => ( aa_hea7994211679605476167unit_o @ ( relH @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(188,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1233_Un__absorb1) ).

thf(1271,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(436,axiom,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
        | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_mod__h__bot__iff_I7_J) ).

thf(2308,plain,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          | ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(325,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_inf_Oabsorb__iff1) ).

thf(1853,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = A ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = A )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(422,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
     => ? [D: produc3658429121746597890et_nat,E: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_mod__starD) ).

thf(2229,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
     => ? [D: produc3658429121746597890et_nat,E: produc3658429121746597890et_nat] :
          ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(383,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1213_Un__mono) ).

thf(2084,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(318,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_Un__absorb) ).

thf(1806,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(434,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
     => ~ ( ? [D: produc3658429121746597890et_nat] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
         => ! [D: produc3658429121746597890et_nat] :
              ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_mod__starE) ).

thf(2299,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
     => ~ ( ? [D: produc3658429121746597890et_nat] : ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ D )
         => ! [D: produc3658429121746597890et_nat] :
              ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(247,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_sup__absorb1) ).

thf(1542,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(448,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_inf_Oidem) ).

thf(2378,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(89,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( ( A = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_sup__bot_Oeq__neutr__iff) ).

thf(863,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) ) )
      & ( ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(119,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_inf__greatest) ).

thf(979,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(24,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] :
      ( ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6031_image__Un) ).

thf(604,plain,
    ! [A: fun_nat_nat,B: set_nat,C: set_nat] :
      ( ( image_nat_nat @ A @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( image_nat_nat @ A @ B ) ) @ ( image_nat_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(331,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_le__infI1) ).

thf(1894,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(477,axiom,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
        & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_mod__h__bot__iff_I6_J) ).

thf(2493,plain,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(258,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_inf__bot__left) ).

thf(1589,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(343,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4724_Diff__Int) ).

thf(1933,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(93,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( ( A = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Un__empty) ).

thf(880,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) ) )
      & ( ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(136,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( ( A = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_sup__eq__bot__iff) ).

thf(1043,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) ) )
      & ( ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(316,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1223_Un__upper1) ).

thf(1801,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(254,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
    <=> ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_subset__empty) ).

thf(1571,plain,
    ! [A: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat )
       => ( A = bot_bot_set_nat ) )
      & ( ( A = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(22,axiom,
    ! [A: nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
     => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5430_ComplD) ).

thf(599,plain,
    ! [A: nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
     => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(367,axiom,
    top_top_assn != bot_bot_assn,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9230_assn__basic__inequalities_I5_J) ).

thf(2025,plain,
    top_top_assn != bot_bot_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(62,axiom,
    ! [A: set_nat] :
      ( ! [B: nat] :
          ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
    <=> ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_all__not__in__conv) ).

thf(758,plain,
    ! [A: set_nat] :
      ( ( ! [B: nat] :
            ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A )
       => ( A = bot_bot_set_nat ) )
      & ( ( A = bot_bot_set_nat )
       => ! [B: nat] :
            ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(87,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_distrib__sup__le) ).

thf(858,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(430,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
    <=> ? [D: heap_e7401611519738050253t_unit,E: set_nat,F: set_nat] :
          ( ( C
            = ( produc7507926704131184380et_nat @ D @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) ) )
          & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
            = bot_bot_set_nat )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ D @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_mod__star__conv) ).

thf(2267,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
       => ? [D: heap_e7401611519738050253t_unit,E: set_nat,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) ) )
            & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
              = bot_bot_set_nat )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ D @ F ) ) ) )
      & ( ? [D: heap_e7401611519738050253t_unit,E: set_nat,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) ) )
            & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ F )
              = bot_bot_set_nat )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
            & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ D @ F ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(295,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_Int__left__commute) ).

thf(1731,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(133,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_Un__left__commute) ).

thf(1029,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(131,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ C ) @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4650_double__diff) ).

thf(1022,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ C ) @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(166,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1430_boolean__algebra_Oconj__disj__distrib) ).

thf(1177,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(139,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_sup_Omono) ).

thf(1061,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(498,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) )
    <=> ( B = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2891_one__assn__raw_Osimps) ).

thf(2578,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) )
       => ( B = bot_bot_set_nat ) )
      & ( ( B = bot_bot_set_nat )
       => ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ ( produc7507926704131184380et_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(73,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ A )
            = ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7384_prod_Omono__neutral__right) ).

thf(811,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
             => ( ( aa_nat_assn @ C @ D )
                = one_one_assn ) )
         => ( ( groups6906906614972039071t_assn @ C @ A )
            = ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(409,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_le__supI1) ).

thf(2182,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(395,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ C ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5179_inf__cancel__left1) ).

thf(2129,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ C ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(441,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr7920380315054183110_nat_o,C: produc3658429121746597890et_nat,D: fun_Pr6460944699146269935_nat_o] :
      ( ( ord_le5018287362838994063_nat_o @ A @ ( accp_P5801069581201407417et_nat @ B ) )
     => ( ! [E: produc3658429121746597890et_nat,F: produc3658429121746597890et_nat] :
            ( ( aa_Pro653082453696054616_nat_o @ A @ E )
           => ( ( aa_Pro653082453696054616_nat_o @ ( aa_Pro7278237734719282863_nat_o @ B @ F ) @ E )
             => ( aa_Pro653082453696054616_nat_o @ A @ F ) ) )
       => ( ( aa_Pro653082453696054616_nat_o @ A @ C )
         => ( ! [E: produc3658429121746597890et_nat] :
                ( ( aa_Pro653082453696054616_nat_o @ A @ E )
               => ( ! [F: produc3658429121746597890et_nat] :
                      ( ( aa_Pro653082453696054616_nat_o @ ( aa_Pro7278237734719282863_nat_o @ B @ F ) @ E )
                     => ( aa_Pro653082453696054616_nat_o @ D @ F ) )
                 => ( aa_Pro653082453696054616_nat_o @ D @ E ) ) )
           => ( aa_Pro653082453696054616_nat_o @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2421_accp__subset__induct) ).

thf(2343,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr7920380315054183110_nat_o,C: produc3658429121746597890et_nat,D: fun_Pr6460944699146269935_nat_o] :
      ( ( ord_le5018287362838994063_nat_o @ A @ ( accp_P5801069581201407417et_nat @ B ) )
     => ( ! [E: produc3658429121746597890et_nat,F: produc3658429121746597890et_nat] :
            ( ( aa_Pro653082453696054616_nat_o @ A @ E )
           => ( ( aa_Pro653082453696054616_nat_o @ ( aa_Pro7278237734719282863_nat_o @ B @ F ) @ E )
             => ( aa_Pro653082453696054616_nat_o @ A @ F ) ) )
       => ( ( aa_Pro653082453696054616_nat_o @ A @ C )
         => ( ! [E: produc3658429121746597890et_nat] :
                ( ( aa_Pro653082453696054616_nat_o @ A @ E )
               => ( ! [F: produc3658429121746597890et_nat] :
                      ( ( aa_Pro653082453696054616_nat_o @ ( aa_Pro7278237734719282863_nat_o @ B @ F ) @ E )
                     => ( aa_Pro653082453696054616_nat_o @ D @ F ) )
                 => ( aa_Pro653082453696054616_nat_o @ D @ E ) ) )
           => ( aa_Pro653082453696054616_nat_o @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(157,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_inf__sup__aci_I7_J) ).

thf(1149,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(115,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7824_finite__UnI) ).

thf(964,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( aa_set_nat_o @ finite_finite_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(29,axiom,
    ! [A: fun_nat_o] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ ( collect_nat @ A ) )
     => ? [B: nat] : ( aa_nat_o @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7761_not__finite__existsD) ).

thf(626,plain,
    ! [A: fun_nat_o] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ ( collect_nat @ A ) )
     => ? [B: nat] : ( aa_nat_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(103,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_Un__subset__iff) ).

thf(915,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(252,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( bot_bot_set_nat
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
    <=> ( ( A = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_sup__bot_Oneutr__eq__iff) ).

thf(1556,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( bot_bot_set_nat
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) ) )
      & ( ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) )
       => ( bot_bot_set_nat
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(486,axiom,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ p ) @ r ) ) @ ( produc7507926704131184380et_nat @ h2 @ as ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_A_K_AR_092_060close_062) ).

thf(2542,plain,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ p ) @ r ) ) @ ( produc7507926704131184380et_nat @ h2 @ as ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(230,axiom,
    ( one_one_assn
    = ( abs_assn @ one_assn_raw ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3036_one__assn__def) ).

thf(1460,plain,
    ( one_one_assn
    = ( abs_assn @ one_assn_raw ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(193,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5191_Compl__Int) ).

thf(1293,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(431,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3106_assn__one__left) ).

thf(2278,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(460,axiom,
    ! [A: assn,B: assn,C: assn,D: assn] :
      ( ( A
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ D )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1383_boolean__algebra__cancel_Oinf1) ).

