%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP256_3 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 07:37:17 AM UTC 2026
% Result : Theorem 64.74s 17.99s
% Output : Refutation 68.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1071
% Syntax : Number of formulae : 2172 ( 610 unt; 0 typ; 1 def)
% Number of atoms : 6001 (2102 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 33652 ( 691 ~; 169 |; 695 &;29142 @)
% ( 285 <=>;2670 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 661 ( 660 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 142 ( 139 usr; 49 con; 0-4 aty)
% Number of variables : 5229 ( 2 ^;4965 !; 211 ?;5229 :)
% ( 0 !>; 0 ?*; 0 @-; 51 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_fu8946524575271555235nteger_type,type,
fun_fu8946524575271555235nteger: $tType ).
thf(fun_fu9160953773549289085nt_int_type,type,
fun_fu9160953773549289085nt_int: $tType ).
thf(fun_fu3460006408547937207nteger_type,type,
fun_fu3460006408547937207nteger: $tType ).
thf(fun_Pr2985126522952997572nteger_type,type,
fun_Pr2985126522952997572nteger: $tType ).
thf(fun_Pr2338235074370512933eger_o_type,type,
fun_Pr2338235074370512933eger_o: $tType ).
thf(fun_fu465145433024125141nt_int_type,type,
fun_fu465145433024125141nt_int: $tType ).
thf(produc1319942482725812455at_nat_type,type,
produc1319942482725812455at_nat: $tType ).
thf(produc1260151622200656695at_nat_type,type,
produc1260151622200656695at_nat: $tType ).
thf(fun_se5282722391638144526_nat_o_type,type,
fun_se5282722391638144526_nat_o: $tType ).
thf(fun_fu1322491050725084261_nat_o_type,type,
fun_fu1322491050725084261_nat_o: $tType ).
thf(fun_Pr4781553364444837327nt_int_type,type,
fun_Pr4781553364444837327nt_int: $tType ).
thf(list_P2959130015091922598nteger_type,type,
list_P2959130015091922598nteger: $tType ).
thf(set_Pr3486312109254157132nteger_type,type,
set_Pr3486312109254157132nteger: $tType ).
thf(fun_Pr7015759342434529115eger_o_type,type,
fun_Pr7015759342434529115eger_o: $tType ).
thf(fun_Pr5940282452322918422_int_o_type,type,
fun_Pr5940282452322918422_int_o: $tType ).
thf(fun_Pr8197042229416165454nteger_type,type,
fun_Pr8197042229416165454nteger: $tType ).
thf(produc2453742332425399446nteger_type,type,
produc2453742332425399446nteger: $tType ).
thf(fun_Pr4194762028118890523eger_o_type,type,
fun_Pr4194762028118890523eger_o: $tType ).
thf(produc3739950874144486240at_nat_type,type,
produc3739950874144486240at_nat: $tType ).
thf(fun_fu7695273699059480439eger_o_type,type,
fun_fu7695273699059480439eger_o: $tType ).
thf(list_P2843741347166045587nt_int_type,type,
list_P2843741347166045587nt_int: $tType ).
thf(set_Pr6700895561065273913nt_int_type,type,
set_Pr6700895561065273913nt_int: $tType ).
thf(fun_Pr3540825087398332590_int_o_type,type,
fun_Pr3540825087398332590_int_o: $tType ).
thf(produc3043004577601930755nt_int_type,type,
produc3043004577601930755nt_int: $tType ).
thf(fun_fu6865642474282033866_int_o_type,type,
fun_fu6865642474282033866_int_o: $tType ).
thf(fun_fu7234941744988193529t_real_type,type,
fun_fu7234941744988193529t_real: $tType ).
thf(fun_fu6383124537394581533et_nat_type,type,
fun_fu6383124537394581533et_nat: $tType ).
thf(fun_fu1569576118606662777et_int_type,type,
fun_fu1569576118606662777et_int: $tType ).
thf(fun_Pr8696298990344678139nt_int_type,type,
fun_Pr8696298990344678139nt_int: $tType ).
thf(list_P1054633106646461488nteger_type,type,
list_P1054633106646461488nteger: $tType ).
thf(set_Pr1200682188532975830nteger_type,type,
set_Pr1200682188532975830nteger: $tType ).
thf(fun_Pr1347628893830317649eger_o_type,type,
fun_Pr1347628893830317649eger_o: $tType ).
thf(fun_Pr4319214966644334570_int_o_type,type,
fun_Pr4319214966644334570_int_o: $tType ).
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_o: $tType ).
thf(fun_fu5323616038969315652_int_o_type,type,
fun_fu5323616038969315652_int_o: $tType ).
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(produc7509114972854644512nteger_type,type,
produc7509114972854644512nteger: $tType ).
thf(fun_fu3422731660242565741eger_o_type,type,
fun_fu3422731660242565741eger_o: $tType ).
thf(list_f4306079564415238026e_term_type,type,
list_f4306079564415238026e_term: $tType ).
thf(set_fu8280898353253485872e_term_type,type,
set_fu8280898353253485872e_term: $tType ).
thf(list_f280343417242313083e_term_type,type,
list_f280343417242313083e_term: $tType ).
thf(fun_Pr5098669352780829690e_term_type,type,
fun_Pr5098669352780829690e_term: $tType ).
thf(set_fu5653557704672872225e_term_type,type,
set_fu5653557704672872225e_term: $tType ).
thf(fun_fu604837885242254216t_real_type,type,
fun_fu604837885242254216t_real: $tType ).
thf(fun_fu9079770784915425324et_nat_type,type,
fun_fu9079770784915425324et_nat: $tType ).
thf(list_P932735248015874751nt_int_type,type,
list_P932735248015874751nt_int: $tType ).
thf(set_Pr4166680992137330533nt_int_type,type,
set_Pr4166680992137330533nt_int: $tType ).
thf(fun_Pr1196100989263358594_int_o_type,type,
fun_Pr1196100989263358594_int_o: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(fun_fu5272517084062245049at_nat_type,type,
fun_fu5272517084062245049at_nat: $tType ).
thf(fun_fu9140019011034226361at_nat_type,type,
fun_fu9140019011034226361at_nat: $tType ).
thf(fun_Pr7763680713840462443e_term_type,type,
fun_Pr7763680713840462443e_term: $tType ).
thf(fun_fu6829939267127632275at_nat_type,type,
fun_fu6829939267127632275at_nat: $tType ).
thf(fun_fu1853463631764337203omplex_type,type,
fun_fu1853463631764337203omplex: $tType ).
thf(produc4788131091073775919nt_int_type,type,
produc4788131091073775919nt_int: $tType ).
thf(fun_fu3656911019502402539omplex_type,type,
fun_fu3656911019502402539omplex: $tType ).
thf(fun_fu260611630652282675omplex_type,type,
fun_fu260611630652282675omplex: $tType ).
thf(fun_fu7433039812794084273omplex_type,type,
fun_fu7433039812794084273omplex: $tType ).
thf(fun_fu2978539155105838238_int_o_type,type,
fun_fu2978539155105838238_int_o: $tType ).
thf(fun_fu8917005985606432553at_nat_type,type,
fun_fu8917005985606432553at_nat: $tType ).
thf(fun_fu232560502794827049at_nat_type,type,
fun_fu232560502794827049at_nat: $tType ).
thf(fun_se7788542033685991124_nat_o_type,type,
fun_se7788542033685991124_nat_o: $tType ).
thf(fun_fu3378010530705604573at_nat_type,type,
fun_fu3378010530705604573at_nat: $tType ).
thf(fun_fu6938252901338612493omplex_type,type,
fun_fu6938252901338612493omplex: $tType ).
thf(fun_fu7724386853639975089omplex_type,type,
fun_fu7724386853639975089omplex: $tType ).
thf(fun_fu6287892695735310827x_real_type,type,
fun_fu6287892695735310827x_real: $tType ).
thf(fun_li6914387844523535256_nat_o_type,type,
fun_li6914387844523535256_nat_o: $tType ).
thf(fun_Pr1253225528153422666at_nat_type,type,
fun_Pr1253225528153422666at_nat: $tType ).
thf(fun_fu8082241605084145771ex_nat_type,type,
fun_fu8082241605084145771ex_nat: $tType ).
thf(fun_fu8020931516743756395ex_nat_type,type,
fun_fu8020931516743756395ex_nat: $tType ).
thf(fun_fu55639602125797389t_real_type,type,
fun_fu55639602125797389t_real: $tType ).
thf(list_P5464809261938338413at_nat_type,type,
list_P5464809261938338413at_nat: $tType ).
thf(produc2703417854250991842on_num_type,type,
produc2703417854250991842on_num: $tType ).
thf(produc7004362771917097900on_nat_type,type,
produc7004362771917097900on_nat: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(fun_Pr1308109350235310159nt_int_type,type,
fun_Pr1308109350235310159nt_int: $tType ).
thf(set_Pr4329608150637261639at_nat_type,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(fun_Pr3059359313727237556_nat_o_type,type,
fun_Pr3059359313727237556_nat_o: $tType ).
thf(fun_fu7903722123778649997at_nat_type,type,
fun_fu7903722123778649997at_nat: $tType ).
thf(fun_fu3351286688164852109at_nat_type,type,
fun_fu3351286688164852109at_nat: $tType ).
thf(fun_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_fu4306744791715064858_rat_o_type,type,
fun_fu4306744791715064858_rat_o: $tType ).
thf(fun_fu6699046866436802030_int_o_type,type,
fun_fu6699046866436802030_int_o: $tType ).
thf(produc6121120109295599847at_nat_type,type,
produc6121120109295599847at_nat: $tType ).
thf(fun_fu5253574275612187245l_real_type,type,
fun_fu5253574275612187245l_real: $tType ).
thf(fun_op1221328669798608686_nat_o_type,type,
fun_op1221328669798608686_nat_o: $tType ).
thf(produc50614890452615238on_num_type,type,
produc50614890452615238on_num: $tType ).
thf(produc1615844007061411358on_nat_type,type,
produc1615844007061411358on_nat: $tType ).
thf(fun_fu5321668254738230545t_real_type,type,
fun_fu5321668254738230545t_real: $tType ).
thf(fun_fu8695033588447641837al_nat_type,type,
fun_fu8695033588447641837al_nat: $tType ).
thf(fun_fu1169599456156577517al_nat_type,type,
fun_fu1169599456156577517al_nat: $tType ).
thf(fun_fu5553606195750802321at_nat_type,type,
fun_fu5553606195750802321at_nat: $tType ).
thf(fun_fu8018396694123807121at_nat_type,type,
fun_fu8018396694123807121at_nat: $tType ).
thf(fun_fu5396388669021241873t_real_type,type,
fun_fu5396388669021241873t_real: $tType ).
thf(fun_fu1051927838966779501t_real_type,type,
fun_fu1051927838966779501t_real: $tType ).
thf(produc3843707927480180839at_nat_type,type,
produc3843707927480180839at_nat: $tType ).
thf(fun_fu4073184632390761289at_nat_type,type,
fun_fu4073184632390761289at_nat: $tType ).
thf(fun_fu9148247276982919825at_nat_type,type,
fun_fu9148247276982919825at_nat: $tType ).
thf(fun_fu3143578834292514029nt_nat_type,type,
fun_fu3143578834292514029nt_nat: $tType ).
thf(fun_fu3180206027003385489at_nat_type,type,
fun_fu3180206027003385489at_nat: $tType ).
thf(fun_fu6398909621167755501nt_nat_type,type,
fun_fu6398909621167755501nt_nat: $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_fu7732904369943091395at_nat_type,type,
fun_fu7732904369943091395at_nat: $tType ).
thf(fun_fu1098312133097393581at_rat_type,type,
fun_fu1098312133097393581at_rat: $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_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(fun_fu1584491925252458057omplex_type,type,
fun_fu1584491925252458057omplex: $tType ).
thf(fun_fu2142003765521078979plex_o_type,type,
fun_fu2142003765521078979plex_o: $tType ).
thf(fun_fu709861064203714431x_real_type,type,
fun_fu709861064203714431x_real: $tType ).
thf(list_f8851413139013959296e_term_type,type,
list_f8851413139013959296e_term: $tType ).
thf(list_P8469869581646625389at_nat_type,type,
list_P8469869581646625389at_nat: $tType ).
thf(set_fu1527098227522870310e_term_type,type,
set_fu1527098227522870310e_term: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(fun_fu3593947265352647275omplex_type,type,
fun_fu3593947265352647275omplex: $tType ).
thf(fun_fu6638204120336560003ex_rat_type,type,
fun_fu6638204120336560003ex_rat: $tType ).
thf(fun_fu2513798379308225899ex_nat_type,type,
fun_fu2513798379308225899ex_nat: $tType ).
thf(fun_fu4692242605864086655ex_int_type,type,
fun_fu4692242605864086655ex_int: $tType ).
thf(fun_se374060482380105870_nat_o_type,type,
fun_se374060482380105870_nat_o: $tType ).
thf(fun_fu3275390434952296369_nat_o_type,type,
fun_fu3275390434952296369_nat_o: $tType ).
thf(fun_fu7523448966510524487plex_o_type,type,
fun_fu7523448966510524487plex_o: $tType ).
thf(fun_fu6714502955005156803_nat_o_type,type,
fun_fu6714502955005156803_nat_o: $tType ).
thf(fun_fu225173491512638659_nat_o_type,type,
fun_fu225173491512638659_nat_o: $tType ).
thf(fun_fu1834022669976960707_nat_o_type,type,
fun_fu1834022669976960707_nat_o: $tType ).
thf(fun_fu4568065243339218371_nat_o_type,type,
fun_fu4568065243339218371_nat_o: $tType ).
thf(fun_fu6212260319156258755_nat_o_type,type,
fun_fu6212260319156258755_nat_o: $tType ).
thf(fun_fu1657029809911482051_nat_o_type,type,
fun_fu1657029809911482051_nat_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_fu9068519094125542729real_o_type,type,
fun_fu9068519094125542729real_o: $tType ).
thf(fun_fu9132278742410140537l_real_type,type,
fun_fu9132278742410140537l_real: $tType ).
thf(list_f628289730585369423e_term_type,type,
list_f628289730585369423e_term: $tType ).
thf(fun_fu7677565902479959693_rat_o_type,type,
fun_fu7677565902479959693_rat_o: $tType ).
thf(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(fun_Co3460408610320954864e_term_type,type,
fun_Co3460408610320954864e_term: $tType ).
thf(set_fu3629540756087427317e_term_type,type,
set_fu3629540756087427317e_term: $tType ).
thf(set_Pr1916528119006554503T_VEBT_type,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(fun_fu6810213084838398785t_real_type,type,
fun_fu6810213084838398785t_real: $tType ).
thf(fun_VE2573032740582156747_nat_o_type,type,
fun_VE2573032740582156747_nat_o: $tType ).
thf(fun_fu6433034133342731997_nat_o_type,type,
fun_fu6433034133342731997_nat_o: $tType ).
thf(fun_fu3930813892005118153_int_o_type,type,
fun_fu3930813892005118153_int_o: $tType ).
thf(fun_fu7187499828406537085al_rat_type,type,
fun_fu7187499828406537085al_rat: $tType ).
thf(fun_fu3768230810189712741al_nat_type,type,
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thf(fun_fu5645595436833112697al_int_type,type,
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thf(fun_fu1620311477532340197t_real_type,type,
fun_fu1620311477532340197t_real: $tType ).
thf(fun_fu4328765270694171897t_real_type,type,
fun_fu4328765270694171897t_real: $tType ).
thf(fun_op7653269905477231939_num_o_type,type,
fun_op7653269905477231939_num_o: $tType ).
thf(fun_op7326680082016885773_nat_o_type,type,
fun_op7326680082016885773_nat_o: $tType ).
thf(fun_op5373868528577402299_nat_o_type,type,
fun_op5373868528577402299_nat_o: $tType ).
thf(fun_op3832135881594366065_nat_o_type,type,
fun_op3832135881594366065_nat_o: $tType ).
thf(fun_fu8391177546919232046_nat_o_type,type,
fun_fu8391177546919232046_nat_o: $tType ).
thf(fun_fu7503566767892366382_int_o_type,type,
fun_fu7503566767892366382_int_o: $tType ).
thf(fun_Pr4799464687642144302_num_o_type,type,
fun_Pr4799464687642144302_num_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_fu6277728343830838362at_nat_type,type,
fun_fu6277728343830838362at_nat: $tType ).
thf(fun_fu5576414621873183578at_nat_type,type,
fun_fu5576414621873183578at_nat: $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_fu6579618355643354601at_rat_type,type,
fun_fu6579618355643354601at_rat: $tType ).
thf(fun_fu5304001865264412401at_rat_type,type,
fun_fu5304001865264412401at_rat: $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_fu1617438229336688381nt_rat_type,type,
fun_fu1617438229336688381nt_rat: $tType ).
thf(fun_co3194742168270691230omplex_type,type,
fun_co3194742168270691230omplex: $tType ).
thf(fun_Co8502721031311864414nteger_type,type,
fun_Co8502721031311864414nteger: $tType ).
thf(fun_fu2849355231831568730at_nat_type,type,
fun_fu2849355231831568730at_nat: $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_fu4149201653251398851plex_o_type,type,
fun_fu4149201653251398851plex_o: $tType ).
thf(fun_fu2620374121714387907_int_o_type,type,
fun_fu2620374121714387907_int_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_fu5587483295140630005real_o_type,type,
fun_fu5587483295140630005real_o: $tType ).
thf(fun_Pr2183138248833747856t_real_type,type,
fun_Pr2183138248833747856t_real: $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_Pr6405077315951356852et_nat_type,type,
fun_Pr6405077315951356852et_nat: $tType ).
thf(fun_Pr3914994171019630096et_int_type,type,
fun_Pr3914994171019630096et_int: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_in2204242111582549184nt_int_type,type,
fun_in2204242111582549184nt_int: $tType ).
thf(fun_Co6597186368970283863nteger_type,type,
fun_Co6597186368970283863nteger: $tType ).
thf(fun_op7210469962420818650on_nat_type,type,
fun_op7210469962420818650on_nat: $tType ).
thf(fun_in5730379987311621695e_term_type,type,
fun_in5730379987311621695e_term: $tType ).
thf(fun_fu3572752990780465756omplex_type,type,
fun_fu3572752990780465756omplex: $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_fu1806770557662746761_nat_o_type,type,
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thf(fun_fu4977034074775808476omplex_type,type,
fun_fu4977034074775808476omplex: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_Pr2478283820680522243nt_int_type,type,
fun_Pr2478283820680522243nt_int: $tType ).
thf(fun_fu8643405727515436425nteger_type,type,
fun_fu8643405727515436425nteger: $tType ).
thf(fun_fu3477889739401271834t_real_type,type,
fun_fu3477889739401271834t_real: $tType ).
thf(fun_fu4045816715887884506omplex_type,type,
fun_fu4045816715887884506omplex: $tType ).
thf(fun_re3844104906058862192omplex_type,type,
fun_re3844104906058862192omplex: $tType ).
thf(fun_in1904380326158164027at_nat_type,type,
fun_in1904380326158164027at_nat: $tType ).
thf(fun_fu5289434066392675523_nat_o_type,type,
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thf(fun_fu4757868175734369219real_o_type,type,
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thf(fun_fu8602227297639178947real_o_type,type,
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thf(fun_fu91202020541382083_nat_o_type,type,
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thf(fun_fu8783008166737851587real_o_type,type,
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thf(fun_na5914473681949881652_nat_o_type,type,
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thf(fun_fu6441209753288909002at_nat_type,type,
fun_fu6441209753288909002at_nat: $tType ).
thf(fun_fu2815703370569351114at_nat_type,type,
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thf(fun_fu15528267131686454x_real_type,type,
fun_fu15528267131686454x_real: $tType ).
thf(fun_fu1590586450949517859at_nat_type,type,
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thf(fun_fu2499394402704830801nteger_type,type,
fun_fu2499394402704830801nteger: $tType ).
thf(fun_fu3628599891403802633nteger_type,type,
fun_fu3628599891403802633nteger: $tType ).
thf(fun_fu5956788528830221615omplex_type,type,
fun_fu5956788528830221615omplex: $tType ).
thf(fun_fu171175841697012900at_nat_type,type,
fun_fu171175841697012900at_nat: $tType ).
thf(fun_fu4165420744652164954omplex_type,type,
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thf(fun_fu2256525824028639322ex_nat_type,type,
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thf(fun_fu6034410707023039066omplex_type,type,
fun_fu6034410707023039066omplex: $tType ).
thf(fun_fu2872202335991144794ex_nat_type,type,
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thf(fun_fu5589980185390252312t_real_type,type,
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thf(fun_fu6436183194761443139_nat_o_type,type,
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thf(fun_fu5646853623633916995_int_o_type,type,
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thf(fun_fu8304507701009772099_nat_o_type,type,
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thf(fun_fu8064956510386623256t_real_type,type,
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thf(fun_fu7493154764834273859_int_o_type,type,
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thf(fun_fu927436805355353155_nat_o_type,type,
fun_fu927436805355353155_nat_o: $tType ).
thf(fun_fu138107234227827011_int_o_type,type,
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thf(fun_re7819166435457029784t_real_type,type,
fun_re7819166435457029784t_real: $tType ).
thf(fun_fu4806068833880117316t_real_type,type,
fun_fu4806068833880117316t_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_na5060536216179792737_nat_o_type,type,
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thf(fun_fu3719611171164834136t_real_type,type,
fun_fu3719611171164834136t_real: $tType ).
thf(set_fi4554929511873752355omplex_type,type,
set_fi4554929511873752355omplex: $tType ).
thf(fun_fu4710970720072501148at_rat_type,type,
fun_fu4710970720072501148at_rat: $tType ).
thf(fun_fu6228432884689642900at_rat_type,type,
fun_fu6228432884689642900at_rat: $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,
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thf(fun_ra2740371568465858076at_rat_type,type,
fun_ra2740371568465858076at_rat: $tType ).
thf(fun_in281396392327853336at_int_type,type,
fun_in281396392327853336at_int: $tType ).
thf(fun_co6147893885205795665omplex_type,type,
fun_co6147893885205795665omplex: $tType ).
thf(fun_Co1981900195452921617nteger_type,type,
fun_Co1981900195452921617nteger: $tType ).
thf(fun_fu9095377814970772604at_nat_type,type,
fun_fu9095377814970772604at_nat: $tType ).
thf(fun_fu4368050222092438908at_nat_type,type,
fun_fu4368050222092438908at_nat: $tType ).
thf(fun_re5512370375968561900l_real_type,type,
fun_re5512370375968561900l_real: $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(fun_fu4971871526818099510l_real_type,type,
fun_fu4971871526818099510l_real: $tType ).
thf(set_Pr6192946355708809607T_VEBT_type,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(list_P6254988961118846195et_nat_type,type,
list_P6254988961118846195et_nat: $tType ).
thf(list_P5578671422887162913nteger_type,type,
list_P5578671422887162913nteger: $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_fu8372050067615010778t_real_type,type,
fun_fu8372050067615010778t_real: $tType ).
thf(fun_fu1521248433810422618al_nat_type,type,
fun_fu1521248433810422618al_nat: $tType ).
thf(fun_se1865396762483378772_nat_o_type,type,
fun_se1865396762483378772_nat_o: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(set_Pr5488025237498180813et_nat_type,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(set_Pr4811707699266497531nteger_type,type,
set_Pr4811707699266497531nteger: $tType ).
thf(fun_fu1994797156054922755_nat_o_type,type,
fun_fu1994797156054922755_nat_o: $tType ).
thf(fun_Pr7211993375558241536eger_o_type,type,
fun_Pr7211993375558241536eger_o: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(fun_fu8066363281484412158at_nat_type,type,
fun_fu8066363281484412158at_nat: $tType ).
thf(fun_fu7177403482836593662at_nat_type,type,
fun_fu7177403482836593662at_nat: $tType ).
thf(fun_fu4911969157638215514t_real_type,type,
fun_fu4911969157638215514t_real: $tType ).
thf(fun_fu8130672751802585526t_real_type,type,
fun_fu8130672751802585526t_real: $tType ).
thf(fun_fu40286998686754419omplex_type,type,
fun_fu40286998686754419omplex: $tType ).
thf(fun_fu3613808716698379563omplex_type,type,
fun_fu3613808716698379563omplex: $tType ).
thf(fun_fu2990765671291504771ex_rat_type,type,
fun_fu2990765671291504771ex_rat: $tType ).
thf(fun_fu705315015666092147ex_nat_type,type,
fun_fu705315015666092147ex_nat: $tType ).
thf(fun_fu4213752561377164075ex_int_type,type,
fun_fu4213752561377164075ex_int: $tType ).
thf(fun_co6883864892131739507omplex_type,type,
fun_co6883864892131739507omplex: $tType ).
thf(fun_fu5776950848406856154at_nat_type,type,
fun_fu5776950848406856154at_nat: $tType ).
thf(fun_fu5586244933174592126at_nat_type,type,
fun_fu5586244933174592126at_nat: $tType ).
thf(fun_fu7773166507867613914nt_nat_type,type,
fun_fu7773166507867613914nt_nat: $tType ).
thf(fun_fu6714665071556184448_rat_o_type,type,
fun_fu6714665071556184448_rat_o: $tType ).
thf(fun_fu570715051317967998at_nat_type,type,
fun_fu570715051317967998at_nat: $tType ).
thf(fun_fu2757636626010989786nt_nat_type,type,
fun_fu2757636626010989786nt_nat: $tType ).
thf(fun_fu2445682883699234307plex_o_type,type,
fun_fu2445682883699234307plex_o: $tType ).
thf(fun_fu3719809307426920623omplex_type,type,
fun_fu3719809307426920623omplex: $tType ).
thf(fun_se2389560805064864136_nat_o_type,type,
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thf(fun_na927404270896789692_nat_o_type,type,
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thf(produc3447558737645232053on_num_type,type,
produc3447558737645232053on_num: $tType ).
thf(produc4953844613479565601on_nat_type,type,
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thf(fun_fu2408719596384163971_nat_o_type,type,
fun_fu2408719596384163971_nat_o: $tType ).
thf(fun_Pr8522397820002030766t_real_type,type,
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thf(set_fi7789364187291644575l_real_type,type,
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thf(fun_Pr3513738403344720850et_nat_type,type,
fun_Pr3513738403344720850et_nat: $tType ).
thf(fun_op493924057549976310_num_o_type,type,
fun_op493924057549976310_num_o: $tType ).
thf(fun_op167334234089630144_nat_o_type,type,
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thf(fun_op6120599277751319488_num_o_type,type,
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thf(fun_op5794009454290973322_nat_o_type,type,
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thf(fun_in8804710076054006414at_nat_type,type,
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thf(fun_fu7631928937237476593t_real_type,type,
fun_fu7631928937237476593t_real: $tType ).
thf(fun_Pr4738963024209204295_int_o_type,type,
fun_Pr4738963024209204295_int_o: $tType ).
thf(fun_Pr7537129237977221859_rat_o_type,type,
fun_Pr7537129237977221859_rat_o: $tType ).
