%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP234_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:05 AM UTC 2026
% Result : Theorem 25.64s 7.91s
% Output : Refutation 26.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 311
% Syntax : Number of formulae : 624 ( 434 unt; 0 typ; 0 def)
% Number of atoms : 1114 ( 962 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 7892 ( 165 ~; 37 |; 116 &;7257 @)
% ( 42 <=>; 275 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 459 ( 458 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 36 con; 0-4 aty)
% Number of variables : 1349 ( 0 ^;1297 !; 32 ?;1349 :)
% ( 0 !>; 0 ?*; 0 @-; 20 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_o: $tType ).
thf(fun_fu1853463631764337203omplex_type,type,
fun_fu1853463631764337203omplex: $tType ).
thf(fun_fu3656911019502402539omplex_type,type,
fun_fu3656911019502402539omplex: $tType ).
thf(fun_fu1415179302847465169at_nat_type,type,
fun_fu1415179302847465169at_nat: $tType ).
thf(fun_fu7668021852929781713at_int_type,type,
fun_fu7668021852929781713at_int: $tType ).
thf(fun_fu165555417558590673at_int_type,type,
fun_fu165555417558590673at_int: $tType ).
thf(fun_fu2295278630349710275d_enat_type,type,
fun_fu2295278630349710275d_enat: $tType ).
thf(fun_fu7433039812794084273omplex_type,type,
fun_fu7433039812794084273omplex: $tType ).
thf(fun_fu6938252901338612493omplex_type,type,
fun_fu6938252901338612493omplex: $tType ).
thf(fun_li6914387844523535256_nat_o_type,type,
fun_li6914387844523535256_nat_o: $tType ).
thf(fun_fu2696391717783642433at_nat_type,type,
fun_fu2696391717783642433at_nat: $tType ).
thf(fun_fu708039595006729209at_int_type,type,
fun_fu708039595006729209at_int: $tType ).
thf(fun_fu4402582520547598677nt_int_type,type,
fun_fu4402582520547598677nt_int: $tType ).
thf(fun_fu8020931516743756395ex_nat_type,type,
fun_fu8020931516743756395ex_nat: $tType ).
thf(fun_fu2556788080963300715ex_int_type,type,
fun_fu2556788080963300715ex_int: $tType ).
thf(fun_fu8001260946965626035ex_int_type,type,
fun_fu8001260946965626035ex_int: $tType ).
thf(fun_fu5040975675184911655d_enat_type,type,
fun_fu5040975675184911655d_enat: $tType ).
thf(set_Pr1542805901266377927at_nat_type,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(produc9217583074051984497at_nat_type,type,
produc9217583074051984497at_nat: $tType ).
thf(fun_fu3351286688164852109at_nat_type,type,
fun_fu3351286688164852109at_nat: $tType ).
thf(fun_fu3636980702898289805at_int_type,type,
fun_fu3636980702898289805at_int: $tType ).
thf(fun_fu7424888833511495217nt_int_type,type,
fun_fu7424888833511495217nt_int: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_fu8695033588447641837al_nat_type,type,
fun_fu8695033588447641837al_nat: $tType ).
thf(fun_fu3562227594288721901al_int_type,type,
fun_fu3562227594288721901al_int: $tType ).
thf(fun_fu8404755328348021045al_int_type,type,
fun_fu8404755328348021045al_int: $tType ).
thf(fun_fu3686806697881729723t_real_type,type,
fun_fu3686806697881729723t_real: $tType ).
thf(produc6392793444374437607at_nat_type,type,
produc6392793444374437607at_nat: $tType ).
thf(fun_fu5553606195750802321at_nat_type,type,
fun_fu5553606195750802321at_nat: $tType ).
thf(fun_fu3518430294936654993at_int_type,type,
fun_fu3518430294936654993at_int: $tType ).
thf(fun_fu6324116013759063093nt_int_type,type,
fun_fu6324116013759063093nt_int: $tType ).
thf(fun_fu4584101141160326545at_int_type,type,
fun_fu4584101141160326545at_int: $tType ).
thf(fun_fu7802804735324696557nt_int_type,type,
fun_fu7802804735324696557nt_int: $tType ).
thf(fun_fu5303113179588540421d_enat_type,type,
fun_fu5303113179588540421d_enat: $tType ).
thf(fun_fu3180206027003385489at_nat_type,type,
fun_fu3180206027003385489at_nat: $tType ).
thf(fun_fu6398909621167755501nt_nat_type,type,
fun_fu6398909621167755501nt_nat: $tType ).
thf(fun_fu8366861321737653343at_nat_type,type,
fun_fu8366861321737653343at_nat: $tType ).
thf(fun_fu2469135700067826619at_int_type,type,
fun_fu2469135700067826619at_int: $tType ).
thf(fun_Pr8877776288780692068_nat_o_type,type,
fun_Pr8877776288780692068_nat_o: $tType ).
thf(fun_fu3064074204415222357nt_int_type,type,
fun_fu3064074204415222357nt_int: $tType ).
thf(fun_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_fu9045186299510176150at_o_o_type,type,
fun_fu9045186299510176150at_o_o: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(fun_fu5235757188046002187enat_o_type,type,
fun_fu5235757188046002187enat_o: $tType ).
thf(fun_fu1584491925252458057omplex_type,type,
fun_fu1584491925252458057omplex: $tType ).
thf(fun_fu7039103635370308747enat_o_type,type,
fun_fu7039103635370308747enat_o: $tType ).
thf(fun_fu4978687986242683275enat_o_type,type,
fun_fu4978687986242683275enat_o: $tType ).
thf(fun_fu709861064203714431x_real_type,type,
fun_fu709861064203714431x_real: $tType ).
thf(list_P8469869581646625389at_nat_type,type,
list_P8469869581646625389at_nat: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(fun_fu3593947265352647275omplex_type,type,
fun_fu3593947265352647275omplex: $tType ).
thf(fun_fu2513798379308225899ex_nat_type,type,
fun_fu2513798379308225899ex_nat: $tType ).
thf(fun_fu4692242605864086655ex_int_type,type,
fun_fu4692242605864086655ex_int: $tType ).
thf(fun_fu7523448966510524487plex_o_type,type,
fun_fu7523448966510524487plex_o: $tType ).
thf(fun_fu7998770217265696895plex_o_type,type,
fun_fu7998770217265696895plex_o: $tType ).
thf(fun_fu2242303475990058951plex_o_type,type,
fun_fu2242303475990058951plex_o: $tType ).
thf(fun_fu1954767945837035587plex_o_type,type,
fun_fu1954767945837035587plex_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_fu961951300032224317real_o_type,type,
fun_fu961951300032224317real_o: $tType ).
thf(fun_fu9132278742410140537l_real_type,type,
fun_fu9132278742410140537l_real: $tType ).
thf(set_Pr1916528119006554503T_VEBT_type,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(fun_fu2073406008148662973_nat_o_type,type,
fun_fu2073406008148662973_nat_o: $tType ).
thf(fun_fu6810213084838398785t_real_type,type,
fun_fu6810213084838398785t_real: $tType ).
thf(fun_fu7636615314495962301enat_o_type,type,
fun_fu7636615314495962301enat_o: $tType ).
thf(fun_fu8808458186726762489_nat_o_type,type,
fun_fu8808458186726762489_nat_o: $tType ).
thf(fun_fu2316129113556059581enat_o_type,type,
fun_fu2316129113556059581enat_o: $tType ).
thf(fun_fu2664588616489632577_int_o_type,type,
fun_fu2664588616489632577_int_o: $tType ).
thf(fun_VE2573032740582156747_nat_o_type,type,
fun_VE2573032740582156747_nat_o: $tType ).
thf(fun_co3732688428756473980omplex_type,type,
fun_co3732688428756473980omplex: $tType ).
thf(fun_fu3768230810189712741al_nat_type,type,
fun_fu3768230810189712741al_nat: $tType ).
thf(fun_fu5645595436833112697al_int_type,type,
fun_fu5645595436833112697al_int: $tType ).
thf(fun_fu1620311477532340197t_real_type,type,
fun_fu1620311477532340197t_real: $tType ).
thf(fun_fu8391177546919232046_nat_o_type,type,
fun_fu8391177546919232046_nat_o: $tType ).
thf(fun_Pr2028404973800837934_nat_o_type,type,
fun_Pr2028404973800837934_nat_o: $tType ).
thf(fun_Pr9018117161326028078_int_o_type,type,
fun_Pr9018117161326028078_int_o: $tType ).
thf(fun_fu7872074469501006851d_enat_type,type,
fun_fu7872074469501006851d_enat: $tType ).
thf(fun_fu3043630359712370243plex_o_type,type,
fun_fu3043630359712370243plex_o: $tType ).
thf(fun_fu4472351043248340291real_o_type,type,
fun_fu4472351043248340291real_o: $tType ).
thf(fun_fu5533088652784741581real_o_type,type,
fun_fu5533088652784741581real_o: $tType ).
thf(fun_fu5935951186182374353at_nat_type,type,
fun_fu5935951186182374353at_nat: $tType ).
thf(fun_fu960360787657196261at_int_type,type,
fun_fu960360787657196261at_int: $tType ).
thf(fun_fu4902120768161409089at_int_type,type,
fun_fu4902120768161409089at_int: $tType ).
thf(fun_fu6652553491520710942omplex_type,type,
fun_fu6652553491520710942omplex: $tType ).
thf(fun_fu973771059875708133nt_nat_type,type,
fun_fu973771059875708133nt_nat: $tType ).
thf(fun_co3194742168270691230omplex_type,type,
fun_co3194742168270691230omplex: $tType ).
thf(fun_fu5273811730930669507plex_o_type,type,
fun_fu5273811730930669507plex_o: $tType ).
thf(fun_fu3780232916559739075_nat_o_type,type,
fun_fu3780232916559739075_nat_o: $tType ).