thf(2418,plain,
    ! [A: assn,B: assn,C: assn,D: assn] :
      ( ( A
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ D )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(288,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat,F: set_nat] :
          ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ E ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ F ) ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_distrib__imp1) ).

thf(1699,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat,F: set_nat] :
          ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ F ) )
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ E ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ F ) ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(77,axiom,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2335_psubsetD) ).

thf(827,plain,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(274,axiom,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ! [C: nat] :
          ( ( aa_nat_o @ A @ C )
         => ( aa_nat_o @ B @ C ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( collect_nat @ A ) ) @ ( collect_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1540_Collect__mono) ).

thf(1643,plain,
    ! [A: fun_nat_o,B: fun_nat_o] :
      ( ! [C: nat] :
          ( ( aa_nat_o @ A @ C )
         => ( aa_nat_o @ B @ C ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( collect_nat @ A ) ) @ ( collect_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(16,axiom,
    ! [A: nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
    <=> ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5399_Compl__iff) ).

thf(563,plain,
    ! [A: nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) )
       => ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B ) )
      & ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ B )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(286,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1218_Un__least) ).

thf(1694,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(354,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Int__Un__eq_I3_J) ).

thf(1973,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(379,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_Int__lower2) ).

thf(2069,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(102,axiom,
    bot_bot_assn != one_one_assn,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2951_assn__basic__inequalities_I3_J) ).

thf(912,plain,
    bot_bot_assn != one_one_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(164,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1200_Int__greatest) ).

thf(1171,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(374,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_sup_Ocobounded2) ).

thf(2051,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(33,axiom,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
     => ~ ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
           => ( A
             != ( image_nat_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6009_subset__imageE) ).

thf(636,plain,
    ! [A: set_nat,B: fun_nat_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( image_nat_nat @ B @ C ) )
     => ~ ! [D: set_nat] :
            ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ C )
           => ( A
             != ( image_nat_nat @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(181,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5196_Compl__Un) ).

thf(1245,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( uminus5710092332889474511et_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ ( uminus5710092332889474511et_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(293,axiom,
    ( bot_bot_assn
    = ( abs_assn @ aTP_Lamm_eo ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2594_bot__assn__def) ).

thf(1726,plain,
    ( bot_bot_assn
    = ( abs_assn @ aTP_Lamm_eo ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(202,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1438_boolean__algebra_Oconj__disj__distrib2) ).

thf(1364,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(241,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_boolean__algebra_Oconj__zero__right) ).

thf(1496,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(435,axiom,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) )
    <=> ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_mod__h__bot__indep) ).

thf(2303,plain,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) )
      & ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(425,axiom,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_eq @ A ) @ B ) @ C )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
        & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10154_ATP_Olambda__463) ).

thf(2239,plain,
    ! [A: assn,B: assn,C: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_eq @ A ) @ B ) @ C )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ C )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ C ) )
       => ( aa_Pro653082453696054616_nat_o @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_eq @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(319,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat,D: $o] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
      <=> D )
     => ~ ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ E @ F ) )
           => ( D
            <=> ~ ? [G: set_nat,H: set_nat] :
                    ( ( F
                      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ G ) @ H ) )
                    & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ G ) @ H )
                      = bot_bot_set_nat )
                    & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ G ) )
                    & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_times__assn__raw_Oelims_I1_J) ).

thf(1809,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat,D: $o] :
      ( ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C )
         => D )
        & ( D
         => ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ A ) @ B ) @ C ) ) )
     => ~ ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ E @ F ) )
           => ( ( D
               => ~ ? [G: set_nat,H: set_nat] :
                      ( ( F
                        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ G ) @ H ) )
                      & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ G ) @ H )
                        = bot_bot_set_nat )
                      & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ G ) )
                      & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ H ) ) ) )
              & ( ~ ? [G: set_nat,H: set_nat] :
                      ( ( F
                        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ G ) @ H ) )
                      & ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ G ) @ H )
                        = bot_bot_set_nat )
                      & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ G ) )
                      & ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ H ) ) )
               => D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(7,axiom,
    ! [A: nat] :
      ~ ( aa_set_nat_o @ ( member_nat @ A ) @ bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_empty__iff) ).

thf(531,plain,
    ! [A: nat] :
      ~ ( aa_set_nat_o @ ( member_nat @ A ) @ bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(12,axiom,
    aa_set_nat_o @ finite_finite_nat @ bot_bot_set_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7794_finite_OemptyI) ).

thf(548,plain,
    aa_set_nat_o @ finite_finite_nat @ bot_bot_set_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(106,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ! [D: assn,E: assn,F: assn] :
          ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ E ) @ F ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ E ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ F ) ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_distrib__imp1) ).

thf(927,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ! [D: assn,E: assn,F: assn] :
          ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ E ) @ F ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ E ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ D ) @ F ) ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(145,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_sup_OcoboundedI1) ).

thf(1081,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(415,axiom,
    ! [A: $o,B: heap_e7401611519738050253t_unit] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) )
    <=> A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2432_mod__h__bot__iff_I1_J) ).

thf(2202,plain,
    ! [A: $o,B: heap_e7401611519738050253t_unit] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) )
       => A )
      & ( A
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ ( produc7507926704131184380et_nat @ B @ bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(233,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_Un__empty__left) ).

thf(1472,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(14,axiom,
    ! [A: set_nat,B: fun_nat_o] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( collect_nat @ B ) )
    <=> ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ( aa_nat_o @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1781_subset__Collect__conv) ).

thf(553,plain,
    ! [A: set_nat,B: fun_nat_o] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( collect_nat @ B ) )
       => ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_nat_o @ B @ C ) ) )
      & ( ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_nat_o @ B @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( collect_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(217,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_Int__Un__eq_I2_J) ).

thf(1413,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(143,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_sup__ge1) ).

thf(1076,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(173,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2126_less__infI1) ).

thf(1208,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(20,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1534_subset__iff) ).

thf(589,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) )
      & ( ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(80,axiom,
    ! [A: nat,B: fun_nat_o] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( collect_nat @ B ) )
    <=> ( aa_nat_o @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_mem__Collect__eq) ).

thf(836,plain,
    ! [A: nat,B: fun_nat_o] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( collect_nat @ B ) )
       => ( aa_nat_o @ B @ A ) )
      & ( ( aa_nat_o @ B @ A )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( collect_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(250,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2459_relH__in__rangeI_I2_J) ).

thf(1551,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(307,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_inf__sup__distrib2) ).

thf(1770,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(86,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_Int__absorb1) ).

thf(855,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(34,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4798_DiffD1) ).

thf(640,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(454,axiom,
    ! [A: assn,B: nat] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ B ) ) @ A )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_nat_assn @ ( power_power_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3563_power__commutes) ).

thf(2397,plain,
    ! [A: assn,B: nat] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_nat_assn @ ( power_power_assn @ A ) @ B ) ) @ A )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_nat_assn @ ( power_power_assn @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(90,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_le__supE) ).

thf(872,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(214,axiom,
    ! [A: assn,B: assn] :
      ( ( ( aa_assn_assn @ uminus_uminus_assn @ A )
        = ( aa_assn_assn @ uminus_uminus_assn @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4835_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff) ).

thf(1400,plain,
    ! [A: assn,B: assn] :
      ( ( ( ( aa_assn_assn @ uminus_uminus_assn @ A )
          = ( aa_assn_assn @ uminus_uminus_assn @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( aa_assn_assn @ uminus_uminus_assn @ A )
          = ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(346,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_inf__sup__aci_I2_J) ).

thf(1941,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(301,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( uminus5710092332889474511et_nat @ A ) ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4939_inf__compl__bot__right) ).

thf(1753,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( uminus5710092332889474511et_nat @ A ) ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(315,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1451_boolean__algebra_Odisj__conj__distrib2) ).

thf(1798,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(6,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
        & ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4776_Diff__iff) ).

thf(525,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(46,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1501_subsetI) ).

thf(690,plain,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(261,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2119_less__infI2) ).

thf(1598,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(49,axiom,
    ! [A: set_nat,B: nat] :
      ( ( A = bot_bot_set_nat )
     => ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_equals0D) ).

thf(705,plain,
    ! [A: set_nat,B: nat] :
      ( ( A = bot_bot_set_nat )
     => ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(447,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3057_comm__monoid__mult__class_Omult__1) ).

thf(2375,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ one_one_assn ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(177,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2168_sup_Oabsorb4) ).

thf(1230,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(237,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4960_boolean__algebra_Ode__Morgan__disj) ).

thf(1484,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ uminus_uminus_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ B ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(403,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_sup__bot__right) ).

thf(2160,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ bot_bot_set_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(242,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_o] :
      ( ! [D: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
         => ( aa_nat_o @ C @ D ) )
    <=> ( ! [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
           => ( aa_nat_o @ C @ D ) )
        & ! [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
           => ( aa_nat_o @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_ball__Un) ).

