%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP232_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 07:37:02 AM UTC 2026
% Result : Theorem 50.82s 16.61s
% Output : Refutation 53.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1131
% Syntax : Number of formulae : 2273 ( 674 unt; 0 typ; 0 def)
% Number of atoms : 6128 (2108 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 36351 ( 681 ~; 174 |; 668 &;31815 @)
% ( 295 <=>;2718 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 484 ( 483 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 50 con; 0-3 aty)
% Number of variables : 5530 ( 0 ^;5286 !; 202 ?;5530 :)
% ( 0 !>; 0 ?*; 0 @-; 42 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_fu8871020438547428127omplex_type,type,
fun_fu8871020438547428127omplex: $tType ).
thf(fun_fu8266604298679398363omplex_type,type,
fun_fu8266604298679398363omplex: $tType ).
thf(fun_fu2828149587716756511BT_nat_type,type,
fun_fu2828149587716756511BT_nat: $tType ).
thf(fun_fu8251827778467837215BT_int_type,type,
fun_fu8251827778467837215BT_int: $tType ).
thf(fun_fu3330635997124576799BT_int_type,type,
fun_fu3330635997124576799BT_int: $tType ).
thf(fun_fu1853463631764337203omplex_type,type,
fun_fu1853463631764337203omplex: $tType ).
thf(fun_fu7433039812794084273omplex_type,type,
fun_fu7433039812794084273omplex: $tType ).
thf(fun_fu4061198407372677825at_nat_type,type,
fun_fu4061198407372677825at_nat: $tType ).
thf(fun_fu6630916859057521017at_int_type,type,
fun_fu6630916859057521017at_int: $tType ).
thf(fun_fu6200680875500743381nt_int_type,type,
fun_fu6200680875500743381nt_int: $tType ).
thf(fun_li6914387844523535256_nat_o_type,type,
fun_li6914387844523535256_nat_o: $tType ).
thf(fun_fu8020931516743756395ex_nat_type,type,
fun_fu8020931516743756395ex_nat: $tType ).
thf(fun_fu2556788080963300715ex_int_type,type,
fun_fu2556788080963300715ex_int: $tType ).
thf(fun_fu8001260946965626035ex_int_type,type,
fun_fu8001260946965626035ex_int: $tType ).
thf(fun_fu155073193946645565VEBT_o_type,type,
fun_fu155073193946645565VEBT_o: $tType ).
thf(fun_fu4141963935195952137T_real_type,type,
fun_fu4141963935195952137T_real: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(produc9217583074051984497at_nat_type,type,
produc9217583074051984497at_nat: $tType ).
thf(fun_fu3351286688164852109at_nat_type,type,
fun_fu3351286688164852109at_nat: $tType ).
thf(fun_fu3636980702898289805at_int_type,type,
fun_fu3636980702898289805at_int: $tType ).
thf(fun_fu7424888833511495217nt_int_type,type,
fun_fu7424888833511495217nt_int: $tType ).
thf(fun_fu4463953228700081077BT_rat_type,type,
fun_fu4463953228700081077BT_rat: $tType ).
thf(fun_fu5586652545743564717BT_nat_type,type,
fun_fu5586652545743564717BT_nat: $tType ).
thf(fun_fu7059288016784409353BT_int_type,type,
fun_fu7059288016784409353BT_int: $tType ).
thf(fun_fu8270842325377534013VEBT_o_type,type,
fun_fu8270842325377534013VEBT_o: $tType ).
thf(fun_fu8695033588447641837al_nat_type,type,
fun_fu8695033588447641837al_nat: $tType ).
thf(fun_fu3562227594288721901al_int_type,type,
fun_fu3562227594288721901al_int: $tType ).
thf(fun_fu8404755328348021045al_int_type,type,
fun_fu8404755328348021045al_int: $tType ).
thf(fun_fu5553606195750802321at_nat_type,type,
fun_fu5553606195750802321at_nat: $tType ).
thf(fun_fu3518430294936654993at_int_type,type,
fun_fu3518430294936654993at_int: $tType ).
thf(fun_fu6324116013759063093nt_int_type,type,
fun_fu6324116013759063093nt_int: $tType ).
thf(fun_fu4584101141160326545at_int_type,type,
fun_fu4584101141160326545at_int: $tType ).
thf(fun_fu7802804735324696557nt_int_type,type,
fun_fu7802804735324696557nt_int: $tType ).
thf(fun_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_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(fun_fu720419882121075617plex_o_type,type,
fun_fu720419882121075617plex_o: $tType ).
thf(fun_fu1633589921238504865VEBT_o_type,type,
fun_fu1633589921238504865VEBT_o: $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(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_fu7523448966510524487plex_o_type,type,
fun_fu7523448966510524487plex_o: $tType ).
thf(fun_fu3480337415675744067nteger_type,type,
fun_fu3480337415675744067nteger: $tType ).
thf(fun_fu2816609810865982204omplex_type,type,
fun_fu2816609810865982204omplex: $tType ).
thf(fun_fu2435797646934184285_nat_o_type,type,
fun_fu2435797646934184285_nat_o: $tType ).
thf(fun_fu1493198444879918881VEBT_o_type,type,
fun_fu1493198444879918881VEBT_o: $tType ).
thf(fun_fu1995833500178483365_int_o_type,type,
fun_fu1995833500178483365_int_o: $tType ).
thf(fun_fu6979804496544055329VEBT_o_type,type,
fun_fu6979804496544055329VEBT_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(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(fun_fu5218021089301596328omplex_type,type,
fun_fu5218021089301596328omplex: $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_co3732688428756473980omplex_type,type,
fun_co3732688428756473980omplex: $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_fu1620311477532340197t_real_type,type,
fun_fu1620311477532340197t_real: $tType ).
thf(fun_fu4328765270694171897t_real_type,type,
fun_fu4328765270694171897t_real: $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_fu8659448316070137091omplex_type,type,
fun_fu8659448316070137091omplex: $tType ).