thf(fun_fu3074144567237359299plex_o_type,type,
fun_fu3074144567237359299plex_o: $tType ).
thf(fun_fu1580565752866428867_nat_o_type,type,
fun_fu1580565752866428867_nat_o: $tType ).
thf(fun_fu2339071201290874307plex_o_type,type,
fun_fu2339071201290874307plex_o: $tType ).
thf(fun_fu810243669753863363_int_o_type,type,
fun_fu810243669753863363_int_o: $tType ).
thf(fun_fu5575653946431489541real_o_type,type,
fun_fu5575653946431489541real_o: $tType ).
thf(fun_fu3519392362395250509real_o_type,type,
fun_fu3519392362395250509real_o: $tType ).
thf(fun_se2100927751953696370t_real_type,type,
fun_se2100927751953696370t_real: $tType ).
thf(fun_fu6813129056075673441_nat_o_type,type,
fun_fu6813129056075673441_nat_o: $tType ).
thf(fun_fu4228744305898656589_int_o_type,type,
fun_fu4228744305898656589_int_o: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_fu875838123782038019d_enat_type,type,
fun_fu875838123782038019d_enat: $tType ).
thf(fun_fu3572752990780465756omplex_type,type,
fun_fu3572752990780465756omplex: $tType ).
thf(fun_fu2357351296865450298t_real_type,type,
fun_fu2357351296865450298t_real: $tType ).
thf(fun_fu4997915388126054052at_nat_type,type,
fun_fu4997915388126054052at_nat: $tType ).
thf(fun_fu2507832243194327296at_int_type,type,
fun_fu2507832243194327296at_int: $tType ).
thf(fun_fu4933388555348682076at_int_type,type,
fun_fu4933388555348682076at_int: $tType ).
thf(produc9211091688327510695T_VEBT_type,type,
produc9211091688327510695T_VEBT: $tType ).
thf(fun_fu9090758901314268781nt_o_o_type,type,
fun_fu9090758901314268781nt_o_o: $tType ).
thf(fun_fu4528473944208963392omplex_type,type,
fun_fu4528473944208963392omplex: $tType ).
thf(fun_fu8173507842404362040omplex_type,type,
fun_fu8173507842404362040omplex: $tType ).
thf(fun_fu6075382464776002713_nat_o_type,type,
fun_fu6075382464776002713_nat_o: $tType ).
thf(fun_fu7440396458814700513_nat_o_type,type,
fun_fu7440396458814700513_nat_o: $tType ).
thf(fun_fu2760153274138146437_int_o_type,type,
fun_fu2760153274138146437_int_o: $tType ).
thf(fun_fu4125167268176844237_int_o_type,type,
fun_fu4125167268176844237_int_o: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_fu5354524256550068955t_real_type,type,
fun_fu5354524256550068955t_real: $tType ).
thf(fun_fu3477889739401271834t_real_type,type,
fun_fu3477889739401271834t_real: $tType ).
thf(fun_fu4045816715887884506omplex_type,type,
fun_fu4045816715887884506omplex: $tType ).
thf(fun_fu5289434066392675523_nat_o_type,type,
fun_fu5289434066392675523_nat_o: $tType ).
thf(fun_fu4757868175734369219real_o_type,type,
fun_fu4757868175734369219real_o: $tType ).
thf(fun_fu7328815047503086531_int_o_type,type,
fun_fu7328815047503086531_int_o: $tType ).
thf(fun_fu8602227297639178947real_o_type,type,
fun_fu8602227297639178947real_o: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_fu1590586450949517859at_nat_type,type,
fun_fu1590586450949517859at_nat: $tType ).
thf(fun_fu3492966305048685787at_int_type,type,
fun_fu3492966305048685787at_int: $tType ).
thf(fun_fu5956788528830221615omplex_type,type,
fun_fu5956788528830221615omplex: $tType ).
thf(fun_re6135230694098607860t_real_type,type,
fun_re6135230694098607860t_real: $tType ).
thf(fun_fu4165420744652164954omplex_type,type,
fun_fu4165420744652164954omplex: $tType ).
thf(fun_fu2872202335991144794ex_nat_type,type,
fun_fu2872202335991144794ex_nat: $tType ).
thf(fun_fu382119191059418038ex_int_type,type,
fun_fu382119191059418038ex_int: $tType ).
thf(fun_fu7350578069724619866ex_int_type,type,
fun_fu7350578069724619866ex_int: $tType ).
thf(fun_fu5589980185390252312t_real_type,type,
fun_fu5589980185390252312t_real: $tType ).
thf(fun_fu6436183194761443139_nat_o_type,type,
fun_fu6436183194761443139_nat_o: $tType ).
thf(fun_fu5646853623633916995_int_o_type,type,
fun_fu5646853623633916995_int_o: $tType ).
thf(fun_fu8304507701009772099_nat_o_type,type,
fun_fu8304507701009772099_nat_o: $tType ).
thf(fun_fu8064956510386623256t_real_type,type,
fun_fu8064956510386623256t_real: $tType ).
thf(fun_fu7493154764834273859_int_o_type,type,
fun_fu7493154764834273859_int_o: $tType ).
thf(fun_fu927436805355353155_nat_o_type,type,
fun_fu927436805355353155_nat_o: $tType ).
thf(fun_fu7336479014630192387t_real_type,type,
fun_fu7336479014630192387t_real: $tType ).
thf(fun_re7819166435457029784t_real_type,type,
fun_re7819166435457029784t_real: $tType ).
thf(fun_fu2115079063411676732t_real_type,type,
fun_fu2115079063411676732t_real: $tType ).
thf(fun_fu4540635375566031512t_real_type,type,
fun_fu4540635375566031512t_real: $tType ).
thf(fun_fu163975356400620604t_real_type,type,
fun_fu163975356400620604t_real: $tType ).
thf(fun_fu3666831194735236760at_nat_type,type,
fun_fu3666831194735236760at_nat: $tType ).
thf(fun_fu1176748049803510004at_int_type,type,
fun_fu1176748049803510004at_int: $tType ).
thf(fun_fu3172963709264267764nt_int_type,type,
fun_fu3172963709264267764nt_int: $tType ).
thf(fun_fu2955637221277575299d_enat_type,type,
fun_fu2955637221277575299d_enat: $tType ).
thf(fun_fu5112335056569181187at_nat_type,type,
fun_fu5112335056569181187at_nat: $tType ).
thf(fun_fu6685514224203069699at_int_type,type,
fun_fu6685514224203069699at_int: $tType ).
thf(fun_Ex8979681104671372885d_enat_type,type,
fun_Ex8979681104671372885d_enat: $tType ).
thf(fun_fu7075445697382584196_int_o_type,type,
fun_fu7075445697382584196_int_o: $tType ).
thf(fun_fu4413992040155564420at_nat_type,type,
fun_fu4413992040155564420at_nat: $tType ).
thf(fun_fu1567874110255095356at_int_type,type,
fun_fu1567874110255095356at_int: $tType ).
thf(fun_fu5519318738670804632at_int_type,type,
fun_fu5519318738670804632at_int: $tType ).
thf(fun_in281396392327853336at_int_type,type,
fun_in281396392327853336at_int: $tType ).
thf(fun_co6147893885205795665omplex_type,type,
fun_co6147893885205795665omplex: $tType ).
thf(fun_fu4368050222092438908at_nat_type,type,
fun_fu4368050222092438908at_nat: $tType ).
thf(fun_fu1877967077160712152at_int_type,type,
fun_fu1877967077160712152at_int: $tType ).
thf(fun_fu3874182736621469912nt_int_type,type,
fun_fu3874182736621469912nt_int: $tType ).
thf(set_Pr3451248702717554689st_nat_type,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(set_Pr765067013931698361st_int_type,type,
set_Pr765067013931698361st_int: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(set_Pr6192946355708809607T_VEBT_type,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(fun_fu8384527901749275179omplex_type,type,
fun_fu8384527901749275179omplex: $tType ).
thf(fun_fu7714627026455246123x_real_type,type,
fun_fu7714627026455246123x_real: $tType ).
thf(fun_fu2338672169953838170al_nat_type,type,
fun_fu2338672169953838170al_nat: $tType ).
thf(fun_fu9071961061876887222al_int_type,type,
fun_fu9071961061876887222al_int: $tType ).
thf(fun_fu86166166672686426al_int_type,type,
fun_fu86166166672686426al_int: $tType ).