thf(1499,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_o] :
      ( ( ! [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
           => ( aa_nat_o @ C @ D ) )
       => ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
             => ( aa_nat_o @ C @ D ) )
          & ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
             => ( aa_nat_o @ C @ D ) ) ) )
      & ( ( ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ A )
             => ( aa_nat_o @ C @ D ) )
          & ! [D: nat] :
              ( ( aa_set_nat_o @ ( member_nat @ D ) @ B )
             => ( aa_nat_o @ C @ D ) ) )
       => ! [D: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
           => ( aa_nat_o @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(224,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4704_Diff__subset__conv) ).

thf(1432,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(312,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_le__infI) ).

thf(1785,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(463,axiom,
    ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ top_top_assn ) @ top_top_assn )
    = top_top_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9229_merge__true__star) ).

thf(2429,plain,
    ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ top_top_assn ) @ top_top_assn )
    = top_top_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(278,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1248_subset__Un__eq) ).

thf(1658,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
          = B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(72,axiom,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1516_in__mono) ).

thf(808,plain,
    ! [A: set_nat,B: set_nat,C: nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
       => ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(282,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_inf__mono) ).

thf(1679,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ D )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(35,axiom,
    ! [A: set_nat] :
      ( ( A != bot_bot_set_nat )
     => ~ ! [B: nat] :
            ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2223_set__notEmptyE) ).

thf(643,plain,
    ! [A: set_nat] :
      ( ( A != bot_bot_set_nat )
     => ~ ! [B: nat] :
            ~ ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(11,axiom,
    ! [A: set_nat] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( A != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7799_infinite__imp__nonempty) ).

thf(544,plain,
    ! [A: set_nat] :
      ( ~ ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( A != bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(376,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_UnI2) ).

thf(2056,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(57,axiom,
    ! [A: nat] :
      ~ ( aa_set_nat_o @ ( member_nat @ A ) @ bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_emptyE) ).

thf(744,plain,
    ! [A: nat] :
      ~ ( aa_set_nat_o @ ( member_nat @ A ) @ bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(487,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ bot_bot_assn ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_mod__false) ).

thf(2543,plain,
    ! [A: produc3658429121746597890et_nat] :
      ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ bot_bot_assn ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(137,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Un__Int__eq_I2_J) ).

thf(1052,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(53,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4781_DiffI) ).

thf(727,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
     => ( ~ ( aa_set_nat_o @ ( member_nat @ A ) @ C )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(147,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ~ ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ D @ E ) )
                & ! [F: heap_e7401611519738050253t_unit,G: set_nat] :
                    ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ G )
                        = bot_bot_set_nat )
                      & ( aa_hea7994211679605476167unit_o @ ( relH @ E @ D ) @ F )
                      & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ F @ E ) )
                      & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ F @ G ) ) )
                   => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ F @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2484_wand__raw_Oelims_I2_J) ).

thf(1094,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ C )
     => ~ ! [D: heap_e7401611519738050253t_unit,E: set_nat] :
            ( ( C
              = ( produc7507926704131184380et_nat @ D @ E ) )
           => ~ ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ D @ E ) )
                & ! [F: heap_e7401611519738050253t_unit,G: set_nat] :
                    ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ E ) @ G )
                        = bot_bot_set_nat )
                      & ( aa_hea7994211679605476167unit_o @ ( relH @ E @ D ) @ F )
                      & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ F @ E ) )
                      & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ F @ G ) ) )
                   => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ F @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ E ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(462,axiom,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
       => ( aa_hea7994211679605476167unit_o @ ( heap_Time_success_a @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2509_hoare__triple__success) ).

thf(2426,plain,
    ! [A: assn,B: heap_Time_Heap_a,C: fun_a_assn,D: heap_e7401611519738050253t_unit,E: set_nat] :
      ( ( hoare_hoare_triple_a @ A @ B @ C )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ D @ E ) )
       => ( aa_hea7994211679605476167unit_o @ ( heap_Time_success_a @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(246,axiom,
    ! [A: set_nat,B: set_nat,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) @ C ) @ D )
    <=> ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ D )
        & ( aa_hea7994211679605476167unit_o @ ( relH @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_relH__dist__union) ).

thf(1536,plain,
    ! [A: set_nat,B: set_nat,C: heap_e7401611519738050253t_unit,D: heap_e7401611519738050253t_unit] :
      ( ( ( aa_hea7994211679605476167unit_o @ ( relH @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) @ C ) @ D )
       => ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ D )
          & ( aa_hea7994211679605476167unit_o @ ( relH @ B @ C ) @ D ) ) )
      & ( ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ C ) @ D )
          & ( aa_hea7994211679605476167unit_o @ ( relH @ B @ C ) @ D ) )
       => ( aa_hea7994211679605476167unit_o @ ( relH @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(179,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_sup__ge2) ).

thf(1240,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(123,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_Un__left__absorb) ).

thf(991,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(220,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_inf_Oassoc) ).

thf(1421,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(471,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2458_models__in__range) ).

thf(2458,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(167,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_inf__sup__distrib1) ).

thf(1180,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(352,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5297_shunt2) ).

thf(1966,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ B ) ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(107,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_sup_Oleft__commute) ).

thf(931,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(251,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5175_inf__cancel__left2) ).

thf(1553,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(349,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_Int__emptyI) ).

thf(1949,plain,
    ! [A: set_nat,B: set_nat] :
      ( ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(336,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_boolean__algebra_Oconj__zero__left) ).

thf(1913,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ bot_bot_set_nat ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(118,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_inf_OcoboundedI1) ).

thf(976,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(19,axiom,
    ! [A: set_nat] :
      ( ? [B: nat] : ( aa_set_nat_o @ ( member_nat @ B ) @ A )
    <=> ( A != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_ex__in__conv) ).

thf(581,plain,
    ! [A: set_nat] :
      ( ( ? [B: nat] : ( aa_set_nat_o @ ( member_nat @ B ) @ A )
       => ( A != bot_bot_set_nat ) )
      & ( ( A != bot_bot_set_nat )
       => ? [B: nat] : ( aa_set_nat_o @ ( member_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(95,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_Int__commute) ).

thf(891,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(129,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4301_diff__shunt__var) ).

thf(1010,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(380,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1424_boolean__algebra_Oconj__disj__distrib) ).

thf(2071,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(296,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2105_inf_Oabsorb4) ).

thf(1734,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(150,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) )
    <=> ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ D ) )
        & ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ F )
                = bot_bot_set_nat )
              & ( aa_hea7994211679605476167unit_o @ ( relH @ D @ C ) @ E )
              & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ D ) )
              & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ F ) ) )
           => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2486_wand__raw_Osimps) ).

thf(1108,plain,
    ! [A: fun_Pr6460944699146269935_nat_o,B: fun_Pr6460944699146269935_nat_o,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) )
       => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ D ) )
          & ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
              ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ F )
                  = bot_bot_set_nat )
                & ( aa_hea7994211679605476167unit_o @ ( relH @ D @ C ) @ E )
                & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ D ) )
                & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ F ) ) )
             => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ F ) ) ) ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ C @ D ) )
          & ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
              ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ D ) @ F )
                  = bot_bot_set_nat )
                & ( aa_hea7994211679605476167unit_o @ ( relH @ D @ C ) @ E )
                & ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ D ) )
                & ( aa_Pro653082453696054616_nat_o @ A @ ( produc7507926704131184380et_nat @ E @ F ) ) )
             => ( aa_Pro653082453696054616_nat_o @ B @ ( produc7507926704131184380et_nat @ E @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ F ) ) ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ A ) @ B ) @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(361,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4861_Compl__disjoint2) ).

thf(1998,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(276,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_le__iff__inf) ).

thf(1649,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = A ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = A )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(443,axiom,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: set_nat,D: assn,E: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ E ) )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ E )
            = bot_bot_set_nat )
         => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ D ) ) @ ( produc7507926704131184380et_nat @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_star__assnI) ).

thf(2352,plain,
    ! [A: assn,B: heap_e7401611519738050253t_unit,C: set_nat,D: assn,E: set_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ B @ C ) )
     => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ B @ E ) )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ E )
            = bot_bot_set_nat )
         => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ D ) ) @ ( produc7507926704131184380et_nat @ B @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(146,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
    <=> ( ( A
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2091_inf_Ostrict__order__iff) ).

thf(1084,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
       => ( ( A
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( A
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) )
          & ( A != B ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(82,axiom,
    ( ( aa_o_assn @ pure_assn @ $false )
    = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2448_pure__false) ).

thf(844,plain,
    ( ( aa_o_assn @ pure_assn @ $false )
    = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(421,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2766_ab__semigroup__mult__class_Omult_Ocommute) ).

thf(2226,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(275,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Int__Un__eq_I1_J) ).

thf(1646,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(198,axiom,
    top_top_assn != one_one_assn,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9231_assn__basic__inequalities_I1_J) ).

thf(1326,plain,
    top_top_assn != one_one_assn,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(184,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_sup_OboundedI) ).

thf(1253,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ C ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(114,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_sup__bot__left) ).