thf(fun_fu3043630359712370243plex_o_type,type,
fun_fu3043630359712370243plex_o: $tType ).
thf(fun_fu4472351043248340291real_o_type,type,
fun_fu4472351043248340291real_o: $tType ).
thf(fun_fu7076988630286034496BT_nat_type,type,
fun_fu7076988630286034496BT_nat: $tType ).
thf(fun_fu4586905485354307740BT_int_type,type,
fun_fu4586905485354307740BT_int: $tType ).
thf(fun_fu6554335974241757432BT_int_type,type,
fun_fu6554335974241757432BT_int: $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_fu3780232916559739075_nat_o_type,type,
fun_fu3780232916559739075_nat_o: $tType ).
thf(fun_fu3074144567237359299plex_o_type,type,
fun_fu3074144567237359299plex_o: $tType ).
thf(fun_fu1580565752866428867_nat_o_type,type,
fun_fu1580565752866428867_nat_o: $tType ).
thf(fun_fu2339071201290874307plex_o_type,type,
fun_fu2339071201290874307plex_o: $tType ).
thf(fun_fu810243669753863363_int_o_type,type,
fun_fu810243669753863363_int_o: $tType ).
thf(fun_se2100927751953696370t_real_type,type,
fun_se2100927751953696370t_real: $tType ).
thf(fun_fu6813129056075673441_nat_o_type,type,
fun_fu6813129056075673441_nat_o: $tType ).
thf(fun_fu4228744305898656589_int_o_type,type,
fun_fu4228744305898656589_int_o: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_Co6597186368970283863nteger_type,type,
fun_Co6597186368970283863nteger: $tType ).
thf(fun_fu3572752990780465756omplex_type,type,
fun_fu3572752990780465756omplex: $tType ).
thf(fun_fu4528473944208963392omplex_type,type,
fun_fu4528473944208963392omplex: $tType ).
thf(fun_fu8198533418994508931T_real_type,type,
fun_fu8198533418994508931T_real: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_fu8643405727515436425nteger_type,type,
fun_fu8643405727515436425nteger: $tType ).
thf(fun_fu4045816715887884506omplex_type,type,
fun_fu4045816715887884506omplex: $tType ).
thf(fun_re3844104906058862192omplex_type,type,
fun_re3844104906058862192omplex: $tType ).
thf(fun_fu2188483506383969923BT_rat_type,type,
fun_fu2188483506383969923BT_rat: $tType ).
thf(fun_fu5238640373165125763BT_nat_type,type,
fun_fu5238640373165125763BT_nat: $tType ).
thf(fun_fu5786399312697532803BT_int_type,type,
fun_fu5786399312697532803BT_int: $tType ).
thf(fun_fu5289434066392675523_nat_o_type,type,
fun_fu5289434066392675523_nat_o: $tType ).
thf(fun_fu4757868175734369219real_o_type,type,
fun_fu4757868175734369219real_o: $tType ).
thf(fun_fu7328815047503086531_int_o_type,type,
fun_fu7328815047503086531_int_o: $tType ).
thf(fun_fu8602227297639178947real_o_type,type,
fun_fu8602227297639178947real_o: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_fu3446001173448610095VEBT_o_type,type,
fun_fu3446001173448610095VEBT_o: $tType ).
thf(fun_fu4682139747248231omplex_type,type,
fun_fu4682139747248231omplex: $tType ).
thf(fun_fu5899661017408545610at_nat_type,type,
fun_fu5899661017408545610at_nat: $tType ).
thf(fun_fu3409577872476818854at_int_type,type,
fun_fu3409577872476818854at_int: $tType ).
thf(fun_fu5405793531937576614nt_int_type,type,
fun_fu5405793531937576614nt_int: $tType ).
thf(fun_fu1590586450949517859at_nat_type,type,
fun_fu1590586450949517859at_nat: $tType ).
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_re6135230694098607860t_real_type,type,
fun_re6135230694098607860t_real: $tType ).
thf(fun_fu2872202335991144794ex_nat_type,type,
fun_fu2872202335991144794ex_nat: $tType ).
thf(fun_fu382119191059418038ex_int_type,type,
fun_fu382119191059418038ex_int: $tType ).
thf(fun_fu7350578069724619866ex_int_type,type,
fun_fu7350578069724619866ex_int: $tType ).
thf(fun_fu5589980185390252312t_real_type,type,
fun_fu5589980185390252312t_real: $tType ).
thf(fun_fu6436183194761443139_nat_o_type,type,
fun_fu6436183194761443139_nat_o: $tType ).
thf(fun_fu5646853623633916995_int_o_type,type,
fun_fu5646853623633916995_int_o: $tType ).
thf(fun_fu8304507701009772099_nat_o_type,type,
fun_fu8304507701009772099_nat_o: $tType ).
thf(fun_fu8064956510386623256t_real_type,type,
fun_fu8064956510386623256t_real: $tType ).
thf(fun_fu7493154764834273859_int_o_type,type,
fun_fu7493154764834273859_int_o: $tType ).
thf(fun_fu927436805355353155_nat_o_type,type,
fun_fu927436805355353155_nat_o: $tType ).
thf(fun_re7819166435457029784t_real_type,type,
fun_re7819166435457029784t_real: $tType ).
thf(fun_fu163975356400620604t_real_type,type,
fun_fu163975356400620604t_real: $tType ).
thf(fun_fu6610162456291744429VEBT_o_type,type,
fun_fu6610162456291744429VEBT_o: $tType ).
thf(fun_fu4911191927098811621T_real_type,type,
fun_fu4911191927098811621T_real: $tType ).
thf(fun_fu14152356423011729BT_rat_type,type,
fun_fu14152356423011729BT_rat: $tType ).
thf(fun_fu7075445697382584196_int_o_type,type,
fun_fu7075445697382584196_int_o: $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,
fun_fu5519318738670804632at_int: $tType ).
thf(fun_ra8505079968215247908at_rat_type,type,
fun_ra8505079968215247908at_rat: $tType ).