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,
fun_fu3043978019632300333x_real: $tType ).
thf(filter6041513312241820739omplex_type,type,
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thf(fun_fu3077872570260440615l_real_type,type,
fun_fu3077872570260440615l_real: $tType ).
thf(fun_op8028897214545316308_nat_o_type,type,
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thf(fun_in7207726656141197838et_nat_type,type,
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thf(fun_Co6226381647958292740nteger_type,type,
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thf(fun_Co3583066429914935172er_nat_type,type,
fun_Co3583066429914935172er_nat: $tType ).
thf(fun_Co1092983284983208416er_int_type,type,
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thf(list_P2623026923184700063T_real_type,type,
list_P2623026923184700063T_real: $tType ).
thf(list_P877281246627933069T_VEBT_type,type,
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thf(fun_fu2497916604042137945plex_o_type,type,
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thf(fun_fu6229866931165912581plex_o_type,type,
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thf(fun_fu4396998534562958809ex_rat_type,type,
fun_fu4396998534562958809ex_rat: $tType ).
thf(produc1828647624359046049st_nat_type,type,
produc1828647624359046049st_nat: $tType ).
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(set_Pr7765410600122031685T_real_type,type,
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thf(set_Pr6019664923565264691T_VEBT_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(set_Pr6227168374412355847list_o_type,type,
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thf(set_li5450038453877631591at_nat_type,type,
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thf(produc8243902056947475879T_VEBT_type,type,
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thf(fun_fu2598743018846156927al_rat_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(fun_li7366011709773453460_nat_o_type,type,
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thf(set_Pr7556676689462069481BT_nat_type,type,
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thf(set_Pr5066593544530342725BT_int_type,type,
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thf(set_Pr8044002425091019955T_VEBT_type,type,
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thf(fun_fu7444430165986413063real_o_type,type,
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thf(fun_fu3532930458344041007omplex_type,type,
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thf(set_se7855581050983116737at_nat_type,type,
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thf(set_Pr5085853215250843933omplex_type,type,
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thf(produc7819656566062154093et_nat_type,type,
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thf(produc8923325533196201883nteger_type,type,
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thf(fun_se4782206882984618170_nat_o_type,type,
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thf(fun_Pr7716844367077540446plex_o_type,type,
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thf(fun_na5873943405026509934VEBT_o_type,type,
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thf(fun_Ex2441982661509597004d_enat_type,type,
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thf(fun_fu6891447142836604759at_o_o_type,type,
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thf(fun_VE2962686792283380846VEBT_o_type,type,
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thf(fun_fu8328862064278946247at_rat_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_fu1008360527747082367nt_rat_type,type,
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thf(fun_fu8905809029841901679nt_nat_type,type,
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thf(fun_ra3995598502166916815at_rat_type,type,
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thf(fun_ra5513060666784058567at_rat_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_fu6176141739774794687_nat_o_type,type,
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thf(fun_fu4302481349826706223omplex_type,type,
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thf(fun_fu7994259084669964039_int_o_type,type,
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thf(fun_fu3558165918884697647omplex_type,type,
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thf(fun_se2170385732985038782_nat_o_type,type,
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thf(fun_se9162176452187397432plex_o_type,type,
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thf(fun_Co2081214437782444048eger_o_type,type,
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thf(fun_fu1358370060594899587plex_o_type,type,
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thf(fun_na7595719129879163854on_num_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_fu7564235448449272366at_o_o_type,type,
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thf(fun_fu6971708032831053102nt_o_o_type,type,
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thf(fun_Pr672294278902479040t_real_type,type,
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thf(list_P3126845725202233233VEBT_o_type,type,
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thf(list_P7495141550334521929T_VEBT_type,type,
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thf(filter2146258269922977983l_real_type,type,
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thf(fun_op1272087013972230845on_nat_type,type,
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thf(fun_fu6510078244439976541real_o_type,type,
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thf(fun_fu3729927046167673097real_o_type,type,
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thf(fun_fu5551332503302594393al_rat_type,type,
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thf(fun_ra4503298312962071866nt_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_Pr1652463973008025892nt_rat_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(set_Pr3175402225741728619VEBT_o_type,type,
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thf(set_Pr7543698050874017315T_VEBT_type,type,
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thf(fun_re7208826350674946562omplex_type,type,
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thf(fun_na7671319193681171066at_nat_type,type,
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thf(fun_li2771310203728655226at_nat_type,type,
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thf(fun_in6553099857819052212t_real_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_fu1771228864347509049real_o_type,type,
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thf(fun_fu4002475321494201261t_real_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(option4927543243414619207at_nat_type,type,
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thf(list_P8689742595348180415l_real_type,type,
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thf(filter1242075044329608583at_nat_type,type,
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thf(fun_se1179353343636554400at_nat_type,type,
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thf(fun_na106483476154090400at_nat_type,type,
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thf(fun_na1591161823130732966omplex_type,type,
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thf(fun_in2630332840903238488et_nat_type,type,
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thf(fun_in7040156458970095540et_int_type,type,
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thf(fun_in1307110748760623106omplex_type,type,
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thf(fun_co3258106519541737638omplex_type,type,
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thf(fun_co7673900812888889602omplex_type,type,
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thf(fun_fu7145897819039579925_nat_o_type,type,
fun_fu7145897819039579925_nat_o: $tType ).
thf(fun_fu3162257917499486297at_rat_type,type,
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thf(fun_fu3473604023002724957_int_o_type,type,
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thf(fun_fu3922030663826099033nt_rat_type,type,
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thf(fun_na7928631014926962227_nat_o_type,type,
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thf(fun_in5570076352459579423_int_o_type,type,
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thf(set_Pr6218003697084177305l_real_type,type,
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thf(list_P6834414599653733731al_nat_type,type,
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thf(list_P4344331454722006975al_int_type,type,
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thf(list_P6863124054624500543t_real_type,type,
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thf(fun_Pr4814023175418636514real_o_type,type,
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thf(produc5170161368751668367T_real_type,type,
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thf(produc3757001726724277373T_VEBT_type,type,
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thf(fun_na7542918316964655096d_enat_type,type,
fun_na7542918316964655096d_enat: $tType ).
thf(set_Pr3510011417693777981al_nat_type,type,
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thf(set_Pr1019928272762051225al_int_type,type,
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thf(set_Pr3538720872664544793t_real_type,type,
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thf(produc7102631898165422375list_o_type,type,
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thf(list_P6011104703257516679at_nat_type,type,
list_P6011104703257516679at_nat: $tType ).
thf(list_P3521021558325789923at_int_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(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,
fun_Pr3238374608701176162_int_o: $tType ).
thf(fun_na5723442673449079972x_real_type,type,
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thf(fun_co8378349014452122532t_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_li2421049240157457050_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_int_set_set_nat_type,type,
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thf(fun_co636942507509095880at_nat_type,type,
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thf(fun_Co8499238673658658103nteger_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,
fun_fu4001317426178549763_nat_o: $tType ).
thf(fun_fu3883539188510166275_int_o_type,type,
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thf(fun_re7681423839302404990l_real_type,type,
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thf(list_P3595434254542482545real_o_type,type,
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thf(list_P5232166724548748803o_real_type,type,
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thf(fun_re4238438383274954274t_real_type,type,
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thf(fun_na6724076748692969250l_real_type,type,
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thf(set_Pr4936984352647145239real_o_type,type,
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thf(set_Pr6573716822653411497o_real_type,type,
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thf(list_P7333126701944960589_nat_o_type,type,
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thf(list_P6285523579766656935_o_nat_type,type,
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thf(list_P3795440434834930179_o_int_type,type,
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thf(set_list_VEBT_VEBT_type,type,
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thf(produc334124729049499915VEBT_o_type,type,
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thf(produc2504756804600209347T_VEBT_type,type,
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thf(fun_real_fun_nat_nat_type,type,
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thf(fun_nat_fun_real_nat_type,type,
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thf(fun_nat_fun_rat_real_type,type,
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thf(fun_nat_fun_int_real_type,type,
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thf(fun_list_VEBT_VEBT_o_type,type,
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thf(fun_int_fun_nat_real_type,type,
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thf(set_Pr2101469702781467981_o_nat_type,type,
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thf(set_Pr8834758594704517033_o_int_type,type,
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thf(produc6271795597528267376eger_o_type,type,
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thf(fun_re7319081385389557872plex_o_type,type,
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thf(fun_co4998825143550818160real_o_type,type,
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thf(fun_rat_fun_rat_rat_type,type,
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thf(fun_rat_fun_nat_rat_type,type,
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thf(fun_num_fun_num_num_type,type,
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thf(fun_nat_fun_nat_rat_type,type,
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thf(fun_nat_fun_nat_nat_type,type,
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thf(fun_nat_fun_nat_int_type,type,
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thf(fun_nat_fun_list_o_o_type,type,
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thf(fun_co8153928105989009288nteger_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(produc2422161461964618553l_real_type,type,
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thf(fun_num_option_num_type,type,
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thf(produc3741383161447143261al_nat_type,type,
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thf(produc8786904178792722361al_int_type,type,
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thf(produc679980390762269497t_real_type,type,
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thf(fun_real_fun_real_o_type,type,
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thf(product_prod_num_num_type,type,
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thf(product_prod_nat_nat_type,type,
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thf(product_prod_nat_int_type,type,
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thf(product_prod_int_int_type,type,
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thf(list_P4002435161011370285od_o_o_type,type,
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thf(fun_re6978948838062957830nteger_type,type,
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thf(fun_list_nat_nat_type,type,
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thf(fun_int_set_real_type,type,
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thf(set_list_complex_type,type,
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thf(fun_VEBT_VEBT_nat_type,type,
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thf(set_Product_prod_o_o_type,type,
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thf(fun_set_nat_nat_type,type,
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thf(fun_nat_set_nat_type,type,
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thf(fun_nat_set_int_type,type,
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thf(fun_nat_Code_integer_type,type,
fun_nat_Code_integer: $tType ).
thf(fun_int_set_nat_type,type,
fun_int_set_nat: $tType ).
thf(fun_int_set_int_type,type,
fun_int_set_int: $tType ).
thf(fun_int_Code_integer_type,type,
fun_int_Code_integer: $tType ).
thf(fun_complex_complex_type,type,
fun_complex_complex: $tType ).
thf(fun_Code_integer_nat_type,type,
fun_Code_integer_nat: $tType ).
thf(fun_Code_integer_int_type,type,
fun_Code_integer_int: $tType ).
thf(set_set_complex_type,type,
set_set_complex: $tType ).
thf(fun_fun_rat_rat_o_type,type,
fun_fun_rat_rat_o: $tType ).
thf(fun_fun_nat_rat_o_type,type,
fun_fun_nat_rat_o: $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_rat_fun_rat_o_type,type,
fun_rat_fun_rat_o: $tType ).
thf(fun_num_fun_num_o_type,type,
fun_num_fun_num_o: $tType ).
thf(fun_nat_fun_nat_o_type,type,
fun_nat_fun_nat_o: $tType ).
thf(fun_nat_fun_int_o_type,type,
fun_nat_fun_int_o: $tType ).
thf(fun_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(option_VEBT_VEBT_type,type,
option_VEBT_VEBT: $tType ).
thf(option_set_nat_type,type,
option_set_nat: $tType ).
thf(fun_option_num_o_type,type,
fun_option_num_o: $tType ).
thf(fun_option_nat_o_type,type,
fun_option_nat_o: $tType ).
thf(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(product_prod_real_o_type,type,
product_prod_real_o: $tType ).
thf(product_prod_o_real_type,type,
product_prod_o_real: $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(product_prod_nat_o_type,type,
product_prod_nat_o: $tType ).
thf(product_prod_o_nat_type,type,
product_prod_o_nat: $tType ).
thf(product_prod_o_int_type,type,
product_prod_o_int: $tType ).
thf(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_rat_type,type,
fun_complex_rat: $tType ).
thf(fun_complex_num_type,type,
fun_complex_num: $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(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(fun_set_rat_o_type,type,
fun_set_rat_o: $tType ).
thf(fun_set_num_o_type,type,
fun_set_num_o: $tType ).
thf(fun_set_nat_o_type,type,
fun_set_nat_o: $tType ).
thf(fun_set_int_o_type,type,
fun_set_int_o: $tType ).
thf(fun_Code_integer_o_type,type,
fun_Code_integer_o: $tType ).
thf(fun_nat_fun_o_o_type,type,
fun_nat_fun_o_o: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(fun_real_real_type,type,
fun_real_real: $tType ).
thf(fun_Extended_enat_o_type,type,
fun_Extended_enat_o: $tType ).
thf(fun_real_rat_type,type,
fun_real_rat: $tType ).
thf(fun_real_num_type,type,
fun_real_num: $tType ).
thf(fun_real_nat_type,type,
fun_real_nat: $tType ).
thf(fun_real_int_type,type,
fun_real_int: $tType ).
thf(fun_rat_real_type,type,
fun_rat_real: $tType ).
thf(fun_num_real_type,type,
fun_num_real: $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(set_list_o_type,type,
set_list_o: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(fun_rat_rat_type,type,
fun_rat_rat: $tType ).
thf(fun_rat_num_type,type,
fun_rat_num: $tType ).
thf(fun_rat_nat_type,type,
fun_rat_nat: $tType ).
thf(fun_rat_int_type,type,
fun_rat_int: $tType ).
thf(fun_num_rat_type,type,
fun_num_rat: $tType ).
thf(fun_num_num_type,type,
fun_num_num: $tType ).
thf(fun_num_nat_type,type,
fun_num_nat: $tType ).
thf(fun_num_int_type,type,
fun_num_int: $tType ).
thf(fun_nat_rat_type,type,
fun_nat_rat: $tType ).
thf(fun_nat_num_type,type,
fun_nat_num: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_int_type,type,
fun_nat_int: $tType ).
thf(fun_list_o_o_type,type,
fun_list_o_o: $tType ).
thf(fun_int_rat_type,type,
fun_int_rat: $tType ).
thf(fun_int_num_type,type,
fun_int_num: $tType ).
thf(fun_int_nat_type,type,
fun_int_nat: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(set_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(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_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(fun_rat_o_type,type,
fun_rat_o: $tType ).
thf(fun_num_o_type,type,
fun_num_o: $tType ).
thf(fun_nat_o_type,type,
fun_nat_o: $tType ).
thf(fun_int_o_type,type,
fun_int_o: $tType ).
thf(fun_o_nat_type,type,
fun_o_nat: $tType ).
thf(fun_o_int_type,type,
fun_o_int: $tType ).
thf(option_o_type,type,
option_o: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(fun_o_o_type,type,
fun_o_o: $tType ).
thf(real_type,type,
real: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(aTP_Lamm_aad_decl,type,
aTP_Lamm_aad: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_aae_decl,type,
aTP_Lamm_aae: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_aax_decl,type,
aTP_Lamm_aax: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_acc_decl,type,
aTP_Lamm_acc: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_acd_decl,type,
aTP_Lamm_acd: fun_nat_nat ).
thf(aTP_Lamm_acq_decl,type,
aTP_Lamm_acq: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_cs_decl,type,
aTP_Lamm_cs: fun_nat_o > fun_nat_fun_nat_o ).
thf(aTP_Lamm_fs_decl,type,
aTP_Lamm_fs: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_he_decl,type,
aTP_Lamm_he: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_ly_decl,type,
aTP_Lamm_ly: fun_nat_nat ).
thf(aTP_Lamm_mb_decl,type,
aTP_Lamm_mb: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mv_decl,type,
aTP_Lamm_mv: fun_nat_nat ).
thf(aTP_Lamm_nz_decl,type,
aTP_Lamm_nz: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_of_decl,type,
aTP_Lamm_of: nat > fun_nat_fun_nat_o ).
thf(aTP_Lamm_tv_decl,type,
aTP_Lamm_tv: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_vn_decl,type,
aTP_Lamm_vn: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xm_decl,type,
aTP_Lamm_xm: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_yi_decl,type,
aTP_Lamm_yi: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_zv_decl,type,
aTP_Lamm_zv: nat > fun_na7928631014926962227_nat_o ).
thf(aTP_Lamm_zx_decl,type,
aTP_Lamm_zx: nat > fun_na7928631014926962227_nat_o ).
thf(binomial_decl,type,
binomial: fun_nat_fun_nat_nat ).
thf(gbinomial_nat_decl,type,
gbinomial_nat: fun_nat_fun_nat_nat ).
thf(bit_se2002935070580805687sk_nat_decl,type,
bit_se2002935070580805687sk_nat: fun_nat_nat ).
thf(bit_se547839408752420682it_nat_decl,type,
bit_se547839408752420682it_nat: fun_nat_fun_nat_nat ).
thf(bit_se2925701944663578781it_nat_decl,type,
bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).
thf(bit_se1148574629649215175it_nat_decl,type,
bit_se1148574629649215175it_nat: fun_nat_fun_nat_o ).
thf(comm_s4663373288045622133er_nat_decl,type,
comm_s4663373288045622133er_nat: fun_nat_fun_nat_nat ).
thf(semiri1408675320244567234ct_nat_decl,type,
semiri1408675320244567234ct_nat: fun_nat_nat ).
thf(at_top_nat_decl,type,
at_top_nat: filter_nat ).
thf(filterlim_nat_nat_decl,type,
filterlim_nat_nat: fun_nat_nat > filter_nat > filter_nat > $o ).
thf(gcd_gcd_nat_decl,type,
gcd_gcd_nat: fun_nat_fun_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(append_nat_decl,type,
append_nat: list_nat > list_nat > list_nat ).
thf(drop_nat_decl,type,
drop_nat: nat > list_nat > list_nat ).
thf(enumerate_VEBT_VEBT_decl,type,
enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(find_nat_decl,type,
find_nat: fun_nat_o > list_nat > option_nat ).
thf(find_VEBT_VEBT_decl,type,
find_VEBT_VEBT: fun_VEBT_VEBT_o > list_VEBT_VEBT > option_VEBT_VEBT ).
thf(last_nat_decl,type,
last_nat: list_nat > nat ).
thf(linord738340561235409698at_nat_decl,type,
linord738340561235409698at_nat: fun_nat_nat > list_nat > list_nat ).
thf(cons_nat_decl,type,
cons_nat: nat > list_nat > list_nat ).
thf(nil_nat_decl,type,
nil_nat: list_nat ).
thf(hd_nat_decl,type,
hd_nat: list_nat > 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_update_nat_decl,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(list_u1324408373059187874T_VEBT_decl,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(nth_o_decl,type,
nth_o: list_o > fun_nat_o ).
thf(nth_nat_decl,type,
nth_nat: fun_li2771310203728655226at_nat ).
thf(nth_Pr6777367263587873994T_VEBT_decl,type,
nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
thf(nth_Pr744662078594809490T_VEBT_decl,type,
nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
thf(nth_Pr4606735188037164562VEBT_o_decl,type,
nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
thf(nth_Pr4953567300277697838T_VEBT_decl,type,
nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
thf(nth_VEBT_VEBT_decl,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(product_o_o_decl,type,
product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
thf(product_o_VEBT_VEBT_decl,type,
product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
thf(produc7156399406898700509T_VEBT_decl,type,
produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(product_VEBT_VEBT_o_decl,type,
product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
thf(produc4743750530478302277T_VEBT_decl,type,
produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(replicate_VEBT_VEBT_decl,type,
replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(take_nat_decl,type,
take_nat: nat > list_nat > list_nat ).
thf(upt_decl,type,
upt: nat > nat > list_nat ).
thf(zip_nat_VEBT_VEBT_decl,type,
zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(zip_VE537291747668921783T_VEBT_decl,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
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(case_nat_nat_decl,type,
case_nat_nat: nat > fun_nat_nat > fun_nat_nat ).
thf(semiri1316708129612266289at_nat_decl,type,
semiri1316708129612266289at_nat: fun_nat_nat ).
thf(semiri8422978514062236437ux_nat_decl,type,
semiri8422978514062236437ux_nat: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(size_size_list_o_decl,type,
size_size_list_o: list_o > nat ).
thf(size_size_list_nat_decl,type,
size_size_list_nat: list_nat > nat ).
thf(size_s1515746228057227161od_o_o_decl,type,
size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
thf(size_s4313452262239582901T_VEBT_decl,type,
size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
thf(size_s9168528473962070013VEBT_o_decl,type,
size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
thf(size_s7466405169056248089T_VEBT_decl,type,
size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
thf(size_s6755466524823107622T_VEBT_decl,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(size_size_option_nat_decl,type,
size_size_option_nat: option_nat > nat ).
thf(some_nat_decl,type,
some_nat: nat > option_nat ).
thf(some_VEBT_VEBT_decl,type,
some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT ).
thf(size_option_nat_decl,type,
size_option_nat: fun_nat_nat > option_nat > nat ).
thf(ord_Least_nat_decl,type,
ord_Least_nat: fun_nat_o > nat ).
thf(ord_less_nat_decl,type,
ord_less_nat: fun_nat_fun_nat_o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: fun_nat_fun_nat_o ).