thf(961,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ bot_bot_set_nat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(450,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2761_mult_Oassoc) ).

thf(2389,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(386,axiom,
    ! [A: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ bot_bot_set_nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1404_bot_Oextremum) ).

thf(2098,plain,
    ! [A: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ bot_bot_set_nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(236,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_sup__inf__distrib2) ).

thf(1481,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ A ) @ C ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(38,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ wand_assn @ A ) @ B )
      = ( abs_assn @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ ( rep_assn @ A ) ) @ ( rep_assn @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2494_wand__assn__def) ).

thf(652,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ wand_assn @ A ) @ B )
      = ( abs_assn @ ( aa_fun2638059832795814268_nat_o @ ( wand_raw @ ( rep_assn @ A ) ) @ ( rep_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(464,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_star__false__right) ).

thf(2431,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ bot_bot_assn )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(400,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_inf__sup__aci_I1_J) ).

thf(2152,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(452,axiom,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h2 @ as2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_M2) ).

thf(2394,plain,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h2 @ as2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(397,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4584_Diff__eq__empty__iff) ).

thf(2135,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(457,axiom,
    ~ ! [A: set_nat,B: set_nat] :
        ( ( as
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
            = bot_bot_set_nat )
         => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h2 @ A ) )
           => ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h2 @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062as1_Aas2_O_A_092_060lbrakk_062as_A_061_Aas1_A_092_060union_062_Aas2_059_Aas1_A_092_060inter_062_Aas2_A_061_A_123_125_059_A_Ih_M_Aas1_J_A_092_060Turnstile_062_AP_059_A_Ih_M_Aas2_J_A_092_060Turnstile_062_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(2406,plain,
    ~ ! [A: set_nat,B: set_nat] :
        ( ( as
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
            = bot_bot_set_nat )
         => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h2 @ A ) )
           => ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(285,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ aTP_Lamm_cz @ A ) @ B )
    <=> ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9844_ATP_Olambda__153) ).

thf(1689,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ aTP_Lamm_cz @ A ) @ B )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A ) )
      & ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ A )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ aTP_Lamm_cz @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(17,axiom,
    ! [A: fun_nat_nat,B: set_nat] :
      ( ( ( image_nat_nat @ A @ B )
        = bot_bot_set_nat )
    <=> ( B = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5897_image__is__empty) ).

thf(568,plain,
    ! [A: fun_nat_nat,B: set_nat] :
      ( ( ( ( image_nat_nat @ A @ B )
          = bot_bot_set_nat )
       => ( B = bot_bot_set_nat ) )
      & ( ( B = bot_bot_set_nat )
       => ( ( image_nat_nat @ A @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(264,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ D )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1395_boolean__algebra__cancel_Osup1) ).

thf(1607,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ D )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(98,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_sup_Oassoc) ).

thf(899,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(370,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_boolean__algebra_Oconj__zero__left) ).

thf(2036,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ bot_bot_assn ) @ A )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(437,axiom,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
    <=> ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
        & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_mod__h__bot__iff_I5_J) ).

thf(2315,plain,
    ! [A: assn,B: assn,C: heap_e7401611519738050253t_unit] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
       => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) )
          & ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ B ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ ( produc7507926704131184380et_nat @ C @ bot_bot_set_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(385,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Un__Int__eq_I3_J) ).

thf(2095,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(44,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4662_Int__Diff) ).

thf(684,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(13,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( groups6906906614972039071t_assn @ C @ B )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ) @ ( groups6906906614972039071t_assn @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7341_prod_Osubset__diff) ).

thf(549,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( groups6906906614972039071t_assn @ C @ B )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) ) ) @ ( groups6906906614972039071t_assn @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(226,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_inf_Oabsorb2) ).

thf(1444,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(52,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ? [D: set_nat] :
          ( ( aa_set_nat_o @ finite_finite_nat @ D )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
          & ( aa_set_nat_o @ C @ D ) )
    <=> ? [D: set_nat] :
          ( ( aa_set_nat_o @ finite_finite_nat @ D )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
          & ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7897_ex__finite__subset__image) ).

thf(716,plain,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ( ? [D: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
            & ( aa_set_nat_o @ C @ D ) )
       => ? [D: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
            & ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) )
      & ( ? [D: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B )
            & ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) )
       => ? [D: set_nat] :
            ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) )
            & ( aa_set_nat_o @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(161,axiom,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7433_prod_Ounion__inter) ).

thf(1161,plain,
    ! [A: set_nat,B: set_nat,C: fun_nat_assn] :
      ( ( aa_set_nat_o @ finite_finite_nat @ A )
     => ( ( aa_set_nat_o @ finite_finite_nat @ B )
       => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) @ ( groups6906906614972039071t_assn @ C @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( groups6906906614972039071t_assn @ C @ A ) ) @ ( groups6906906614972039071t_assn @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(398,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat,C: assn,D: assn] :
      ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
     => ( ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ F )
              = bot_bot_set_nat )
           => ( ( aa_hea7994211679605476167unit_o @ ( relH @ B @ A ) @ E )
             => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ B ) )
               => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ C ) @ ( produc7507926704131184380et_nat @ E @ F ) )
                 => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ E @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ F ) ) ) ) ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ wand_assn @ C ) @ D ) ) @ ( produc7507926704131184380et_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2443_wand__assnI) ).

thf(2142,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat,C: assn,D: assn] :
      ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ A @ B ) )
     => ( ! [E: heap_e7401611519738050253t_unit,F: set_nat] :
            ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ F )
              = bot_bot_set_nat )
           => ( ( aa_hea7994211679605476167unit_o @ ( relH @ B @ A ) @ E )
             => ( ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ E @ B ) )
               => ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ C ) @ ( produc7507926704131184380et_nat @ E @ F ) )
                 => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ D ) @ ( produc7507926704131184380et_nat @ E @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ F ) ) ) ) ) ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ wand_assn @ C ) @ D ) ) @ ( produc7507926704131184380et_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(27,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ A )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4565_Diff__cancel) ).

thf(620,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ A )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(190,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Un__Int__eq_I4_J) ).

thf(1280,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(401,axiom,
    ( ( aa_o_assn @ pure_assn @ $true )
    = one_one_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2949_pure__true) ).

thf(2155,plain,
    ( ( aa_o_assn @ pure_assn @ $true )
    = one_one_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(423,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( abs_assn @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ ( rep_assn @ A ) ) @ ( rep_assn @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2504_times__assn__def) ).

thf(2233,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( abs_assn @ ( aa_fun2638059832795814268_nat_o @ ( times_assn_raw @ ( rep_assn @ A ) ) @ ( rep_assn @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(269,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
    <=> ( A = bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5185_subset__Compl__self__eq) ).

thf(1625,plain,
    ! [A: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) )
       => ( A = bot_bot_set_nat ) )
      & ( ( A = bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( uminus5710092332889474511et_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(207,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4699_Diff__partition) ).

thf(1380,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(328,axiom,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ B )
    <=> ( ( ( produc8586169260539613262et_nat @ B )
          = bot_bot_set_nat )
        & A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9385_mod__pure) ).

thf(1876,plain,
    ! [A: $o,B: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ B )
       => ( ( ( produc8586169260539613262et_nat @ B )
            = bot_bot_set_nat )
          & A ) )
      & ( ( ( ( produc8586169260539613262et_nat @ B )
            = bot_bot_set_nat )
          & A )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_o_assn @ pure_assn @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(182,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4953_inf__compl__bot__left1) ).

thf(1248,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(55,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4654_Diff__Int__distrib2) ).

thf(735,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(428,axiom,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2894_one__assn__raw_Oelims_I3_J) ).

thf(2258,plain,
    ! [A: produc3658429121746597890et_nat] :
      ( ~ ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
     => ~ ! [B: heap_e7401611519738050253t_unit,C: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ B @ C ) )
           => ( C = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(153,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2460_relH__in__rangeI_I1_J) ).

thf(1133,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( aa_Pro653082453696054616_nat_o @ in_range @ ( produc7507926704131184380et_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(255,axiom,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_inf__idem) ).

thf(1578,plain,
    ! [A: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(351,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( bot_bot_set_nat
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
    <=> ( ( A = bot_bot_set_nat )
        & ( B = bot_bot_set_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_bot__eq__sup__iff) ).

thf(1957,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( bot_bot_set_nat
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
       => ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) ) )
      & ( ( ( A = bot_bot_set_nat )
          & ( B = bot_bot_set_nat ) )
       => ( bot_bot_set_nat
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(79,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4581_Un__Diff__cancel) ).

thf(833,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(116,axiom,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
    <=> ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
        & ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Int__iff) ).

thf(967,plain,
    ! [A: nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
       => ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( member_nat @ A ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ( aa_set_nat_o @ ( member_nat @ A ) @ C ) )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(364,axiom,
    ! [A: $o] :
      ( ( ( aa_o_assn @ pure_assn @ A )
        = bot_bot_assn )
    <=> ~ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2447_pure__assn__eq__false__iff) ).