thf(fun_fu734372843349436973enat_o_type,type,
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thf(fun_fu746971108421118025t_real_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(fun_fu1994797156054922755_nat_o_type,type,
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thf(fun_fu8066363281484412158at_nat_type,type,
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thf(fun_fu5576280136552685402at_int_type,type,
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thf(fun_fu7572495796013443162nt_int_type,type,
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thf(fun_fu7383104390662542801enat_o_type,type,
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thf(fun_fu8278438252182731309enat_o_type,type,
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thf(fun_fu4016676428956456173at_nat_type,type,
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thf(fun_fu1526593284024729417at_int_type,type,
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thf(fun_fu40286998686754419omplex_type,type,
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thf(fun_fu705315015666092147ex_nat_type,type,
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thf(fun_fu4213752561377164075ex_int_type,type,
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thf(fun_na6632006986671646835omplex_type,type,
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thf(fun_co6883864892131739507omplex_type,type,
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thf(fun_fu3096161788242865370at_int_type,type,
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thf(fun_fu5283083362935887158nt_int_type,type,
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thf(fun_fu570715051317967998at_nat_type,type,
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thf(fun_fu2757636626010989786nt_nat_type,type,
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thf(fun_fu3719809307426920623omplex_type,type,
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thf(fun_se2389560805064864136_nat_o_type,type,
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thf(fun_na927404270896789692_nat_o_type,type,
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thf(fun_fu2408719596384163971_nat_o_type,type,
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thf(produc7248412053542808358at_nat_type,type,
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thf(fun_Pr4738963024209204295_int_o_type,type,
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thf(fun_na3970208099681795815_nat_o_type,type,
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thf(fun_fu806425790188207109plex_o_type,type,
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thf(fun_fu3043978019632300333x_real_type,type,
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thf(fun_se6072594010446775118enat_o_type,type,
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thf(fun_fu3077872570260440615l_real_type,type,
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thf(fun_fu9148622857633396327enat_o_type,type,
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thf(fun_fu6122667721776870753plex_o_type,type,
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thf(fun_fu6229866931165912581plex_o_type,type,
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thf(fun_fu1553612835185860561ex_nat_type,type,
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thf(fun_fu8286901727108909613ex_int_type,type,
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thf(produc1828647624359046049st_nat_type,type,
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thf(produc1186641810826059865st_int_type,type,
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thf(fun_re8542384036533109323t_real_type,type,
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thf(fun_re4112884445705685835l_real_type,type,
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thf(list_P7037539587688870467BT_nat_type,type,
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thf(list_P4547456442757143711BT_int_type,type,
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thf(list_P5647936690300460905T_VEBT_type,type,
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thf(list_P7524865323317820941T_VEBT_type,type,
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thf(produc8243902056947475879T_VEBT_type,type,
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thf(fun_fu3214020956574444655al_nat_type,type,
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thf(fun_fu3737244727311182119al_int_type,type,
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thf(fun_fu6899955116716589935t_real_type,type,
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thf(fun_fu121957152452960295t_real_type,type,
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thf(fun_re4756235295228751087t_real_type,type,
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thf(fun_na5225841814499866095t_real_type,type,
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thf(set_Pr7556676689462069481BT_nat_type,type,
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thf(fun_fu3532930458344041007omplex_type,type,
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thf(fun_li1025265955262268170_nat_o_type,type,
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thf(fun_na7718645245721260691t_real_type,type,
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thf(fun_na5873943405026509934VEBT_o_type,type,
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thf(fun_na1154345429118027792d_enat_type,type,
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thf(fun_Ex2441982661509597004d_enat_type,type,
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thf(fun_fu7002938529518989751at_nat_type,type,
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thf(fun_fu8464300013002972271at_int_type,type,
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thf(fun_fu8905809029841901679nt_nat_type,type,
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thf(fun_fu1143798476471108391nt_int_type,type,
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thf(fun_na3244735409550470327at_nat_type,type,
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thf(fun_na7654559027617327379at_int_type,type,
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thf(fun_na2382631619178260847at_int_type,type,
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thf(fun_in6793278964266839919at_int_type,type,
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thf(fun_in1521351555827773387at_int_type,type,
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thf(fun_fu4302481349826706223omplex_type,type,
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thf(fun_se2170385732985038782_nat_o_type,type,
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thf(fun_fu1358370060594899587plex_o_type,type,
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thf(fun_na4030263931958639548enat_o_type,type,
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thf(fun_fu3022329567491847689real_o_type,type,
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thf(fun_fu4478067837645853357l_real_type,type,
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thf(fun_Pr672294278902479040t_real_type,type,
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thf(fun_fu1852998413150313061real_o_type,type,
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thf(fun_fu3729927046167673097real_o_type,type,
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thf(fun_fu2707946803925496145al_nat_type,type,
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thf(fun_fu217863658993769389al_int_type,type,
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thf(fun_Pr2602117396471556196at_nat_type,type,
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thf(fun_Pr7647638413817135296at_int_type,type,
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thf(fun_na1476630412504255114at_nat_type,type,
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thf(fun_in4514472496968388910at_nat_type,type,
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thf(fun_in4211310926729683942nt_int_type,type,
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thf(fun_re7208826350674946562omplex_type,type,
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thf(fun_na819858167508000762st_nat_type,type,
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thf(fun_co286204877037288194omplex_type,type,
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thf(fun_fu6621322437453427393_nat_o_type,type,
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thf(fun_fu4185471554550717449_int_o_type,type,
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thf(fun_fu7030473000426307245t_real_type,type,
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thf(fun_na2418085665696872764plex_o_type,type,
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thf(fun_Ex239764483819389678enat_o_type,type,
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thf(option4927543243414619207at_nat_type,type,
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thf(filter1242075044329608583at_nat_type,type,
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thf(fun_na1591161823130732966omplex_type,type,
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thf(fun_co3258106519541737638omplex_type,type,
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thf(fun_fu5477517762487726877_nat_o_type,type,
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thf(fun_fu8207122332086543297_nat_o_type,type,
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thf(fun_fu7052161110045437101at_int_type,type,
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thf(fun_fu1805223966450871909_int_o_type,type,
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thf(fun_fu4534828536049688329_int_o_type,type,
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thf(fun_fu1078644964449000785nt_nat_type,type,
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thf(fun_na7928631014926962227_nat_o_type,type,
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thf(fun_na2978037997607195054t_real_type,type,
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thf(fun_na7542918316964655096d_enat_type,type,
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thf(fun_na40478436225343698at_nat_type,type,
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thf(fun_na6773767328148392750at_int_type,type,
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thf(fun_in5181886200629118930at_int_type,type,
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thf(fun_Ex7123704652682714774at_nat_type,type,
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thf(fun_Ex4633621507750988018at_int_type,type,
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thf(fun_Ex6820543082444009806nt_int_type,type,
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thf(list_P6011104703257516679at_nat_type,type,
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thf(list_P3521021558325789923at_int_type,type,
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thf(list_P8198026277950538467nt_nat_type,type,
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thf(list_P5707943133018811711nt_int_type,type,
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thf(produc9072475918466114483BT_nat_type,type,
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thf(produc4894624898956917775BT_int_type,type,
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thf(produc8025551001238799321T_VEBT_type,type,
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thf(produc1531783533982839933T_VEBT_type,type,
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thf(fun_se2161501677553633980real_o_type,type,
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thf(fun_li1940556759920501533BT_nat_type,type,
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thf(set_Pr1261947904930325089at_nat_type,type,
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thf(set_Pr958786334691620121nt_int_type,type,
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thf(fun_fu9050450510664235267real_o_type,type,
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thf(fun_Pr4796943543331071514_nat_o_type,type,
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thf(fun_Pr3238374608701176162_int_o_type,type,
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thf(fun_na5723442673449079972x_real_type,type,
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thf(fun_na7234455742697417626_nat_o_type,type,
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thf(fun_na7306406234920378942_int_o_type,type,
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thf(fun_VE6480751511521678896_nat_o_type,type,
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thf(fun_na6887940067898170868VEBT_o_type,type,
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thf(fun_na1142814060743658952omplex_type,type,
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thf(fun_na8457291176974909128ex_nat_type,type,
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thf(fun_na5967208032043182372ex_int_type,type,
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thf(fun_in3657390099950231424ex_int_type,type,
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thf(fun_co636942507509095880at_nat_type,type,
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thf(fun_co7370231399432144932at_int_type,type,
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thf(fun_co333780937270390912nt_int_type,type,
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thf(fun_se382663106265794036_nat_o_type,type,
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thf(fun_se867122708194164540_int_o_type,type,
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thf(fun_na8563630686737515764_nat_o_type,type,
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thf(fun_co1148497455491383662plex_o_type,type,
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thf(fun_fu4001317426178549763_nat_o_type,type,
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thf(fun_fu3883539188510166275_int_o_type,type,
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thf(fun_re1486040982601698206enat_o_type,type,
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thf(fun_na6724076748692969250l_real_type,type,
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thf(fun_in3542000807660726686enat_o_type,type,
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thf(fun_Ex6161781345015750782_nat_o_type,type,
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thf(fun_Ex3916636377345304866_int_o_type,type,
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thf(set_list_VEBT_VEBT_type,type,
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thf(fun_Ex5852502975177633731d_enat_type,type,
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thf(fun_nat_fun_int_int_type,type,
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thf(fun_int_fun_nat_nat_type,type,
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thf(fun_int_fun_nat_int_type,type,
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thf(fun_int_fun_int_int_type,type,
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thf(fun_set_set_nat_o_type,type,
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thf(fun_na1554462459066888140plex_o_type,type,
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thf(fun_in5065666251602127472plex_o_type,type,
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thf(fun_co5676208753217392844_nat_o_type,type,
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thf(fun_co3431063785546946928_int_o_type,type,
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thf(set_li5464603477888414924d_enat_type,type,
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thf(fun_num_option_num_type,type,
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thf(fun_li827083013690791791enat_o_type,type,
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thf(fun_Ex3741802288643809319omplex_type,type,
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thf(fun_co6496365337113880337d_enat_type,type,
fun_co6496365337113880337d_enat: $tType ).
thf(set_se7270636423289371942d_enat_type,type,
set_se7270636423289371942d_enat: $tType ).
thf(fun_se8123728892507317397enat_o_type,type,
fun_se8123728892507317397enat_o: $tType ).
thf(fun_real_fun_real_o_type,type,
fun_real_fun_real_o: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_nat_int_type,type,
product_prod_nat_int: $tType ).
thf(product_prod_int_nat_type,type,
product_prod_int_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(fun_set_nat_real_type,type,
fun_set_nat_real: $tType ).
thf(fun_real_set_nat_type,type,
fun_real_set_nat: $tType ).
thf(fun_nat_list_nat_type,type,
fun_nat_list_nat: $tType ).
thf(fun_list_nat_nat_type,type,
fun_list_nat_nat: $tType ).
thf(fun_list_int_nat_type,type,
fun_list_int_nat: $tType ).
thf(set_list_complex_type,type,
set_list_complex: $tType ).
thf(fun_VEBT_VEBT_nat_type,type,
fun_VEBT_VEBT_nat: $tType ).
thf(fun_real_fun_nat_o_type,type,
fun_real_fun_nat_o: $tType ).