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(order_mono_nat_nat_decl,type,
order_mono_nat_nat: fun_nat_nat > $o ).
thf(power_power_nat_decl,type,
power_power_nat: fun_nat_fun_nat_nat ).
thf(produc2982872950893828659T_VEBT_decl,type,
produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
thf(produc599794634098209291T_VEBT_decl,type,
produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
thf(produc8721562602347293563VEBT_o_decl,type,
produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
thf(produc537772716801021591T_VEBT_decl,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(algebr934650988132801477me_nat_decl,type,
algebr934650988132801477me_nat: fun_nat_fun_nat_o ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
thf(dvd_dvd_nat_decl,type,
dvd_dvd_nat: fun_nat_fun_nat_o ).
thf(modulo_modulo_nat_decl,type,
modulo_modulo_nat: fun_nat_fun_nat_nat ).
thf(zero_n2687167440665602831ol_nat_decl,type,
zero_n2687167440665602831ol_nat: $o > nat ).
thf(set_fo2584398358068434914at_nat_decl,type,
set_fo2584398358068434914at_nat: fun_nat_fun_nat_nat > nat > fun_nat_fun_nat_nat ).
thf(vEBT_Leaf_decl,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
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_VEBT_valid_decl,type,
vEBT_VEBT_valid: vEBT_VEBT > fun_nat_o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_o ).
thf(vEBT_set_vebt_decl,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_vebt_buildup_decl,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(vEBT_vebt_delete_decl,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
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_set_vebt_decl,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > fun_nat_o ).
thf(vEBT_vebt_maxt_decl,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(aa_list_o_o_decl,type,
aa_list_o_o: fun_list_o_o > list_o > $o ).
thf(aa_lis1299702591413342011at_nat_decl,type,
aa_lis1299702591413342011at_nat: fun_li2771310203728655226at_nat > list_nat > fun_nat_nat ).
thf(aa_list_VEBT_VEBT_o_decl,type,
aa_list_VEBT_VEBT_o: fun_list_VEBT_VEBT_o > list_VEBT_VEBT > $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_nat_fun_nat_o_decl,type,
aa_nat_fun_nat_o: fun_nat_fun_nat_o > nat > fun_nat_o ).
thf(aa_nat_fun_nat_nat_decl,type,
aa_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).
thf(aa_nat8314798964848609180_nat_o_decl,type,
aa_nat8314798964848609180_nat_o: fun_na7928631014926962227_nat_o > nat > fun_nat_fun_nat_o ).
thf(aa_nat1925708948643195573VEBT_o_decl,type,
aa_nat1925708948643195573VEBT_o: fun_na6887940067898170868VEBT_o > nat > fun_VEBT_VEBT_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(m_decl,type,
m: nat ).
thf(ma_decl,type,
ma: nat ).
thf(maxi_decl,type,
maxi: 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(sk11_decl,type,
sk11: nat > nat > nat ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: nat,B: nat] :
@+[C: nat] :
( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ).
thf(286,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n2687167440665602831ol_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4666_take__bit__of__1) ).
thf(2452,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n2687167440665602831ol_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(936,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1353_less__eqE) ).
thf(5593,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(243,axiom,
! [A: nat] : ( A @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7917_fact__le__power) ).
thf(2263,plain,
! [A: nat] : ( A @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(559,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3404_less__diff__conv) ).
thf(3798,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(477,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9263_less__mask) ).
thf(3449,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(978,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1429_add__le__mono) ).
thf(5778,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1024,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_valid__tree__deg__neq__0) ).
thf(6014,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7992_fact__mono__nat) ).
thf(1110,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3142_div__nat__eqI) ).
thf(1686,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(951,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_dual__order_Ostrict__implies__not__eq) ).
thf(5659,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(113,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_3005_vebt__insert_Osimps_I2_J) ).
thf(1665,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)],[113]) ).
thf(320,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2028_zero__le__power) ).
thf(2630,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(1044,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_3260_diff__commute) ).
thf(6085,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)],[1044]) ).
thf(723,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_2276_mult__Suc__right) ).
thf(4560,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)],[723]) ).
thf(591,axiom,
! [A: nat,B: nat,C: fun_nat_fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( E @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1795_transitive__stepwise__le) ).
thf(3962,plain,
! [A: nat,B: nat,C: fun_nat_fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( E @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(456,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( summary @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
<=> ( ( B @ ( summary @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__C4_OIH_C_I2_J) ).
thf(3345,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( summary @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( A != B ) )
=> ( B @ ( A @ ( summary @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( summary @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( ( B @ ( summary @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(702,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4175_dvd__1__iff__1) ).
thf(4464,plain,
! [A: nat] :
( ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_linorder__linear) ).
thf(2341,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4310_le__imp__power__dvd) ).
thf(2072,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(615,axiom,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_less__induct) ).
thf(4062,plain,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(278,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3663_max_OboundedI) ).
thf(2412,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(40,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2799_zero__less__one__class_Ozero__le__one) ).
thf(1237,plain,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(387,axiom,
! [A: nat,B: fun_nat_o] :
( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
<=> ( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( A @ ( B @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1775_Ex__less__Suc) ).
thf(2921,plain,
! [A: nat,B: fun_nat_o] :
( ( ( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( A @ ( B @ aa_nat_o ) ) )
=> ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( A @ ( B @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(660,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_1197_add_Oright__neutral) ).
thf(4290,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)],[660]) ).
thf(537,axiom,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6471_of__nat__0__less__iff) ).
thf(3698,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(576,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_VEBT_VEBT ) )
= ( C @ ( B @ nth_VEBT_VEBT ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_nth__equalityI) ).
thf(3863,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_VEBT_VEBT ) )
= ( C @ ( B @ nth_VEBT_VEBT ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(954,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_antisym__conv3) ).
thf(5676,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(282,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4387_dvd__power__iff) ).
thf(2427,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(186,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__zero__eq) ).
thf(1982,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(504,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_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_8013_fact__diff__Suc) ).
thf(3566,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_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)],[504]) ).
thf(759,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_2530_mult__0) ).
thf(4728,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)],[759]) ).
thf(129,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3687_max_Oabsorb__iff2) ).
thf(1750,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(672,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_linorder__cases) ).
thf(4339,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(574,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2872_mult__left__less__imp__less) ).
thf(3858,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(143,axiom,
~ ( one_one_nat @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4262_not__is__unit__0) ).
thf(1808,plain,
~ ( one_one_nat @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(400,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3144_dividend__less__times__div) ).
thf(3040,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(3,axiom,
! [A: list_nat,B: nat] :
( ( B @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ ( A @ list_update_nat ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list__update__id) ).
thf(1073,plain,
! [A: list_nat,B: nat] :
( ( B @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ ( A @ list_update_nat ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1016,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2364_less__1__mult) ).
thf(5982,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(668,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 ) ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat] :
( A
!= ( D @ ( 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_4092_mod__eq__nat1E) ).
thf(4326,plain,
! [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 ) ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat] :
( A
!= ( D @ ( 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)],[668]) ).
thf(370,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = B ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1387_add__mono__thms__linordered__field_I2_J) ).
thf(2854,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = B ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(736,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_3478_mult__eq__if) ).
thf(4623,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)],[736]) ).
thf(464,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_order__less__irrefl) ).
thf(3382,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(532,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_add__le__cancel__right) ).
thf(3680,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(210,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3124_div__le__dividend) ).
thf(2077,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1027,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_2398_mult_Oleft__commute) ).
thf(6022,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)],[1027]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2045_power__le__imp__le__base) ).
thf(1211,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1037,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_valid__0__not) ).
thf(6063,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(406,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( D @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( 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 @ ( A @ ( B @ ( minus_minus_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 ) )
= E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3455_nat__eq__add__iff1) ).
thf(3072,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) )
= E )
=> ( ( D @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( 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 @ ( A @ ( B @ ( minus_minus_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 ) )
= E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(172,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_dual__order_Otrans) ).
thf(1924,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1,conjecture,
na @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_invar_vebt @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( na @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1072,plain,
~ ( na @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1045,axiom,
xa = ma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_True) ).
thf(6088,plain,
xa = ma,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(6089,plain,
xa = ma,
inference(lifteq,[status(thm)],[6088]) ).
thf(1065,axiom,
m = na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C4_Ohyps_C_I3_J) ).
thf(6153,plain,
m = na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(6154,plain,
na = m,
inference(lifteq,[status(thm)],[6153]) ).
thf(6177,plain,
~ ( m @ ( m @ ( ma @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(rewrite,[status(thm)],[1072,6089,6154]) ).
thf(840,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ vEBT_vebt_buildup @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_buildup__gives__valid) ).
thf(5141,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ vEBT_vebt_buildup @ vEBT_invar_vebt @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3647_max_Omono) ).
thf(1522,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(712,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3071_div__less) ).
thf(4515,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(562,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1725_Suc__le__mono) ).
thf(3813,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(268,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: $o,F: $o] :
( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
!= ( F @ ( E @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3285_VEBT_Odistinct_I1_J) ).
thf(2381,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: $o,F: $o] :
( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
!= ( F @ ( E @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(874,axiom,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) )
=> ( D @ ( C @ aa_nat_o ) ) ) ) )
=> ( A @ ( C @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1896_inc__induct) ).
thf(5292,plain,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) )
=> ( D @ ( C @ aa_nat_o ) ) ) ) )
=> ( A @ ( C @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(827,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3442_diff__Suc__less) ).
thf(5069,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(272,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7993_fact__ge__self) ).
thf(2395,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(383,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_2845_Suc__eq__plus1__left) ).
thf(2908,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)],[383]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_order_Oorder__iff__strict) ).
thf(1422,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(590,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_4023_bits__mod__0) ).
thf(3959,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)],[590]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_le__neq__implies__less) ).
thf(2099,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(859,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_less__not__refl2) ).
thf(5224,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(884,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( D @ ( A @ aa_nat_o ) ) )
& ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ex__least__nat__le) ).
thf(5348,plain,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( D @ ( A @ aa_nat_o ) ) )
& ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(1025,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_nz @ 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_9634_ATP_Olambda__303) ).
thf(6017,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_nz @ 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)],[1025]) ).
thf(83,axiom,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ zero_n2687167440665602831ol_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6459_of__nat__of__bool) ).
thf(1486,plain,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ zero_n2687167440665602831ol_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(716,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6433_of__nat__add) ).
thf(4532,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(920,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_2187_mult__is__0) ).
thf(5501,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)],[920]) ).
thf(138,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2948_power__less__imp__less__exp) ).
thf(1788,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_le__cases3) ).
thf(1671,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(623,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_4033_mod__by__1) ).
thf(4090,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)],[623]) ).
thf(548,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ size_s6755466524823107622T_VEBT )
= ( A @ size_s6755466524823107622T_VEBT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_length__list__update) ).
thf(3745,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ size_s6755466524823107622T_VEBT )
= ( A @ size_s6755466524823107622T_VEBT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(422,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_1370_comm__monoid__add__class_Oadd__0) ).
thf(3135,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)],[422]) ).
thf(156,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1524_verit__comp__simplify1_I2_J) ).
thf(1867,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(960,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1894_le__less__Suc__eq) ).
thf(5701,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = A )
=> ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(695,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3340_diff__le__mono2) ).
thf(4440,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(962,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_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_3247_diff__Suc__diff__eq1) ).
thf(5713,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_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)],[962]) ).
thf(953,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_15_not__min__Null__member) ).
thf(5674,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)],[953]) ).
thf(131,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_linorder__le__cases) ).
thf(1761,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(819,axiom,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( C @ ( A @ aa_nat_o ) )
=> ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_infinite__descent0) ).
thf(5005,plain,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( C @ ( A @ aa_nat_o ) )
=> ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(450,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( A @ upt ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9171_nth__upt) ).
thf(3313,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( A @ upt ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(961,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_1762_nat__induct) ).
thf(5708,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)],[961]) ).
thf(265,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_3036_max__nat_Oeq__neutr__iff) ).
thf(2360,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)],[265]) ).
thf(570,axiom,
zero_zero_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8733_zero__natural_Orsp) ).
thf(3848,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3667_max_Oorder__iff) ).
thf(1497,plain,
! [A: nat,B: nat] :
( ( ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(929,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1448_add__nonneg__nonneg) ).
thf(5550,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3756_discrete) ).
thf(1608,plain,
! [A: nat,B: nat] :
( ( ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(739,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2813_mult__less__mono1) ).
thf(4633,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(688,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1335_add__mono__thms__linordered__semiring_I3_J) ).
thf(4403,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(473,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_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_3407_Nat_Odiff__add__assoc) ).
thf(3429,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_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)],[473]) ).
thf(932,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3405_le__diff__conv) ).
thf(5565,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(728,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mb @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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_9876_ATP_Olambda__545) ).
thf(4575,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mb @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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)],[728]) ).
thf(1003,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3333_less__imp__diff__less) ).
thf(5906,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(58,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_3112_nat__add__max__right) ).
thf(1310,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)],[58]) ).
thf(460,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_1414_add__eq__self__zero) ).
thf(3365,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)],[460]) ).
thf(789,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_deg__not__0) ).
thf(4870,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(347,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4320_dvd__diffD1) ).
thf(2740,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(49,axiom,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7851_fact__0) ).
thf(1274,plain,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1275,plain,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(lifteq,[status(thm)],[1274]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4319_less__eq__dvd__minus) ).
thf(2141,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(508,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6560_of__nat__diff) ).
thf(3577,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(200,axiom,
! [A: nat,B: nat,C: list_nat,D: nat] :
( ( ( C @ ( B @ cons_nat ) @ ( A @ cons_nat ) )
= ( D @ ( A @ upt ) ) )
<=> ( ( C @ ( B @ cons_nat ) )
= ( D @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9182_upt__conv__Cons__Cons) ).
thf(2042,plain,
! [A: nat,B: nat,C: list_nat,D: nat] :
( ( ( ( C @ ( B @ cons_nat ) )
= ( D @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) )
=> ( ( C @ ( B @ cons_nat ) @ ( A @ cons_nat ) )
= ( D @ ( A @ upt ) ) ) )
& ( ( ( C @ ( B @ cons_nat ) @ ( A @ cons_nat ) )
= ( D @ ( A @ upt ) ) )
=> ( ( C @ ( B @ cons_nat ) )
= ( D @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(968,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_less__mono__imp__le__mono) ).
thf(5740,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(491,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1511_add__pos__nonneg) ).
thf(3502,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(706,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6527_of__nat__less__0__iff) ).
thf(4496,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(619,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6927_binomial__eq__0) ).
thf(4079,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_gcd_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_8800_gcd__nat_Oeq__neutr__iff) ).
thf(1366,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( gcd_gcd_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)],[67]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( divide_divide_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_3754_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq) ).
thf(1518,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( divide_divide_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)],[87]) ).
thf(38,axiom,
zero_zero_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1550_le__numeral__extra_I3_J) ).
thf(1228,plain,
zero_zero_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(30,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_3065_max__0__1_I2_J) ).
thf(1196,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)],[30]) ).
thf(1061,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_24_in__children__def) ).
thf(6138,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)],[1061]) ).
thf(553,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8983_mult__nat__left__at__top) ).
thf(3766,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(599,axiom,
! [A: nat,B: nat,C: vEBT_VEBT] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ replicate_VEBT_VEBT ) @ nth_VEBT_VEBT ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4505_nth__replicate) ).
thf(3994,plain,
! [A: nat,B: nat,C: vEBT_VEBT] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ replicate_VEBT_VEBT ) @ nth_VEBT_VEBT ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_order__le__imp__less__or__eq) ).
thf(1127,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(582,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2687_mult__right__mono) ).
thf(3915,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(300,axiom,
! [A: $o,B: $o] :
( ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4634_of__bool__less__eq__iff) ).
thf(2548,plain,
! [A: $o,B: $o] :
( ( ( A
=> B )
=> ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
=> B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(969,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_2010_power__Suc__0) ).
thf(5745,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)],[969]) ).
thf(753,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4057_mod__less__eq__dividend) ).
thf(4679,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(176,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3101_max__def) ).
thf(1935,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(587,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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_6965_choose__reduce__nat) ).
thf(3947,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[587]) ).
thf(627,axiom,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
<=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4502_Ball__set__replicate) ).
thf(4124,plain,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(990,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_2123_mult__zero__left) ).
thf(5825,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)],[990]) ).
thf(965,axiom,
! [A: fun_nat_o,B: nat,C: fun_nat_o,D: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( E @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( E @ ( C @ aa_nat_o ) ) )
=> ( ( A @ ord_Least_nat )
= ( C @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9259_Least__Suc2) ).
thf(5723,plain,
! [A: fun_nat_o,B: nat,C: fun_nat_o,D: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( ( E @ ( C @ aa_nat_o ) )
=> ( E @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( E @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( E @ ( C @ aa_nat_o ) ) ) )
=> ( ( A @ ord_Least_nat )
= ( C @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(274,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3659_max_OboundedE) ).
thf(2400,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(810,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8294_pochhammer__pos) ).
thf(4963,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(183,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( aTP_Lamm_acd @ map_nat_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9185_map__decr__upt) ).
thf(1967,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( aTP_Lamm_acd @ map_nat_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(711,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( B @ ( minus_minus_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_3372_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(4511,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( B @ ( minus_minus_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)],[711]) ).
thf(649,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_4020_mod__0) ).
thf(4249,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)],[649]) ).
thf(930,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1391_add__mono__thms__linordered__field_I1_J) ).
thf(5553,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(719,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3451_nat__diff__add__eq1) ).
thf(4546,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(715,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3700_less__max__iff__disj) ).
thf(4524,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(675,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3128_less__mult__imp__div__less) ).
thf(4348,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(724,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_35_list__update__id) ).
thf(4563,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)],[724]) ).
thf(507,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( A @ aa_nat_nat ) @ ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1884_lift__Suc__antimono__le) ).
thf(3574,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( A @ aa_nat_nat ) @ ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(849,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1476_add__mono__thms__linordered__field_I3_J) ).
thf(5188,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1038,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aae @ 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_9475_ATP_Olambda__144) ).
thf(6066,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aae @ 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)],[1038]) ).
thf(425,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1792_not__less__eq__eq) ).
thf(3148,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_Orderings_Oorder__eq__iff) ).
thf(1313,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(379,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1904_less__add__Suc2) ).
thf(2897,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(648,axiom,
! [A: nat,B: fun_nat_o] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) ) )
=> ( A @ ( B @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2958_nat__induct__non__zero) ).
thf(4243,plain,
! [A: nat,B: fun_nat_o] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) ) )
=> ( A @ ( B @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(446,axiom,
! [A: list_o,B: list_o] :
( ( A = B )
<=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_o @ aa_nat_o ) )
<=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_list__eq__iff__nth__eq) ).
thf(3248,plain,
! [A: list_o,B: list_o] :
( ( ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(646,axiom,
! [A: nat,B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ ( B @ nth_VEBT_VEBT ) @ member_VEBT_VEBT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_nth__mem) ).
thf(4238,plain,
! [A: nat,B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ ( B @ nth_VEBT_VEBT ) @ member_VEBT_VEBT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(435,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1431_trans__le__add1) ).
thf(3204,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2981_self__le__power) ).
thf(2039,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(447,axiom,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( A @ aa_nat_o ) )
<=> ( F @ ( B @ aa_nat_o ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( C @ aa_nat_o ) )
<=> ( F @ ( D @ aa_nat_o ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) )
<=> ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1612_pinf_I2_J) ).
thf(3275,plain,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( B @ aa_nat_o ) )
=> ( F @ ( A @ aa_nat_o ) ) )
& ( ( F @ ( A @ aa_nat_o ) )
=> ( F @ ( B @ aa_nat_o ) ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( D @ aa_nat_o ) )
=> ( F @ ( C @ aa_nat_o ) ) )
& ( ( F @ ( C @ aa_nat_o ) )
=> ( F @ ( D @ aa_nat_o ) ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) )
=> ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) ) )
& ( ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) )
=> ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(337,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7873_fact__nonzero) ).
thf(2698,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(421,axiom,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ ( C @ ( B @ nth_VEBT_VEBT ) @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 )
= ( B @ set_VEBT_VEBT2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_set__swap) ).
thf(3131,plain,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ ( C @ ( B @ nth_VEBT_VEBT ) @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 )
= ( B @ set_VEBT_VEBT2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(872,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2876_mult__strict__mono) ).
thf(5284,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(534,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1905_less__add__Suc1) ).
thf(3689,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(258,axiom,
~ ( one_one_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2542_less__numeral__extra_I4_J) ).
thf(2339,plain,
~ ( one_one_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(756,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_2522_mult__left__cancel) ).
thf(4692,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)],[756]) ).
thf(1048,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_3263_diff__right__commute) ).
thf(6095,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)],[1048]) ).
thf(246,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_order_Ostrict__implies__order) ).
thf(2269,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(745,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_2278_nat__mult__div__cancel__disj) ).
thf(4654,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)],[745]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4377_is__unit__div__mult__cancel__right) ).
thf(1264,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(332,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2844_One__nat__def) ).
thf(2681,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(2682,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= one_one_nat ),
inference(lifteq,[status(thm)],[2681]) ).
thf(419,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4063_unique__euclidean__semiring__numeral__class_Opos__mod__bound) ).
thf(3125,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(471,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_gr0I) ).
thf(3410,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(98,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3543_max_Obounded__iff) ).
thf(1577,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(79,axiom,
! [A: fun_nat_o,B: list_nat,C: nat] :
( ( ( B @ ( A @ find_nat ) )
= ( C @ some_nat ) )
<=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( C
= ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ( B @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1685_find__Some__iff) ).
thf(1455,plain,
! [A: fun_nat_o,B: list_nat,C: nat] :
( ( ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( C
= ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ( B @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ find_nat ) )
= ( C @ some_nat ) ) )
& ( ( ( B @ ( A @ find_nat ) )
= ( C @ some_nat ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( C
= ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ( B @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(848,axiom,
! [A: fun_list_o_o,B: list_o] :
( ! [C: list_o] :
( ! [D: list_o] :
( ( C @ size_size_list_o @ ( D @ size_size_list_o @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_o_o ) ) )
=> ( C @ ( A @ aa_list_o_o ) ) )
=> ( B @ ( A @ aa_list_o_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_length__induct) ).
thf(5182,plain,
! [A: fun_list_o_o,B: list_o] :
( ! [C: list_o] :
( ! [D: list_o] :
( ( C @ size_size_list_o @ ( D @ size_size_list_o @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_o_o ) ) )
=> ( C @ ( A @ aa_list_o_o ) ) )
=> ( B @ ( A @ aa_list_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(569,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C
= ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3472_div__if) ).
thf(3845,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C
= ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(948,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) )
<=> ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_all__set__conv__all__nth) ).
thf(5640,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o] :
( ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(410,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8816_gcd__non__0__nat) ).
thf(3089,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(290,axiom,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4729_of__bool__def) ).
thf(2466,plain,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_dual__order_Oantisym) ).
thf(2126,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4398_dvd__mult__cancel2) ).
thf(1132,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = one_one_nat )
=> ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(401,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1891_le__imp__less__Suc) ).
thf(3043,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2037_power__less__imp__less__base) ).
thf(1922,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(1006,axiom,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( B
= ( D @ ( suc @ aa_nat_nat ) ) )
=> ( D @ ( C @ aa_nat_o ) ) )
=> ( ! [D: nat] :
( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) )
=> ( D @ ( C @ aa_nat_o ) ) ) )
=> ( A @ ( C @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1784_strict__inc__induct) ).
thf(5925,plain,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( B
= ( D @ ( suc @ aa_nat_nat ) ) )
=> ( D @ ( C @ aa_nat_o ) ) )
=> ( ! [D: nat] :
( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) )
=> ( D @ ( C @ aa_nat_o ) ) ) )
=> ( A @ ( C @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(667,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_zero__reorient) ).
thf(4317,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)],[667]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3683_max_Oabsorb__iff1) ).
thf(1115,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(579,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1893_less__Suc__eq__le) ).
thf(3902,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(588,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_order_Ostrict__implies__not__eq) ).
thf(3951,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(652,axiom,
! [A: nat] :
? [B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Ex__list__of__length) ).
thf(4265,plain,
! [A: nat] :
? [B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(270,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( D @ ( C @ ( B @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= E )
=> ( E
= ( @+[F: nat] :
( ( ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F
= ( D @ ( B @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8035_fold__atLeastAtMost__nat_Oelims) ).
thf(2388,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( D @ ( C @ ( B @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= E )
=> ( E
= ( @+[F: nat] :
( ( ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F
= ( D @ ( B @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ upt ) )
= nil_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9168_upt__conv__Nil) ).
thf(1100,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ upt ) )
= nil_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(413,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9226_coprime__diff__one__left__nat) ).
thf(3099,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(881,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2750_zero__less__mult__pos2) ).
thf(5338,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(342,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2061_power__eq__imp__eq__base) ).
thf(2713,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(600,axiom,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1417_not__add__less1) ).
thf(3998,plain,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(483,axiom,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ enumerate_VEBT_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( A @ ( B @ nth_VEBT_VEBT ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1561_nth__enumerate__eq) ).
thf(3463,plain,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ enumerate_VEBT_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( A @ ( B @ nth_VEBT_VEBT ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(465,axiom,
! [A: nat] : ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6524_of__nat__0__le__iff) ).
thf(3385,plain,
! [A: nat] : ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(231,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1584_pinf_I8_J) ).
thf(2169,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(5,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ upt ) )
= nil_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9173_upt__0) ).
thf(1087,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ upt ) )
= nil_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(852,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6545_of__nat__mono) ).
thf(5199,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ upt ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9186_upt__add__eq__append) ).
thf(1147,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ upt ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_antisym) ).
thf(1247,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(679,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_neq0__conv) ).
thf(4358,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(895,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_not__less0) ).
thf(5397,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(943,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1285_add__gr__0) ).
thf(5622,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(546,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1403_add__strict__right__mono) ).
thf(3734,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(629,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3399_Suc__diff__le) ).
thf(4141,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(196,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_3134_div__add__self1) ).
thf(2024,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)],[196]) ).
thf(1049,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_17_bit__split__inv) ).
thf(6098,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)],[1049]) ).
thf(394,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4293_dvd__eq__mod__eq__0) ).