thf(2008,plain,
    ! [A: $o] :
      ( ( ( ( aa_o_assn @ pure_assn @ A )
          = bot_bot_assn )
       => ~ A )
      & ( ~ A
       => ( ( aa_o_assn @ pure_assn @ A )
          = bot_bot_assn ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(357,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
      = bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4589_Diff__disjoint) ).

thf(1986,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ B ) @ A ) )
      = bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(496,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_assn__times__comm) ).

thf(2572,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(290,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_inf__sup__aci_I8_J) ).

thf(1710,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(330,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Int__Un__eq_I4_J) ).

thf(1891,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(420,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_inf_Oleft__commute) ).

thf(2223,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ C ) )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(505,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inf__right__idem) ).

thf(2619,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(162,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_sup__left__commute) ).

thf(1165,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(489,axiom,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( hoare_new_addrs @ A @ B @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_new__addr__refl) ).

thf(2549,plain,
    ! [A: heap_e7401611519738050253t_unit,B: set_nat] :
      ( ( hoare_new_addrs @ A @ B @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(71,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ A )
    <=> ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
       != bot_bot_set_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4740_disjoint__alt__simp3) ).

thf(801,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ A )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
         != bot_bot_set_nat ) )
      & ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
         != bot_bot_set_nat )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(358,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2098_inf_Ostrict__boundedE) ).

thf(1989,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
     => ~ ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
         => ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(97,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_distrib__inf__le) ).

thf(897,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ C ) ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(216,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_le__infI2) ).

thf(1410,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(64,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4660_Diff__Int2) ).

thf(767,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(459,axiom,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h @ as2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062) ).

thf(2417,plain,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ r ) @ ( produc7507926704131184380et_nat @ h @ as2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(342,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_inf_OcoboundedI2) ).

thf(1930,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ C ) @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(321,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ! [D: assn,E: assn,F: assn] :
          ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ E ) @ F ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ E ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ F ) ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_distrib__imp2) ).

thf(1829,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ! [D: assn,E: assn,F: assn] :
          ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ E ) @ F ) )
          = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ E ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ D ) @ F ) ) )
     => ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ B ) @ C ) )
        = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ sup_sup_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B ) ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(18,axiom,
    ! [A: nat,B: set_nat,C: fun_nat_o] :
      ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( collect_nat @ C ) ) )
    <=> ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
        & ( aa_nat_o @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1807_Int__Collect) ).

thf(575,plain,
    ! [A: nat,B: set_nat,C: fun_nat_o] :
      ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( collect_nat @ C ) ) )
       => ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ( aa_nat_o @ C @ A ) ) )
      & ( ( ( aa_set_nat_o @ ( member_nat @ A ) @ B )
          & ( aa_nat_o @ C @ A ) )
       => ( aa_set_nat_o @ ( member_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ ( collect_nat @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(158,axiom,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ A )
       => ( aa_hea7994211679605476167unit_o @ ( relH @ D @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1250_relH__subset) ).

thf(1152,plain,
    ! [A: set_nat,B: heap_e7401611519738050253t_unit,C: heap_e7401611519738050253t_unit,D: set_nat] :
      ( ( aa_hea7994211679605476167unit_o @ ( relH @ A @ B ) @ C )
     => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ A )
       => ( aa_hea7994211679605476167unit_o @ ( relH @ D @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(88,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4719_Int__Diff__Un) ).

thf(860,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(501,axiom,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B )
    <=> ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
        & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4882_mod__not__dist) ).

thf(2600,plain,
    ! [A: assn,B: produc3658429121746597890et_nat] :
      ( ( ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B )
       => ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
          & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) ) )
      & ( ( ( aa_Pro653082453696054616_nat_o @ in_range @ B )
          & ~ ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ A ) @ B ) )
       => ( aa_Pro653082453696054616_nat_o @ ( rep_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(355,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
    <=> ( B
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_sup_Oorder__iff) ).

thf(1976,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
       => ( B
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) ) )
      & ( ( B
          = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ A ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(480,axiom,
    ( ( hoare_new_addrs @ h2 @ as @ h )
    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) ) @ as2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062) ).

thf(2507,plain,
    ( ( hoare_new_addrs @ h2 @ as @ h )
    = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) ) @ as2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(340,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_inf_Ocobounded2) ).

thf(1925,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(446,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ aTP_Lamm_fs @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10737_ATP_Olambda__1046) ).

thf(2372,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ aTP_Lamm_fs @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(25,axiom,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ! [D: set_nat] :
          ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) ) )
         => ( aa_set_nat_o @ C @ D ) )
    <=> ! [D: set_nat] :
          ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
            & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B ) )
         => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7907_all__finite__subset__image) ).

thf(607,plain,
    ! [A: fun_nat_nat,B: set_nat,C: fun_set_nat_o] :
      ( ( ! [D: set_nat] :
            ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
              & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) ) )
           => ( aa_set_nat_o @ C @ D ) )
       => ! [D: set_nat] :
            ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
              & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B ) )
           => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) ) )
      & ( ! [D: set_nat] :
            ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
              & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ B ) )
           => ( aa_set_nat_o @ C @ ( image_nat_nat @ A @ D ) ) )
       => ! [D: set_nat] :
            ( ( ( aa_set_nat_o @ finite_finite_nat @ D )
              & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( image_nat_nat @ A @ B ) ) )
           => ( aa_set_nat_o @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(21,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4658_Diff__Diff__Int) ).

thf(596,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(206,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_inf__sup__ord_I1_J) ).

thf(1378,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(485,axiom,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_assn__times__assoc) ).

thf(2539,plain,
    ! [A: assn,B: assn,C: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ B ) ) @ C )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ A ) @ ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ times_times_assn @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(291,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
        = bot_bot_set_nat )
    <=> ! [C: nat] :
          ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
         => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_disjoint__iff) ).

thf(1713,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat )
       => ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) ) )
      & ( ! [C: nat] :
            ( ( aa_set_nat_o @ ( member_nat @ C ) @ A )
           => ~ ( aa_set_nat_o @ ( member_nat @ C ) @ B ) )
       => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B )
          = bot_bot_set_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(120,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_sup__left__idem) ).

thf(982,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(127,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_sup_Oabsorb2) ).

thf(1004,plain,
    ! [A: set_nat,B: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(297,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2144_sup_Ostrict__coboundedI1) ).

thf(1737,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(381,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1437_boolean__algebra_Odisj__conj__distrib) ).

thf(2074,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ B ) @ C ) )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(253,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
    <=> ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
        & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_sup_Obounded__iff) ).

thf(1565,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C )
       => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) ) )
      & ( ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ C )
          & ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ B ) @ C ) )
       => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(377,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ minus_minus_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5100_minus__assn__def) ).

thf(2059,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ minus_minus_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ ( aa_assn_assn @ uminus_uminus_assn @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(218,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_inf__sup__ord_I3_J) ).

thf(1416,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(61,axiom,
    ! [A: set_nat] :
      ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ bot_bot_set_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2073_bot_Oextremum__strict) ).

thf(755,plain,
    ! [A: set_nat] :
      ~ ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_set_nat @ A ) @ bot_bot_set_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(442,axiom,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h2 @ as1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_M1) ).

thf(2351,plain,
    aa_Pro653082453696054616_nat_o @ ( rep_assn @ p ) @ ( produc7507926704131184380et_nat @ h2 @ as1 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(412,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_inf__le2) ).

thf(2191,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(474,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_inf__sup__aci_I1_J) ).

thf(2470,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(438,axiom,
    ! [A: produc3658429121746597890et_nat,B: $o] :
      ( ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
      <=> B )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( B
            <=> ( D != bot_bot_set_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2892_one__assn__raw_Oelims_I1_J) ).

thf(2321,plain,
    ! [A: produc3658429121746597890et_nat,B: $o] :
      ( ( ( ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A )
         => B )
        & ( B
         => ( aa_Pro653082453696054616_nat_o @ one_assn_raw @ A ) ) )
     => ~ ! [C: heap_e7401611519738050253t_unit,D: set_nat] :
            ( ( A
              = ( produc7507926704131184380et_nat @ C @ D ) )
           => ( ( B
               => ( D != bot_bot_set_nat ) )
              & ( ( D != bot_bot_set_nat )
               => B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(347,axiom,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_Int__lower1) ).

thf(1944,plain,
    ! [A: set_nat,B: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ inf_inf_set_nat @ A ) @ B ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(203,axiom,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ A )
      = bot_bot_assn ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4935_boolean__algebra_Oconj__cancel__left) ).

thf(1367,plain,
    ! [A: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ ( aa_assn_assn @ uminus_uminus_assn @ A ) ) @ A )
      = bot_bot_assn ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(110,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ A )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1400_boolean__algebra__cancel_Osup2) ).

thf(940,plain,
    ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
      ( ( A
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) )
     => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ A )
        = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(239,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_sup_OcoboundedI2) ).