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_fu4368050222092438908at_nat_type,type,
fun_fu4368050222092438908at_nat: $tType ).
thf(fun_fu1877967077160712152at_int_type,type,
fun_fu1877967077160712152at_int: $tType ).
thf(fun_fu3874182736621469912nt_int_type,type,
fun_fu3874182736621469912nt_int: $tType ).
thf(fun_re5512370375968561900l_real_type,type,
fun_re5512370375968561900l_real: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $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_fu9071961061876887222al_int_type,type,
fun_fu9071961061876887222al_int: $tType ).
thf(fun_fu86166166672686426al_int_type,type,
fun_fu86166166672686426al_int: $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_Pr4811707699266497531nteger_type,type,
set_Pr4811707699266497531nteger: $tType ).
thf(fun_fu1994797156054922755_nat_o_type,type,
fun_fu1994797156054922755_nat_o: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(fun_fu8066363281484412158at_nat_type,type,
fun_fu8066363281484412158at_nat: $tType ).
thf(fun_fu5576280136552685402at_int_type,type,
fun_fu5576280136552685402at_int: $tType ).
thf(fun_fu7572495796013443162nt_int_type,type,
fun_fu7572495796013443162nt_int: $tType ).
thf(fun_se4683600015404540110VEBT_o_type,type,
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thf(fun_fu6329627000648617163VEBT_o_type,type,
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thf(fun_fu40286998686754419omplex_type,type,
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thf(fun_fu3613808716698379563omplex_type,type,
fun_fu3613808716698379563omplex: $tType ).
thf(fun_fu2990765671291504771ex_rat_type,type,
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thf(fun_fu705315015666092147ex_nat_type,type,
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thf(fun_fu4213752561377164075ex_int_type,type,
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thf(fun_na6632006986671646835omplex_type,type,
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thf(fun_co6883864892131739507omplex_type,type,
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thf(fun_fu3096161788242865370at_int_type,type,
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thf(fun_fu5283083362935887158nt_int_type,type,
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thf(fun_fu570715051317967998at_nat_type,type,
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thf(fun_fu2757636626010989786nt_nat_type,type,
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thf(fun_fu2445682883699234307plex_o_type,type,
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thf(fun_fu3719809307426920623omplex_type,type,
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thf(fun_se2389560805064864136_nat_o_type,type,
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thf(fun_na927404270896789692_nat_o_type,type,
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thf(fun_fu2408719596384163971_nat_o_type,type,
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thf(produc7248412053542808358at_nat_type,type,
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thf(set_fi7789364187291644575l_real_type,type,
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thf(fun_fu7631928937237476593t_real_type,type,
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thf(fun_na3970208099681795815_nat_o_type,type,
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thf(fun_fu806425790188207109plex_o_type,type,
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thf(fun_fu3043978019632300333x_real_type,type,
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thf(fun_VE2006399705683203104omplex_type,type,
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thf(fun_co3541073130412562976omplex_type,type,
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thf(filter6041513312241820739omplex_type,type,
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thf(fun_fu3077872570260440615l_real_type,type,
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thf(fun_Co6226381647958292740nteger_type,type,
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thf(fun_Co3583066429914935172er_nat_type,type,
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thf(fun_Co1092983284983208416er_int_type,type,
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thf(fun_re8542384036533109323t_real_type,type,
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thf(fun_re4112884445705685835l_real_type,type,
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thf(list_P7037539587688870467BT_nat_type,type,
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thf(list_P4547456442757143711BT_int_type,type,
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thf(list_P5647936690300460905T_VEBT_type,type,
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thf(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_fu6899955116716589935t_real_type,type,
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thf(fun_fu121957152452960295t_real_type,type,
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thf(fun_re4756235295228751087t_real_type,type,
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thf(fun_na5225841814499866095t_real_type,type,
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thf(set_Pr7556676689462069481BT_nat_type,type,
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thf(fun_fu7444430165986413063real_o_type,type,
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thf(fun_fu3532930458344041007omplex_type,type,
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thf(fun_li1025265955262268170_nat_o_type,type,
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thf(set_Pr5085853215250843933omplex_type,type,
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thf(produc8923325533196201883nteger_type,type,
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thf(fun_Pr7716844367077540446plex_o_type,type,
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thf(fun_na7718645245721260691t_real_type,type,
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thf(fun_na5873943405026509934VEBT_o_type,type,
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thf(fun_Ex2441982661509597004d_enat_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_fu1143798476471108391nt_int_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_na1148497095348402375at_rat_type,type,
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thf(fun_na3244735409550470327at_nat_type,type,
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thf(fun_na7654559027617327379at_int_type,type,
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thf(fun_na2382631619178260847at_int_type,type,
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thf(fun_in6793278964266839919at_int_type,type,
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thf(fun_in1521351555827773387at_int_type,type,
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thf(fun_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_Co2081214437782444048eger_o_type,type,
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thf(fun_fu1358370060594899587plex_o_type,type,
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thf(fun_fu3022329567491847689real_o_type,type,
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thf(fun_fu4478067837645853357l_real_type,type,
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thf(fun_Pr672294278902479040t_real_type,type,
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thf(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(list_P8526636022914148096eger_o_type,type,
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thf(fun_fu5551332503302594393al_rat_type,type,
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thf(fun_Pr2602117396471556196at_nat_type,type,
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thf(fun_Pr7647638413817135296at_int_type,type,
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thf(fun_na1476630412504255114at_nat_type,type,
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thf(fun_in4514472496968388910at_nat_type,type,
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thf(fun_in4211310926729683942nt_int_type,type,
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thf(fun_re7208826350674946562omplex_type,type,
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thf(fun_co286204877037288194omplex_type,type,
fun_co286204877037288194omplex: $tType ).