thf(2989,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( A != zero_zero_nat )
=> ! [C: nat] :
( B
!= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4332_unit__dvdE) ).
thf(1356,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( A != zero_zero_nat )
=> ! [C: nat] :
( B
!= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1357,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
? [C: nat] :
( B
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(miniscope,[status(thm)],[1356]) ).
thf(1358,plain,
! [B: nat,A: nat] :
( ( ( B
= ( A @ ( B @ sk11 ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ~ ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A != zero_zero_nat )
| ~ ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(cnf,[status(esa)],[1357]) ).
thf(1359,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ~ ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(cnfConj,[status(thm)],[1358]) ).
thf(1361,plain,
! [A: nat] :
( ~ ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != zero_zero_nat ) ),
inference(lifteq,[status(thm)],[1359]) ).
thf(1362,plain,
~ ( one_one_nat @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(simp,[status(thm)],[1361]) ).
thf(687,axiom,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) )
<=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4499_Bex__set__replicate) ).
thf(4390,plain,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) ) )
& ( ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) )
=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(832,axiom,
! [A: nat] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9223_coprime__Suc__0__right) ).
thf(5091,plain,
! [A: nat] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(770,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_bot__nat__0_Onot__eq__extremum) ).
thf(4793,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(822,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_3342_diff__add__inverse) ).
thf(5020,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)],[822]) ).
thf(1028,axiom,
treeList @ size_s6755466524823107622T_VEBT @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062) ).
thf(6025,plain,
treeList @ size_s6755466524823107622T_VEBT @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(764,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_4042_bits__mod__div__trivial) ).
thf(4756,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)],[764]) ).
thf(981,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3382_add__le__imp__le__diff) ).
thf(5792,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(192,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1574_minf_I8_J) ).
thf(2007,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(234,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_2185_mult_Oright__neutral) ).
thf(2178,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)],[234]) ).
thf(1001,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7907_fact__less__mono) ).
thf(5888,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(662,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_acd @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9334_ATP_Olambda__3) ).
thf(4297,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_acd @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(601,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_3302_diff__diff__eq) ).
thf(4001,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)],[601]) ).
thf(479,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6540_of__nat__less__imp__less) ).
thf(3453,plain,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_order__antisym__conv) ).
thf(1334,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1060,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aad @ 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_9483_ATP_Olambda__152) ).
thf(6135,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aad @ 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)],[1060]) ).
thf(495,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2011_nat__zero__less__power__iff) ).
thf(3525,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(1020,axiom,
xa != mi,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_xmi) ).
thf(5993,plain,
xa != mi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(5994,plain,
xa != mi,
inference(polarity_switch,[status(thm)],[5993]) ).
thf(5995,plain,
xa != mi,
inference(lifteq,[status(thm)],[5994]) ).
thf(6176,plain,
mi != ma,
inference(rewrite,[status(thm)],[5995,6089]) ).
thf(519,axiom,
! [A: list_VEBT_VEBT,B: list_o] :
( ( B @ ( A @ product_VEBT_VEBT_o ) @ size_s9168528473962070013VEBT_o )
= ( B @ size_size_list_o @ ( A @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4202_length__product) ).
thf(3621,plain,
! [A: list_VEBT_VEBT,B: list_o] :
( ( B @ ( A @ product_VEBT_VEBT_o ) @ size_s9168528473962070013VEBT_o )
= ( B @ size_size_list_o @ ( A @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(825,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3146_split__div) ).
thf(5032,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(21,axiom,
! [A: nat,B: list_nat,C: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( B @ list_update_nat ) ) )
= B )
<=> ( ( A @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_list__update__same__conv) ).
thf(1151,plain,
! [A: nat,B: list_nat,C: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( A @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= C )
=> ( ( C @ ( A @ ( B @ list_update_nat ) ) )
= B ) )
& ( ( ( C @ ( A @ ( B @ list_update_nat ) ) )
= B )
=> ( ( A @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(354,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3236_zero__less__diff) ).
thf(2777,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2338_power__increasing__iff) ).
thf(1183,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(993,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_1996_power__0__Suc) ).
thf(5834,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)],[993]) ).
thf(239,axiom,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ~ ( B @ ( C @ aa_nat_o ) )
=> ? [D: nat] :
( ! [E: nat] :
( ! [F: nat] :
( ( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( F @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( F @ ( C @ aa_nat_o ) ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ! [E: nat] :
( ( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( E @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( E @ ( C @ aa_nat_o ) ) )
& ( B @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_complete__interval) ).
thf(2237,plain,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ~ ( B @ ( C @ aa_nat_o ) )
=> ? [D: nat] :
( ! [E: nat] :
( ! [F: nat] :
( ( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( F @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( F @ ( C @ aa_nat_o ) ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ! [E: nat] :
( ( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( E @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( E @ ( C @ aa_nat_o ) ) )
& ( B @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(814,axiom,
! [A: nat] :
? [B: list_o] :
( ( B @ size_size_list_o )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Ex__list__of__length) ).
thf(4988,plain,
! [A: nat] :
? [B: list_o] :
( ( B @ size_size_list_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(316,axiom,
! [A: fun_nat_o] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( A @ ord_Least_nat )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9257_Least__eq__0) ).
thf(2616,plain,
! [A: fun_nat_o] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( A @ ord_Least_nat )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(179,axiom,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2791_not__one__le__zero) ).
thf(1946,plain,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(952,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_2138_mult__cancel__left) ).
thf(5663,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)],[952]) ).
thf(358,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1787_le__SucE) ).
thf(2794,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(799,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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4192_dvd__times__right__cancel__iff) ).
thf(4903,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(696,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3214_diff__diff__cancel) ).
thf(4443,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(729,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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_1436_add__nonpos__eq__0__iff) ).
thf(4578,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( 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)],[729]) ).
thf(937,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_8867_Suc__funpow) ).
thf(5597,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)],[937]) ).
thf(605,axiom,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ~ ( C @ ( A @ aa_nat_o ) )
=> ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_infinite__descent) ).
thf(4018,plain,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ~ ( C @ ( A @ aa_nat_o ) )
=> ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(468,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3401_less__diff__iff) ).
thf(3393,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(820,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_order__less__imp__not__less) ).
thf(5013,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(879,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_3210_Suc__diff__diff) ).
thf(5333,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)],[879]) ).
thf(427,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_2128_mult__zero__right) ).
thf(3163,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)],[427]) ).
thf(505,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ order_mono_nat_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9042_mono__times__nat) ).
thf(3569,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ order_mono_nat_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1017,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_9165_drop__upt) ).
thf(5985,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)],[1017]) ).
thf(585,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1890_less__Suc__eq__0__disj) ).
thf(3923,plain,
! [A: nat,B: nat] :
( ( ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) )
| ( A = zero_zero_nat ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(411,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1395_add__strict__mono) ).
thf(3093,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(555,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1757_nat_Odistinct_I1_J) ).
thf(3771,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(572,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3398_diff__less) ).
thf(3851,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(467,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3500_le__div__geq) ).
thf(3389,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(24,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_bot__nat__0_Oextremum) ).
thf(1169,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(497,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( comm_s4663373288045622133er_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_8335_pochhammer__product) ).
thf(3537,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( comm_s4663373288045622133er_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)],[497]) ).
thf(249,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) )
<=> ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4719_split__of__bool__asm) ).
thf(2281,plain,
! [A: fun_nat_o,B: $o] :
( ( ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) )
=> ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) ) )
& ( ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) )
=> ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(858,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3545_div__geq) ).
thf(5220,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(292,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2538_zero__neq__one) ).
thf(2481,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(2482,plain,
zero_zero_nat != one_one_nat,
inference(polarity_switch,[status(thm)],[2481]) ).
thf(2483,plain,
zero_zero_nat != one_one_nat,
inference(lifteq,[status(thm)],[2482]) ).
thf(777,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1420_trans__less__add1) ).
thf(4825,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(323,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4476_take__bit__of__0) ).
thf(2639,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( A != zero_zero_nat )
=> ! [C: nat] :
( ( C != zero_zero_nat )
=> ( ( one_one_nat @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( ( C @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( ( C @ ( A @ ( times_times_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 ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4383_is__unitE) ).
thf(1405,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( A != zero_zero_nat )
=> ! [C: nat] :
( ( C != zero_zero_nat )
=> ( ( one_one_nat @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( ( C @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( ( C @ ( A @ ( times_times_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 ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(742,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3397_Suc__diff__Suc) ).
thf(4643,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(377,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2013_power__eq__0__iff) ).
thf(2884,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(613,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_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_3370_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(4055,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_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)],[613]) ).
thf(885,axiom,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4652_zero__less__of__bool__iff) ).
thf(5353,plain,
! [A: $o] :
( ( A
=> ( A @ zero_n2687167440665602831ol_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ zero_n2687167440665602831ol_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(1053,axiom,
( ( treeList @ size_s6755466524823107622T_VEBT )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ size_s6755466524823107622T_VEBT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_091high_Ax_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_Ax_An_J_A_Ilow_Ax_An_J_093_J_092_060close_062) ).
thf(6110,plain,
( ( treeList @ size_s6755466524823107622T_VEBT )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ size_s6755466524823107622T_VEBT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(892,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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_3018_div__mult__self__is__m) ).
thf(5384,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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)],[892]) ).
thf(492,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_4069_mod__Suc) ).
thf(3505,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)],[492]) ).
thf(162,axiom,
! [A: $o] : ( A @ zero_n2687167440665602831ol_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4710_zero__less__eq__of__bool) ).
thf(1886,plain,
! [A: $o] : ( A @ zero_n2687167440665602831ol_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(622,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_4036_bits__mod__by__1) ).
thf(4087,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)],[622]) ).
thf(281,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3091_max__absorb2) ).
thf(2424,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(531,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_2221_nonzero__mult__div__cancel__left) ).
thf(3676,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)],[531]) ).
thf(224,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_leI) ).
thf(2137,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(589,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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_2426_nat__mult__div__cancel1) ).
thf(3955,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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)],[589]) ).
thf(444,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1407_add__less__imp__less__left) ).
thf(3243,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(512,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( aTP_Lamm_ly @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9088_diff__Suc) ).
thf(3588,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( aTP_Lamm_ly @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_le__trans) ).
thf(1697,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(502,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_3081_div__mult__self2) ).
thf(3559,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)],[502]) ).
thf(987,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3400_diff__less__mono) ).
thf(5819,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(515,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1343_add__mono__thms__linordered__semiring_I1_J) ).
thf(3606,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(437,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ some_nat @ ( A @ size_option_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4455_option_Osize__gen_I2_J) ).
thf(3211,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ some_nat @ ( A @ size_option_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(271,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2956_power__increasing) ).
thf(2392,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(1051,axiom,
? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_notemp) ).
thf(6103,plain,
? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(730,axiom,
! [A: nat,B: nat] :
( ( ( A @ some_nat )
= ( B @ some_nat ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_option_Oinject) ).
thf(4588,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ some_nat )
= ( B @ some_nat ) ) )
& ( ( ( A @ some_nat )
= ( B @ some_nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(620,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3715_max_Ostrict__coboundedI1) ).
thf(4082,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(704,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3335_le__diff__iff) ).
thf(4483,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(958,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2912_mult__less__le__imp__less) ).
thf(5695,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(757,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4366_mod__greater__zero__iff__not__dvd) ).
thf(4700,plain,
! [A: nat,B: nat] :
( ( ~ ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(1012,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6419_of__nat__eq__0__iff) ).
thf(5961,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(732,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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4189_dvd__times__left__cancel__iff) ).
thf(4604,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(638,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3526_max_Oabsorb4) ).
thf(4199,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(448,axiom,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_nat__less__induct) ).
thf(3301,plain,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(596,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_2233_nonzero__mult__div__cancel__right) ).
thf(3984,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)],[596]) ).
thf(907,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_4027_mod__mult__self2__is__0) ).
thf(5443,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)],[907]) ).
thf(905,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1452_add__increasing2) ).
thf(5438,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1036,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_1318_group__cancel_Oadd1) ).
thf(6058,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)],[1036]) ).
thf(722,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_2847_Suc__eq__plus1) ).
thf(4557,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)],[722]) ).
thf(1047,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_tv @ 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_9547_ATP_Olambda__216) ).
thf(6092,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_tv @ 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)],[1047]) ).
thf(641,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1788_le__SucI) ).
thf(4216,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(513,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( 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_4098_unique__euclidean__semiring__numeral__class_Omod__mult2__eq) ).
thf(3591,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( 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)],[513]) ).
thf(1026,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_valid__eq1) ).
thf(6020,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(689,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2710_mult__mono_H) ).
thf(4407,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(291,axiom,
! [A: nat] :
( ( ( one_one_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4506_take__bit__of__1__eq__0__iff) ).
thf(2473,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( one_one_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( one_one_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(795,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_3402_diff__add__0) ).
thf(4888,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)],[795]) ).
thf(77,axiom,
! [A: list_nat,B: list_nat] :
( ( A = B )
<=> ( ! [C: nat] :
( ( A @ size_size_list_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
& ( ( A @ size_size_list_nat )
= ( B @ size_size_list_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_list__eq__iff__nth__eq) ).
thf(1438,plain,
! [A: list_nat,B: list_nat] :
( ( ( ! [C: nat] :
( ( A @ size_size_list_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
& ( ( A @ size_size_list_nat )
= ( B @ size_size_list_nat ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ! [C: nat] :
( ( A @ size_size_list_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
& ( ( A @ size_size_list_nat )
= ( B @ size_size_list_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(995,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_linorder__neq__iff) ).
thf(5839,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(542,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_vn @ aa_nat_fun_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9528_ATP_Olambda__197) ).
thf(3720,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_vn @ aa_nat_fun_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(899,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_2527_mult__right__cancel) ).
thf(5411,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)],[899]) ).
thf(618,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_dual__order_Ostrict__trans) ).
thf(4076,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(346,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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_7943_fact__num__eq__if) ).
thf(2737,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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)],[346]) ).
thf(998,axiom,
! [A: vEBT_VEBT,B: fun_VEBT_VEBT_o,C: list_VEBT_VEBT] :
( ( ( A @ some_VEBT_VEBT )
= ( C @ ( B @ find_VEBT_VEBT ) ) )
<=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
& ( A
= ( D @ ( C @ nth_VEBT_VEBT ) ) )
& ( D @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) )
& ( C @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1677_find__Some__iff2) ).
thf(5862,plain,
! [A: vEBT_VEBT,B: fun_VEBT_VEBT_o,C: list_VEBT_VEBT] :
( ( ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
& ( A
= ( D @ ( C @ nth_VEBT_VEBT ) ) )
& ( D @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) )
& ( C @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ some_VEBT_VEBT )
= ( C @ ( B @ find_VEBT_VEBT ) ) ) )
& ( ( ( A @ some_VEBT_VEBT )
= ( C @ ( B @ find_VEBT_VEBT ) ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
& ( A
= ( D @ ( C @ nth_VEBT_VEBT ) ) )
& ( D @ ( C @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) )
& ( C @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(238,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4399_dvd__minus__add) ).
thf(2232,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(252,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8001_dvd__fact) ).
thf(2307,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(928,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_1223_zero__eq__add__iff__both__eq__0) ).
thf(5540,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)],[928]) ).
thf(212,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8812_gcd__diff2__nat) ).
thf(2083,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(607,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6532_of__nat__neq__0) ).
thf(4031,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(126,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_2418_comm__monoid__mult__class_Omult__1) ).
thf(1736,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)],[126]) ).
thf(318,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3695_max_OcoboundedI2) ).
thf(2621,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(614,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3229_le__add__diff__inverse) ).
thf(4059,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(134,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_2180_mult__1) ).
thf(1768,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)],[134]) ).
thf(205,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_le__refl) ).
thf(2061,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(500,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_3212_diff__0__eq__0) ).
thf(3550,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)],[500]) ).
thf(189,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_3033_max__nat_Oright__neutral) ).
thf(2000,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)],[189]) ).
thf(339,axiom,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6454_of__nat__1) ).
thf(2705,plain,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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 ) ) )
<=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4367_mod__eq__dvd__iff__nat) ).
thf(1387,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) ) ) )
& ( ( ( 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 ) ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1031,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_1288_add__right__imp__eq) ).
thf(6032,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)],[1031]) ).
thf(982,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6475_of__nat__less__of__nat__power__cancel__iff) ).
thf(5794,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(96,axiom,
! [A: nat] :
~ ( ( zero_zero_nat != A )
& ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4247_gcd__nat_Oextremum__strict) ).
thf(1570,plain,
! [A: nat] :
~ ( ( zero_zero_nat != A )
& ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(650,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9225_coprime__diff__one__right__nat) ).
thf(4252,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(714,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2731_mult__pos__neg) ).
thf(4521,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(913,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6439_of__nat__mult) ).
thf(5470,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(393,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4076_mod__if) ).
thf(2986,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(436,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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_6968_binomial__addition__formula) ).
thf(3207,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[436]) ).
thf(41,axiom,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7860_fact__Suc__0) ).
thf(1238,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(284,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_le0) ).
thf(2441,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(940,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_order__less__not__sym) ).
thf(5611,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(966,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2672_mult__nonneg__nonpos) ).
thf(5734,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(944,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1428_le__Suc__ex) ).
thf(5630,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(302,axiom,
! [A: $o,B: $o] :
( ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B
& ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4648_of__bool__less__iff) ).
thf(2560,plain,
! [A: $o,B: $o] :
( ( ( B
& ~ A )
=> ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
& ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(240,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_226_min__Null__member) ).
thf(2249,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)],[240]) ).
thf(1022,axiom,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( zero_zero_nat @ ( A @ ( aTP_Lamm_mv @ semiri8422978514062236437ux_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6603_of__nat__code) ).
thf(6000,plain,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( zero_zero_nat @ ( A @ ( aTP_Lamm_mv @ semiri8422978514062236437ux_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(311,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_order__le__less__trans) ).
thf(2596,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(818,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4317_dvd__pos__nat) ).
thf(5002,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( 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_6935_choose__mult) ).
thf(1123,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( 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)],[15]) ).
thf(921,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1421_trans__less__add2) ).
thf(5512,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(707,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1399_add__strict__left__mono) ).
thf(4499,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(314,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_dual__order_Ostrict__iff__not) ).
thf(2606,plain,
! [A: nat,B: nat] :
( ( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(426,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= B )
=> ( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4556_replicate__eqI) ).
thf(3154,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= B )
=> ( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(698,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1493_pos__add__strict) ).
thf(4449,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(831,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1240_nat__add__left__cancel__le) ).
thf(5085,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(971,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_3346_diff__mult__distrib) ).
thf(5754,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)],[971]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_dual__order_Oeq__iff) ).
thf(2150,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(633,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_2507_mult__not__zero) ).
thf(4160,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)],[633]) ).
thf(528,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_order__less__trans) ).
thf(3664,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(449,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1874_lift__Suc__mono__less__iff) ).
thf(3307,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(1007,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_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_3366_diff__add) ).
thf(5937,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_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)],[1007]) ).
thf(561,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2773_mult__strict__right__mono) ).
thf(3810,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(490,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2548_mult__le__mono2) ).
thf(3499,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(541,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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4362_dvd__mult__cancel) ).
thf(3718,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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(853,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4251_dvd__diff__nat) ).
thf(5201,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1988_power__mono__iff) ).
thf(2313,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(168,axiom,
! [A: $o] : ( one_one_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4714_of__bool__less__eq__one) ).
thf(1910,plain,
! [A: $o] : ( one_one_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(922,axiom,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2544_le__cube) ).
thf(5515,plain,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(976,axiom,
! [A: nat] :
( ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_not__gr0) ).
thf(5769,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(428,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_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_3373_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(3166,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_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)],[428]) ).
thf(433,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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_1440_add__nonneg__eq__0__iff) ).
thf(3191,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( 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)],[433]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2837_one__le__power) ).
thf(1938,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(999,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_2188_mult__0__right) ).
thf(5879,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)],[999]) ).
thf(373,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2735_mult__pos__pos) ).
thf(2872,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(685,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( aTP_Lamm_aax @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8984_mult__nat__right__at__top) ).
thf(4385,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( aTP_Lamm_aax @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_nless__le) ).
thf(1951,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(911,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2787_nat__mult__le__cancel1) ).
thf(5460,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(1018,axiom,
( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_hprolist) ).
thf(5988,plain,
( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(107,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_less__eq__nat_Osimps_I1_J) ).
thf(1624,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(499,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1652_minf_I4_J) ).
thf(3546,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_less__imp__le__nat) ).
thf(1159,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(496,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_dual__order_Oasym) ).
thf(3535,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(151,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_2163_div__by__0) ).
thf(1836,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)],[151]) ).
thf(838,axiom,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( A @ aa_nat_o ) )
<=> ( F @ ( B @ aa_nat_o ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( C @ aa_nat_o ) )
<=> ( F @ ( D @ aa_nat_o ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) )
<=> ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1642_minf_I2_J) ).
thf(5113,plain,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( B @ aa_nat_o ) )
=> ( F @ ( A @ aa_nat_o ) ) )
& ( ( F @ ( A @ aa_nat_o ) )
=> ( F @ ( B @ aa_nat_o ) ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( D @ aa_nat_o ) )
=> ( F @ ( C @ aa_nat_o ) ) )
& ( ( F @ ( C @ aa_nat_o ) )
=> ( F @ ( D @ aa_nat_o ) ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) )
=> ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) ) )
& ( ( ( F @ ( C @ aa_nat_o ) )
| ( F @ ( A @ aa_nat_o ) ) )
=> ( ( F @ ( D @ aa_nat_o ) )
| ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(235,axiom,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
<=> ( ( B
<=> D )
& ( A
<=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3167_VEBT_Oinject_I2_J) ).
thf(2181,plain,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) )
=> ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) ) )
& ( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
=> ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(692,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_1331_verit__sum__simplify) ).
thf(4417,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)],[692]) ).
thf(762,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_o @ aa_nat_o ) )
<=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_nth__equalityI) ).
thf(4740,plain,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1070,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_1314_group__cancel_Oadd2) ).
thf(6168,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)],[1070]) ).
thf(398,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4079_unique__euclidean__semiring__numeral__class_Opos__mod__sign) ).
thf(3028,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(544,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_gr__implies__not__zero) ).
thf(3727,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_order_Ostrict__iff__order) ).
thf(1281,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(701,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1430_add__le__mono1) ).
thf(4461,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(529,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3453_nat__le__add__iff1) ).
thf(3667,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(219,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4248_gcd__nat_Oextremum__unique) ).
thf(2112,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3125_div__le__mono) ).
thf(1291,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(514,axiom,
! [A: nat,B: fun_nat_o] :
( ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
<=> ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( zero_zero_nat @ ( B @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1888_All__less__Suc2) ).
thf(3595,plain,
! [A: nat,B: fun_nat_o] :
( ( ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( zero_zero_nat @ ( B @ aa_nat_o ) ) )
=> ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
=> ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( zero_zero_nat @ ( B @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(476,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( 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_8817_bezout__nat) ).
thf(3445,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( 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)],[476]) ).
thf(1046,axiom,
( ( maxi @ some_nat )
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ vEBT_vebt_maxt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_maxidef) ).
thf(6090,plain,
( ( maxi @ some_nat )
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ vEBT_vebt_maxt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(11,axiom,
! [A: nat,B: nat,C: list_nat,D: nat] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_nth__list__update__neq) ).
thf(1106,plain,
! [A: nat,B: nat,C: list_nat,D: nat] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(545,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ hd_nat )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9164_hd__upt) ).
thf(3731,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ hd_nat )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(518,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6423_of__nat__less__iff) ).
thf(3615,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(869,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_less__irrefl__nat) ).
thf(5270,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(901,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2664_mult__nonneg__nonpos2) ).
thf(5423,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(946,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_linorder__neqE) ).
thf(5635,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(611,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3378_add__le__add__imp__diff__le) ).
thf(4048,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(625,axiom,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( A @ aa_nat_o ) )
<=> ( F @ ( B @ aa_nat_o ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( C @ aa_nat_o ) )
<=> ( F @ ( D @ aa_nat_o ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) )
<=> ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1637_minf_I1_J) ).
thf(4095,plain,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( B @ aa_nat_o ) )
=> ( F @ ( A @ aa_nat_o ) ) )
& ( ( F @ ( A @ aa_nat_o ) )
=> ( F @ ( B @ aa_nat_o ) ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( D @ aa_nat_o ) )
=> ( F @ ( C @ aa_nat_o ) ) )
& ( ( F @ ( C @ aa_nat_o ) )
=> ( F @ ( D @ aa_nat_o ) ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( E @ ( F @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) )
=> ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) ) )
& ( ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) )
=> ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(780,axiom,
! [A: nat,B: nat] :
? [C: nat] :
! [D: nat] :
( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4272_pinf_I10_J) ).