thf(fun_real_fun_int_o_type,type,
fun_real_fun_int_o: $tType ).
thf(fun_nat_fun_real_o_type,type,
fun_nat_fun_real_o: $tType ).
thf(fun_list_complex_o_type,type,
fun_list_complex_o: $tType ).
thf(fun_int_fun_real_o_type,type,
fun_int_fun_real_o: $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_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_set_int_type,type,
fun_nat_set_int: $tType ).
thf(fun_complex_complex_type,type,
fun_complex_complex: $tType ).
thf(set_set_complex_type,type,
set_set_complex: $tType ).
thf(fun_fun_int_int_o_type,type,
fun_fun_int_int_o: $tType ).
thf(fun_set_complex_o_type,type,
fun_set_complex_o: $tType ).
thf(fun_re6065469302365115155d_enat_type,type,
fun_re6065469302365115155d_enat: $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_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_Ex1451620480498224165t_real_type,type,
fun_Ex1451620480498224165t_real: $tType ).
thf(option_VEBT_VEBT_type,type,
option_VEBT_VEBT: $tType ).
thf(option_set_nat_type,type,
option_set_nat: $tType ).
thf(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(fun_in5914218760682845459d_enat_type,type,
fun_in5914218760682845459d_enat: $tType ).
thf(fun_Ex7660298398204468809at_nat_type,type,
fun_Ex7660298398204468809at_nat: $tType ).
thf(fun_Ex3482447378695272101at_int_type,type,
fun_Ex3482447378695272101at_int: $tType ).
thf(option_Extended_enat_type,type,
option_Extended_enat: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(fun_real_complex_type,type,
fun_real_complex: $tType ).
thf(fun_complex_real_type,type,
fun_complex_real: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(set_list_int_type,type,
set_list_int: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(fun_set_real_o_type,type,
fun_set_real_o: $tType ).
thf(fun_list_nat_o_type,type,
fun_list_nat_o: $tType ).
thf(fun_list_int_o_type,type,
fun_list_int_o: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(fun_VEBT_VEBT_o_type,type,
fun_VEBT_VEBT_o: $tType ).
thf(fun_nat_complex_type,type,
fun_nat_complex: $tType ).
thf(fun_int_complex_type,type,
fun_int_complex: $tType ).
thf(fun_complex_nat_type,type,
fun_complex_nat: $tType ).
thf(fun_complex_int_type,type,
fun_complex_int: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $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(list_Extended_enat_type,type,
list_Extended_enat: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(set_Extended_enat_type,type,
set_Extended_enat: $tType ).
thf(fun_char_nat_type,type,
fun_char_nat: $tType ).
thf(fun_real_real_type,type,
fun_real_real: $tType ).
thf(fun_nat_char_type,type,
fun_nat_char: $tType ).
thf(fun_Extended_enat_o_type,type,
fun_Extended_enat_o: $tType ).
thf(fun_real_nat_type,type,
fun_real_nat: $tType ).
thf(fun_real_int_type,type,
fun_real_int: $tType ).
thf(fun_nat_real_type,type,
fun_nat_real: $tType ).
thf(fun_int_real_type,type,
fun_int_real: $tType ).
thf(list_complex_type,type,
list_complex: $tType ).
thf(fun_num_num_type,type,
fun_num_num: $tType ).
thf(fun_num_nat_type,type,
fun_num_nat: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_int_type,type,
fun_nat_int: $tType ).
thf(fun_int_nat_type,type,
fun_int_nat: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(set_complex_type,type,
set_complex: $tType ).
thf(option_real_type,type,
option_real: $tType ).
thf(filter_real_type,type,
filter_real: $tType ).
thf(fun_complex_o_type,type,
fun_complex_o: $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(filter_nat_type,type,
filter_nat: $tType ).
thf(fun_o_fun_o_o_type,type,
fun_o_fun_o_o: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $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(fun_real_o_type,type,
fun_real_o: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $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(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(extended_enat_type,type,
extended_enat: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(fun_o_o_type,type,
fun_o_o: $tType ).
thf(char_type,type,
char: $tType ).
thf(real_type,type,
real: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(aTP_Lamm_aaa_decl,type,
aTP_Lamm_aaa: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_aas_decl,type,
aTP_Lamm_aas: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_aba_decl,type,
aTP_Lamm_aba: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_abl_decl,type,
aTP_Lamm_abl: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_cd_decl,type,
aTP_Lamm_cd: fun_nat_nat ).
thf(aTP_Lamm_ko_decl,type,
aTP_Lamm_ko: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_la_decl,type,
aTP_Lamm_la: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mw_decl,type,
aTP_Lamm_mw: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_py_decl,type,
aTP_Lamm_py: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_rp_decl,type,
aTP_Lamm_rp: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_tl_decl,type,
aTP_Lamm_tl: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_tp_decl,type,
aTP_Lamm_tp: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_tz_decl,type,
aTP_Lamm_tz: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ua_decl,type,
aTP_Lamm_ua: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ue_decl,type,
aTP_Lamm_ue: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ul_decl,type,
aTP_Lamm_ul: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_zi_decl,type,
aTP_Lamm_zi: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_zj_decl,type,
aTP_Lamm_zj: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_zl_decl,type,
aTP_Lamm_zl: nat > fun_na8563630686737515764_nat_o ).
thf(aTP_Lamm_zy_decl,type,
aTP_Lamm_zy: fun_nat_fun_nat_nat ).
thf(binomial_decl,type,
binomial: fun_nat_fun_nat_nat ).
thf(finite_card_set_nat_decl,type,
finite_card_set_nat: set_set_nat > nat ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: fun_nat_fun_nat_nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(times_times_nat_decl,type,
times_times_nat: fun_nat_fun_nat_nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(drop_nat_decl,type,
drop_nat: nat > list_nat > list_nat ).
thf(find_VEBT_VEBT_decl,type,
find_VEBT_VEBT: fun_VEBT_VEBT_o > list_VEBT_VEBT > option_VEBT_VEBT ).
thf(linord738340561235409698at_nat_decl,type,
linord738340561235409698at_nat: fun_nat_nat > list_nat > list_nat ).
thf(map_nat_nat_decl,type,
map_nat_nat: fun_nat_nat > list_nat > list_nat ).
thf(set_VEBT_VEBT2_decl,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(tl_nat_decl,type,
tl_nat: list_nat > list_nat ).
thf(list_u1324408373059187874T_VEBT_decl,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(nth_VEBT_VEBT_decl,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(upt_decl,type,
upt: nat > nat > list_nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(compow_fun_nat_nat_decl,type,
compow_fun_nat_nat: nat > fun_nat_nat > fun_nat_nat ).
thf(nat_triangle_decl,type,
nat_triangle: fun_nat_nat ).
thf(none_P5556105721700978146at_nat_decl,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(some_P7363390416028606310at_nat_decl,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(ord_le4337996190870823476T_VEBT_decl,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ord_max_nat_decl,type,
ord_max_nat: fun_nat_fun_nat_nat ).
thf(power_power_nat_decl,type,
power_power_nat: fun_nat_fun_nat_nat ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: nat > fun_na1476630412504255114at_nat ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
thf(modulo_modulo_nat_decl,type,
modulo_modulo_nat: fun_nat_fun_nat_nat ).
thf(collect_set_nat_decl,type,
collect_set_nat: fun_set_nat_o > set_set_nat ).
thf(vEBT_Node_decl,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > fun_nat_o ).
thf(vEBT_VEBT_high_decl,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
thf(vEBT_V5917875025757280293ildren_decl,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > fun_nat_o ).
thf(vEBT_VEBT_low_decl,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_o ).
thf(vEBT_vebt_insert_decl,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(vEBT_VEBT_bit_concat_decl,type,
vEBT_VEBT_bit_concat: nat > fun_nat_fun_nat_nat ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: fun_VEBT_VEBT_o ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > fun_nat_o ).
thf(aa_nat_o_decl,type,
aa_nat_o: fun_nat_o > nat > $o ).
thf(aa_nat_nat_decl,type,
aa_nat_nat: fun_nat_nat > nat > nat ).
thf(aa_nat7603221163087113075at_nat_decl,type,
aa_nat7603221163087113075at_nat: fun_na1476630412504255114at_nat > nat > product_prod_nat_nat ).
thf(aa_nat_fun_nat_nat_decl,type,
aa_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).
thf(aa_nat_fun_set_nat_o_decl,type,
aa_nat_fun_set_nat_o: fun_na8563630686737515764_nat_o > nat > fun_set_nat_o ).
thf(aa_VEBT_VEBT_o_decl,type,
aa_VEBT_VEBT_o: fun_VEBT_VEBT_o > vEBT_VEBT > $o ).
thf(member_VEBT_VEBT_decl,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(deg_decl,type,
deg: nat ).
thf(i_decl,type,
i: nat ).
thf(m_decl,type,
m: nat ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(na_decl,type,
na: nat ).
thf(summary_decl,type,
summary: vEBT_VEBT ).
thf(treeList_decl,type,
treeList: list_VEBT_VEBT ).
thf(xa_decl,type,
xa: nat ).
thf(266,axiom,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_member @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__C161_C) ).
thf(1411,plain,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_member @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(170,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2464_Suc__mult__cancel1) ).
thf(1024,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(279,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_cd @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8838_ATP_Olambda__719) ).
thf(1454,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_cd @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(41,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2269_mult_Oright__neutral) ).
thf(468,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2325_div__mult__mult1__if) ).
thf(481,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(257,axiom,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_even__odd__cases) ).
thf(1369,plain,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(212,axiom,
! [A: product_prod_nat_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
~ ( D @ ( C @ ( B @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1588_VEBT__internal_OminNull_Osimps_I5_J) ).
thf(1190,plain,
! [A: product_prod_nat_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
~ ( D @ ( C @ ( B @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(219,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ( ( B @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_set__update__subsetI) ).