thf(set_Pr448751882837621926eger_o_type,type,
set_Pr448751882837621926eger_o: $tType ).
thf(fun_fu6621322437453427393_nat_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_VE597728521808591204at_nat_type,type,
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thf(fun_VE7331017413731640256at_int_type,type,
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thf(fun_VE294566951569886236nt_int_type,type,
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thf(fun_na6208021027755453088BT_nat_type,type,
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thf(fun_na3717937882823726332BT_int_type,type,
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thf(fun_na2418085665696872764plex_o_type,type,
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thf(fun_in1463024724634152352BT_int_type,type,
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thf(option4927543243414619207at_nat_type,type,
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thf(filter1242075044329608583at_nat_type,type,
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thf(fun_VE7631951351884037842plex_o_type,type,
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thf(fun_na8135612474337863287nteger_type,type,
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thf(fun_na1591161823130732966omplex_type,type,
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thf(fun_co9003232526696249554VEBT_o_type,type,
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thf(fun_co3258106519541737638omplex_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(fun_Pr4814023175418636514real_o_type,type,
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thf(fun_na7542918316964655096d_enat_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(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_VE3165209603783583043T_VEBT_type,type,
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thf(fun_Pr4796943543331071514_nat_o_type,type,
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thf(fun_Pr3238374608701176162_int_o_type,type,
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thf(fun_co8378349014452122532t_real_type,type,
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thf(fun_VE9219535225822561060nteger_type,type,
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thf(fun_na7234455742697417626_nat_o_type,type,
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thf(fun_na7306406234920378942_int_o_type,type,
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thf(fun_VE6480751511521678896_nat_o_type,type,
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thf(fun_VE4235606543851232980_int_o_type,type,
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thf(fun_na6887940067898170868VEBT_o_type,type,
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thf(fun_na1142814060743658952omplex_type,type,
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thf(fun_na8457291176974909128ex_nat_type,type,
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thf(fun_na5967208032043182372ex_int_type,type,
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thf(fun_in4578122135805219920VEBT_o_type,type,
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thf(fun_in3657390099950231424ex_int_type,type,
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thf(fun_co636942507509095880at_nat_type,type,
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thf(fun_co7370231399432144932at_int_type,type,
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thf(fun_co333780937270390912nt_int_type,type,
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thf(fun_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,
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thf(fun_fu3883539188510166275_int_o_type,type,
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thf(fun_re7681423839302404990l_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(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_list_VEBT_VEBT_o_type,type,
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thf(produc6271795597528267376eger_o_type,type,
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thf(fun_VE5569070535936029429omplex_type,type,
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thf(fun_re7319081385389557872plex_o_type,type,
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thf(fun_co4340422964966740447T_VEBT_type,type,
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thf(fun_set_VEBT_VEBT_o_type,type,
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thf(fun_nat_fun_list_o_o_type,type,
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fun_in5065666251602127472plex_o: $tType ).
thf(fun_co5676208753217392844_nat_o_type,type,
fun_co5676208753217392844_nat_o: $tType ).
thf(fun_co3431063785546946928_int_o_type,type,
fun_co3431063785546946928_int_o: $tType ).
thf(fun_Co480733329897759773un_o_o_type,type,
fun_Co480733329897759773un_o_o: $tType ).
thf(fun_VEBT_VEBT_real_type,type,
fun_VEBT_VEBT_real: $tType ).
thf(fun_real_fun_real_o_type,type,
fun_real_fun_real_o: $tType ).
thf(fun_real_VEBT_VEBT_type,type,
fun_real_VEBT_VEBT: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(list_P4002435161011370285od_o_o_type,type,
list_P4002435161011370285od_o_o: $tType ).
thf(fun_set_nat_real_type,type,
fun_set_nat_real: $tType ).
thf(fun_re6978948838062957830nteger_type,type,
fun_re6978948838062957830nteger: $tType ).
thf(set_list_complex_type,type,
set_list_complex: $tType ).
thf(fun_VEBT_VEBT_rat_type,type,
fun_VEBT_VEBT_rat: $tType ).
thf(fun_VEBT_VEBT_num_type,type,
fun_VEBT_VEBT_num: $tType ).
thf(fun_VEBT_VEBT_nat_type,type,
fun_VEBT_VEBT_nat: $tType ).
thf(fun_VEBT_VEBT_int_type,type,
fun_VEBT_VEBT_int: $tType ).
thf(fun_real_fun_nat_o_type,type,
fun_real_fun_nat_o: $tType ).
thf(fun_real_fun_int_o_type,type,
fun_real_fun_int_o: $tType ).
thf(fun_nat_fun_real_o_type,type,
fun_nat_fun_real_o: $tType ).
thf(fun_list_complex_o_type,type,
fun_list_complex_o: $tType ).
thf(fun_int_fun_real_o_type,type,
fun_int_fun_real_o: $tType ).
thf(fun_int_VEBT_VEBT_type,type,
fun_int_VEBT_VEBT: $tType ).
thf(fun_set_nat_nat_type,type,
fun_set_nat_nat: $tType ).
thf(fun_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_set_int_type,type,
fun_nat_set_int: $tType ).
thf(fun_nat_Code_integer_type,type,
fun_nat_Code_integer: $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_nat_rat_o_type,type,
fun_fun_nat_rat_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(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(fun_real_complex_type,type,
fun_real_complex: $tType ).
thf(fun_complex_real_type,type,
fun_complex_real: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(set_list_int_type,type,
set_list_int: $tType ).
thf(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(list_Code_integer_type,type,
list_Code_integer: $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(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(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(filter_nat_type,type,
filter_nat: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $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(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_a_decl,type,
aTP_Lamm_a: set_VEBT_VEBT > fun_VEBT_VEBT_o ).