thf(4840,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(603,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1662_minf_I7_J) ).
thf(4012,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(442,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3248_Suc__diff__1) ).
thf(3237,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(861,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_3343_diff__cancel2) ).
thf(5233,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)],[861]) ).
thf(776,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3238_diff__is__0__eq) ).
thf(4817,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(592,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1472_add__le__less__mono) ).
thf(3968,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1040,axiom,
~ ! [A: nat] :
( ( A @ some_nat )
!= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ vEBT_vebt_maxt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxi_O_ASome_Amaxi_A_061_Avebt__maxt_A_ItreeList_091high_Ax_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_Ax_An_J_A_Ilow_Ax_An_J_093_A_B_Ahigh_Ax_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(6075,plain,
~ ! [A: nat] :
( ( A @ some_nat )
!= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ vEBT_vebt_maxt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(484,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8807_gcd__pos__nat) ).
thf(3467,plain,
! [A: nat,B: nat] :
( ( ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) )
=> ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(557,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6914_binomial__eq__0__iff) ).
thf(3784,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1050,axiom,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082__C4_Ohyps_C_I4_J) ).
thf(6101,plain,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(472,axiom,
! [A: nat,B: fun_na6887940067898170868VEBT_o] :
( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
<=> ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Skolem__list__nth) ).
thf(3413,plain,
! [A: nat,B: fun_na6887940067898170868VEBT_o] :
( ( ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) )
=> ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
=> ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(367,axiom,
! [A: nat,B: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3396_diff__less__Suc) ).
thf(2841,plain,
! [A: nat,B: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(61,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_3106_max__add__distrib__left) ).
thf(1328,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)],[61]) ).
thf(341,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_order__eq__refl) ).
thf(2709,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(184,axiom,
! [A: vEBT_VEBT,B: nat,C: nat,D: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( A @ vEBT_vebt_maxt )
= ( C @ some_nat ) )
=> ( ( D @ ( A @ vEBT_vebt_member @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_maxt__corr__help) ).
thf(1970,plain,
! [A: vEBT_VEBT,B: nat,C: nat,D: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( A @ vEBT_vebt_maxt )
= ( C @ some_nat ) )
=> ( ( D @ ( A @ vEBT_vebt_member @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(740,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_3306_add__implies__diff) ).
thf(4636,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)],[740]) ).
thf(335,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4244_dvd__0__left) ).
thf(2692,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2488_mult__le__one) ).
thf(1587,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(644,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2908_mult__le__less__imp__less) ).
thf(4233,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(538,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( 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_2048_zero__power) ).
thf(3704,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( 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)],[538]) ).
thf(160,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_209_both__member__options__equiv__member) ).
thf(1878,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)],[160]) ).
thf(344,axiom,
! [A: nat] :
( ( one_one_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6449_of__nat__1__eq__iff) ).
thf(2726,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ) )
& ( ( one_one_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(804,axiom,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) ) ) ) )
=> ( B @ ( C @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1897_dec__induct) ).
thf(4930,plain,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) ) ) ) )
=> ( B @ ( C @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3137_div__greater__zero__iff) ).
thf(1719,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(371,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3447_less__diff__conv2) ).
thf(2858,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(713,axiom,
! [A: nat] :
( ( A @ some_nat @ size_size_option_nat )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1955_option_Osize_I4_J) ).
thf(4518,plain,
! [A: nat] :
( ( A @ some_nat @ size_size_option_nat )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(786,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1484_add__neg__neg) ).
thf(4860,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(470,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4061_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend) ).
thf(3407,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(836,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6983_gbinomial__0_I2_J) ).
thf(5107,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(127,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_neq__if__length__neq) ).
thf(1739,plain,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(540,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3246_diff__Suc__diff__eq2) ).
thf(3714,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(1074,plain,
! [B: nat,A: list_nat] :
( ( B @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ ( A @ list_update_nat ) ) )
= A ),
inference(cnf,[status(esa)],[1073]) ).
thf(1075,plain,
! [B: nat,A: list_nat] :
( ( B @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ ( A @ list_update_nat ) ) )
= A ),
inference(lifteq,[status(thm)],[1074]) ).
thf(718,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2807_zero__less__one) ).
thf(4545,plain,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(99,axiom,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Ex__list__of__length) ).
thf(1584,plain,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(261,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7899_fact__dvd) ).
thf(2349,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2969_power__strict__decreasing) ).
thf(1567,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(752,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1503_add__nonneg__pos) ).
thf(4676,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(556,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_zero__less__iff__neq__zero) ).
thf(3775,plain,
! [A: nat] :
( ( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(424,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1785_not__less__less__Suc__eq) ).
thf(3141,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A = B )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(475,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1765_Suc__neq__Zero) ).
thf(3441,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_order__le__neq__trans) ).
thf(2455,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4360_dvd__imp__le) ).
thf(1700,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1069,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_1322_add__mono__thms__linordered__semiring_I4_J) ).
thf(6164,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)],[1069]) ).
thf(315,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2973_power__decreasing) ).
thf(2613,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2053_nat__one__le__power) ).
thf(1810,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(139,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6444_of__nat__eq__1__iff) ).
thf(1791,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ) )
& ( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(543,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = B ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1339_add__mono__thms__linordered__semiring_I2_J) ).
thf(3723,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = B ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(525,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_2133_mult__eq__0__iff) ).
thf(3643,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)],[525]) ).
thf(788,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_mv @ 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_9338_ATP_Olambda__7) ).
thf(4867,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_mv @ 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)],[788]) ).
thf(328,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6928_binomial__symmetric) ).
thf(2666,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6905_zero__less__binomial__iff) ).
thf(1889,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(775,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_ly @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9229_sort__upt) ).
thf(4814,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_ly @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(392,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_1215_add__cancel__right__left) ).
thf(2978,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)],[392]) ).
thf(325,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_3110_max__add__distrib__right) ).
thf(2649,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)],[325]) ).
thf(772,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = C )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_ord__less__eq__trans) ).
thf(4804,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = C )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(526,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1433_nat__le__iff__add) ).
thf(3654,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(404,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1460_add__increasing) ).
thf(3059,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1058,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ ( A @ produc4743750530478302277T_VEBT ) @ size_s7466405169056248089T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT @ ( A @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4201_length__product) ).
thf(6129,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ ( A @ produc4743750530478302277T_VEBT ) @ size_s7466405169056248089T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT @ ( A @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(307,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8810_gcd__le2__nat) ).
thf(2581,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(563,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2034_nat__power__less__imp__less) ).
thf(3819,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(955,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4176_dvd__1__left) ).
thf(5683,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(363,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_1205_add__cancel__left__left) ).
thf(2813,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)],[363]) ).
thf(352,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_1220_add__cancel__right__right) ).
thf(2766,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)],[352]) ).
thf(824,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_of @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9789_ATP_Olambda__458) ).
thf(5026,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_of @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_of @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(350,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_3490_power__eq__if) ).
thf(2756,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)],[350]) ).
thf(147,axiom,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4167_dvd__0__right) ).
thf(1825,plain,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(391,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1790_le__Suc__eq) ).
thf(2968,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(826,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2788_Suc__mult__less__cancel1) ).
thf(5063,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(870,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_4014_mod__self) ).
thf(5273,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)],[870]) ).
thf(996,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1632_pinf_I7_J) ).
thf(5850,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(517,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( plus_plus_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_3239_Nat_Oadd__diff__assoc) ).
thf(3611,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( plus_plus_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)],[517]) ).
thf(295,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2952_power__strict__increasing) ).
thf(2519,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(915,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( B @ ( minus_minus_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_3408_Nat_Odiff__add__assoc2) ).
thf(5481,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( B @ ( minus_minus_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)],[915]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_dual__order_Ostrict__implies__order) ).
thf(1297,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(498,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
& ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1495_less__imp__add__positive) ).
thf(3541,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
& ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(890,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2815_Suc__mult__le__cancel1) ).
thf(5374,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(251,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8283_pochhammer__0) ).
thf(2304,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
<=> ( B
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4343_dvd__div__eq__mult) ).
thf(1530,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) )
& ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( B
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(91,axiom,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3161_Leaf__0__not) ).
thf(1539,plain,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(710,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1780_less__antisym) ).
thf(4508,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(616,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_1797_add__Suc) ).
thf(4068,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)],[616]) ).
thf(891,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4437_list__decode_Ocases) ).
thf(5380,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(114,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_2942_power__0__left) ).
thf(1668,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)],[114]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( 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 = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2269_power__inject__exp) ).
thf(1974,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = C )
=> ( ( B @ ( 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 ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(1014,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1444_add__nonpos__nonpos) ).
thf(5973,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(919,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_2549_add__mult__distrib2) ).
thf(5498,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)],[919]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).
thf(1192,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(175,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3651_max_OorderE) ).
thf(1932,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(439,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1257_add__le__same__cancel2) ).
thf(3222,plain,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(191,axiom,
suc @ order_mono_nat_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9041_mono__Suc) ).
thf(2006,plain,
suc @ order_mono_nat_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4489_take__bit__0) ).
thf(1799,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(975,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_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_3225_le__add__diff__inverse2) ).
thf(5766,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_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)],[975]) ).
thf(989,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1786_Suc__leD) ).
thf(5823,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(876,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_1901_add__is__1) ).
thf(5305,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)],[876]) ).
thf(552,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1265_add__less__same__cancel1) ).
thf(3760,plain,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(857,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6516_mult__of__nat__commute) ).
thf(5217,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(631,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1777_not__less__eq) ).
thf(4152,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(939,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_1706_nat_Oinject) ).
thf(5603,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)],[939]) ).
thf(409,axiom,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1793_full__nat__induct) ).
thf(3083,plain,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( C @ ( D @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(434,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3237_diff__is__0__eq_H) ).
thf(3201,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(643,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1776_less__Suc__eq) ).
thf(4223,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(266,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = C )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_ord__le__eq__trans) ).
thf(2370,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = C )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(89,axiom,
! [A: $o] :
( ( one_one_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4656_of__bool__less__one__iff) ).
thf(1525,plain,
! [A: $o] :
( ( ~ A
=> ( one_one_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(865,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_not__less__iff__gr__or__eq) ).
thf(5245,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(717,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_1237_add__is__0) ).
thf(4535,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)],[717]) ).
thf(520,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_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_4077_le__mod__geq) ).
thf(3624,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( minus_minus_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)],[520]) ).
thf(811,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1432_trans__le__add2) ).
thf(4966,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(933,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1770_Suc__lessD) ).
thf(5571,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(967,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_6912_binomial__1) ).
thf(5737,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)],[967]) ).
thf(900,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3496_power__minus__mult) ).
thf(5419,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(602,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4296_mod__eq__0__iff__dvd) ).
thf(4004,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_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 ) )
= zero_zero_nat )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(720,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_size__neq__size__imp__neq) ).
thf(4550,plain,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B != A )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_nle__le) ).
thf(1857,plain,
! [A: nat,B: nat] :
( ( ( ( B != A )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B != A )
& ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(931,axiom,
! [A: nat] :
( ( zero_zero_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6414_of__nat__0__eq__iff) ).
thf(5557,plain,
! [A: nat] :
( ( ( zero_zero_nat = A )
=> ( zero_zero_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(338,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_2394_nat__mult__1) ).
thf(2702,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)],[338]) ).
thf(503,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2546_mult__le__mono) ).
thf(3563,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(636,axiom,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2811_not__one__less__zero) ).
thf(4195,plain,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(493,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2780_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(3508,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_antisym__conv1) ).
thf(1895,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1004,axiom,
! [A: nat,B: fun_nat_o] :
( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
<=> ( ? [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( zero_zero_nat @ ( B @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1886_Ex__less__Suc2) ).
thf(5909,plain,
! [A: nat,B: fun_nat_o] :
( ( ( ? [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( zero_zero_nat @ ( B @ aa_nat_o ) ) )
=> ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ? [C: nat] :
( ( C @ ( B @ aa_nat_o ) )
& ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ? [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( zero_zero_nat @ ( B @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(568,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_neq__if__length__neq) ).
thf(3841,plain,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(816,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2727_mult__neg__pos) ).
thf(4995,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(125,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_2018_power__not__zero) ).
thf(1732,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)],[125]) ).
thf(727,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2714_mult__mono) ).
thf(4572,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3691_max_OcoboundedI1) ).
thf(1278,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(539,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3531_max__less__iff__conj) ).
thf(3707,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(683,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1365_add__le__imp__le__right) ).
thf(4380,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(458,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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_6966_times__binomial__minus1__eq) ).
thf(3358,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[458]) ).
thf(308,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__antisym) ).
thf(2585,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(1013,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_3084_div__mult__self1) ).
thf(5969,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)],[1013]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8026_binomial__fact__lemma) ).
thf(1483,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(746,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1427_add__leD2) ).
thf(4657,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(313,axiom,
! [A: nat,B: list_nat,C: nat,D: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( A @ ( B @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( @+[E: nat] :
( ( ( A != D )
=> ( E
= ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = D )
=> ( E = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nth__list__update) ).
thf(2602,plain,
! [A: nat,B: list_nat,C: nat,D: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( A @ ( B @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( @+[E: nat] :
( ( ( A != D )
=> ( E
= ( D @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = D )
=> ( E = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(558,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1273_less__add__same__cancel1) ).
thf(3792,plain,
! [A: nat,B: nat] :
( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(533,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8806_gcd__Suc__0) ).
thf(3686,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1035,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_acq @ aa_nat_o ) )
<=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9509_ATP_Olambda__178) ).
thf(6052,plain,
! [A: fun_nat_o,B: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_acq @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_acq @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(378,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_set__update__memI) ).
thf(2894,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(896,axiom,
( ( ma @ ( xa @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( xa @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44__092_060open_062mi_A_092_060le_062_Ax_A_092_060and_062_Ax_A_092_060le_062_Ama_092_060close_062) ).
thf(5400,plain,
( ( ma @ ( xa @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( xa @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8870_bit__push__bit__iff__nat) ).
thf(1631,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(389,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1235_add__less__cancel__right) ).
thf(2936,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(112,axiom,
! [A: nat,B: fun_nat_o,C: list_nat] :
( ( ( A @ some_nat )
= ( C @ ( B @ find_nat ) ) )
<=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( A
= ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( C @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1679_find__Some__iff2) ).
thf(1648,plain,
! [A: nat,B: fun_nat_o,C: list_nat] :
( ( ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( A
= ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( C @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ some_nat )
= ( C @ ( B @ find_nat ) ) ) )
& ( ( ( A @ some_nat )
= ( C @ ( B @ find_nat ) ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) )
& ( A
= ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) )
& ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) )
& ( C @ size_size_list_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(803,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B != A )
& ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3710_max_Ostrict__order__iff) ).
thf(4919,plain,
! [A: nat,B: nat] :
( ( ( ( B != A )
& ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B != A )
& ( B
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(1021,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_set__vebt__set__vebt_H__valid) ).
thf(5996,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(1029,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_acc @ 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_9485_ATP_Olambda__154) ).
thf(6026,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_acc @ 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)],[1029]) ).
thf(790,axiom,
! [A: nat,B: nat,C: $o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_order__less__imp__triv) ).
thf(4872,plain,
! [A: nat,B: nat,C: $o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(382,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nth__list__update__eq) ).
thf(2904,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(677,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1425_le__add2) ).
thf(4354,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(10,axiom,
! [A: list_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ list_update_nat ) ) @ size_size_list_nat )
= ( A @ size_size_list_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_length__list__update) ).
thf(1103,plain,
! [A: list_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ list_update_nat ) ) @ size_size_list_nat )
= ( A @ size_size_list_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,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_2147_bits__div__0) ).
thf(1548,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)],[92]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6934_zero__less__binomial) ).
thf(1927,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(197,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_279_subset__code_I1_J) ).
thf(2028,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)],[197]) ).
thf(345,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2977_power__le__imp__le__exp) ).
thf(2734,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1000,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2552_nat__mult__less__cancel1) ).
thf(5882,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(416,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_2826_mult__Suc) ).
thf(3111,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)],[416]) ).
thf(455,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9224_coprime__Suc__0__left) ).
thf(3343,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8304_pochhammer__nonneg) ).
thf(2260,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(807,axiom,
! [A: fun_nat_o,B: nat,C: nat,D: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( A @ aa_nat_o ) )
=> ( C @ ( E @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( D @ ( A @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4070_mod__induct) ).
thf(4943,plain,
! [A: fun_nat_o,B: nat,C: nat,D: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( A @ aa_nat_o ) )
=> ( C @ ( E @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( D @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(653,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2763_mult__strict__left__mono) ).
thf(4268,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(452,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3445_nat__diff__split) ).
thf(3319,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(523,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1622_pinf_I4_J) ).
thf(3636,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(161,axiom,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2846_plus__1__eq__Suc) ).
thf(1884,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8811_gcd__le1__nat) ).
thf(1784,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(443,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3332_diff__less__mono2) ).
thf(3240,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(356,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_3038_div__mult__mult1__if) ).
thf(2789,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)],[356]) ).
thf(195,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4340_div__dvd__iff__mult) ).
thf(2016,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(771,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1889_gr0__implies__Suc) ).
thf(4801,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(992,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2927_n__less__m__mult__n) ).
thf(5831,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(578,axiom,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2545_le__square) ).
thf(3900,plain,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(834,axiom,
! [A: nat,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_list__ball__nth) ).
thf(5099,plain,
! [A: nat,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(481,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1488_add__pos__pos) ).
thf(3458,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(343,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B != A )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_dual__order_Ostrict__iff__order) ).
thf(2716,plain,
! [A: nat,B: nat] :
( ( ( ( B != A )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B != A )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(733,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3705_max_Ostrict__boundedE) ).
thf(4612,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(336,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3655_max_OorderI) ).
thf(2695,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(959,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_3177_zero__diff) ).
thf(5698,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)],[959]) ).
thf(964,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_2512_divisors__zero) ).
thf(5720,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)],[964]) ).
thf(630,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2322_nat__mult__le__cancel__disj) ).
thf(4144,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(466,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( B @ size_s6755466524823107622T_VEBT @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_length__pos__if__in__set) ).
thf(3387,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( B @ size_s6755466524823107622T_VEBT @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(817,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_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_3336_Nat_Odiff__diff__eq) ).
thf(4998,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_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)],[817]) ).
thf(748,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_ord__eq__less__trans) ).
thf(4662,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(150,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_2403_mult_Ocomm__neutral) ).
thf(1833,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)],[150]) ).
thf(554,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_3198_add__diff__cancel__left_H) ).
thf(3768,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)],[554]) ).
thf(170,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6488_of__nat__power__le__of__nat__cancel__iff) ).
thf(1916,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(408,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2904_mult__right__le__imp__le) ).
thf(3081,plain,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2965_power__Suc__less__one) ).
thf(1929,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(1008,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_3186_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(5940,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)],[1008]) ).
thf(550,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1239_nat__add__left__cancel__less) ).
thf(3751,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(536,axiom,
! [A: nat,B: nat,C: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1456_add__decreasing2) ).
thf(3695,plain,
! [A: nat,B: nat,C: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(396,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_1900_one__is__add) ).
thf(3002,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)],[396]) ).
thf(454,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_dual__order_Oirrefl) ).
thf(3340,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(488,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_6913_binomial__0__Suc) ).
thf(3487,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)],[488]) ).
thf(845,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1647_minf_I3_J) ).
thf(5158,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(429,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3334_eq__diff__iff) ).
thf(3170,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(645,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2883_mult__right__less__imp__less) ).
thf(4236,plain,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(642,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( D @ ( A @ aa_nat_o ) ) )
& ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1934_ex__least__nat__less) ).
thf(4218,plain,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( D @ ( A @ aa_nat_o ) ) )
& ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(351,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( D @ ( divide_divide_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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4334_dvd__div__div__eq__mult) ).
thf(2759,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( 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 ) ) )
=> ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( D @ ( 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 @ ( D @ ( divide_divide_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 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(850,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3368_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(5190,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_order__antisym) ).
thf(1765,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(6,axiom,
! [A: list_nat,B: nat,C: nat] :
( ( B @ ( A @ size_size_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ list_update_nat ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_list__update__beyond) ).
thf(1090,plain,
! [A: list_nat,B: nat,C: nat] :
( ( B @ ( A @ size_size_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ list_update_nat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(784,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_order__less__imp__not__eq) ).
thf(4854,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(301,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_2840_power__0) ).
thf(2557,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)],[301]) ).
thf(741,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_less__nat__zero__code) ).
thf(4640,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = A )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_dual__order_Oorder__iff__strict) ).
thf(1638,plain,
! [A: nat,B: nat] :
( ( ( ( B = A )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = A )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(457,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_287_set__update__subsetI) ).
thf(3355,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)],[457]) ).
thf(903,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1351_add__left__mono) ).
thf(5432,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(304,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_3030_max__Suc__Suc) ).
thf(2573,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)],[304]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4321_dvd__diffD) ).
thf(2148,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(211,axiom,
! [A: nat,B: list_nat,C: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( A @ ( B @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_nth__list__update__eq) ).
thf(2079,plain,
! [A: nat,B: list_nat,C: nat] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( A @ ( B @ list_update_nat ) ) @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(841,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( A @ ord_Least_nat )
= ( A @ aTP_Lamm_acq @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9258_Least__Suc) ).
thf(5143,plain,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( A @ ord_Least_nat )
= ( A @ aTP_Lamm_acq @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(681,axiom,
! [A: nat] :
( ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_not__gr__zero) ).
thf(4369,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(279,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7998_fact__ge__Suc__0__nat) ).
thf(2415,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(878,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2277_less__one) ).
thf(5325,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(1054,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_1300_add_Ocommute) ).
thf(6112,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)],[1054]) ).
thf(917,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_2517_no__zero__divisors) ).
thf(5491,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)],[917]) ).
thf(329,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4199_pow__divides__pow__iff) ).
thf(2669,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(663,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3337_diff__le__mono) ).
thf(4300,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(431,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( ( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( C = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1490_canonically__ordered__monoid__add__class_OlessE) ).
thf(3182,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( ( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( C = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(767,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1887_gr0__conv__Suc) ).
thf(4773,plain,
! [A: nat] :
( ( ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(57,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8803_gcd__nat_Oright__neutral) ).
thf(1307,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: nat] : ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9261_less__eq__mask) ).
thf(1194,plain,
! [A: nat] : ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1062,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_xm @ 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_9646_ATP_Olambda__315) ).
thf(6144,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_xm @ 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)],[1062]) ).
thf(414,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_4045_mod__by__Suc__0) ).
thf(3101,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)],[414]) ).
thf(769,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2694_mult__left__mono) ).
thf(4790,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(324,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_order_Ostrict__iff__not) ).
thf(2642,plain,
! [A: nat,B: nat] :
( ( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3748_div__positive) ).
thf(2229,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(319,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_linorder__not__le) ).
thf(2624,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(864,axiom,
one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2931_zero__less__two) ).
thf(5244,plain,
one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(735,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_3344_Nat_Odiff__cancel) ).
thf(4620,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)],[735]) ).
thf(97,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_3032_max__0L) ).
thf(1574,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)],[97]) ).
thf(1063,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_1326_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(6147,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)],[1063]) ).
thf(353,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_58_list__update__overwrite) ).
thf(2774,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)],[353]) ).
thf(778,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2052_power__gt__expt) ).
thf(4828,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(801,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_4030_mod__mult__self1__is__0) ).
thf(4914,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)],[801]) ).
thf(216,axiom,
! [A: nat,B: nat] : ( B @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4520_take__bit__nat__less__eq__self) ).
thf(2097,plain,
! [A: nat,B: nat] : ( B @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4350_is__unit__power__iff) ).
thf(1771,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( one_one_nat @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
| ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(898,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1617_pinf_I3_J) ).
thf(5407,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(640,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_yi @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9464_ATP_Olambda__133) ).
thf(4213,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_yi @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(734,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( @+[E: vEBT_VEBT] :
( ( ( A != D )
=> ( E
= ( D @ ( B @ nth_VEBT_VEBT ) ) ) )
& ( ( A = D )
=> ( E = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nth__list__update) ).
thf(4616,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( @+[E: vEBT_VEBT] :
( ( ( A != D )
=> ( E
= ( D @ ( B @ nth_VEBT_VEBT ) ) ) )
& ( ( A = D )
=> ( E = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(833,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9260_mask__nat__positive__iff) ).
thf(5093,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(926,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3452_nat__le__add__iff2) ).
thf(5531,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(749,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1782_less__trans__Suc) ).
thf(4667,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(423,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2928_n__less__n__mult__m) ).
thf(3138,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(942,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3139_div__less__iff__less__mult) ).
thf(5616,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(68,axiom,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4246_gcd__nat_Oextremum) ).
thf(1376,plain,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(888,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1766_Zero__neq__Suc) ).