thf(1211,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ( ( B @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(52,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2274_mult__1) ).
thf(523,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2979_Suc__mod__mult__self2) ).
thf(1290,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(300,axiom,
( ( xa @ ( summary @ ( treeList @ ( deg @ ( ma @ ( mi @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ ( deg @ ( ma @ ( mi @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( xa @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1465__C10_C) ).
thf(1522,plain,
( ( xa @ ( summary @ ( treeList @ ( deg @ ( ma @ ( mi @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ ( deg @ ( ma @ ( mi @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( xa @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(275,axiom,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nsprop) ).
thf(1443,plain,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(265,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2341_one__eq__mult__iff) ).
thf(1401,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(308,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2380_mult_Ocommute) ).
thf(1544,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3347_mod__div__decomp) ).
thf(1205,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(304,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_py @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8340_ATP_Olambda__221) ).
thf(1533,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_py @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6728_binomial__Suc__Suc__eq__times) ).
thf(1305,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(17,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2895_mod__0) ).
thf(379,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(232,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1438_triangle__Suc) ).
thf(1269,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(125,axiom,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32__C0_C) ).
thf(878,plain,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2107_div__add__self2) ).
thf(511,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2953_mod__div__trivial) ).
thf(385,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1510_nat__add__max__right) ).
thf(1137,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(59,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2003_bits__div__by__0) ).
thf(550,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(234,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zj @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8316_ATP_Olambda__197) ).
thf(1275,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zj @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3126_mod__add__cong) ).
thf(945,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2901_mod__add__self2) ).
thf(930,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= B )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= B )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3274_mod__Suc) ).
thf(1063,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= B )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= B )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1480_max__nat_Oeq__neutr__iff) ).
thf(340,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(214,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2978_Suc__mod__mult__self3) ).
thf(1196,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3396_div__mod__decomp) ).
thf(1001,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3559_add__diff__cancel__left_H) ).
thf(1386,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2603_power__Suc2) ).
thf(1366,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(30,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_add_Oright__neutral) ).
thf(436,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(153,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3716_diff__diff__eq) ).
thf(973,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2471_add__mult__distrib2) ).
thf(885,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(174,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2424_crossproduct__noteq) ).
thf(1046,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( C != D )
& ( A != B ) ) )
& ( ( ( C != D )
& ( A != B ) )
=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2903_mod__add__self1) ).
thf(1287,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(65,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2259_mult__zero__right) ).
thf(570,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(231,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3724_zero__induct__lemma) ).
thf(1264,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(296,axiom,
( i
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
thf(1511,plain,
( i
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(110,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1389_list__decode_Ocases) ).
thf(802,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(12,axiom,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2166_plus__1__eq__Suc) ).
thf(357,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3826_diff__Suc__eq__diff__pred) ).
thf(949,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(38,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_add_Ocomm__neutral) ).
thf(460,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1887_nat__power__eq__Suc__0__iff) ).
thf(853,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__is__1) ).
thf(1247,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(123,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_zero__induct) ).
thf(870,plain,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(166,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2980_Suc__mod__mult__self1) ).
thf(1013,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2364_div__mult__self1) ).
thf(325,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(264,axiom,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1564_vebt__member_Osimps_I4_J) ).
thf(1398,plain,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_add__eq__0__iff__both__eq__0) ).
thf(416,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2395_mult__left__cancel) ).
thf(591,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(172,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1467_deg__SUcn__Node) ).
thf(1040,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(77,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2105_div__add__self1) ).
thf(646,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3122_mod__add__right__eq) ).
thf(1151,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(259,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3569_Suc__diff__diff) ).
thf(1383,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_zero__eq__add__iff__both__eq__0) ).
thf(806,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6718_choose__mult__lemma) ).
thf(1302,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(100,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3545_diff__zero) ).
thf(756,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2342_mult__eq__1__iff) ).
thf(1373,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(32,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Suc__neq__Zero) ).
thf(443,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2290_mult__is__0) ).
thf(602,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(205,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3565_add__diff__cancel__right_H) ).
thf(1169,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(35,axiom,
( ( one_one_nat @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2034_max__0__1_I1_J) ).
thf(453,plain,
( ( one_one_nat @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(81,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2362_div__mult__self2) ).
thf(660,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2472_add__mult__distrib) ).
thf(998,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6739_binomial__absorption) ).
thf(1104,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(49,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1390_vebt__buildup_Ocases) ).
thf(507,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(191,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2618_mult__Suc) ).
thf(1119,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(104,axiom,
! [A: fun_nat_o] :
( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
=> ? [B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ~ ( B @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1391_exists__least__lemma) ).
thf(774,plain,
! [A: fun_nat_o] :
( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
=> ? [B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ~ ( B @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(180,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3737_diff__cancel2) ).
thf(1074,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3817_diff__add__0) ).
thf(920,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2246_mult__cancel__right) ).
thf(678,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A = C )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = C )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(215,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6681_binomial__0__Suc) ).
thf(1199,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(15,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1864_div__by__0) ).
thf(366,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(91,axiom,
! [A: nat] :
( ( A @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2891_mod__self) ).
thf(714,plain,
! [A: nat] :
( ( A @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3138_mod__Suc__eq) ).
thf(942,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(31,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2358_div__mult__self4) ).
thf(439,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(246,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_tz @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8177_ATP_Olambda__58) ).
thf(1311,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_tz @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2292_nat__mult__eq__1__iff) ).
thf(534,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(109,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Zero__neq__Suc) ).
thf(798,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(175,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6715_Suc__times__binomial) ).
thf(1057,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(203,axiom,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1587_vebt__insert_Osimps_I3_J) ).
thf(1163,plain,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2963_mod__mult__self1) ).
thf(1091,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(115,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2180_power__0__left) ).
thf(825,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_abl @ aa_nat_fun_nat_nat ) @ map_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7984_map__add__upt) ).
thf(952,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_abl @ aa_nat_fun_nat_nat ) @ map_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(299,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_add__right__imp__eq) ).
thf(1519,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(252,axiom,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not__min__Null__member) ).
thf(1355,plain,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3351_mod__div__mult__eq) ).
thf(1217,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3236_div__add1__eq) ).
thf(1238,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(223,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__Suc) ).
thf(1223,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2480_nat__mult__max__right) ).
thf(894,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6690_binomial__Suc__Suc) ).
thf(1021,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(105,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1481_max__nat_Oleft__neutral) ).
thf(778,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(270,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_add__left__cancel) ).
thf(1423,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( A = B )
=> ( ~ ? [F: nat] : ( F @ ( E @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ! [F: vEBT_VEBT] :
( ( D @ set_VEBT_VEBT2 @ ( F @ member_VEBT_VEBT ) )
=> ~ ? [G: nat] : ( G @ ( F @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1468_mi__eq__ma__no__ch) ).
thf(1032,plain,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( A = B )
=> ( ~ ? [F: nat] : ( F @ ( E @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ! [F: vEBT_VEBT] :
( ( D @ set_VEBT_VEBT2 @ ( F @ member_VEBT_VEBT ) )
=> ~ ? [G: nat] : ( G @ ( F @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(311,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2375_mult_Oassoc) ).
thf(1555,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_cd @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8000_sort__upt) ).
thf(1296,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_cd @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aaa @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8259_ATP_Olambda__140) ).
thf(1457,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aaa @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(47,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2289_mult__0__right) ).
thf(493,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2957_mod__mult__self4) ).
thf(1128,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(236,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2479_nat__mult__max__left) ).
thf(1281,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2345_mult__Suc__right) ).
thf(1392,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_add__cancel__right__left) ).
thf(842,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(64,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_old_Onat_Odistinct_I2_J) ).
thf(566,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(46,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2089_one__reorient) ).
thf(484,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_nat = A ) )
& ( ( one_one_nat = A )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subset__code_I1_J) ).
thf(329,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) )
=> ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) )
& ( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ko @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8628_ATP_Olambda__509) ).
thf(1178,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ko @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3736_Nat_Odiff__cancel) ).
thf(1360,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_add__eq__self__zero) ).
thf(650,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_nat_Oinject) ).
thf(1111,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(20,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2096_zero__neq__one) ).
thf(388,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3137_mod__Suc__Suc__eq) ).
thf(989,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(87,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2893_mod__by__0) ).
thf(697,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(307,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ aTP_Lamm_zl @ aa_nat_fun_set_nat_o ) @ collect_set_nat @ finite_card_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7690_binomial__def) ).
thf(1541,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ aTP_Lamm_zl @ aa_nat_fun_set_nat_o ) @ collect_set_nat @ finite_card_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(42,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_valid__tree__deg__neq__0) ).
thf(471,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(202,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2165_Suc__eq__plus1) ).
thf(1160,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2961_mod__mult__self2) ).
thf(933,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2329_div__mult__mult1) ).
thf(642,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(220,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3556_add__diff__cancel__left) ).
thf(1214,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(167,axiom,
~ ( i @ ( summary @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__C163_C) ).
thf(1016,plain,
~ ( i @ ( summary @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(152,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_min__Null__member) ).
thf(970,plain,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(58,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1995_div__by__Suc__0) ).
thf(547,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2391_mult__right__cancel) ).
thf(706,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(267,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_tp @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8449_ATP_Olambda__330) ).
thf(1414,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_tp @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(53,axiom,
( aTP_Lamm_cd
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3102_lambda__one) ).
thf(526,plain,
( aTP_Lamm_cd
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2409_mult__not__zero) ).
thf(515,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6723_Suc__times__binomial__add) ).
thf(1131,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(278,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_add_Oleft__commute) ).
thf(1451,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(97,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2164_One__nat__def) ).
thf(738,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1509_nat__add__max__left) ).
thf(1060,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(37,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2897_bits__mod__0) ).
thf(457,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3739_diff__add__inverse2) ).