thf(aTP_Lamm_aao_decl,type,
aTP_Lamm_aao: nat > fun_na8563630686737515764_nat_o ).
thf(aTP_Lamm_aba_decl,type,
aTP_Lamm_aba: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_abd_decl,type,
aTP_Lamm_abd: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_abz_decl,type,
aTP_Lamm_abz: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_acy_decl,type,
aTP_Lamm_acy: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_acz_decl,type,
aTP_Lamm_acz: fun_nat_nat ).
thf(aTP_Lamm_adf_decl,type,
aTP_Lamm_adf: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_cg_decl,type,
aTP_Lamm_cg: fun_nat_nat ).
thf(aTP_Lamm_eo_decl,type,
aTP_Lamm_eo: set_VEBT_VEBT > fun_VEBT_VEBT_o ).
thf(aTP_Lamm_fd_decl,type,
aTP_Lamm_fd: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_kn_decl,type,
aTP_Lamm_kn: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_lv_decl,type,
aTP_Lamm_lv: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mg_decl,type,
aTP_Lamm_mg: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_na_decl,type,
aTP_Lamm_na: fun_nat_nat ).
thf(aTP_Lamm_ng_decl,type,
aTP_Lamm_ng: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_os_decl,type,
aTP_Lamm_os: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_qw_decl,type,
aTP_Lamm_qw: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_sv_decl,type,
aTP_Lamm_sv: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_sz_decl,type,
aTP_Lamm_sz: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_th_decl,type,
aTP_Lamm_th: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ui_decl,type,
aTP_Lamm_ui: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_uq_decl,type,
aTP_Lamm_uq: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xw_decl,type,
aTP_Lamm_xw: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xx_decl,type,
aTP_Lamm_xx: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xy_decl,type,
aTP_Lamm_xy: nat > fun_nat_fun_nat_nat ).
thf(binomial_decl,type,
binomial: fun_nat_fun_nat_nat ).
thf(gbinomial_nat_decl,type,
gbinomial_nat: fun_nat_fun_nat_nat ).
thf(bit_se2925701944663578781it_nat_decl,type,
bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).
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(finite_card_set_nat_decl,type,
finite_card_set_nat: set_set_nat > nat ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: fun_nat_fun_nat_nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(times_times_nat_decl,type,
times_times_nat: fun_nat_fun_nat_nat ).
thf(uminus5710092332889474511et_nat_decl,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(drop_nat_decl,type,
drop_nat: nat > list_nat > list_nat ).
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(map_nat_nat_decl,type,
map_nat_nat: fun_nat_nat > list_nat > list_nat ).
thf(set_VEBT_VEBT2_decl,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(tl_nat_decl,type,
tl_nat: list_nat > list_nat ).
thf(list_u1324408373059187874T_VEBT_decl,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(nth_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(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(upt_decl,type,
upt: nat > nat > list_nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(compow_fun_nat_nat_decl,type,
compow_fun_nat_nat: nat > fun_nat_nat > fun_nat_nat ).
thf(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(nat_triangle_decl,type,
nat_triangle: fun_nat_nat ).
thf(bot_bo1642239108664514429BT_nat_decl,type,
bot_bo1642239108664514429BT_nat: set_Pr7556676689462069481BT_nat ).
thf(bot_bo4779999733149731012_nat_o_decl,type,
bot_bo4779999733149731012_nat_o: fun_VE6480751511521678896_nat_o ).
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 > fun_set_VEBT_VEBT_o ).
thf(ord_max_nat_decl,type,
ord_max_nat: fun_nat_fun_nat_nat ).
thf(power_power_nat_decl,type,
power_power_nat: fun_nat_fun_nat_nat ).
thf(produc738532404422230701BT_nat_decl,type,
produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
thf(produc537772716801021591T_VEBT_decl,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
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(collect_nat_decl,type,
collect_nat: fun_nat_o > set_nat ).
thf(collect_set_nat_decl,type,
collect_set_nat: fun_set_nat_o > set_set_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_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: fun_VE6480751511521678896_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_membermima_decl,type,
vEBT_VEBT_membermima: fun_VE6480751511521678896_nat_o ).
thf(vEBT_V5719532721284313246member_decl,type,
vEBT_V5719532721284313246member: fun_VE6480751511521678896_nat_o ).
thf(vEBT_VEBT_valid_decl,type,
vEBT_VEBT_valid: fun_VE6480751511521678896_nat_o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: fun_VE6480751511521678896_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_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: fun_VE6480751511521678896_nat_o ).
thf(aa_nat_o_decl,type,
aa_nat_o: fun_nat_o > nat > $o ).
thf(aa_nat_nat_decl,type,
aa_nat_nat: fun_nat_nat > nat > nat ).
thf(aa_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_nat_fun_set_nat_o_decl,type,
aa_nat_fun_set_nat_o: fun_na8563630686737515764_nat_o > nat > fun_set_nat_o ).
thf(aa_set_VEBT_VEBT_o_decl,type,
aa_set_VEBT_VEBT_o: fun_set_VEBT_VEBT_o > set_VEBT_VEBT > $o ).
thf(aa_VEBT_VEBT_o_decl,type,
aa_VEBT_VEBT_o: fun_VEBT_VEBT_o > vEBT_VEBT > $o ).
thf(aa_VEB2314620471664397097_nat_o_decl,type,
aa_VEB2314620471664397097_nat_o: fun_VE6480751511521678896_nat_o > vEBT_VEBT > fun_nat_o ).
thf(member373505688050248522BT_nat_decl,type,
member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
thf(member_VEBT_VEBT_decl,type,
member_VEBT_VEBT: vEBT_VEBT > fun_set_VEBT_VEBT_o ).
thf(deg_decl,type,
deg: nat ).
thf(m_decl,type,
m: nat ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(na_decl,type,
na: nat ).
thf(summary_decl,type,
summary: vEBT_VEBT ).