thf(1490,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ B )
     => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(15,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4666_set__diff__diff__left) ).

thf(560,plain,
    ! [A: set_nat,B: set_nat,C: set_nat] :
      ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ B ) ) @ C )
      = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ minus_minus_set_nat @ A ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(389,axiom,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( abs_assn @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_eq @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2598_inf__assn__def) ).

thf(2106,plain,
    ! [A: assn,B: assn] :
      ( ( aa_assn_assn @ ( aa_ass954072293579886259n_assn @ inf_inf_assn @ A ) @ B )
      = ( abs_assn @ ( aa_ass4243947775541419017_nat_o @ ( aTP_Lamm_eq @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(384,axiom,
    ! [A: fun_se1909708154429037836et_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) )
     => ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) )
       => ( ! [D: set_nat,E: set_nat,F: set_nat] :
              ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ D )
             => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ F ) @ D )
               => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ E ) @ F ) ) @ D ) ) )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C )
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_sup__unique) ).

thf(2087,plain,
    ! [A: fun_se1909708154429037836et_nat,B: set_nat,C: set_nat] :
      ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ D ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) )
     => ( ! [D: set_nat,E: set_nat] : ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ D ) @ E ) )
       => ( ! [D: set_nat,E: set_nat,F: set_nat] :
              ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ E ) @ D )
             => ( ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ F ) @ D )
               => ( aa_set_nat_o @ ( aa_set7861427066675100071_nat_o @ ord_less_eq_set_nat @ ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ E ) @ F ) ) @ D ) ) )
         => ( ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ sup_sup_set_nat @ B ) @ C )
            = ( aa_set_nat_set_nat @ ( aa_set2309701074089104077et_nat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(2834,plain,
    $false,
    inference(cvc4,[status(thm)],[2163,2452,1469,1190,1168,2109,1767,1105,846,2559,777,666,2199,1322,1665,1995,2263,909,628,2595,2499,2077,1750,1211,1158,2210,730,2622,2381,994,1728,1205,1142,655,1971,677,1305,1437,1041,2395,2062,1939,2248,1756,2448,2434,1233,2476,1919,747,1640,945,1954,2042,538,1458,2575,1078,1788,1426,1001,1391,973,1475,1803,1127,1782,2020,841,1601,1386,2400,1529,1904,1703,1055,2039,1826,2185,2562,934,1992,2126,1462,2356,1907,2501,1860,2217,1545,2552,1319,1347,770,2520,1773,1100,1847,1922,817,902,2169,2403,2222,924,789,1632,2122,937,1383,2034,2555,2616,1946,1418,2236,623,1682,1136,1581,2335,1183,1283,687,2437,2281,877,1447,2523,1622,1394,1526,998,988,2103,2392,507,1697,1242,849,1863,2473,534,1067,798,1074,1604,1274,1723,894,952,820,1487,2606,2015,1174,1676,693,630,1619,2150,1370,2132,2414,2445,1032,2565,852,1296,1836,1656,1407,710,1687,1457,522,830,889,2179,1740,1910,1592,1983,650,1017,1064,1227,2509,1397,2245,1350,1936,2157,2115,1762,2100,2359,1375,1329,753,1424,2053,1584,2613,1214,1889,1612,1155,2460,1493,701,2536,738,1266,1668,2465,2006,1429,779,1759,647,1776,1263,2125,985,515,1478,2546,508,921,541,765,1286,1515,1026,2338,1202,792,633,1779,1187,674,2423,662,906,2001,750,2176,2585,824,1747,601,1251,618,1764,1548,1927,2028,1595,1833,1007,1916,2048,2188,2568,875,958,1795,1124,1256,1615,1389,1139,2193,2220,2293,713,1635,2442,2166,1897,1638,1271,2308,1853,2229,2084,1806,2299,1542,2378,863,979,604,1894,2493,1589,1933,880,1043,1801,1571,599,2025,758,858,2267,1731,1029,1022,1177,1061,2578,811,2182,2129,2343,1149,964,626,915,1556,2542,1460,1293,2278,2418,1699,827,1643,563,1694,1973,2069,912,1171,2051,636,1245,1726,1364,1496,2303,2239,1809,531,548,927,1081,2202,1472,553,1413,1076,1208,589,836,1551,1770,855,640,2397,872,1400,1941,1753,1798,525,690,1598,705,2375,1230,1484,2160,1499,1432,1785,2429,1658,808,1679,643,544,2056,744,2543,1052,727,1094,2426,1536,1240,991,1421,2458,1180,1966,931,1553,1949,1913,976,581,891,1010,2071,1734,1108,1998,1649,2352,1084,844,2226,1646,1326,1253,961,2389,2098,1481,652,2431,2152,2394,2135,2406,1689,568,1607,899,2036,2315,2095,684,549,1444,716,1161,2142,620,1280,2155,2233,1625,1380,1876,1248,735,2258,1133,1578,1957,833,967,2008,1986,2572,1710,1891,2223,2619,1165,2549,801,1989,897,1410,767,2417,1930,1829,575,1152,860,2600,1976,2507,1925,2372,607,596,1378,2539,1713,982,1004,1737,2074,1565,2059,1416,755,2351,2191,2470,2321,1944,1367,940,1490,560,2106,2087]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : ITP213_3 : TPTP v8.2.0. Released v8.0.0.
% 0.13/0.17  % Command  : run_Leo-III %s %d
% 0.17/0.39  % Computer : n015.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit : 300
% 0.17/0.39  % WCLimit  : 300
% 0.17/0.39  % DateTime : Sat May 18 17:30:24 EDT 2024
% 0.17/0.39  % CPUTime  : 
% 1.03/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 5.87/2.33  % [INFO] 	 Parsing done (1396ms). 
% 6.10/2.35  % [INFO] 	 Running in sequential loop mode. 
% 6.65/2.61  % [INFO] 	 eprover registered as external prover. 
% 6.65/2.62  % [INFO] 	 cvc4 registered as external prover. 
% 6.65/2.62  % [INFO] 	 Scanning for conjecture ... 
% 10.85/3.72  % [INFO] 	 Found a conjecture (or negated_conjecture) and 10775 axioms. Running axiom selection ... 
% 12.21/4.10  % [INFO] 	 Axiom selection finished. Selected 504 axioms (removed 10271 axioms). 
% 13.30/4.37  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 13.30/4.40  % [INFO] 	 Type checking passed. 
% 13.30/4.40  % [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 ... 
% 25.65/7.69  % External prover 'cvc4' found a proof!
% 25.65/7.69  % [INFO] 	 Killing All external provers ... 
% 25.65/7.69  % Time passed: 7123ms (effective reasoning time: 5339ms)
% 25.65/7.69  % 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)>