thf(1202,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2447_comm__semiring__class_Odistrib) ).
thf(1241,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3615_diff__add__zero) ).
thf(1187,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(129,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2967_mod__by__Suc__0) ).
thf(888,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2828_left__add__mult__distrib) ).
thf(926,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(283,axiom,
! [A: vEBT_VEBT] :
( ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__C11_C) ).
thf(1466,plain,
! [A: vEBT_VEBT] :
( ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(179,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3128_mod__add__eq) ).
thf(1071,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3741_diff__mult__distrib) ).
thf(1278,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2327_div__mult__mult2) ).
thf(412,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2404_divisors__zero) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(288,axiom,
( ( na @ ( suc @ aa_nat_nat ) )
= m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__C8_C) ).
thf(1483,plain,
( ( na @ ( suc @ aa_nat_nat ) )
= m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2815_nat__mult__div__cancel__disj) ).
thf(573,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_add__cancel__left__left) ).
thf(689,plain,
! [A: nat,B: nat] :
( ( ( A = zero_zero_nat )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(201,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_aba @ aa_nat_o ) )
<=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8293_ATP_Olambda__174) ).
thf(1154,plain,
! [A: fun_nat_o,B: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_aba @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_aba @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(113,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1485_max__0R) ).
thf(819,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6716_Suc__times__binomial__eq) ).
thf(1007,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1921_power__not__zero) ).
thf(402,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(95,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2473_nat__mult__1) ).
thf(732,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(261,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3355_mult__div__mod__eq) ).
thf(1389,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3685_right__diff__distrib_H) ).
thf(1125,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2598_power__Suc) ).
thf(875,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(148,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mw @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8636_ATP_Olambda__517) ).
thf(958,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mw @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(224,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3864_minus__mod__eq__div__mult) ).
thf(1226,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(290,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3655_diff__commute) ).
thf(1488,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( suc @ map_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7983_map__Suc__upt) ).
thf(936,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( suc @ map_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3896_mult__eq__if) ).
thf(382,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
( ( i @ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( i @ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
!= ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(313,plain,
( ( i @ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
!= ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(189,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( A
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3713_add__implies__diff) ).
thf(1107,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( A
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(40,axiom,
( ( zero_zero_nat @ ( one_one_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2030_max__0__1_I2_J) ).
thf(466,plain,
( ( zero_zero_nat @ ( one_one_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(10,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_old_Onat_Oexhaust) ).
thf(350,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(83,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2006_div__by__1) ).
thf(672,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2288_mult__cancel1) ).
thf(391,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(294,axiom,
! [A: list_VEBT_VEBT,B: nat] :
( ( B @ ( A @ nth_VEBT_VEBT ) @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list__update__id) ).
thf(1503,plain,
! [A: list_VEBT_VEBT,B: nat] :
( ( B @ ( A @ nth_VEBT_VEBT ) @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_nat__arith_Osuc1) ).
thf(979,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2250_mult__cancel__left) ).
thf(784,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(301,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ue @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8435_ATP_Olambda__316) ).
thf(1524,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ue @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(292,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_add__right__cancel) ).
thf(1492,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(207,axiom,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1586_vebt__member_Osimps_I3_J) ).
thf(1175,plain,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(133,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1507_max__add__distrib__right) ).
thf(900,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(23,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1883_power__Suc0__right) ).
thf(406,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3860_minus__mult__div__eq__mod) ).
thf(880,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3689_left__diff__distrib_H) ).
thf(1043,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_nat_OdiscI) ).
thf(616,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3834_nat__minus__add__max) ).
thf(1122,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(70,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3570_diff__0__eq__0) ).
thf(599,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(273,axiom,
na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tc) ).
thf(1439,plain,
na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_old_Onat_Oinject) ).
thf(1080,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2287_mult__cancel2) ).
thf(631,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(112,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3549_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(816,plain,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__is__0) ).
thf(621,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(88,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2414_comm__monoid__mult__class_Omult__1) ).
thf(700,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2432_combine__common__factor) ).
thf(964,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(281,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3656_diff__right__commute) ).
thf(1460,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(240,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2933_mod__mult__self1__is__0) ).
thf(1293,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3397_mod__mult2__eq) ).
thf(983,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(285,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ vEBT_VEBT_bit_concat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bit__split__inv) ).
thf(1474,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ vEBT_VEBT_bit_concat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(157,axiom,
! [A: nat] :
( ( suc @ ( A @ compow_fun_nat_nat ) )
= ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7741_Suc__funpow) ).
thf(986,plain,
! [A: nat] :
( ( suc @ ( A @ compow_fun_nat_nat ) )
= ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3726_diffs0__imp__equal) ).
thf(563,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(286,axiom,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__C162_C) ).
thf(1477,plain,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(79,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2419_mult_Ocomm__neutral) ).
thf(653,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(178,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( A != zero_zero_nat )
=> ( ( ( D != E )
& ( B = C ) )
=> ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2577_add__scale__eq__noteq) ).
thf(1066,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( A != zero_zero_nat )
=> ( ( ( D != E )
& ( B = C ) )
=> ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(276,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ upt ) @ ( A @ drop_nat ) )
= ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7961_drop__upt) ).
thf(1445,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ upt ) @ ( A @ drop_nat ) )
= ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(36,axiom,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1486_triangle__0) ).
thf(455,plain,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(127,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] : ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1823_VEBT__internal_OminNull_Osimps_I4_J) ).
thf(883,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] : ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(84,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1483_max__nat_Oright__neutral) ).
thf(675,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(218,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6682_binomial__1) ).
thf(1208,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(55,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3725_minus__nat_Odiff__0) ).
thf(531,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_add__0) ).
thf(795,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(269,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_add_Oassoc) ).
thf(1420,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(196,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2959_mod__mult__self3) ).
thf(1134,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ul @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8498_ATP_Olambda__379) ).
thf(939,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ul @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3562_add__diff__cancel__right) ).
thf(1018,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2318_nonzero__mult__div__cancel__left) ).
thf(553,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1479_max__Suc__Suc) ).
thf(1181,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(310,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( A = B ) )
=> ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_add__mono__thms__linordered__semiring_I4_J) ).
thf(1551,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( A = B ) )
=> ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(27,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_old_Onat_Odistinct_I1_J) ).
thf(426,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(204,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3353_mod__mult__div__eq) ).
thf(1166,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(309,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( B @ ( C @ nth_VEBT_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_nth__list__update__neq) ).
thf(1547,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( B @ ( C @ nth_VEBT_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(61,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1874_power__0__Suc) ).
thf(557,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(298,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( D @ ( B @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_list__update__overwrite) ).
thf(1516,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( D @ ( B @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(303,axiom,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57__C3_C) ).
thf(1531,plain,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(24,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_comm__monoid__add__class_Oadd__0) ).
thf(409,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(92,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2160_power__0) ).
thf(717,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(226,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2167_Suc__eq__plus1__left) ).
thf(1235,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(39,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_not0__implies__Suc) ).
thf(463,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(248,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o,D: fun_VEBT_VEBT_o] :
( ( A = B )
=> ( ! [E: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( E @ member_VEBT_VEBT ) )
=> ( ( E @ ( C @ aa_VEBT_VEBT_o ) )
<=> ( E @ ( D @ aa_VEBT_VEBT_o ) ) ) )
=> ( ( A @ ( C @ find_VEBT_VEBT ) )
= ( B @ ( D @ find_VEBT_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1794_find__cong) ).
thf(1317,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o,D: fun_VEBT_VEBT_o] :
( ( A = B )
=> ( ! [E: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( E @ member_VEBT_VEBT ) )
=> ( ( ( E @ ( D @ aa_VEBT_VEBT_o ) )
=> ( E @ ( C @ aa_VEBT_VEBT_o ) ) )
& ( ( E @ ( C @ aa_VEBT_VEBT_o ) )
=> ( E @ ( D @ aa_VEBT_VEBT_o ) ) ) ) )
=> ( ( A @ ( C @ find_VEBT_VEBT ) )
= ( B @ ( D @ find_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(67,axiom,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_nat__induct) ).
thf(576,plain,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(306,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zy @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8266_ATP_Olambda__147) ).
thf(1538,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zy @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2310_nonzero__mult__div__cancel__right) ).
thf(359,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zi @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8317_ATP_Olambda__198) ).
thf(1220,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_zi @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(57,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1822_vebt__member_Osimps_I2_J) ).
thf(544,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_member @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(89,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2937_mod__by__1) ).
thf(703,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(305,axiom,
( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_insprop) ).
thf(1536,plain,
( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2399_no__zero__divisors) ).
thf(656,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(72,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1870_div__0) ).
thf(613,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(237,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3343_cancel__div__mod__rules_I2_J) ).
thf(1284,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(121,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2465_mult__0) ).
thf(864,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__Suc__right) ).
thf(1272,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_add_Ocommute) ).
thf(1485,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(295,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_group__cancel_Oadd2) ).
thf(1506,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2437_distrib__right) ).
thf(1094,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3315_nat__mod__eq__iff) ).
thf(1140,plain,
! [A: nat,B: nat,C: nat] :
( ( ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(34,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Nat_Oadd__0__right) ).
thf(450,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(14,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2001_bits__div__0) ).
thf(363,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2291_nat__1__eq__mult__iff) ).
thf(581,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Zero__not__Suc) ).
thf(759,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(130,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3633_diff__Suc__1) ).
thf(891,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(277,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2370_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1448,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3302_mod__eq__0D) ).
thf(1010,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3893_add__eq__if) ).
thf(771,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2442_distrib__left) ).
thf(976,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_one__is__add) ).
thf(903,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(149,axiom,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6667_binomial__Suc__n) ).
thf(961,plain,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3904_power__eq__if) ).
thf(319,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(187,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1504_max__add__distrib__left) ).
thf(1101,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3738_diff__add__inverse) ).