thf(5367,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(348,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2795_linordered__nonzero__semiring__class_Ozero__le__one) ).
thf(2742,plain,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(693,axiom,
! [A: fun_VEBT_VEBT_o,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( ( B @ ( A @ find_VEBT_VEBT ) )
= ( C @ some_VEBT_VEBT ) )
<=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) ) )
& ( C
= ( D @ ( B @ nth_VEBT_VEBT ) ) )
& ( D @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) )
& ( B @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1683_find__Some__iff) ).
thf(4420,plain,
! [A: fun_VEBT_VEBT_o,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) ) )
& ( C
= ( D @ ( B @ nth_VEBT_VEBT ) ) )
& ( D @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) )
& ( B @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ find_VEBT_VEBT ) )
= ( C @ some_VEBT_VEBT ) ) )
& ( ( ( B @ ( A @ find_VEBT_VEBT ) )
= ( C @ some_VEBT_VEBT ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( D @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( E @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) ) )
& ( C
= ( D @ ( B @ nth_VEBT_VEBT ) ) )
& ( D @ ( B @ nth_VEBT_VEBT ) @ ( A @ aa_VEBT_VEBT_o ) )
& ( B @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(793,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_less__not__refl) ).
thf(4882,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(800,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4071_mod__less__divisor) ).
thf(4911,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(188,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( E @ ( A @ aa_nat_o ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( D @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Nat_Oex__has__greatest__nat) ).
thf(1993,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ? [D: nat] :
( ! [E: nat] :
( ( E @ ( A @ aa_nat_o ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( D @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(760,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1724_Suc__less__eq) ).
thf(4731,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(146,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_size__neq__size__imp__neq) ).
thf(1821,plain,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(656,axiom,
! [A: nat,B: nat] :
? [C: nat] :
! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4277_minf_I9_J) ).
thf(4277,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(670,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_3190_add__diff__cancel__right_H) ).
thf(4332,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)],[670]) ).
thf(912,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4100_Suc__times__mod__eq) ).
thf(5466,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(1034,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_1184_add__left__cancel) ).
thf(6044,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)],[1034]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4397_dvd__mult__cancel1) ).
thf(2252,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = one_one_nat )
=> ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_linorder__not__less) ).
thf(1381,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(257,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_le__eq__less__or__eq) ).
thf(2329,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(223,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2065_power__eq__iff__eq__base) ).
thf(2129,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_less__or__eq__imp__le) ).
thf(2343,plain,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(830,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1499_add__neg__nonpos) ).
thf(5082,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(726,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_1727_add__Suc__right) ).
thf(4569,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)],[726]) ).
thf(797,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2676_mult__nonneg__nonneg) ).
thf(4897,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(699,axiom,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4072_gcd__nat__induct) ).
thf(4452,plain,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(277,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_linorder__le__less__linear) ).
thf(2410,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(894,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_2785_add__scale__eq__noteq) ).
thf(5392,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)],[894]) ).
thf(60,axiom,
! [A: nat,B: list_VEBT_VEBT,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_VEBT_VEBT_o ) @ nth_Pr4606735188037164562VEBT_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc8721562602347293563VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4129_product__nth) ).
thf(1325,plain,
! [A: nat,B: list_VEBT_VEBT,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_VEBT_VEBT_o ) @ nth_Pr4606735188037164562VEBT_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc8721562602347293563VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(783,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( A @ vEBT_vebt_maxt )
= ( C @ some_nat ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_maxt__member) ).
thf(4850,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( A @ vEBT_vebt_maxt )
= ( C @ some_nat ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(478,axiom,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6409_of__nat__0) ).
thf(3451,plain,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(950,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_3242_diff__Suc__1) ).
thf(5656,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)],[950]) ).
thf(1041,axiom,
~ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_False) ).
thf(6080,plain,
~ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_delete ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(593,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3450_nat__diff__add__eq2) ).
thf(3971,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(510,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1627_pinf_I5_J) ).
thf(3583,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(384,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_22__C4_Ohyps_C_I6_J) ).
thf(2911,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)],[384]) ).
thf(721,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3374_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(4554,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2498_power__less__power__Suc) ).
thf(1112,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(306,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3141_div__less__dividend) ).
thf(2578,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( @+[D: nat] :
( ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( D = zero_zero_nat ) )
& ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( D = one_one_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 )
@ ( ord_less_eq_nat @ aa_nat_fun_nat_o )
@ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4107_verit__le__mono__div) ).
thf(1213,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( @+[D: nat] :
( ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( D = zero_zero_nat ) )
& ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( D = one_one_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 )
@ ( ord_less_eq_nat @ aa_nat_fun_nat_o )
@ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_verit__comp__simplify1_I3_J) ).
thf(2086,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(708,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__not__refl3) ).
thf(4502,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(225,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_dual__order_Orefl) ).
thf(2139,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(621,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_order__less__asym_H) ).
thf(4085,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_dual__order_Ostrict__trans2) ).
thf(2633,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(298,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_nat__less__le) ).
thf(2535,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(875,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1898_Suc__le__eq) ).
thf(5299,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(957,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1424_le__add1) ).
thf(5693,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(1030,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_1292_add__left__imp__eq) ).
thf(6029,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)],[1030]) ).
thf(580,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9184_upt__conv__Cons) ).
thf(3908,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3539_max_Oabsorb2) ).
thf(2069,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(489,axiom,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1565_Euclid__induct) ).
thf(3490,plain,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(486,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1761_old_Onat_Oexhaust) ).
thf(3480,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_order__class_Oorder__eq__iff) ).
thf(1171,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(209,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_zero__le) ).
thf(2075,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(782,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6428_of__nat__le__iff) ).
thf(4844,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(882,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_gr__implies__not0) ).
thf(5340,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(31,axiom,
! [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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8818_bezout__gcd__nat_H) ).
thf(1198,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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(153,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__0__eq) ).
thf(1841,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(521,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_fs @ 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_9879_ATP_Olambda__548) ).
thf(3627,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_fs @ 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)],[521]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2935_power__le__one) ).
thf(2171,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1015,axiom,
! [A: fun_list_VEBT_VEBT_o,B: list_VEBT_VEBT] :
( ! [C: list_VEBT_VEBT] :
( ! [D: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( D @ size_s6755466524823107622T_VEBT @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( C @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ aa_list_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_length__induct) ).
thf(5976,plain,
! [A: fun_list_VEBT_VEBT_o,B: list_VEBT_VEBT] :
( ! [C: list_VEBT_VEBT] :
( ! [D: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( D @ size_s6755466524823107622T_VEBT @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( C @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ aa_list_VEBT_VEBT_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(359,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1277_less__add__same__cancel2) ).
thf(2797,plain,
! [A: nat,B: nat] :
( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(310,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4401_mod__nat__eqI) ).
thf(2592,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4300_dvd__power__le) ).
thf(1435,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ( B = one_one_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4391_dvd__power) ).
thf(1726,plain,
! [A: nat,B: nat] :
( ( ( B = one_one_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(66,axiom,
! [A: nat,B: nat] : ( A @ ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3129_div__times__less__eq__dividend) ).
thf(1364,plain,
! [A: nat,B: nat] : ( A @ ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2041_power__inject__base) ).
thf(1250,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(430,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_3075_div__mult__self4) ).
thf(3178,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)],[430]) ).
thf(737,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1759_old_Onat_Odistinct_I1_J) ).
thf(4626,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(918,axiom,
! [A: nat,B: nat,C: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1464_add__decreasing) ).
thf(5495,plain,
! [A: nat,B: nat,C: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(839,axiom,
! [A: nat] :
? [B: nat] : ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_gt__ex) ).
thf(5139,plain,
! [A: nat] :
? [B: nat] : ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(632,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_order_Oasym) ).
thf(4158,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_order_Ostrict__trans2) ).
thf(1805,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(628,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_1764_zero__induct) ).
thf(4136,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)],[628]) ).
thf(158,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_210_valid__member__both__member__options) ).
thf(1873,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)],[158]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3096_max__absorb1) ).
thf(1208,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(700,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3521_max_Oabsorb3) ).
thf(4458,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(166,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4519_take__bit__tightened__less__eq__nat) ).
thf(1905,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(972,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ size_size_list_nat )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9166_length__upt) ).
thf(5757,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ size_size_list_nat )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(612,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1419_add__less__mono1) ).
thf(4052,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(792,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1356_add__right__mono) ).
thf(4879,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(584,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1361_add__le__imp__le__left) ).
thf(3921,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(974,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_4039_mod__div__trivial) ).
thf(5763,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)],[974]) ).
thf(886,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zv @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9990_ATP_Olambda__659) ).
thf(5358,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zv @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zv @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(93,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_2191_nat__mult__eq__1__iff) ).
thf(1551,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)],[93]) ).
thf(571,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1480_add__mono__thms__linordered__field_I4_J) ).
thf(3849,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1043,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_valid__eq2) ).
thf(6083,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ upt ) )
= nil_nat )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9170_upt__eq__Nil__conv) ).
thf(1076,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ upt ) )
= nil_nat ) )
& ( ( ( B @ ( A @ upt ) )
= nil_nat )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(904,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_order_Ostrict__trans) ).
thf(5435,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_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_7913_fact__mod) ).
thf(1626,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_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)],[108]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_leD) ).
thf(2054,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(180,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2484_mult__left__le) ).
thf(1948,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(385,axiom,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) ) ) )
=> ( B @ ( C @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1794_nat__induct__at__least) ).
thf(2914,plain,
! [A: nat,B: nat,C: fun_nat_o] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_nat_o ) )
=> ( D @ ( suc @ aa_nat_nat ) @ ( C @ aa_nat_o ) ) ) )
=> ( B @ ( C @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(399,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat,E: nat] :
( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4364_bezout__add__strong__nat) ).
thf(3031,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat,E: nat] :
( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(586,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3126_Euclidean__Division_Odiv__eq__0__iff) ).
thf(3936,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(130,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8801_gcd__nat_Oleft__neutral) ).
thf(1758,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(255,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_3114_nat__mult__max__right) ).
thf(2318,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)],[255]) ).
thf(247,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3127_Suc__div__le__mono) ).
thf(2271,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(326,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3162_deg__1__Leafy) ).
thf(2652,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(731,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1261_add__le__same__cancel1) ).
thf(4598,plain,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(595,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6467_of__nat__Suc) ).
thf(3981,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(635,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_1809_find__cong) ).
thf(4177,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)],[635]) ).
thf(594,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1253_le__add__same__cancel1) ).
thf(3975,plain,
! [A: nat,B: nat] :
( ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_order__neq__le__trans) ).
thf(1990,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(725,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ upt ) @ ( B @ take_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9167_take__upt) ).
thf(4566,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ upt ) @ ( B @ take_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(847,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ~ ( ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3446_nat__diff__split__asm) ).
thf(5165,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ~ ( ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ~ ( ? [D: nat] :
( ~ ( D @ ( A @ aa_nat_o ) )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(480,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7996_fact__less__mono__nat) ).
thf(3455,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(80,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
<=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3164_deg1Leaf) ).
thf(1472,plain,
! [A: vEBT_VEBT] :
( ( ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) )
=> ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(755,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 ) ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat] :
( C
!= ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4093_mod__eq__nat2E) ).
thf(4688,plain,
! [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 ) ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat] :
( C
!= ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(369,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_4066_mod__eq__self__iff__div__eq__0) ).
thf(2846,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)],[369]) ).
thf(1055,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_11_deg__deg__n) ).
thf(6115,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)],[1055]) ).
thf(380,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_not__less__zero) ).
thf(2899,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(634,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1779_Suc__less__eq2) ).
thf(4168,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1059,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_1664_deg__SUcn__Node) ).
thf(6132,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)],[1059]) ).
thf(506,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_1375_add_Ocomm__neutral) ).
thf(3571,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)],[506]) ).
thf(390,axiom,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( A @ aa_nat_o ) )
<=> ( F @ ( B @ aa_nat_o ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( C @ aa_nat_o ) )
<=> ( F @ ( D @ aa_nat_o ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) )
<=> ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1607_pinf_I1_J) ).
thf(2942,plain,
! [A: fun_nat_o,B: fun_nat_o,C: fun_nat_o,D: fun_nat_o] :
( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( B @ aa_nat_o ) )
=> ( F @ ( A @ aa_nat_o ) ) )
& ( ( F @ ( A @ aa_nat_o ) )
=> ( F @ ( B @ aa_nat_o ) ) ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( F @ ( D @ aa_nat_o ) )
=> ( F @ ( C @ aa_nat_o ) ) )
& ( ( F @ ( C @ aa_nat_o ) )
=> ( F @ ( D @ aa_nat_o ) ) ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) )
=> ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) ) )
& ( ( ( F @ ( C @ aa_nat_o ) )
& ( F @ ( A @ aa_nat_o ) ) )
=> ( ( F @ ( D @ aa_nat_o ) )
& ( F @ ( B @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(128,axiom,
! [A: $o] :
( ( ( A @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
<=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4644_of__bool__eq__0__iff) ).
thf(1743,plain,
! [A: $o] :
( ( ~ A
=> ( ( A @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ) )
& ( ( ( A @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(1744,plain,
( ( ~ $true
=> ( ( $true @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ) )
& ( ( ( $true @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
=> ~ $true ) ),
inference(instance,[status(thm)],[1743]) ).
thf(1745,plain,
( ( $true @ zero_n2687167440665602831ol_nat )
!= zero_zero_nat ),
inference(simp,[status(thm)],[1744]) ).
thf(1748,plain,
( ( $true @ zero_n2687167440665602831ol_nat )
!= zero_zero_nat ),
inference(lifteq,[status(thm)],[1745]) ).
thf(524,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_3413_nat__minus__add__max) ).
thf(3640,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)],[524]) ).
thf(273,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_2154_div__0) ).
thf(2397,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)],[273]) ).
thf(751,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_4074_mod__eq__0D) ).
thf(4673,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)],[751]) ).
thf(438,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6463_of__nat__le__0__iff) ).
thf(3214,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4352_unit__imp__mod__eq__0) ).
thf(2012,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(309,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4517_take__bit__tightened) ).
thf(2588,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(970,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1231_add__less__cancel__left) ).
thf(5748,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(567,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_2529_Suc__mult__cancel1) ).
thf(3833,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)],[567]) ).
thf(440,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2273_nat__mult__less__cancel__disj) ).
thf(3228,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(364,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_2190_mult__cancel2) ).
thf(2821,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)],[364]) ).
thf(276,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_3113_nat__mult__max__left) ).
thf(2407,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)],[276]) ).
thf(682,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1515_add__strict__increasing) ).
thf(4377,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(738,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_3475_add__eq__if) ).
thf(4630,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)],[738]) ).
thf(516,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_2005_power__Suc0__right) ).
thf(3608,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)],[516]) ).
thf(334,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_2388_nat__mult__1__right) ).
thf(2689,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)],[334]) ).
thf(908,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4082_unique__euclidean__semiring__numeral__class_Omod__less) ).
thf(5446,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(597,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_1796_add__Suc__shift) ).
thf(3988,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)],[597]) ).
thf(1792,plain,
( ! [A: nat] :
( ( A = one_one_nat )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ) )
& ! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
=> ( A = one_one_nat ) ) ),
inference(miniscope,[status(thm)],[1791]) ).
thf(1793,plain,
! [B: nat,A: nat] :
( ( ( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
| ( B != one_one_nat ) )
& ( ( A = one_one_nat )
| ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= one_one_nat ) ) ),
inference(cnf,[status(esa)],[1792]) ).
thf(1795,plain,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
| ( A != one_one_nat ) ),
inference(cnfConj,[status(thm)],[1793]) ).
thf(1797,plain,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
| ( A != one_one_nat ) ),
inference(lifteq,[status(thm)],[1795]) ).
thf(1798,plain,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(simp,[status(thm)],[1797]) ).
thf(1039,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_he @ aa_nat_o ) )
<=> ~ ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9553_ATP_Olambda__222) ).
thf(6069,plain,
! [A: fun_nat_o,B: nat] :
( ( ~ ( B @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_he @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_he @ aa_nat_o ) )
=> ~ ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(547,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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_2551_nat__mult__eq__cancel1) ).
thf(3737,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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)],[547]) ).
thf(462,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_3213_diff__self__eq__0) ).
thf(3376,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)],[462]) ).
thf(988,axiom,
ma @ ( mi @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_mimapr) ).
thf(5822,plain,
ma @ ( mi @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(182,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
= ( B @ size_size_list_nat ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_nth__equalityI) ).
thf(1961,plain,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
= ( B @ size_size_list_nat ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(608,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( C @ ( 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 @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1422_less__add__eq__less) ).
thf(4035,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( C @ ( 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 @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(805,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4194_dvd__imp__mod__0) ).
thf(4937,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(267,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2355_power__decreasing__iff) ).
thf(2375,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(893,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1767_Zero__not__Suc) ).
thf(5388,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(680,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_9194_tl__upt) ).
thf(4366,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)],[680]) ).
thf(178,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_ord__eq__le__trans) ).
thf(1941,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(829,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1737_less__Suc0) ).
thf(5074,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(924,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1741_n__not__Suc__n) ).
thf(5523,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(331,axiom,
! [A: nat,B: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ size_s6755466524823107622T_VEBT )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4480_length__replicate) ).
thf(2678,plain,
! [A: nat,B: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ size_s6755466524823107622T_VEBT )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(122,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8805_gcd__0__left__nat) ).
thf(1716,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(75,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6992_gbinomial__0_I1_J) ).
thf(1432,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(386,axiom,
! [A: nat,B: nat] :
? [C: nat] :
! [D: nat] :
( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4267_pinf_I9_J) ).
thf(2920,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(821,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: vEBT_VEBT] :
( ! [D: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_all__nth__imp__all__set) ).
thf(5015,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: vEBT_VEBT] :
( ! [D: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(157,axiom,
! [A: nat,B: list_VEBT_VEBT,C: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ zip_VE537291747668921783T_VEBT ) @ nth_Pr4953567300277697838T_VEBT ) )
= ( A @ ( C @ nth_VEBT_VEBT ) @ ( A @ ( B @ nth_VEBT_VEBT ) @ produc537772716801021591T_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1665_nth__zip) ).
thf(1869,plain,
! [A: nat,B: list_VEBT_VEBT,C: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ zip_VE537291747668921783T_VEBT ) @ nth_Pr4953567300277697838T_VEBT ) )
= ( A @ ( C @ nth_VEBT_VEBT ) @ ( A @ ( B @ nth_VEBT_VEBT ) @ produc537772716801021591T_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(871,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1903_less__iff__Suc__add) ).
thf(5276,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(566,axiom,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3427_invar__vebt_Ointros_I1_J) ).
thf(3828,plain,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(791,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_174_list__update__swap) ).
thf(4875,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)],[791]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_order_Otrans) ).
thf(2354,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(327,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_order__less__le) ).
thf(2656,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(397,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
<=> ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3375_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(3019,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) )
& ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(407,axiom,
! [A: nat,B: nat] :
? [C: nat] :
! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( B @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4282_minf_I10_J) ).
thf(3080,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(303,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_3131_div__add__self2) ).
thf(2569,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)],[303]) ).
thf(694,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 ) ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat] :
( A
= ( D @ ( 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_4094_nat__mod__eq__lemma) ).
thf(4437,plain,
! [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 ) ) )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat] :
( A
= ( D @ ( 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)],[694]) ).
thf(647,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1416_add__less__mono) ).
thf(4240,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9188_upt__rec) ).
thf(2092,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3679_le__max__iff__disj) ).
thf(1813,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(535,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_less__imp__neq) ).
thf(3691,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(417,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7948_fact__reduce) ).
thf(3114,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(149,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( D @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4305_power__le__dvd) ).
thf(1830,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( D @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_order__less__imp__le) ).
thf(1763,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(299,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( comm_s4663373288045622133er_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_8309_pochhammer__0__left) ).
thf(2545,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( comm_s4663373288045622133er_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)],[299]) ).
thf(312,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2087_power__strict__mono) ).
thf(2599,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(768,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_in__set__conv__nth) ).
thf(4781,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) ) )
& ( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(761,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( suc @ aa_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1772_Suc__lessI) ).
thf(4737,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( suc @ aa_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7894_fact__mono) ).
thf(1130,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(947,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1415_add__lessD1) ).
thf(5638,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2024_power__mono) ).
thf(1218,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(909,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1519_add__strict__increasing2) ).
thf(5450,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(855,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1533_verit__comp__simplify1_I1_J) ).
thf(5208,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(154,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4162_nat__dvd__1__iff__1) ).
thf(1849,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(809,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( plus_plus_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_3371_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(4959,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( plus_plus_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)],[809]) ).
thf(366,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_3194_add__diff__cancel__right) ).
thf(2838,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)],[366]) ).
thf(141,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_2150_bits__div__by__0) ).
thf(1802,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)],[141]) ).
thf(120,axiom,
! [A: vEBT_VEBT] :
( ! [B: option4927543243414619207at_nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
!= ( E @ ( D @ ( C @ ( B @ vEBT_Node ) ) ) ) )
=> ~ ! [B: $o,C: $o] :
( A
!= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3286_VEBT_Oexhaust) ).
thf(1702,plain,
! [A: vEBT_VEBT] :
( ! [B: option4927543243414619207at_nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
!= ( E @ ( D @ ( C @ ( B @ vEBT_Node ) ) ) ) )
=> ~ ! [B: $o,C: $o] :
( A
!= ( C @ ( B @ vEBT_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(815,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_neq__if__length__neq) ).
thf(4991,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(945,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1657_minf_I5_J) ).
thf(5633,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(956,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2323_mult__le__cancel2) ).
thf(5685,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(673,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1507_add__nonpos__neg) ).
thf(4342,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(963,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
@ zero_n2687167440665602831ol_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4658_Suc__0__mod__eq) ).
thf(5717,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
@ zero_n2687167440665602831ol_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(469,axiom,
! [A: fun_nat_o] :
( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
<=> ? [B: nat] :
( ! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ aa_nat_o ) ) )
& ( B @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_exists__least__iff) ).
thf(3398,plain,
! [A: fun_nat_o] :
( ( ? [B: nat] :
( ! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ aa_nat_o ) ) )
& ( B @ ( A @ aa_nat_o ) ) )
=> ? [B: nat] : ( B @ ( A @ aa_nat_o ) ) )
& ( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
=> ? [B: nat] :
( ! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( A @ aa_nat_o ) ) )
& ( B @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(691,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_acc @ 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_9178_map__add__upt) ).
thf(4414,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_acc @ 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)],[691]) ).
thf(330,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_dual__order_Ostrict__trans1) ).
thf(2675,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(203,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8804_gcd__0__nat) ).
thf(2056,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(842,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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_3087_div__mult__self1__is__m) ).
thf(5147,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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)],[842]) ).
thf(941,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1869_lift__Suc__mono__less) ).
thf(5613,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(863,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_6351_exists__least__lemma) ).
thf(5240,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)],[863]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4285_dvd__div__eq__0__iff) ).
thf(1221,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(705,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8753_bit__Suc__0__iff) ).
thf(4488,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2961_power__Suc__le__self) ).
thf(2357,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(368,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1789_Suc__le__D) ).
thf(2843,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(227,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3918_max__def__raw) ).
thf(2145,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = A ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(910,axiom,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ! [D: nat] : ( D @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_linorder__less__wlog) ).
thf(5453,plain,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ! [D: nat] : ( D @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(1746,plain,
( ( ~ $false
=> ( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ) )
& ( ( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
=> ~ $false ) ),
inference(instance,[status(thm)],[1743]) ).
thf(1747,plain,
( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ),
inference(simp,[status(thm)],[1746]) ).
thf(1749,plain,
( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[1747]) ).
thf(986,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_1222_add__eq__0__iff__both__eq__0) ).
thf(5809,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)],[986]) ).
thf(639,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_2189_mult__cancel1) ).
thf(4202,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)],[639]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9189_upt__Suc) ).
thf(1094,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_less__le__not__le) ).
thf(1140,plain,
! [A: nat,B: nat] :
( ( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(624,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1426_add__leD1) ).
thf(4093,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(418,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_1569_add__0__iff) ).
thf(3117,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)],[418]) ).
thf(887,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4290_mod__0__imp__dvd) ).
thf(5364,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(361,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2814_mult__less__mono2) ).
thf(2807,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(1068,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_2423_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(6161,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)],[1068]) ).
thf(1052,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_3329_zero__induct__lemma) ).
thf(6105,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)],[1052]) ).
thf(245,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2985_one__less__power) ).
thf(2266,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(42,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ 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 ) @ ( C @ ( A @ ( power_power_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_3466_power__diff) ).
thf(1240,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ 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 ) @ ( C @ ( A @ ( power_power_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)],[42]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_eq__imp__le) ).
thf(1617,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(374,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_3078_div__mult__self3) ).
thf(2875,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)],[374]) ).