thf(treeList_decl,type,
treeList: list_VEBT_VEBT ).
thf(426,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/sandbox2/benchmark/theBenchmark.p',fact_245_add__mono__thms__linordered__field_I4_J) ).
thf(3021,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)],[426]) ).
thf(608,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__not__refl3) ).
thf(3873,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)],[608]) ).
thf(611,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/sandbox2/benchmark/theBenchmark.p',fact_1621_pinf_I4_J) ).
thf(3883,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)],[611]) ).
thf(951,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_adf @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9543_Least__Suc) ).
thf(5593,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_adf @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(847,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6741_of__nat__eq__0__iff) ).
thf(5136,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)],[847]) ).
thf(644,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/sandbox2/benchmark/theBenchmark.p',fact_681_ord__less__eq__trans) ).
thf(4062,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)],[644]) ).
thf(1028,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/sandbox2/benchmark/theBenchmark.p',fact_6762_of__nat__mult) ).
thf(5950,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)],[1028]) ).
thf(888,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3319_mod__add__cong) ).
thf(5320,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(629,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/sandbox2/benchmark/theBenchmark.p',fact_4912_diff__less) ).
thf(3979,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)],[629]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',fact_588_Orderings_Oorder__eq__iff) ).
thf(1982,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)],[184]) ).
thf(1046,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/sandbox2/benchmark/theBenchmark.p',fact_4208_diff__Suc__Suc) ).
thf(6042,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)],[1046]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_3921_nat__mult__dvd__cancel1) ).
thf(1879,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)],[164]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',fact_133_Nat_Oex__has__greatest__nat) ).
thf(1337,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)],[47]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',fact_4705_eq__diff__iff) ).
thf(1718,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)],[130]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',fact_233_add__less__le__mono) ).
thf(2094,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)],[211]) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_1850_power__strict__mono) ).
thf(1411,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)],[64]) ).
thf(1077,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/sandbox2/benchmark/theBenchmark.p',fact_111_group__cancel_Oadd2) ).
thf(6167,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)],[1077]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_4739_zero__less__eq__of__bool) ).
thf(1469,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)],[79]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',fact_2417_split__mult__neg__le) ).
thf(1369,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)],[53]) ).
thf(18,axiom,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3486_dvd__0__right) ).
thf(1190,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)],[18]) ).
thf(905,axiom,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C0_C) ).
thf(5390,plain,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(1112,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/sandbox2/benchmark/theBenchmark.p',fact_72_add__left__imp__eq) ).
thf(6285,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)],[1112]) ).
thf(508,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/sandbox2/benchmark/theBenchmark.p',fact_2985_less__SucE) ).
thf(3397,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)],[508]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',fact_3497_dvd__1__iff__1) ).
thf(2559,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)],[314]) ).
thf(1065,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3289_mod__mult__self4) ).
thf(6121,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1078,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ui @ 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/sandbox2/benchmark/theBenchmark.p',fact_9895_ATP_Olambda__332) ).
thf(6172,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ui @ 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)],[1078]) ).
thf(1106,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_both__member__options__equiv__member) ).
thf(6263,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(767,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/sandbox2/benchmark/theBenchmark.p',fact_6888_of__nat__less__0__iff) ).
thf(4728,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)],[767]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_6838_of__nat__le__of__nat__power__cancel__iff) ).
thf(1818,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)],[150]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_3890_dvd__div__iff__mult) ).
thf(1295,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)],[39]) ).
thf(640,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/sandbox2/benchmark/theBenchmark.p',fact_9495_upt__eq__Cons__conv) ).
thf(4037,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)],[640]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A = B )
| ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4051_gcd__nat_Oorder__iff__strict) ).
thf(1924,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( ( A != B )
& ( 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 ) ) )
& ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
| ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_order__eq__refl) ).
thf(2104,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)],[214]) ).
thf(981,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/sandbox2/benchmark/theBenchmark.p',fact_2280_no__zero__divisors) ).
thf(5718,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)],[981]) ).
thf(1075,axiom,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6731_of__nat__0) ).
thf(6162,plain,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',fact_4353_diff__is__0__eq) ).
thf(2495,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)],[302]) ).
thf(1013,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/sandbox2/benchmark/theBenchmark.p',fact_2306_distrib__right) ).
thf(5878,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)],[1013]) ).
thf(424,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3832_dvd__div__unit__iff) ).
thf(3012,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 @ ( 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)],[424]) ).
thf(867,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/sandbox2/benchmark/theBenchmark.p',fact_5129_add__eq__if) ).
thf(5224,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)],[867]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',fact_573_dual__order_Oantisym) ).
thf(1142,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)],[5]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',fact_8119_binomial__symmetric) ).
thf(2380,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)],[275]) ).
thf(895,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3395_mod__mult2__eq) ).
thf(5348,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(930,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2969_not0__implies__Suc) ).
thf(5501,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(921,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_set__vebt__set__vebt_H__valid) ).
thf(5454,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(464,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_dual__order_Orefl) ).
thf(3185,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)],[464]) ).
thf(1017,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4103_diff__zero) ).
thf(5898,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)],[1017]) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',fact_2496_mult__pos__neg2) ).
thf(3317,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)],[490]) ).
thf(726,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/sandbox2/benchmark/theBenchmark.p',fact_126_infinite__descent) ).
thf(4500,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)],[726]) ).
thf(92,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2570_linordered__nonzero__semiring__class_Ozero__le__one) ).
thf(1522,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)],[92]) ).
thf(730,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/sandbox2/benchmark/theBenchmark.p',fact_3171_max_Ostrict__coboundedI1) ).
thf(4515,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)],[730]) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',fact_3359_unique__euclidean__semiring__numeral__class_Omod__less) ).
thf(2395,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)],[279]) ).
thf(1005,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/sandbox2/benchmark/theBenchmark.p',fact_5132_mult__eq__if) ).
thf(5842,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)],[1005]) ).