% 25.65/7.70  % Axioms used in derivation (504): fact_4959_boolean__algebra_Ode__Morgan__disj, fact_4565_Diff__cancel, fact_9253_top__assn__def, fact_4927_boolean__algebra_Oconj__cancel__right, fact_2421_accp__subset__induct, fact_499_Int__commute, fact_1185_Int__mono, fact_5430_ComplD, fact_5191_Compl__Int, fact_4678_subset__minus__empty, fact_138_inf__sup__absorb, fact_2597_sup__assn__def, fact_7839_finite__psubset__induct, fact_1176_Int__subset__iff, fact_572_inf_OcoboundedI2, fact_2119_less__infI2, fact_1400_boolean__algebra__cancel_Osup2, fact_1437_boolean__algebra_Odisj__conj__distrib, fact_1151_boolean__algebra_Oconj__zero__left, fact_7761_not__finite__existsD, fact_146_sup__inf__absorb, fact_791_sup_OcoboundedI2, fact_1383_boolean__algebra__cancel_Oinf1, fact_415_inf__assoc, fact_724_le__infI1, fact_388_equals0D, fact_1486_disjoint__mono, fact_4729_Diff__Un, fact_4933_boolean__algebra_Oconj__cancel__left, fact_3460_one__assn__raw_Opelims_I3_J, fact_2252_subset__emptyI, fact_5877_image__empty, fact_2218_memb__imp__not__empty, fact_6062_image__Int__subset, fact_3604_left__right__inverse__power, fact_2507_Set_Ois__empty__def, fact_2444_pure__assn__eq__conv, fact_100_Int__Un__eq_I3_J, fact_927_sup__least, fact_7443_prod_OInt__Diff, fact_539_Un__assoc, fact_7747_finite__Un, fact_7794_finite_OemptyI, fact_478_inf__sup__aci_I5_J, fact_7341_prod_Osubset__diff, fact_2077_inf_Ostrict__coboundedI2, fact_895_sup__unique, fact_7838_infinite__Un, fact_580_inf_OcoboundedI1, fact_7814_rev__finite__subset, fact_35_mod__star__conv, fact_7897_ex__finite__subset__image, fact_4865_Compl__disjoint, fact_555_UnI2, fact_90_assn__times__comm, fact_3036_one__assn__def, fact_7806_finite__subset, fact_7877_finite__surj, fact_4662_Int__Diff, fact_983_le__supI, fact_266_mod__or__dist, fact_935_sup__mono, fact_5185_subset__Compl__self__eq, fact_267_star__false__left, fact_660_inf__absorb1, fact_1027_disjoint__iff, fact_7887_finite__subset__image, fact_1074_distrib__imp1, fact_201_inf_Oleft__idem, fact_1194_Int__absorb1, fact_1157_times__assn__raw_Osimps, fact_4719_Int__Diff__Un, fact_2594_bot__assn__def, fact_967_sup__ge2, fact_5175_inf__cancel__left2, fact_4648_Diff__subset, fact_296_le__sup__iff, fact_421_inf_Oassoc, fact_943_sup_Omono, fact_2535_Rep__assn__inverse, fact_1218_Un__least, fact_6009_subset__imageE, fact_1248_subset__Un__eq, fact_463_sup_Ocommute, fact_9229_merge__true__star, fact_1781_subset__Collect__conv, fact_4650_double__diff, fact_2509_hoare__triple__success, fact_604_inf_Ocobounded2, fact_513_IntD1, fact_887_sup_Oabsorb1, fact_620_inf_Oorder__iff, fact_2607_pure__assn__def, fact_6024_image__mono, fact_360_sup__bot__right, fact_277_le__inf__iff, fact_453_sup_Oleft__commute, fact_2893_one__assn__raw_Oelims_I2_J, fact_34_hoare__triple__preI, fact_1072_distrib__imp2, fact_2640_pure__assn__raw_Oelims_I3_J, fact_1250_relH__subset, fact_10737_ATP_Olambda__1046, fact_2176_sup_Oabsorb3, fact_191_inf_Oright__idem, fact_1395_boolean__algebra__cancel_Osup1, fact_4835_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff, fact_503_Int__assoc, fact_1516_in__mono, fact_7799_infinite__imp__nonempty, fact_1527_subset__eq, fact_4953_inf__compl__bot__left1, fact_458_sup__commute, fact_2486_wand__raw_Osimps, fact_2136_sup_Ostrict__coboundedI2, fact_2445_merge__pure__star, fact_2583_Abs__assn__eqI_I1_J, fact_1255_Un__Int__assoc__eq, fact_2_M2, fact_430_inf__sup__aci_I2_J, fact_5394_ComplI, fact_426_inf__sup__aci_I1_J, fact_4873_Diff__Compl, fact_2892_one__assn__raw_Oelims_I1_J, fact_4714_Un__Diff__Int, fact_4871_inter__compl__diff__conv, fact_1014_disjoint__iff__not__equal, fact_373_star__or__dist1, fact_5887_empty__is__image, fact_311_inf__bot__left, fact_5181_inf__cancel__left1, fact_4691_Int__Diff__disjoint, fact_4967_boolean__algebra_Ode__Morgan__conj, fact_4803_DiffE, fact_115_Un__Int__eq_I4_J, fact_206_inf__idem, fact_195_inf__left__idem, fact_700_inf_OorderI, fact_2761_mult_Oassoc, fact_186_inf__right__idem, fact_6269_prod_Oempty, fact_2152_sup_Ostrict__order__iff, fact_807_sup_Oabsorb__iff2, fact_483_inf__sup__aci_I6_J, fact_23_mod__starD, fact_772_inf__sup__ord_I1_J, fact_301_inf__bot__right, fact_951_le__supI2, fact_12__092_060open_062relH_Aas2_Ah_Ah_H_092_060close_062, fact_871_sup__absorb1, fact_8__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_A_K_AR_092_060close_062, fact_823_sup_Ocobounded2, fact_393_emptyE, fact_1145_boolean__algebra_Oconj__zero__right, fact_2098_inf_Ostrict__boundedE, fact_2461_relH__refl, fact_3106_assn__one__left, fact_401_inf_Oleft__commute, fact_325_sup__bot_Oneutr__eq__iff, fact_628_inf__greatest, fact_588_inf_Oabsorb__iff2, fact_740_le__infI, fact_1228_Un__upper2, fact_183_empty__iff, fact_1064_inf__sup__distrib1, fact_5169_diff__eq, fact_1444_boolean__algebra_Oconj__disj__distrib2, fact_1431_boolean__algebra_Odisj__conj__distrib, fact_363_mod__h__bot__iff_I7_J, fact_166_empty__Collect__eq, fact_2447_pure__assn__eq__false__iff, fact_596_inf_Oabsorb__iff1, fact_2192_less__supI1, fact_1094_Un__empty__left, fact_269_inf_Obounded__iff, fact_29_relH__dist__union, fact_4675_psubset__imp__ex__mem, fact_28_mod__h__bot__indep, fact_1404_bot_Oextremum, fact_563_UnI1, fact_7433_prod_Ounion__inter, fact_4935_boolean__algebra_Oconj__cancel__left, fact_36_star__assnI, fact_518_IntE, fact_10154_ATP_Olambda__463, fact_676_inf_Oabsorb1, fact_305_inf__bot__right, fact_353_bot__eq__sup__iff, fact_210_inf_Oidem, fact_144_inf__sup__absorb, fact_9230_assn__basic__inequalities_I5_J, fact_1213_Un__mono, fact_879_sup_Oabsorb2, fact_400_inf_Oleft__commute, fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062as1_Aas2_O_A_092_060lbrakk_062as_A_061_Aas1_A_092_060union_062_Aas2_059_Aas1_A_092_060inter_062_Aas2_A_061_A_123_125_059_A_Ih_M_Aas1_J_A_092_060Turnstile_062_AP_059_A_Ih_M_Aas2_J_A_092_060Turnstile_062_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_1087_Un__empty__right, fact_2450_in__range__empty, fact_1382_boolean__algebra__cancel_Oinf1, fact_959_le__supI1, fact_105_Int__Un__eq_I2_J, fact_332_sup__bot_Oleft__neutral, fact_10752_ATP_Olambda__1061, fact_223_sup__left__idem, fact_1807_Int__Collect, fact_855_sup_OboundedE, fact_383_equals0I, fact_1048_sup__inf__distrib1, fact_7739_finite__Int, fact_7831_Un__infinite, fact_975_sup__ge1, fact_9962_ATP_Olambda__271, fact_1534_subset__iff, fact_410_inf_Ocommute, fact_2922_mult_Oright__neutral, fact_4569_empty__Diff, fact_2126_less__infI1, fact_435_inf__sup__aci_I3_J, fact_4941_inf__compl__bot__right, fact_497_Int__left__absorb, fact_218_sup_Oright__idem, fact_4833_boolean__algebra__class_Oboolean__algebra_Odouble__compl, fact_110_Int__Un__eq_I1_J, fact_2951_assn__basic__inequalities_I3_J, fact_7637_prod_Ounion__diff2, fact_27__092_060open_062as_A_061_Aas1_A_092_060union_062_Aas2_092_060close_062, fact_9252_mod__star__trueE, fact_5173_inf__cancel__left2, fact_7384_prod_Omono__neutral__right, fact_1233_Un__absorb1, fact_531_Un__commute, fact_7608_prod_Ounion__disjoint, fact_1414_bot_Oextremum__uniqueI, fact_1056_inf__sup__distrib2, fact_178_all__not__in__conv, fact_9929_ATP_Olambda__238, fact_1451_boolean__algebra_Odisj__conj__distrib2, fact_468_sup__assoc, fact_173_Collect__empty__eq, fact_692_inf__unique, fact_5305_shunt1, fact_1115_Int__Un__distrib, fact_2225_inter__eq__subsetI, fact_527_Un__left__absorb, fact_228_sup_Oleft__idem, fact_125_Un__Int__eq_I2_J, fact_1154_times__assn__raw_Oelims_I3_J, fact_3057_comm__monoid__mult__class_Omult__1, fact_2458_models__in__range, fact_4666_set__diff__diff__left, fact_4695_Diff__triv, fact_9235_mod__true, fact_411_inf_Ocommute, fact_2432_mod__h__bot__iff_I1_J, fact_243_Int__iff, fact_9387_mod__star__trueE_H, fact_4654_Diff__Int__distrib2, fact_2894_one__assn__raw_Oelims_I3_J, fact_2766_ab__semigroup__mult__class_Omult_Ocommute, fact_7374_prod_Omono__neutral__left, fact_847_sup_OboundedI, fact