thf(1244,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(106,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_plus__nat_Oadd__0) ).
thf(781,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(250,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2428_crossproduct__eq) ).
thf(1341,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_add__cancel__right__right) ).
thf(748,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2935_mod__mult__self2__is__0) ).
thf(995,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(312,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_add__left__imp__eq) ).
thf(1558,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(291,axiom,
( m
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ vEBT_invar_vebt
@ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C12_C) ).
thf(1491,plain,
( m
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ vEBT_invar_vebt
@ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(29,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6691_binomial__n__0) ).
thf(433,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(245,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Suc__inject) ).
thf(1308,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3866_minus__div__mult__eq__mod) ).
thf(1193,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3233_mod__eq__self__iff__div__eq__0) ).
thf(763,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(297,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_rp @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8350_ATP_Olambda__231) ).
thf(1513,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_rp @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abl @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8268_ATP_Olambda__149) ).
thf(1440,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abl @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(138,axiom,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C1_C) ).
thf(929,plain,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3345_cancel__div__mod__rules_I1_J) ).
thf(1077,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2620_mult__eq__self__implies__10) ).
thf(478,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(33,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1888_power__Suc__0) ).
thf(447,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_nat_Odistinct_I1_J) ).
thf(315,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3573_diff__diff__left) ).
thf(967,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(186,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_n__not__Suc__n) ).
thf(1097,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(225,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
<=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_both__member__options__equiv__member) ).
thf(1229,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) )
& ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(263,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( D @ ( D @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1674_vebt__insert_Osimps_I4_J) ).
thf(1395,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( D @ ( D @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(122,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1484_max__0L) ).
thf(867,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(287,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2385_mult_Oleft__commute) ).
thf(1480,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(96,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2012_div__self) ).
thf(735,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(302,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( E @ ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( A @ ( E @ ( B @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_list__update__swap) ).
thf(1527,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( E @ ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( A @ ( E @ ( B @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ua @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8176_ATP_Olambda__57) ).
thf(1148,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ua @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(272,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_la @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8641_ATP_Olambda__522) ).
thf(1436,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_la @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(249,axiom,
( ( xa != ma )
& ( xa != mi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_mimaxrel) ).
thf(1335,plain,
( ( xa != ma )
& ( xa != mi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_add__cancel__left__right) ).
thf(664,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2827_nat__mult__eq__cancel__disj) ).
thf(828,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(93,axiom,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1648_vebt__insert_Osimps_I2_J) ).
thf(720,plain,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3862_minus__mod__eq__mult__div) ).
thf(955,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3357_div__mult1__eq) ).
thf(1363,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(247,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3349_div__mult__mod__eq) ).
thf(1314,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(206,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1466_deg__deg__n) ).
thf(1172,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(132,axiom,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ~ ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__C5_C) ).
thf(897,plain,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ~ ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2360_div__mult__self3) ).
thf(474,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(117,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3543_zero__diff) ).
thf(839,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(98,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1392_add__0__iff) ).
thf(740,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(251,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3124_mod__add__left__eq) ).
thf(1352,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(54,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_valid__0__not) ).
thf(528,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ tl_nat )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7959_tl__upt) ).
thf(1357,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ tl_nat )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(159,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_valid__member__both__member__options) ).
thf(992,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(114,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2474_nat__mult__1__right) ).
thf(822,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(119,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2264_mult__zero__left) ).
thf(850,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(242,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3740_diff__mult__distrib2) ).
thf(1299,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1482_max__nat_Oneutr__eq__iff) ).
thf(369,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_tl @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8274_ATP_Olambda__155) ).
thf(1500,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_tl @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(94,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_zero__reorient) ).
thf(723,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat = A ) )
& ( ( zero_zero_nat = A )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(271,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_group__cancel_Oadd1) ).
thf(1431,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2977_Suc__mod__mult__self4) ).
thf(1004,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(5,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3571_diff__self__eq__0) ).
thf(322,plain,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2939_bits__mod__by__1) ).
thf(337,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1396_verit__sum__simplify) ).
thf(354,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_add__Suc__shift) ).
thf(923,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3568_diff__Suc__Suc) ).
thf(1184,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(282,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aas @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8265_ATP_Olambda__146) ).
thf(1463,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aas @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2955_bits__mod__div__trivial) ).
thf(560,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(183,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2609_power__add) ).
thf(1088,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(284,axiom,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_in__children__def) ).
thf(1468,plain,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) )
=> ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2254_mult__eq__0__iff) ).
thf(496,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(268,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1417,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1565,plain,
$false,
inference(e,[status(thm)],[1411,1024,1454,468,481,1369,1190,1211,523,1290,1522,1443,1401,1544,1205,1533,1305,379,1269,878,511,385,1137,550,1275,945,930,1063,340,1196,1001,1386,1366,436,973,885,1046,1287,570,1264,1511,802,357,949,460,853,1247,870,1013,325,1398,416,591,1040,646,1151,1383,806,1302,756,1373,443,602,1169,453,660,998,1104,507,1119,774,1074,920,678,1199,366,714,942,439,1311,534,798,1057,1163,1091,825,952,1519,1355,1217,1238,1223,894,1021,778,1423,1032,1555,1296,1457,493,1128,1281,1392,842,566,484,329,1178,1360,650,1111,388,989,697,1541,471,1160,933,642,1214,1016,970,547,706,1414,526,515,1131,1451,738,1060,457,1202,1241,1187,888,926,1466,1071,1278,412,430,1483,573,689,1154,819,1007,402,732,1389,1125,875,958,1226,1488,936,382,313,1107,466,350,672,391,1503,979,784,1524,1492,1175,900,406,880,1043,616,1122,599,1439,1080,631,816,621,700,964,1460,1293,983,1474,986,563,1477,653,1066,1445,455,883,675,1208,531,795,1420,1134,939,1018,553,1181,1551,426,1166,1547,557,1516,1531,409,717,1235,463,1317,576,1538,359,1220,544,703,1536,656,613,1284,864,1272,1485,1506,1094,1140,450,363,581,759,891,1448,1010,771,976,903,961,319,1101,1244,781,1341,748,995,1558,1491,433,1308,1193,763,1513,1440,929,1077,478,447,315,967,1097,1229,1395,867,1480,735,1527,1148,1436,1335,664,828,720,955,1363,1314,1172,897,474,839,740,1352,528,1357,992,822,850,1299,369,1500,723,1431,1004,322,337,354,923,1184,1463,560,1088,1468,496,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP234_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n011.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 18:22:43 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 8.05/2.82 % [INFO] Parsing done (1855ms).
% 8.05/2.84 % [INFO] Running in sequential loop mode.
% 9.00/3.22 % [INFO] eprover registered as external prover.
% 9.00/3.22 % [INFO] Scanning for conjecture ...
% 12.53/4.14 % [INFO] Found a conjecture (or negated_conjecture) and 8869 axioms. Running axiom selection ...
% 14.64/4.79 % [INFO] Axiom selection finished. Selected 310 axioms (removed 8559 axioms).
% 15.42/4.96 % [INFO] Problem is typed first-order (TPTP TFF).
% 15.42/4.98 % [INFO] Type checking passed.
% 15.42/4.99 % [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 ...
% 25.64/7.90 % External prover 'e' found a proof!
% 25.64/7.91 % [INFO] Killing All external provers ...