thf(547,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/sandbox2/benchmark/theBenchmark.p',fact_3075_one__less__mult) ).
thf(3549,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)],[547]) ).
thf(74,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( plus_plus_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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3748_dvd__add__left__iff) ).
thf(1443,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 ) )
=> ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( C @ ( plus_plus_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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',fact_8753_fact__ge__Suc__0__nat) ).
thf(1808,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)],[147]) ).
thf(1087,axiom,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3777_set__vebt__def) ).
thf(6199,plain,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(706,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/sandbox2/benchmark/theBenchmark.p',fact_2935_zero__less__Suc) ).
thf(4391,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)],[706]) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',fact_1037_order__less__le__trans) ).
thf(2947,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)],[410]) ).
thf(625,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/sandbox2/benchmark/theBenchmark.p',fact_431_infinite__descent0) ).
thf(3959,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)],[625]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',fact_4211_diff__diff__cancel) ).
thf(1793,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)],[144]) ).
thf(510,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_less__not__refl) ).
thf(3402,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(751,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2336_zero__neq__one) ).
thf(4623,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(711,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_dual__order_Oirrefl) ).
thf(4408,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3810_mult__unit__dvd__iff_H) ).
thf(1655,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( 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 @ ( 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)],[120]) ).
thf(769,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/sandbox2/benchmark/theBenchmark.p',fact_3176_max_Ostrict__coboundedI2) ).
thf(4739,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)],[769]) ).
thf(572,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/sandbox2/benchmark/theBenchmark.p',fact_6901_less__imp__of__nat__less) ).
thf(3648,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)],[572]) ).
thf(651,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/sandbox2/benchmark/theBenchmark.p',fact_488_add__pos__pos) ).
thf(4110,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)],[651]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',fact_1025_order__neq__le__trans) ).
thf(1999,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)],[186]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',fact_3919_dvd__imp__le) ).
thf(2933,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)],[405]) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',fact_955_dual__order_Ostrict__iff__order) ).
thf(2141,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)],[223]) ).
thf(288,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/sandbox2/benchmark/theBenchmark.p',fact_3007_transitive__stepwise__le) ).
thf(2434,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)],[288]) ).
thf(600,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 @ aa_set_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_nth__mem) ).
thf(3826,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 @ aa_set_VEBT_VEBT_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(678,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/sandbox2/benchmark/theBenchmark.p',fact_1636_minf_I1_J) ).
thf(4247,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)],[678]) ).
thf(554,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/sandbox2/benchmark/theBenchmark.p',fact_5127_div__if) ).
thf(3577,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)],[554]) ).
thf(843,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/sandbox2/benchmark/theBenchmark.p',fact_2975_nat__induct) ).
thf(5120,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)],[843]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_3791_minf_I9_J) ).
thf(1426,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_1088_order__le__imp__less__or__eq) ).
thf(1608,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)],[111]) ).
thf(754,axiom,
! [A: nat] :
( ( one_one_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6772_of__nat__1__eq__iff) ).
thf(4633,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)],[754]) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',fact_3006_nat__induct__at__least) ).
thf(2607,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)],[323]) ).
thf(342,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3536_unit__div) ).
thf(2686,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( A @ ( divide_divide_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)],[342]) ).
thf(745,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1488_max__0R) ).
thf(4575,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)],[745]) ).
thf(1019,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/sandbox2/benchmark/theBenchmark.p',fact_9477_length__upt) ).
thf(5906,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)],[1019]) ).
thf(621,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_less__nat__zero__code) ).
thf(3942,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)],[621]) ).
thf(636,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/sandbox2/benchmark/theBenchmark.p',fact_683_less__induct) ).
thf(4011,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)],[636]) ).
thf(1130,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/sandbox2/benchmark/theBenchmark.p',fact_11_bit__split__inv) ).
thf(6359,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)],[1130]) ).
thf(402,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/sandbox2/benchmark/theBenchmark.p',fact_939_order_Ostrict__iff__not) ).
thf(2918,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)],[402]) ).
thf(978,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/sandbox2/benchmark/theBenchmark.p',fact_2937_one__eq__mult__iff) ).
thf(5701,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)],[978]) ).
thf(564,axiom,
~ ( one_one_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2340_less__numeral__extra_I4_J) ).
thf(3616,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)],[564]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_228_le__add2) ).
thf(1233,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)],[29]) ).
thf(580,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/sandbox2/benchmark/theBenchmark.p',fact_2163_power__strict__decreasing__iff) ).
thf(3693,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)],[580]) ).
thf(1056,axiom,
! [A: nat] :
( ( A @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3264_mod__self) ).
thf(6078,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)],[1056]) ).
thf(1100,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/sandbox2/benchmark/theBenchmark.p',fact_4534_diff__commute) ).
thf(6241,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)],[1100]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',fact_2871_div__le__dividend) ).
thf(3121,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)],[445]) ).
thf(528,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/sandbox2/benchmark/theBenchmark.p',fact_7068_pochhammer__pos) ).
thf(3481,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)],[528]) ).
thf(992,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3343_div__add1__eq) ).
thf(5782,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(1126,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/sandbox2/benchmark/theBenchmark.p',fact_52_add__left__cancel) ).
thf(6336,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)],[1126]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',fact_4774_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(1954,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)],[179]) ).
thf(963,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3379_cancel__div__mod__rules_I1_J) ).
thf(5636,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(88,axiom,
! [A: nat,B: nat] :
? [C: nat,D: nat,E: nat] :
( ( ( ( E @ ( 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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
| ( ( E @ ( 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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) )
& ( 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/sandbox2/benchmark/theBenchmark.p',fact_4929_bezout1__nat) ).
thf(1507,plain,
! [A: nat,B: nat] :
? [C: nat,D: nat,E: nat] :
( ( ( ( E @ ( 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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
| ( ( E @ ( 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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) )
& ( 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)],[88]) ).