_3462_one__assn__raw_Opelims_I1_J, fact_4939_inf__compl__bot__right, fact_130_Un__Int__eq_I1_J, fact_2448_pure__false, fact_88_one__assn__raw_Ocases, fact_4658_Diff__Diff__Int, fact_732_inf__mono, fact_5339_uminus__assn__def, fact_2584_Abs__assn__eqI_I2_J, fact_543_ball__Un, fact_1174_empty__subsetI, fact_2084_inf_Ostrict__coboundedI1, fact_1445_boolean__algebra_Odisj__conj__distrib2, fact_2335_psubsetD, fact_1430_boolean__algebra_Oconj__disj__distrib, fact_2643_pure__assn__raw_Osimps, fact_999_inf__sup__ord_I3_J, fact_1223_Un__upper1, fact_1141_boolean__algebra_Oconj__zero__right, fact_95_Int__Un__eq_I4_J, fact_547_bex__Un, fact_2067_bot_Onot__eq__extremum, fact_211_inf_Oidem, fact_5100_minus__assn__def, fact_2641_pure__assn__raw_Oelims_I2_J, fact_5999_subset__image__iff, fact_4771_Diff__idemp, fact_644_inf_OboundedE, fact_4798_DiffD1, fact_1022_Int__empty__left, fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062, fact_4584_Diff__eq__empty__iff, fact_1105_Int__Un__distrib2, fact_159_sup__bot__left, fact_288_sup_Obounded__iff, fact_919_le__iff__sup, fact_799_sup_OcoboundedI1, fact_4589_Diff__disjoint, fact_2504_times__assn__def, fact_205_inf__idem, fact_1034_sup__inf__distrib2, fact_1007_inf__sup__ord_I4_J, fact_4951_inf__compl__bot__left1, fact_748_le__infE, fact_2484_wand__raw_Oelims_I2_J, fact_32_relH__trans, fact_1100_Un__Int__distrib2, fact_346_sup__eq__bot__iff, fact_3461_one__assn__raw_Opelims_I2_J, fact_10137_ATP_Olambda__446, fact_4683_disjoint__alt__simp2, fact_4577_Un__Diff__cancel2, fact_4966_boolean__algebra_Ode__Morgan__conj, fact_31_relH__sym, fact_2771_ab__semigroup__mult__class_Omult_Oleft__commute, fact_2891_one__assn__raw_Osimps, fact_7802_all__subset__image, fact_2452_in__range__dist__union, fact_3062_mult_Ocomm__neutral, fact_24_mod__starE, fact_3422_mod__emp__simp, fact_9231_assn__basic__inequalities_I1_J, fact_612_inf_Ocobounded1, fact_5289_sup__neg__inf, fact_10_Rep__assn__inject, fact_7597_prod_Ounion__inter__neutral, fact_2443_wand__assnI, fact_4573_Diff__empty, fact_5281_inf__shunt, fact_2160_sup_Ostrict__boundedE, fact_2949_pure__true, fact_4793_DiffD2, fact_523_Un__left__commute, fact_405_inf__commute, fact_420_inf_Oassoc, fact_5897_image__is__empty, fact_1147_boolean__algebra_Oconj__zero__left, fact_265_UnCI, fact_2451_mod__pure__star__dist, fact_9257_mod__h__bot__iff_I2_J, fact_9844_ATP_Olambda__153, fact_69_mem__Collect__eq, fact_839_sup_Oorder__iff, fact_1197_Int__absorb2, fact_307_inf__bot__left, fact_378_ex__in__conv, fact_5179_inf__cancel__left1, fact_4740_disjoint__alt__simp3, fact_2112_inf_Oabsorb3, fact_1058_inf__sup__distrib1, fact_5196_Compl__Un, fact_2073_bot_Oextremum__strict, fact_1238_Un__absorb2, fact_1200_Int__greatest, fact_372_mod__false, fact_4704_Diff__subset__conv, fact_4960_boolean__algebra_Ode__Morgan__disj, fact_903_sup_OorderI, fact_362_mod__h__bot__iff_I6_J, fact_1207_Int__Collect__mono, fact_911_sup_OorderE, fact_9386_mod__emp, fact_25_assms, fact_425_inf__sup__aci_I1_J, fact_416_inf__assoc, fact_7907_all__finite__subset__image, fact_668_inf_Oabsorb2, fact_374_star__or__dist2, fact_11_mod__h__bot__iff_I5_J, fact_1587_Collect__mono__iff, fact_436_inf__sup__aci_I3_J, fact_6031_image__Un, fact_2449_merge__pure__and, fact_863_sup__absorb2, fact_33_mod__relH, fact_1170_subset__empty, fact_5399_Compl__iff, fact_395_inf__left__commute, fact_2598_inf__assn__def, fact_652_inf__absorb2, fact_5315_disjoint__eq__subset__Compl, fact_5168_diff__eq, fact_2485_wand__raw_Oelims_I1_J, fact_0_DJ, fact_2105_inf_Oabsorb4, fact_1042_sup__inf__distrib1, fact_493_inf__sup__aci_I8_J, fact_1540_Collect__mono, fact_2459_relH__in__rangeI_I2_J, fact_257_Un__iff, fact_318_sup__bot_Oright__neutral, fact_2091_inf_Ostrict__order__iff, fact_3553_power__commuting__commutes, fact_185_inf__right__idem, fact_2223_set__notEmptyE, fact_406_inf__commute, fact_1182_Un__subset__iff, fact_196_inf__left__idem, fact_431_inf__sup__aci_I2_J, fact_152_sup__inf__absorb, fact_4656_Diff__Int__distrib, fact_1388_boolean__algebra__cancel_Oinf2, fact_1409_bot_Oextremum__unique, fact_501_Int__absorb, fact_2144_sup_Ostrict__coboundedI1, fact_3135_lambda__one, fact_1136_distrib__inf__le, fact_7824_finite__UnI, fact_2927_mult__1, fact_4776_Diff__iff, fact_2462_in__range__subset, fact_4699_Diff__partition, fact_2446_merge__pure__or, fact_1424_boolean__algebra_Oconj__disj__distrib, fact_7_MDL, fact_4724_Diff__Int, fact_4301_diff__shunt__var, fact_1018_Int__empty__right, fact_81_Collect__cong, fact_9251_mod__star__trueI, fact_1156_times__assn__raw_Oelims_I1_J, fact_1126_distrib__sup__le, fact_4882_mod__not__dist, fact_4670_Un__Diff, fact_1110_Un__Int__distrib, fact_495_Int__left__commute, fact_1491_disjointI, fact_2494_wand__assn__def, fact_89_assn__times__assoc, fact_6_M1, fact_780_inf__sup__ord_I2_J, fact_9385_mod__pure, fact_1438_boolean__algebra_Oconj__disj__distrib2, fact_815_sup_Oabsorb__iff1, fact_268_star__false__right, fact_120_Un__Int__eq_I3_J, fact_1040_sup__inf__distrib2, fact_4861_Compl__disjoint2, fact_2416_accp__subset, fact_190_inf_Oright__idem, fact_535_Un__absorb, fact_3563_power__commutes, fact_2642_pure__assn__raw_Oelims_I1_J, fact_571_UnE, fact_4646_Diff__mono, fact_2950_pure__assn__eq__emp__iff, fact_1155_times__assn__raw_Oelims_I2_J, fact_488_inf__sup__aci_I7_J, fact_6071_image__diff__subset, fact_684_le__iff__inf, fact_1521_subsetD, fact_4880_Compl__Diff__eq, fact_3_DJN, fact_441_inf__sup__aci_I4_J, fact_1050_inf__sup__distrib2, fact_708_inf_OorderE, fact_233_sup__idem, fact_1501_subsetI, fact_508_IntD2, fact_4581_Un__Diff__cancel, fact_2184_less__supI2, fact_4781_DiffI, fact_448_sup__left__commute, fact_4660_Diff__Int2, fact_2168_sup_Oabsorb4, fact_396_inf__left__commute, fact_1080_distrib__imp1, fact_3558_power__mult__distrib, fact_2483_wand__raw_Oelims_I3_J, fact_1032_Int__emptyI, fact_5_new__addr__refl, fact_371_mod__and__dist, fact_136_Un__empty, fact_9813_ATP_Olambda__122, fact_1243_subset__UnE, fact_7810_infinite__super, fact_440_inf__sup__aci_I4_J, fact_2460_relH__in__rangeI_I1_J, fact_4945_inf__compl__bot__left2, fact_473_sup_Oassoc, fact_756_inf__le2, fact_2433_hoare__triple__effect, fact_1422_boolean__algebra_Odisj__zero__right, fact_764_inf__le1, fact_200_inf_Oleft__idem, fact_248_IntI, fact_4929_boolean__algebra_Oconj__cancel__right, fact_339_sup__bot_Oeq__neutr__iff, fact_1188_Int__lower1, fact_4687_disjoint__alt__simp1, fact_991_le__supE, fact_238_sup_Oidem, fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062, fact_1387_boolean__algebra__cancel_Oinf2, fact_1066_distrib__imp2, fact_636_inf_OboundedI, fact_4947_inf__compl__bot__left2, fact_1120_Un__Int__crazy, fact_831_sup_Ocobounded1, fact_1191_Int__lower2, fact_2260_not__psubset__empty, fact_1458_inf__Some, fact_716_le__infI2, fact_5297_shunt2
% 25.65/7.70  % No. of inferences in proof: 1012
% 25.65/7.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7123 ms resp. 5339 ms w/o parsing
% 26.53/7.90  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.79/7.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------