thf(288,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ~ ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3484_power__diff__power__eq) ).
thf(2458,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ~ ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(551,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__neqE__nat) ).
thf(3757,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(766,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1902_less__imp__Suc__add) ).
thf(4770,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1033,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_2413_mult_Oassoc) ).
thf(6041,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)],[1033]) ).
thf(977,axiom,
ma @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__C4_Ohyps_C_I7_J) ).
thf(5777,plain,
ma @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_order_Ostrict__trans1) ).
thf(1913,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(432,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2657_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(3188,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(743,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( C @ ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1496_mono__nat__linear__lb) ).
thf(4646,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( C @ ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(474,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( D
= ( E @ ( C @ ( A @ ( B @ ( minus_minus_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_3454_nat__eq__add__iff2) ).
thf(3433,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( D
= ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) ) )
=> ( ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( D
= ( E @ ( C @ ( A @ ( B @ ( minus_minus_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)],[474]) ).
thf(657,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_2550_add__mult__distrib) ).
thf(4278,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)],[657]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7929_choose__dvd) ).
thf(1839,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(744,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_4017_mod__by__0) ).
thf(4651,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)],[744]) ).
thf(253,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_3031_max__0R) ).
thf(2310,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)],[253]) ).
thf(934,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_1210_add__cancel__left__right) ).
thf(5573,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)],[934]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3535_max_Oabsorb1) ).
thf(1781,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(35,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7878_fact__ge__zero) ).
thf(1216,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(349,axiom,
! [A: $o,B: $o,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_vebt_delete ) )
= ( B @ ( A @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3394_vebt__delete_Osimps_I3_J) ).
thf(2743,plain,
! [A: $o,B: $o,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_vebt_delete ) )
= ( B @ ( A @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(395,axiom,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( suc @ aa_nat_nat ) @ ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1763_diff__induct) ).
thf(2997,plain,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat] : ( zero_zero_nat @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat] :
( ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( suc @ aa_nat_nat ) @ ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(27,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3163_deg__1__Leaf) ).
thf(1189,plain,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(403,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_3211_diff__Suc__Suc) ).
thf(3056,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)],[403]) ).
thf(236,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_2245_div__self) ).
thf(2226,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)],[236]) ).
thf(78,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1589_pinf_I6_J) ).
thf(1453,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(916,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3477_nat__less__add__iff1) ).
thf(5485,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( C @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(665,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3473_Suc__pred_H) ).
thf(4310,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(357,axiom,
! [A: nat] : ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2833_less__add__one) ).
thf(2792,plain,
! [A: nat] : ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(285,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2392_one__reorient) ).
thf(2443,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)],[285]) ).
thf(248,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_bot__nat__0_Oextremum__unique) ).
thf(2273,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3751_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(2174,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(565,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_1742_Suc__inject) ).
thf(3825,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)],[565]) ).
thf(610,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_add__le__cancel__left) ).
thf(4042,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1023,axiom,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ! [B: nat,C: nat] :
( ( C @ ( B @ ( A @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
<=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( B != C ) ) )
& ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C4_OIH_C_I1_J) ).
thf(6003,plain,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ! [B: nat,C: nat] :
( ( ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( B != C ) )
=> ( C @ ( B @ ( A @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ vEBT_vebt_delete ) @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
& ( B != C ) ) ) )
& ( na @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(441,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6536_less__imp__of__nat__less) ).
thf(3235,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(43,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bot__nat__0_Oextremum__uniqueI) ).
thf(1244,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(812,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_1705_old_Onat_Oinject) ).
thf(4969,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)],[812]) ).
thf(527,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_order__less__asym) ).
thf(3662,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(867,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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4177_nat__mult__dvd__cancel__disj) ).
thf(5258,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(50,axiom,
! [A: nat,B: nat,C: 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4400_power__dvd__imp__le) ).
thf(1276,plain,
! [A: nat,B: nat,C: 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(101,axiom,
! [A: nat,B: fun_nat_fun_nat_o] :
( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat] : ( D @ ( C @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
<=> ? [C: list_nat] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( D @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ size_size_list_nat )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Skolem__list__nth) ).
thf(1590,plain,
! [A: nat,B: fun_nat_fun_nat_o] :
( ( ? [C: list_nat] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( D @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ size_size_list_nat )
= A ) )
=> ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat] : ( D @ ( C @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat] : ( D @ ( C @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ? [C: list_nat] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ ( D @ ( B @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ size_size_list_nat )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(626,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_linorder__less__linear) ).
thf(4121,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(581,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( plus_plus_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_3240_Nat_Oadd__diff__assoc2) ).
thf(3911,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( plus_plus_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)],[581]) ).
thf(46,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( ( A != zero_zero_nat )
& ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4249_gcd__nat_Onot__eq__extremum) ).
thf(1253,plain,
! [A: nat] :
( ( ( ( A != zero_zero_nat )
& ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A != zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(340,axiom,
! [A: nat,B: nat] : ( B @ ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3130_times__div__less__eq__dividend) ).
thf(2707,plain,
! [A: nat,B: nat] : ( B @ ( 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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(64,axiom,
! [A: nat,B: vEBT_VEBT,C: nat,D: vEBT_VEBT] :
( ( ( B @ ( A @ replicate_VEBT_VEBT ) )
= ( D @ ( C @ replicate_VEBT_VEBT ) ) )
<=> ( ( ( A != zero_zero_nat )
=> ( B = D ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4479_replicate__eq__replicate) ).
thf(1341,plain,
! [A: nat,B: vEBT_VEBT,C: nat,D: vEBT_VEBT] :
( ( ( ( ( A != zero_zero_nat )
=> ( B = D ) )
& ( A = C ) )
=> ( ( B @ ( A @ replicate_VEBT_VEBT ) )
= ( D @ ( C @ replicate_VEBT_VEBT ) ) ) )
& ( ( ( B @ ( A @ replicate_VEBT_VEBT ) )
= ( D @ ( C @ replicate_VEBT_VEBT ) ) )
=> ( ( ( A != zero_zero_nat )
=> ( B = D ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(487,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4026_mod__less) ).
thf(3484,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(297,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2502_power__gt1__lemma) ).
thf(2532,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(754,axiom,
! [A: fun_nat_o,B: nat] :
( ? [C: nat] : ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ? [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
& ( zero_zero_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4329_unity__coeff__ex) ).
thf(4681,plain,
! [A: fun_nat_o,B: nat] :
( ( ? [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
& ( zero_zero_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ? [C: nat] : ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ? [C: nat] : ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ? [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
& ( zero_zero_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(983,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_gr__zeroI) ).
thf(5800,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(453,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_32_nth__list__update__neq) ).
thf(3336,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)],[453]) ).
thf(902,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4361_nat__mult__dvd__cancel1) ).
thf(5426,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6929_binomial__le__pow) ).
thf(1629,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(415,axiom,
! [A: nat,B: nat,C: 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2274_mult__less__cancel2) ).
thf(3104,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(598,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3145_dividend__less__div__times) ).
thf(3991,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(549,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_3410_diff__Suc__eq__diff__pred) ).
thf(3748,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)],[549]) ).
thf(860,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_inthall) ).
thf(5228,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(522,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
!= ( A @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
!= ( C @ ( suc @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1769_Nat_OlessE) ).
thf(3630,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
!= ( A @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
!= ( C @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(835,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_3181_diff__zero) ).
thf(5104,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)],[835]) ).
thf(461,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1358_le__iff__add) ).
thf(3368,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(798,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_2366_mult__eq__self__implies__10) ).
thf(4900,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)],[798]) ).
thf(388,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1899_Suc__leI) ).
thf(2934,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(938,axiom,
! [A: nat,B: list_VEBT_VEBT,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ produc4743750530478302277T_VEBT ) @ nth_Pr4953567300277697838T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc537772716801021591T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4128_product__nth) ).
thf(5600,plain,
! [A: nat,B: list_VEBT_VEBT,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ produc4743750530478302277T_VEBT ) @ nth_Pr4953567300277697838T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc537772716801021591T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(1005,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1347_add__mono) ).
thf(5922,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zx @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9988_ATP_Olambda__657) ).
thf(1491,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zx @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( D @ ( C @ ( B @ ( A @ aTP_Lamm_zx @ aa_nat8314798964848609180_nat_o ) @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4346_unit__div__eq__0__iff) ).
thf(1689,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(637,axiom,
! [A: nat,B: nat] : ( B @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4073_mod__Suc__le__divisor) ).
thf(4197,plain,
! [A: nat,B: nat] : ( B @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(765,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_2009_nat__power__eq__Suc__0__iff) ).
thf(4759,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)],[765]) ).
thf(121,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_3034_max__nat_Oneutr__eq__iff) ).
thf(1706,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)],[121]) ).
thf(230,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_antisym__conv2) ).
thf(2162,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(828,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3338_diff__le__self) ).
thf(5072,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(851,axiom,
! [A: nat] :
~ ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1791_Suc__n__not__le__n) ).
thf(5196,plain,
! [A: nat] :
~ ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(880,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1411_add__less__imp__less__right) ).
thf(5336,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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2939_power__gt1) ).
thf(2009,plain,
! [A: nat,B: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(991,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_3345_diff__mult__distrib2) ).
thf(5828,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)],[991]) ).
thf(846,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_3330_minus__nat_Odiff__0) ).
thf(5162,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)],[846]) ).
thf(661,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4091_div__less__mono) ).
thf(4293,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(511,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3720_max_Ostrict__coboundedI2) ).
thf(3585,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(1056,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_1180_add__right__cancel) ).
thf(6118,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)],[1056]) ).
thf(979,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4318_dvd__minus__self) ).
thf(5781,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2612_power__Suc__less) ).
thf(1294,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4380_is__unit__div__mult__cancel__left) ).
thf(2462,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(994,axiom,
~ ( zero_zero_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_less__numeral__extra_I3_J) ).
thf(5837,plain,
~ ( zero_zero_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(823,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( minus_minus_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_4075_mod__geq) ).
thf(5023,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( minus_minus_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)],[823]) ).
thf(686,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_3006_vebt__insert_Osimps_I3_J) ).
thf(4387,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)],[686]) ).
thf(305,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3671_max_Ocobounded1) ).
thf(2576,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(381,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2900_mult__left__le__imp__le) ).
thf(2902,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8813_gcd__diff1__nat) ).
thf(2120,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(856,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1249_le__add__same__cancel2) ).
thf(5211,plain,
! [A: nat,B: nat] :
( ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8024_fact__div__fact__le__pow) ).
thf(2095,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(697,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1879_lift__Suc__mono__le) ).
thf(4446,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_nat ) @ ( D @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_nat ) @ ( B @ ( A @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(923,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1269_add__less__same__cancel2) ).
thf(5517,plain,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(250,axiom,
! [A: nat,B: fun_nat_o,C: nat] :
( ! [D: nat] :
( ( D @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ aa_nat_o ) ) )
=> ( ! [D: nat] :
( ( A @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( B @ aa_nat_o ) ) )
=> ( D @ ( B @ aa_nat_o ) ) ) )
=> ( C @ ( B @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_nat__descend__induct) ).
thf(2294,plain,
! [A: nat,B: fun_nat_o,C: nat] :
( ! [D: nat] :
( ( D @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( B @ aa_nat_o ) ) )
=> ( ! [D: nat] :
( ( A @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [E: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( B @ aa_nat_o ) ) )
=> ( D @ ( B @ aa_nat_o ) ) ) )
=> ( C @ ( B @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_order__less__le__trans) ).
thf(2036,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(873,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1760_nat_OdiscI) ).
thf(5287,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(23,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ~ ! [E: nat] :
( ( E @ ( A @ aa_nat_o ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_bounded__Max__nat) ).
thf(1161,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ( C @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ! [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
=> ~ ! [E: nat] :
( ( E @ ( A @ aa_nat_o ) )
=> ( D @ ( E @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( A @ aTP_Lamm_vn @ set_fo2584398358068434914at_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_8267_pochhammer__code) ).
thf(1614,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( A @ aTP_Lamm_vn @ set_fo2584398358068434914at_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)],[104]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6552_of__nat__max) ).
thf(2123,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(678,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1895_Suc__le__lessD) ).
thf(4356,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(773,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1723_Suc__mono) ).
thf(4809,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(927,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2032_zero__less__power) ).
thf(5537,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(296,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_2192_nat__1__eq__mult__iff) ).
thf(2522,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)],[296]) ).
thf(159,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_order__refl) ).
thf(1876,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(781,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1768_not0__implies__Suc) ).
thf(4841,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1064,axiom,
! [A: list_o,B: list_o] :
( ( B @ ( A @ product_o_o ) @ size_s1515746228057227161od_o_o )
= ( B @ size_size_list_o @ ( A @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4206_length__product) ).
thf(6150,plain,
! [A: list_o,B: list_o] :
( ( B @ ( A @ product_o_o ) @ size_s1515746228057227161od_o_o )
= ( B @ size_size_list_o @ ( A @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(973,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( ( A @ vEBT_vebt_maxt )
= ( B @ some_nat ) )
=> ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_maxbmo) ).
thf(5760,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( A @ vEBT_vebt_maxt )
= ( B @ some_nat ) )
=> ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(405,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_2271_one__eq__mult__iff) ).
thf(3062,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)],[405]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_not__le__imp__less) ).
thf(1908,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(190,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_3111_nat__add__max__left) ).
thf(2003,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)],[190]) ).
thf(463,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_3341_diff__add__inverse2) ).
thf(3379,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)],[463]) ).
thf(997,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6491_of__nat__zero__less__power__iff) ).
thf(5852,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(609,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1773_less__SucE) ).
thf(4039,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_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_8802_gcd__nat_Oneutr__eq__iff) ).
thf(2102,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_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)],[218]) ).
thf(802,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2746_zero__less__mult__pos) ).
thf(4917,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(294,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3675_max_Ocobounded2) ).
thf(2517,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(333,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2334_power__strict__decreasing__iff) ).
thf(2683,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(604,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( plus_plus_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_3369_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(4014,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( plus_plus_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)],[604]) ).
thf(703,axiom,
! [A: vEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4496_in__set__replicate) ).
thf(4472,plain,
! [A: vEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) ) )
& ( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(269,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_order__trans) ).
thf(2385,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(758,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
<=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_VEBT_Oinject_I1_J) ).
thf(4706,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(575,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7882_fact__not__neg) ).
thf(3860,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(750,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_9180_map__Suc__upt) ).
thf(4670,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)],[750]) ).
thf(494,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( ? [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
& ( D @ ( suc @ aa_nat_nat ) @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C = zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3147_split__div_H) ).
thf(3511,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ? [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
& ( D @ ( suc @ aa_nat_nat ) @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C = zero_zero_nat ) ) )
=> ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( ? [D: nat] :
( ( D @ ( A @ aa_nat_o ) )
& ( D @ ( suc @ aa_nat_nat ) @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(651,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_2143_mult__cancel__right) ).
thf(4254,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)],[651]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9190_upt__Suc__append) ).
thf(1097,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(774,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_less__zeroE) ).
thf(4811,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(868,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2829_add__mono1) ).
thf(5268,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3140_div__eq__dividend__iff) ).
thf(1229,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = one_one_nat )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1010,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8814_gcd__nat_Oelims) ).
thf(5954,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_order__le__less) ).
thf(1395,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(889,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3367_le__add__diff) ).
thf(5371,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(925,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_1798_nat__arith_Osuc1) ).
thf(5527,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)],[925]) ).
thf(201,axiom,
! [A: nat,B: list_nat,C: list_VEBT_VEBT] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ zip_nat_VEBT_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( A @ ( C @ nth_VEBT_VEBT ) @ ( A @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1673_nth__zip) ).
thf(2050,plain,
! [A: nat,B: list_nat,C: list_VEBT_VEBT] :
( ( B @ size_size_list_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ zip_nat_VEBT_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( A @ ( C @ nth_VEBT_VEBT ) @ ( A @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(794,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_bot__nat__0_Oextremum__strict) ).
thf(4885,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8034_binomial__altdef__nat) ).
thf(1480,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(664,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 ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2321_one__le__mult__iff) ).
thf(4303,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(676,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_3044_div__mult__mult1) ).
thf(4350,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)],[676]) ).
thf(897,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n2687167440665602831ol_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4662_take__bit__of__Suc__0) ).
thf(5404,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n2687167440665602831ol_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1019,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aax @ 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_9482_ATP_Olambda__151) ).
thf(5990,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aax @ 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)],[1019]) ).
thf(560,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6479_of__nat__power__less__of__nat__cancel__iff) ).
thf(3804,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(606,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2275_nat__0__less__mult__iff) ).
thf(4024,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6484_of__nat__le__of__nat__power__cancel__iff) ).
thf(1561,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(906,axiom,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1738_zero__less__Suc) ).
thf(5441,plain,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4514_dvd__antisym) ).
thf(2404,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(317,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7890_fact__ge__1) ).
thf(2619,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(402,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_nat__neq__iff) ).
thf(3045,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(837,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_1238_Nat_Oadd__0__right) ).
thf(5110,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)],[837]) ).
thf(355,axiom,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4560_replicate__length__same) ).
thf(2783,plain,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(564,axiom,
! [A: nat,B: nat,C: fun_VEBT_VEBT_o,D: vEBT_VEBT] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_VEBT_VEBT_o ) )
=> ( A @ ( D @ ( B @ replicate_VEBT_VEBT ) @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4475_intind) ).
thf(3822,plain,
! [A: nat,B: nat,C: fun_VEBT_VEBT_o,D: vEBT_VEBT] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_VEBT_VEBT_o ) )
=> ( A @ ( D @ ( B @ replicate_VEBT_VEBT ) @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(322,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_6915_binomial__n__0) ).
thf(2636,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)],[322]) ).
thf(658,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
!= ( C @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1771_Suc__lessE) ).
thf(4281,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
!= ( C @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(659,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_size__neq__size__imp__neq) ).
thf(4286,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(485,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2803_less__numeral__extra_I1_J) ).
thf(3479,plain,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(280,axiom,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ! [D: nat,E: nat] :
( ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_linorder__wlog) ).
thf(2417,plain,
! [A: fun_nat_fun_nat_o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ! [D: nat,E: nat] :
( ( D @ ( E @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( D @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(530,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_3231_diff__add__zero) ).
thf(3673,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)],[530]) ).
thf(877,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_1227_add__0) ).
thf(5322,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)],[877]) ).
thf(206,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3143_less__eq__div__iff__mult__less__eq) ).
thf(2063,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2318_power__strict__increasing__iff) ).
thf(1268,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(843,axiom,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2680_split__mult__neg__le) ).
thf(5151,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( zero_zero_nat @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(69,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[E: nat] :
( ( ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E
= ( D @ ( B @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8036_fold__atLeastAtMost__nat_Osimps) ).
thf(1378,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( B @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[E: nat] :
( ( ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E
= ( D @ ( B @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( one_one_nat @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(935,axiom,
! [A: nat,B: nat,C: nat,D: list_nat] :
( ( ( B @ ( A @ upt ) )
= ( D @ ( C @ cons_nat ) ) )
<=> ( ( ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) )
= D )
& ( A = C )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9187_upt__eq__Cons__conv) ).
thf(5581,plain,
! [A: nat,B: nat,C: nat,D: list_nat] :
( ( ( ( ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) )
= D )
& ( A = C )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ upt ) )
= ( D @ ( C @ cons_nat ) ) ) )
& ( ( ( B @ ( A @ upt ) )
= ( D @ ( C @ cons_nat ) ) )
=> ( ( ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) )
= D )
& ( A = C )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(709,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7886_fact__gt__zero) ).
thf(4506,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1011,axiom,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8752_not__bit__Suc__0__Suc) ).
thf(5958,plain,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(747,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_3331_diffs0__imp__equal) ).
thf(4659,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)],[747]) ).
thf(862,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_3041_div__mult__mult2) ).
thf(5236,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)],[862]) ).
thf(372,axiom,
! [A: nat,B: nat,C: fun_nat_fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) )
=> ( B @ ( A @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1783_less__Suc__induct) ).
thf(2864,plain,
! [A: nat,B: nat,C: fun_nat_fun_nat_o] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat] : ( D @ ( suc @ aa_nat_nat ) @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( E @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( F @ ( E @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( F @ ( D @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) )
=> ( B @ ( A @ ( C @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(56,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4173_dvd__0__left__iff) ).
thf(1299,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(914,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) )
= B )
<=> ( ( A @ ( B @ nth_VEBT_VEBT ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_list__update__same__conv) ).
thf(5473,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( A @ ( B @ nth_VEBT_VEBT ) )
= C )
=> ( ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) )
= B ) )
& ( ( ( C @ ( A @ ( B @ list_u1324408373059187874T_VEBT ) ) )
= B )
=> ( ( A @ ( B @ nth_VEBT_VEBT ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(883,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1758_old_Onat_Odistinct_I2_J) ).
thf(5344,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(459,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3245_Suc__pred) ).
thf(3362,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(362,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2668_mult__nonpos__nonneg) ).
thf(2810,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(854,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( B @ ( A @ size_s6755466524823107622T_VEBT @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_list__update__beyond) ).
thf(5204,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( B @ ( A @ size_s6755466524823107622T_VEBT @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(420,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2926_one__less__mult) ).
thf(3128,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(984,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4090_mod__le__divisor) ).
thf(5803,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(148,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4250_gcd__nat_Oextremum__uniqueI) ).
thf(1827,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1066,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_2408_mult_Ocommute) ).
thf(6155,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)],[1066]) ).
thf(360,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_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_3241_Nat_Odiff__diff__right) ).
thf(2803,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_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)],[360]) ).
thf(985,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_1413_plus__nat_Oadd__0) ).
thf(5806,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)],[985]) ).
thf(684,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2547_mult__le__mono1) ).
thf(4382,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(244,axiom,
one_one_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2533_le__numeral__extra_I4_J) ).
thf(2265,plain,
one_one_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(577,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( E @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4096_split__mod) ).
thf(3869,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( E @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( B @ ( A @ aa_nat_o ) ) ) )
=> ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( ( ( C != zero_zero_nat )
=> ! [D: nat,E: nat] :
( ( C @ ( E @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( E @ ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( E @ ( A @ aa_nat_o ) ) ) ) )
& ( ( C = zero_zero_nat )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(445,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8815_gcd__nat_Osimps) ).
thf(3245,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(690,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_order__less__imp__not__eq2) ).
thf(4410,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(779,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
<=> ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3409_Nat_Ole__imp__diff__is__add) ).
thf(4831,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) )
& ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( B
= ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1042,axiom,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__C4_Ohyps_C_I1_J) ).
thf(6082,plain,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(669,axiom,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1722_lessI) ).
thf(4330,plain,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(1002,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( A = B )
<=> ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_VEBT_VEBT ) )
= ( C @ ( B @ nth_VEBT_VEBT ) ) ) )
& ( ( A @ size_s6755466524823107622T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_list__eq__iff__nth__eq) ).
thf(5891,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_VEBT_VEBT ) )
= ( C @ ( B @ nth_VEBT_VEBT ) ) ) )
& ( ( A @ size_s6755466524823107622T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_VEBT_VEBT ) )
= ( C @ ( B @ nth_VEBT_VEBT ) ) ) )
& ( ( A @ size_s6755466524823107622T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(617,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3339_le__diff__iff_H) ).
thf(4071,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(165,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_3035_max__nat_Oleft__neutral) ).
thf(1902,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)],[165]) ).
thf(293,axiom,
! [A: $o,B: $o,C: nat] :
( ( C @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_VEBT_valid @ aa_nat_o ) )
<=> ( C = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3412_VEBT__internal_Ovalid_H_Osimps_I1_J) ).
thf(2484,plain,
! [A: $o,B: $o,C: nat] :
( ( ( C = one_one_nat )
=> ( C @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_VEBT_valid @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_VEBT_valid @ aa_nat_o ) )
=> ( C = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1885,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(lifteq,[status(thm)],[1884]) ).
thf(674,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ last_nat )
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9267_last__upt) ).
thf(4345,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ last_nat )
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(1057,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_1296_add_Oleft__commute) ).
thf(6126,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)],[1057]) ).
thf(86,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) )
<=> ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4724_split__of__bool) ).
thf(1505,plain,
! [A: fun_nat_o,B: $o] :
( ( ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) )
=> ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) ) )
& ( ( B @ zero_n2687167440665602831ol_nat @ ( A @ aa_nat_o ) )
=> ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(654,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4316_nat__dvd__not__less) ).
thf(4271,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(583,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2887_mult__strict__mono_H) ).
thf(3918,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(106,axiom,
! [A: nat,B: list_nat,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ produc7156399406898700509T_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4136_product__nth) ).