% 25.64/7.91 % Time passed: 7360ms (effective reasoning time: 5055ms)
% 25.64/7.91 % 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)>
% 25.64/7.91 % Axioms used in derivation (310): fact_8265_ATP_Olambda__146, fact_3571_diff__self__eq__0, fact_6716_Suc__times__binomial__eq, fact_33__C163_C, fact_2577_add__scale__eq__noteq, fact_2375_mult_Oassoc, fact_3860_minus__mult__div__eq__mod, fact_2953_mod__div__trivial, fact_940_add__right__imp__eq, fact_3124_mod__add__left__eq, fact_2414_comm__monoid__mult__class_Omult__1, fact_3864_minus__mod__eq__div__mult, fact_6739_binomial__absorption, fact_1874_power__0__Suc, fact_2935_mod__mult__self2__is__0, fact_8449_ATP_Olambda__330, fact_8641_ATP_Olambda__522, fact_1674_vebt__insert_Osimps_I4_J, fact_867_add__cancel__left__left, fact_3355_mult__div__mod__eq, fact_2618_mult__Suc, fact_2370_ab__semigroup__mult__class_Omult__ac_I1_J, fact_2291_nat__1__eq__mult__iff, fact_3741_diff__mult__distrib, fact_875_add__cancel__right__left, fact_3345_cancel__div__mod__rules_I1_J, fact_3236_div__add1__eq, fact_151_old_Onat_Odistinct_I1_J, fact_2464_Suc__mult__cancel1, fact_3726_diffs0__imp__equal, fact_6691_binomial__n__0, fact_1507_max__add__distrib__right, fact_1390_vebt__buildup_Ocases, fact_1481_max__nat_Oleft__neutral, fact_3543_zero__diff, fact_1564_vebt__member_Osimps_I4_J, fact_2603_power__Suc2, fact_1392_add__0__iff, fact_2254_mult__eq__0__iff, fact_2903_mod__add__self1, fact_1995_div__by__Suc__0, fact_2978_Suc__mod__mult__self3, fact_2246_mult__cancel__right, fact_8628_ATP_Olambda__509, fact_2_bit__split__inv, fact_2980_Suc__mod__mult__self1, fact_3102_lambda__one, fact_1870_div__0, fact_6728_binomial__Suc__Suc__eq__times, fact_3_tc, fact_2287_mult__cancel2, fact_7690_binomial__def, fact_2096_zero__neq__one, fact_1794_find__cong, fact_933_add_Oleft__commute, fact_8350_ATP_Olambda__231, fact_1483_max__nat_Oright__neutral, fact_1586_vebt__member_Osimps_I3_J, fact_150_nat_OdiscI, fact_2290_mult__is__0, fact_2395_mult__left__cancel, fact_6718_choose__mult__lemma, fact_2358_div__mult__self4, fact_8435_ATP_Olambda__316, fact_992_add_Ocomm__neutral, fact_3862_minus__mod__eq__mult__div, fact_2967_mod__by__Suc__0, fact_3397_mod__mult2__eq, fact_1468_mi__eq__ma__no__ch, fact_887_add__0, fact_7_list__update__id, fact_3274_mod__Suc, fact_2362_div__mult__self2, fact_15_nsprop, fact_2034_max__0__1_I1_J, fact_3128_mod__add__eq, fact_143_nat__induct, fact_61_valid__tree__deg__neq__0, fact_2292_nat__mult__eq__1__iff, fact_27_both__member__options__equiv__member, fact_63_old_Onat_Oinject, fact_3126_mod__add__cong, fact_2318_nonzero__mult__div__cancel__left, fact_138_Suc__neq__Zero, fact_137_Zero__neq__Suc, fact_8259_ATP_Olambda__140, fact_3896_mult__eq__if, fact_2342_mult__eq__1__iff, fact_6723_Suc__times__binomial__add, fact_2893_mod__by__0, fact_3556_add__diff__cancel__left, fact_2979_Suc__mod__mult__self2, fact_2897_bits__mod__0, fact_3351_mod__div__mult__eq, fact_1484_max__0L, fact_8268_ATP_Olambda__149, fact_2409_mult__not__zero, fact_3315_nat__mod__eq__iff, fact_1486_triangle__0, fact_1465__C10_C, fact_64_nat_Oinject, fact_2479_nat__mult__max__left, fact_2167_Suc__eq__plus1__left, fact_1467_deg__SUcn__Node, fact_6681_binomial__0__Suc, fact_2289_mult__0__right, fact_2963_mod__mult__self1, fact_8636_ATP_Olambda__517, fact_2380_mult_Ocommute, fact_2891_mod__self, fact_3655_diff__commute, fact_2827_nat__mult__eq__cancel__disj, fact_7961_drop__upt, fact_3349_div__mult__mod__eq, fact_142_one__is__add, fact_18_list__update__swap, fact_1485_max__0R, fact_24_not__min__Null__member, fact_3725_minus__nat_Odiff__0, fact_135_add__Suc__shift, fact_2404_divisors__zero, fact_1510_nat__add__max__right, fact_1888_power__Suc__0, fact_2895_mod__0, fact_2937_mod__by__1, fact_8340_ATP_Olambda__221, fact_8274_ATP_Olambda__155, fact_7959_tl__upt, fact_2012_div__self, fact_2341_one__eq__mult__iff, fact_1921_power__not__zero, fact_3302_mod__eq__0D, fact_21_in__children__def, fact_3817_diff__add__0, fact_1509_nat__add__max__left, fact_2288_mult__cancel1, fact_1887_nat__power__eq__Suc__0__iff, fact_2424_crossproduct__noteq, fact_136_Zero__not__Suc, fact_8000_sort__upt, fact_2001_bits__div__0, fact_3565_add__diff__cancel__right_H, fact_3122_mod__add__right__eq, fact_937_add__left__imp__eq, fact_917_group__cancel_Oadd2, fact_2030_max__0__1_I2_J, fact_1389_list__decode_Ocases, fact_860_add_Oright__neutral, fact_146_add__Suc, fact_2180_power__0__left, fact_11__C162_C, fact_2933_mod__mult__self1__is__0, fact_2428_crossproduct__eq, fact_3826_diff__Suc__eq__diff__pred, fact_2447_comm__semiring__class_Odistrib, fact_2364_div__mult__self1, fact_2160_power__0, fact_3396_div__mod__decomp, fact_2391_mult__right__cancel, fact_2437_distrib__right, fact_3740_diff__mult__distrib2, fact_153_nat_Odistinct_I1_J, fact_91_add__Suc__right, fact_2345_mult__Suc__right, fact_2609_power__add, fact_2598_power__Suc, fact_35__C8_C, fact_3893_add__eq__if, fact_144_Suc__inject, fact_847_add__right__cancel, fact_900_zero__reorient, fact_3615_diff__add__zero, fact_8316_ATP_Olambda__197, fact_2828_left__add__mult__distrib, fact_3738_diff__add__inverse, fact_1480_max__nat_Oeq__neutr__iff, fact_1587_vebt__insert_Osimps_I3_J, fact_32__C0_C, fact_92_Nat_Oadd__0__right, fact_2360_div__mult__self3, fact_3633_diff__Suc__1, fact_2105_div__add__self1, fact_60_even__odd__cases, fact_2977_Suc__mod__mult__self4, fact_871_add__cancel__left__right, fact_3568_diff__Suc__Suc, fact_1823_VEBT__internal_OminNull_Osimps_I4_J, fact_2274_mult__1, fact_3739_diff__add__inverse2, fact_2329_div__mult__mult1, fact_1479_max__Suc__Suc, fact_6682_binomial__1, fact_2901_mod__add__self2, fact_57__C3_C, fact_139_zero__induct, fact_3562_add__diff__cancel__right, fact_3716_diff__diff__eq, fact_4__C161_C, fact_2473_nat__mult__1, fact_93_add__is__0, fact_2269_mult_Oright__neutral, fact_905_ab__semigroup__add__class_Oadd__ac_I1_J, fact_3137_mod__Suc__Suc__eq, fact_6690_binomial__Suc__Suc, fact_23__C12_C, fact_3724_zero__induct__lemma, fact_1648_vebt__insert_Osimps_I2_J, fact_8176_ATP_Olambda__57, fact_6715_Suc__times__binomial, fact_2432_combine__common__factor, fact_8266_ATP_Olambda__147, fact_3737_diff__cancel2, fact_1822_vebt__member_Osimps_I2_J, fact_2164_One__nat__def, fact_2474_nat__mult__1__right, fact_3685_right__diff__distrib_H, fact_7741_Suc__funpow, fact_2471_add__mult__distrib2, fact_2472_add__mult__distrib, fact_3138_mod__Suc__eq, fact_3569_Suc__diff__diff, fact_1438_triangle__Suc, fact_929_add_Ocommute, fact_2419_mult_Ocomm__neutral, fact_913_group__cancel_Oadd1, fact_844_add__left__cancel, fact_62_valid__0__not, fact_149_nat__arith_Osuc1, fact_2310_nonzero__mult__div__cancel__right, fact_145_add__is__1, fact_2815_nat__mult__div__cancel__disj, fact_885_zero__eq__add__iff__both__eq__0, fact_1504_max__add__distrib__left, fact_2327_div__mult__mult2, fact_3233_mod__eq__self__iff__div__eq__0, fact_2442_distrib__left, fact_921_add_Oassoc, fact_28_valid__member__both__member__options, fact_2165_Suc__eq__plus1, fact_987_comm__monoid__add__class_Oadd__0, fact_1883_power__Suc0__right, fact_140_n__not__Suc__n, fact_3689_left__diff__distrib_H, fact_2003_bits__div__by__0, fact_3834_nat__minus__add__max, fact_2399_no__zero__divisors, fact_879_add__cancel__right__right, fact_29__C5_C, fact_1466_deg__deg__n, fact_2264_mult__zero__left, fact_3559_add__diff__cancel__left_H, fact_3573_diff__diff__left, fact_1391_exists__least__lemma, fact_2089_one__reorient, fact_14_list__update__overwrite, fact_3549_cancel__comm__monoid__add__class_Odiff__cancel, fact_1_insprop, fact_8838_ATP_Olambda__719, fact_3545_diff__zero, fact_2957_mod__mult__self4, fact_2107_div__add__self2, fact_16__C11_C, fact_148_plus__nat_Oadd__0, fact_3343_cancel__div__mod__rules_I2_J, fact_1588_VEBT__internal_OminNull_Osimps_I5_J, fact_147_old_Onat_Oexhaust, fact_2250_mult__cancel__left, fact_8177_ATP_Olambda__58, fact_2961_mod__mult__self2, fact_1864_div__by__0, fact_883_add__eq__0__iff__both__eq__0, fact_134_add__eq__self__zero, fact_2955_bits__mod__div__trivial, fact_3713_add__implies__diff, fact_2325_div__mult__mult1__if, fact_25_min__Null__member, fact_0_True, fact_2006_div__by__1, fact_1396_verit__sum__simplify, fact_8498_ATP_Olambda__379, fact_3904_power__eq__if, fact_7984_map__add__upt, fact_2480_nat__mult__max__right, fact_3347_mod__div__decomp, fact_2166_plus__1__eq__Suc, fact_6667_binomial__Suc__n, fact_3357_div__mult1__eq, fact_2939_bits__mod__by__1, fact_133_not0__implies__Suc, fact_909_add__mono__thms__linordered__semiring_I4_J, fact_2385_mult_Oleft__commute, fact_8317_ATP_Olambda__198, fact_34_mimaxrel, fact_10_nth__list__update__neq, fact_26__C1_C, fact_2959_mod__mult__self3, fact_3656_diff__right__commute, fact_1482_max__nat_Oneutr__eq__iff, fact_268_set__update__subsetI, fact_7983_map__Suc__upt, fact_2465_mult__0, fact_3736_Nat_Odiff__cancel, fact_8293_ATP_Olambda__174, fact_3353_mod__mult__div__eq, fact_2259_mult__zero__right, fact_3866_minus__div__mult__eq__mod, fact_3570_diff__0__eq__0, fact_152_old_Onat_Odistinct_I2_J, fact_224_subset__code_I1_J, fact_2620_mult__eq__self__implies__10
% 25.64/7.91 % No. of inferences in proof: 624
% 25.64/7.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7360 ms resp. 5055 ms w/o parsing
% 26.74/8.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.74/8.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------