thf(1621,plain,
! [A: nat,B: list_nat,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ produc7156399406898700509T_VEBT ) @ nth_Pr744662078594809490T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( nth_nat @ aa_lis1299702591413342011at_nat ) @ aa_nat_nat ) @ produc599794634098209291T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(671,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_1701_even__odd__cases) ).
thf(4335,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)],[671]) ).
thf(375,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1781_Suc__less__SucD) ).
thf(2879,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(256,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4337_dvd__div__iff__mult) ).
thf(2321,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(376,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1468_add__less__le__mono) ).
thf(2881,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(949,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_cs @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9806_ATP_Olambda__475) ).
thf(5649,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_cs @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_cs @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(808,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_2272_mult__eq__1__iff) ).
thf(4949,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)],[808]) ).
thf(365,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3406_Nat_Ole__diff__conv2) ).
thf(2832,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(204,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1579_minf_I6_J) ).
thf(2059,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(813,axiom,
! [A: nat,B: fun_nat_o] :
( ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
<=> ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
& ( A @ ( B @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1778_All__less__Suc) ).
thf(4977,plain,
! [A: nat,B: fun_nat_o] :
( ( ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
& ( A @ ( B @ aa_nat_o ) ) )
=> ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
=> ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) )
& ( A @ ( B @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(787,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1906_less__natE) ).
thf(4863,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(1032,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) )
<=> ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_valid__eq) ).
thf(6035,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) ) )
& ( ( B @ ( A @ vEBT_VEBT_valid @ aa_nat_o ) )
=> ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(501,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1892_less__eq__Suc__le) ).
thf(3553,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(785,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1383_add__mono__thms__linordered__field_I5_J) ).
thf(4858,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( D @ ( 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_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(806,axiom,
! [A: list_o,B: list_VEBT_VEBT] :
( ( B @ ( A @ product_o_VEBT_VEBT ) @ size_s4313452262239582901T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT @ ( A @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4205_length__product) ).
thf(4940,plain,
! [A: list_o,B: list_VEBT_VEBT] :
( ( B @ ( A @ product_o_VEBT_VEBT ) @ size_s4313452262239582901T_VEBT )
= ( B @ size_s6755466524823107622T_VEBT @ ( A @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(62,axiom,
! [A: nat,B: list_o,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_VEBT_VEBT ) @ nth_Pr6777367263587873994T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ produc2982872950893828659T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4132_product__nth) ).
thf(1331,plain,
! [A: nat,B: list_o,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_VEBT_VEBT ) @ nth_Pr6777367263587873994T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ produc2982872950893828659T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(102,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_3069_max__0__1_I1_J) ).
thf(1606,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)],[102]) ).
thf(1009,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_2425_nat__mult__eq__cancel__disj) ).
thf(5943,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)],[1009]) ).
thf(844,axiom,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1418_not__add__less2) ).
thf(5155,plain,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(509,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_3202_add__diff__cancel__left) ).
thf(3580,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)],[509]) ).
thf(482,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1774_less__SucI) ).
thf(3461,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(1071,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_1310_add_Oassoc) ).
thf(6173,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)],[1071]) ).
thf(655,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3392_linordered__semidom__class_Oadd__diff__inverse) ).
thf(4274,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1067,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_ly @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10069_ATP_Olambda__738) ).
thf(6158,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_ly @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(796,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3476_nat__less__add__iff2) ).
thf(4891,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( E @ ( C @ ( A @ ( B @ ( minus_minus_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 ) @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(980,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2739_mult__pos__neg2) ).
thf(5789,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( zero_zero_nat @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(412,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_3070_div__by__Suc__0) ).
thf(3096,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)],[412]) ).
thf(573,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_1756_vebt__buildup_Ocases) ).
thf(3854,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)],[573]) ).
thf(283,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3138_div__le__mono2) ).
thf(2438,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(763,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3474_Suc__diff__eq__diff__pred) ).
thf(4752,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(666,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1423_add__leE) ).
thf(4313,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(866,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_3215_diff__diff__left) ).
thf(5255,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)],[866]) ).
thf(451,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3403_add__diff__inverse__nat) ).
thf(3316,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1528_verit__la__disequality) ).
thf(2351,plain,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(10484,plain,
$false,
inference(e,[status(thm)],[2452,5593,2263,3798,3449,5778,6014,1110,1686,5659,1665,2630,6085,4560,3962,3345,4464,2341,2072,4062,2412,1237,2921,4290,3698,3863,5676,2427,1982,3566,4728,1750,4339,3858,1808,3040,1073,5982,4326,2854,4623,3382,3680,2077,6022,1211,6063,3072,1924,6177,5141,1522,4515,3813,2381,5292,5069,2395,2908,1422,3959,2099,5224,5348,6017,1486,4532,5501,1788,1671,4090,3745,3135,1867,6089,5701,4440,5713,5674,1761,5005,3313,5708,2360,3848,1497,5550,1608,4633,4403,3429,5565,4575,5906,1310,3365,4870,2740,1275,2141,3577,2042,5740,3502,4496,4079,1366,1518,1228,1196,6138,3766,3994,1127,3915,2548,5745,4679,1935,3947,4124,5825,5723,2400,4963,1967,4511,4249,5553,4546,4524,4348,4563,3574,5188,6066,3148,1313,2897,4243,3248,4238,3204,2039,3275,2698,3131,5284,3689,2339,4692,6095,2269,4654,1264,2682,3125,3410,1577,1455,5182,3845,5640,3089,2466,2126,1132,3043,1922,5925,4317,1115,3902,3951,4265,2388,1100,3099,5338,2713,3998,3463,3385,2169,1087,5199,1147,1247,4358,5397,5622,3734,4141,2024,6098,2989,1362,4390,5091,4793,5020,6025,4756,5792,2007,2178,5888,4297,4001,3453,1334,6135,3525,6176,3621,5032,1151,2777,1183,5834,2237,4988,2616,1946,5663,2794,4903,4443,4578,5597,4018,3393,5013,5333,3163,3569,5985,3923,3093,3771,3851,3389,1169,3537,2281,5220,2483,1072,4825,2639,1405,4643,2884,4055,5353,6110,5384,3505,1886,4087,2424,3676,2137,3955,3243,3588,1697,3559,5819,3606,3211,2392,6103,4588,4082,4483,5695,4700,5961,4604,4199,3301,3984,5443,5438,6058,4557,6092,4216,3591,6020,4407,2473,4888,1438,5839,3720,5411,4076,2737,5862,2232,2307,5540,2083,4031,1736,2621,4059,1768,2061,3550,2000,2705,1387,6032,5794,1570,4252,4521,5470,2986,3207,1238,1274,2441,5611,5734,5630,2560,2249,6000,2596,5002,1123,5512,4499,2606,3154,4449,5085,5754,2150,4160,3664,3307,5937,3810,3499,3718,5201,2313,1910,5515,5769,3166,3191,1938,5879,2872,4385,1951,5460,5988,1624,3546,1159,3535,1836,5113,2181,4417,4740,6168,3028,3727,1281,4461,3667,2112,1291,5993,3595,3445,6090,1106,3731,3615,5270,6153,5423,5635,4048,4095,4840,4012,3237,5233,4817,3968,6075,3467,3784,6101,3413,2841,1328,2709,1970,4636,2692,1587,4233,3704,1878,2726,4930,1719,2858,4518,4860,3407,5107,1739,3714,1075,4545,1584,2349,1567,4676,3775,3141,3441,2455,1700,6164,2613,1810,1791,3723,3643,4867,2666,1889,4814,2978,2649,4804,3654,3059,6129,2581,3819,5683,2813,2766,5026,2756,1825,2968,5063,5273,5850,3611,2519,5481,1297,2681,3541,5374,2304,1530,1539,4508,4068,5380,1668,1974,5973,5498,1192,1932,3222,2006,1799,5766,5823,5305,3760,5217,4152,5603,3083,3201,4223,2370,1525,5245,4535,3624,4966,5571,5737,5419,4004,4550,1857,5557,2702,3563,4195,3508,1895,5909,3841,4995,1732,4572,1278,3707,4380,3358,2585,5969,1483,4657,2602,3792,3686,6052,2894,5400,1631,2936,1648,4919,5996,6026,4872,2904,4354,1103,1548,1927,2028,2734,5882,3111,3343,2260,4943,4268,3319,3636,1884,1784,3240,2789,2016,4801,5831,3900,5099,3458,2716,4612,2695,5698,5720,4144,3387,4998,4662,1833,3768,1916,3081,1929,5940,3751,3695,3002,3340,3487,5158,3170,4236,4218,2759,5190,1765,1090,4854,2557,4640,1638,3355,5432,1356,2573,2148,2079,5143,4369,2415,5325,6112,5491,2669,4300,3182,4773,1307,1194,6144,3101,4790,2642,2229,2624,5244,4620,1574,6147,2774,4828,4914,2097,1771,5407,4213,4616,5093,5531,4667,6154,3138,5616,1376,5367,2742,4420,4882,4911,1993,4731,1821,4277,4332,5466,6044,2252,1381,2329,2129,2343,5082,4569,4897,4452,2410,5392,1325,4850,3451,5656,6080,3971,3583,2911,4554,1112,2578,1213,2481,2086,4502,2139,4085,2633,2535,5299,5693,6029,3908,2069,3490,3480,1171,2075,4844,5340,1198,1841,3627,2171,5976,2797,2592,1435,1726,1364,1250,3178,4626,5495,5139,4158,1805,4136,1873,1208,4458,1905,5757,4052,4879,3921,5763,5358,1551,3849,6083,1076,5435,1626,2054,1948,2914,3031,3936,1758,2318,2271,2652,4598,3981,6088,4177,3975,1990,4566,5165,3455,1472,4688,2846,6115,2899,4168,6132,3571,2942,1748,3640,2397,4673,3214,2012,2588,5748,3833,3228,2821,2407,4377,4630,3608,2689,5446,3988,1798,6069,3737,3376,5822,1961,4035,4937,2375,5388,1743,4366,1941,5074,5523,2678,1716,1432,2920,5015,1869,5276,3828,4875,2354,2656,3019,3080,2569,4437,4240,2092,1813,3691,3114,1830,1763,2545,2599,4781,4737,1130,5638,1218,5450,5208,1849,4959,2838,1802,1702,4991,5633,5685,4342,5717,3398,4414,2675,2056,5147,5613,5240,1221,4488,2357,2843,2145,5453,1749,5809,4202,1094,1140,4093,3117,5364,2807,6161,6105,2266,1240,1617,2875,2458,3757,4770,6041,5777,1913,3188,4646,3433,4278,1839,4651,2310,5573,1781,1216,2743,2997,1189,3056,2226,1453,5485,4310,2792,2443,2273,2174,3825,4042,6003,3235,1244,4969,3662,5258,1276,1590,4121,3911,1253,2707,1341,3484,2532,4681,5800,3336,5426,1629,3104,3991,3748,5228,3630,5104,3368,4900,2934,5600,5922,1491,1689,4197,4759,1706,2162,5072,5196,5336,2009,5828,5162,4293,3585,6118,5781,1294,2462,5837,5023,4387,2576,2902,2120,5211,2095,4446,5517,2294,2036,5287,1161,1614,2123,4356,4809,5537,2522,1876,4841,6150,5760,3062,1908,2003,3379,5852,4039,2102,4917,2517,2683,4014,4472,2385,4706,3860,4670,3511,4254,1097,4811,5268,1229,5954,1395,5371,5527,2050,4885,1480,4303,4350,5404,5990,3804,4024,1561,5441,2404,2619,3045,5110,2783,3822,2636,4281,4286,3479,2417,3673,5322,2063,1268,5151,1378,5581,4506,5958,4659,5236,2864,1299,5473,5344,3362,2810,5204,3128,5803,1827,6155,2803,5806,4382,2265,3869,3245,4410,4831,6082,4330,5891,4071,1902,2484,1885,4345,6126,1505,4271,3918,1621,4335,2879,2321,2881,5649,4949,2832,2059,4977,4863,6035,3553,4858,4940,1331,1606,5943,5155,3580,3461,6173,4274,6158,4891,5789,3096,3854,2438,4752,4313,5255,3316,2351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP256_3 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.13/0.44 % Computer : n020.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8046.5625MB
% 0.13/0.44 % OS : Linux 6.8.0-71-generic
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Fri Sep 25 18:38:19 UTC 2026
% 0.13/0.44 % CPUTime :
% 0.13/0.44 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
% 0.84/1.04 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.47/2.88 % [INFO] Parsing done (1832ms).
% 7.84/2.90 % [INFO] Running in sequential loop mode.
% 8.13/3.09 % [INFO] eprover registered as external prover.
% 8.13/3.09 % [INFO] Scanning for conjecture ...
% 11.64/3.91 % [INFO] Found a conjecture (or negated_conjecture) and 10103 axioms. Running axiom selection ...
% 13.75/4.57 % [INFO] Axiom selection finished. Selected 1069 axioms (removed 9034 axioms).
% 15.48/4.95 % [INFO] Problem is typed first-order (TPTP TFF).
% 15.48/4.98 % [INFO] Type checking passed.
% 15.48/4.98 % [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 ...
% 64.74/17.97 % External prover 'e' found a proof!
% 64.74/17.98 % [INFO] Killing All external provers ...
% 64.74/17.98 % Time passed: 17391ms (effective reasoning time: 15073ms)
% 64.74/17.98 % 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)>
% 64.74/17.99 % Axioms used in derivation (1069): fact_2334_power__strict__decreasing__iff, fact_7878_fact__ge__zero, fact_3081_div__mult__self2, fact_8813_gcd__diff1__nat, fact_1627_pinf_I5_J, fact_1724_Suc__less__eq, fact_2488_mult__le__one, fact_3475_add__eq__if, fact_4069_mod__Suc, fact_3679_le__max__iff__disj, fact_8800_gcd__nat_Oeq__neutr__iff, fact_4107_verit__le__mono__div, fact_3412_VEBT__internal_Ovalid_H_Osimps_I1_J, fact_2274_mult__less__cancel2, fact_2138_mult__cancel__left, fact_1657_minf_I5_J, fact_3202_add__diff__cancel__left, fact_1792_not__less__eq__eq, fact_1422_less__add__eq__less, fact_4397_dvd__mult__cancel1, fact_6516_mult__of__nat__commute, fact_4340_div__dvd__iff__mult, fact_181_less__zeroE, fact_1318_group__cancel_Oadd1, fact_3413_nat__minus__add__max, fact_9485_ATP_Olambda__154, fact_3071_div__less, fact_1888_All__less__Suc2, fact_1550_le__numeral__extra_I3_J, fact_1176_verit__comp__simplify1_I3_J, fact_4499_Bex__set__replicate, fact_8267_pochhammer__code, fact_1778_All__less__Suc, fact_3337_diff__le__mono, fact_3473_Suc__pred_H, fact_8036_fold__atLeastAtMost__nat_Osimps, fact_18__C4_OIH_C_I2_J, fact_1896_inc__induct, fact_3146_split__div, fact_8752_not__bit__Suc__0__Suc, fact_473_order_Ostrict__trans, fact_2484_mult__left__le, fact_3005_vebt__insert_Osimps_I2_J, fact_2900_mult__left__le__imp__le, fact_180_gr__implies__not0, fact_2272_mult__eq__1__iff, fact_7913_fact__mod, fact_707_order_Ostrict__implies__order, fact_4479_replicate__eq__replicate, fact_4074_mod__eq__0D, fact_2657_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_4656_of__bool__less__one__iff, fact_162_size__neq__size__imp__neq, fact_3345_diff__mult__distrib2, fact_753_order__neq__le__trans, fact_305_ord__eq__le__trans, fact_3096_max__absorb1, fact_6454_of__nat__1, fact_1227_add__0, fact_6351_exists__least__lemma, fact_3399_Suc__diff__le, fact_3687_max_Oabsorb__iff2, fact_9223_coprime__Suc__0__right, fact_3500_le__div__geq, fact_4194_dvd__imp__mod__0, fact_3091_max__absorb2, fact_1231_add__less__cancel__left, fact_2394_nat__mult__1, fact_1168_less__numeral__extra_I3_J, fact_6524_of__nat__0__le__iff, fact_3539_max_Oabsorb2, fact_1934_ex__least__nat__less, fact_1770_Suc__lessD, fact_735_linorder__not__less, fact_60_le0, fact_3225_le__add__diff__inverse2, fact_291_nle__le, fact_4192_dvd__times__right__cancel__iff, fact_3163_deg__1__Leaf, fact_4175_dvd__1__iff__1, fact_29_buildup__gives__valid, fact_4096_split__mod, fact_2846_plus__1__eq__Suc, fact_4075_mod__geq, fact_3_valid__eq, fact_3142_div__nat__eqI, fact_3332_diff__less__mono2, fact_4027_mod__mult__self2__is__0, fact_1511_add__pos__nonneg, fact_137_nth__mem, fact_6968_binomial__addition__formula, fact_8818_bezout__gcd__nat_H, fact_2013_power__eq__0__iff, fact_3374_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_441_ord__less__eq__trans, fact_2948_power__less__imp__less__exp, fact_3247_diff__Suc__diff__eq1, fact_4201_length__product, fact_1894_le__less__Suc__eq, fact_1428_le__Suc__ex, fact_713_dual__order_Ostrict__implies__order, fact_765_order__less__le__trans, fact_1788_le__SucI, fact_1617_pinf_I3_J, fact_6433_of__nat__add, fact_1515_add__strict__increasing, fact_192_list__eq__iff__nth__eq, fact_4320_dvd__diffD1, fact_3455_nat__eq__add__iff1, fact_3144_dividend__less__times__div, fact_1383_add__mono__thms__linordered__field_I5_J, fact_6488_of__nat__power__le__of__nat__cancel__iff, fact_3751_unique__euclidean__semiring__numeral__class_Odiv__less, fact_2883_mult__right__less__imp__less, fact_4480_length__replicate, fact_599_leD, fact_1761_old_Onat_Oexhaust, fact_208_maxidef, fact_1426_add__leD1, fact_1781_Suc__less__SucD, fact_2788_Suc__mult__less__cancel1, fact_9088_diff__Suc, fact_2425_nat__mult__eq__cancel__disj, fact_3241_Nat_Odiff__diff__right, fact_2552_nat__mult__less__cancel1, fact_204_list__update__same__conv, fact_3245_Suc__pred, fact_4162_nat__dvd__1__iff__1, fact_4496_in__set__replicate, fact_4437_list__decode_Ocases, fact_6467_of__nat__Suc, fact_1784_strict__inc__induct, fact_3346_diff__mult__distrib, fact_4519_take__bit__tightened__less__eq__nat, fact_1783_less__Suc__induct, fact_6965_choose__reduce__nat, fact_2826_mult__Suc, fact_315_order__antisym, fact_3263_diff__right__commute, fact_3406_Nat_Ole__diff__conv2, fact_4502_Ball__set__replicate, fact_4189_dvd__times__left__cancel__iff, fact_741_order__less__imp__le, fact_1285_add__gr__0, fact_412_order__antisym__conv, fact_156_less__irrefl__nat, fact_3087_div__mult__self1__is__m, fact_8283_pochhammer__0, fact_1774_less__SucI, fact_7943_fact__num__eq__if, fact_8812_gcd__diff2__nat, fact_200_nth__equalityI, fact_468_linorder__less__wlog, fact_2403_mult_Ocomm__neutral, fact_3474_Suc__diff__eq__diff__pred, fact_4364_bezout__add__strong__nat, fact_2143_mult__cancel__right, fact_6934_zero__less__binomial, fact_9261_less__eq__mask, fact_6536_less__imp__of__nat__less, fact_2507_mult__not__zero, fact_462_dual__order_Oirrefl, fact_325_order__trans, fact_3378_add__le__add__imp__diff__le, fact_2547_mult__le__mono1, fact_2795_linordered__nonzero__semiring__class_Ozero__le__one, fact_6428_of__nat__le__iff, fact_1533_verit__comp__simplify1_I1_J, fact_1375_add_Ocomm__neutral, fact_4455_option_Osize__gen_I2_J, fact_4401_mod__nat__eqI, fact_6479_of__nat__power__less__of__nat__cancel__iff, fact_8753_bit__Suc__0__iff, fact_6966_times__binomial__minus1__eq, fact_9165_drop__upt, fact_3143_less__eq__div__iff__mult__less__eq, fact_4167_dvd__0__right, fact_2037_power__less__imp__less__base, fact_1456_add__decreasing2, fact_3162_deg__1__Leafy, fact_6915_binomial__n__0, fact_4132_product__nth, fact_344_dual__order_Otrans, fact_2048_zero__power, fact_4343_dvd__div__eq__mult, fact_2780_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_2785_add__scale__eq__noteq, fact_179_infinite__descent0, fact_47_nth__list__update, fact_2163_div__by__0, fact_35_list__update__id, fact_4093_mod__eq__nat2E, fact_6929_binomial__le__pow, fact_3392_linordered__semidom__class_Oadd__diff__inverse, fact_1387_add__mono__thms__linordered__field_I2_J, fact_8035_fold__atLeastAtMost__nat_Oelims, fact_15_not__min__Null__member, fact_4205_length__product, fact_3410_diff__Suc__eq__diff__pred, fact_3366_diff__add, fact_3032_max__0L, fact_1417_not__add__less1, fact_334_dual__order_Oeq__iff, fact_2548_mult__le__mono2, fact_3035_max__nat_Oleft__neutral, fact_2028_zero__le__power, fact_2961_power__Suc__le__self, fact_2981_self__le__power, fact_4092_mod__eq__nat1E, fact_6444_of__nat__eq__1__iff, fact_151_zero__reorient, fact_431_order_Oasym, fact_158_less__not__refl2, fact_4057_mod__less__eq__dividend, fact_1353_less__eqE, fact_4199_pow__divides__pow__iff, fact_810_linorder__le__less__linear, fact_3526_max_Oabsorb4, fact_1239_nat__add__left__cancel__less, fact_1897_dec__induct, fact_4070_mod__induct, fact_3490_power__eq__if, fact_3531_max__less__iff__conj, fact_4648_of__bool__less__iff, fact_3748_div__positive, fact_3396_diff__less__Suc, fact_4317_dvd__pos__nat, fact_3330_minus__nat_Odiff__0, fact_2150_bits__div__by__0, fact_1249_le__add__same__cancel2, fact_178_gr__zeroI, fact_3476_nat__less__add__iff2, fact_194_Skolem__list__nth, fact_1782_less__trans__Suc, fact_339_dual__order_Oantisym, fact_1261_add__le__same__cancel1, fact_464_exists__least__iff, fact_3369_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_1589_pinf_I6_J, fact_185_bot__nat__0_Oextremum__strict, fact_4560_replicate__length__same, fact_4475_intind, fact_7894_fact__mono, fact_4091_div__less__mono, fact_9338_ATP_Olambda__7, fact_3130_times__div__less__eq__dividend, fact_4176_dvd__1__left, fact_7882_fact__not__neg, fact_2045_power__le__imp__le__base, fact_1607_pinf_I1_J, fact_4076_mod__if, fact_3329_zero__induct__lemma, fact_2813_mult__less__mono1, fact_4337_dvd__div__iff__mult, fact_0__C4_Ohyps_C_I3_J, fact_187_length__induct, fact_1760_nat_OdiscI, fact_4247_gcd__nat_Oextremum__strict, fact_1524_verit__comp__simplify1_I2_J, fact_747_order__le__neq__trans, fact_1269_add__less__same__cancel2, fact_1904_less__add__Suc2, fact_22__C4_Ohyps_C_I6_J, fact_637_not__le__imp__less, fact_7929_choose__dvd, fact_221_order__refl, fact_4177_nat__mult__dvd__cancel__disj, fact_1425_le__add2, fact_3101_max__def, fact_4329_unity__coeff__ex, fact_1436_add__nonpos__eq__0__iff, fact_9164_hd__upt, fact_4014_mod__self, fact_2942_power__0__left, fact_3339_le__diff__iff_H, fact_9990_ATP_Olambda__659, fact_3496_power__minus__mult, fact_9257_Least__eq__0, fact_2840_power__0, fact_27_nth__list__update__eq, fact_4506_take__bit__of__1__eq__0__iff, fact_4020_mod__0, fact_3407_Nat_Odiff__add__assoc, fact_6419_of__nat__eq__0__iff, fact_3242_diff__Suc__1, fact_177_not__less__zero, fact_4094_nat__mod__eq__lemma, fact_1528_verit__la__disequality, fact_2024_power__mono, fact_4476_take__bit__of__0, fact_1565_Euclid__induct, fact_3140_div__eq__dividend__iff, 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fact_1874_lift__Suc__mono__less__iff, fact_170_Ex__list__of__length, fact_573_order__less__imp__triv
% 64.74/17.99 % No. of inferences in proof: 2171
% 64.74/17.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17391 ms resp. 15073 ms w/o parsing
% 68.52/18.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 68.52/18.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------