thf(858,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8120_choose__mult__lemma) ).
thf(5192,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',fact_2998_Suc__leD) ).
thf(2763,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)],[364]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',fact_5081_less__diff__conv2) ).
thf(2227,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)],[244]) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',fact_3544_dvd__imp__mod__0) ).
thf(2010,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)],[188]) ).
thf(207,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5704_take__bit__add) ).
thf(2082,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',fact_1031_order__le__less__trans) ).
thf(3140,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)],[452]) ).
thf(1012,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_neq__if__length__neq) ).
thf(5874,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)],[1012]) ).
thf(773,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/sandbox2/benchmark/theBenchmark.p',fact_430_gr__implies__not0) ).
thf(4760,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)],[773]) ).
thf(750,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/sandbox2/benchmark/theBenchmark.p',fact_4758_split__of__bool__asm) ).
thf(4610,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)],[750]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',fact_9492_upt__conv__Cons) ).
thf(2405,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)],[282]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_172_add__mono__thms__linordered__semiring_I3_J) ).
thf(1887,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)],[166]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',fact_3463_nat__dvd__1__iff__1) ).
thf(1196,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)],[20]) ).
thf(1070,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3394_div__mod__decomp) ).
thf(6138,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_1661_minf_I7_J) ).
thf(3836,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(568,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/sandbox2/benchmark/theBenchmark.p',fact_2593_mult__less__mono1) ).
thf(3629,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)],[568]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_1651_minf_I4_J) ).
thf(3350,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(868,axiom,
! [A: nat] :
( ( zero_zero_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6736_of__nat__0__eq__iff) ).
thf(5227,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)],[868]) ).
thf(570,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/sandbox2/benchmark/theBenchmark.p',fact_215_add__less__mono1) ).
thf(3634,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)],[570]) ).
thf(874,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/sandbox2/benchmark/theBenchmark.p',fact_1959_mult__cancel2) ).
thf(5252,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)],[874]) ).
thf(1103,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_uq @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9909_ATP_Olambda__346) ).
thf(6251,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_uq @ 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)],[1103]) ).
thf(634,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/sandbox2/benchmark/theBenchmark.p',fact_27_add__less__cancel__left) ).
thf(3994,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)],[634]) ).
thf(172,axiom,
! [A: nat,B: nat] :
? [C: nat,D: nat,E: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_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/sandbox2/benchmark/theBenchmark.p',fact_3864_bezout__add__nat) ).
thf(1914,plain,
! [A: nat,B: nat] :
? [C: nat,D: nat,E: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_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)],[172]) ).
thf(699,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/sandbox2/benchmark/theBenchmark.p',fact_1626_pinf_I5_J) ).
thf(4371,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)],[699]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',fact_2658_mult__right__le__imp__le) ).
thf(1441,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)],[73]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',fact_1399_minf_I6_J) ).
thf(2020,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)],[190]) ).
thf(540,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/sandbox2/benchmark/theBenchmark.p',fact_835_nth__list__update) ).
thf(3513,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)],[540]) ).
thf(859,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7106_pochhammer__rec_H) ).
thf(5195,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1001,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6715_of__nat__eq__iff) ).
thf(5825,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',fact_2344_mult__le__mono) ).
thf(1921,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)],[173]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',fact_5134_mod__nat__eqI) ).
thf(2173,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)],[231]) ).
thf(1119,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/sandbox2/benchmark/theBenchmark.p',fact_115_group__cancel_Oadd1) ).
thf(6306,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)],[1119]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',fact_3763_gcd__nat_Onot__eq__extremum) ).
thf(2819,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)],[379]) ).
thf(877,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/sandbox2/benchmark/theBenchmark.p',fact_315_add__is__0) ).
thf(5269,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)],[877]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_3858_dvd__pos__nat) ).
thf(1623,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)],[115]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',fact_1825_power__eq__imp__eq__base) ).
thf(1482,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)],[83]) ).
thf(776,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
<=> ? [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/sandbox2/benchmark/theBenchmark.p',fact_509_in__set__conv__nth) ).
thf(4775,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 @ aa_set_VEBT_VEBT_o ) ) )
& ( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ? [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)],[776]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',fact_882_nless__le) ).
thf(2869,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)],[388]) ).
thf(938,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/sandbox2/benchmark/theBenchmark.p',fact_2940_mult__Suc__right) ).
thf(5553,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)],[938]) ).
thf(472,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/sandbox2/benchmark/theBenchmark.p',fact_4910_diff__less__Suc) ).
thf(3221,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)],[472]) ).
thf(916,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3321_mod__add__left__eq) ).
thf(5429,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(793,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/sandbox2/benchmark/theBenchmark.p',fact_2508_mult__neg__pos) ).
thf(4866,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)],[793]) ).
thf(741,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1926_bits__div__by__0) ).
thf(4563,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)],[741]) ).
thf(1045,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3291_mod__mult__self3) ).
thf(6039,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(1108,axiom,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__C3_C) ).
thf(6274,plain,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',fact_3131_max_Ocobounded2) ).
thf(2755,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)],[361]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_3336_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend) ).
thf(1871,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)],[161]) ).
thf(598,axiom,
! [A: $o] :
( ( ( A @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
<=> ~ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4224_of__bool__eq__0__iff) ).
thf(3816,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)],[598]) ).
thf(3817,plain,
( ( ~ $true
=> ( ( $true @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ) )
& ( ( ( $true @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
=> ~ $true ) ),
inference(instance,[status(thm)],[3816]) ).
thf(3818,plain,
( ( $true @ zero_n2687167440665602831ol_nat )
!= zero_zero_nat ),
inference(simp,[status(thm)],[3817]) ).
thf(3821,plain,
( ( $true @ zero_n2687167440665602831ol_nat )
!= zero_zero_nat ),
inference(lifteq,[status(thm)],[3818]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_3496_dvd__1__left) ).
thf(1826,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)],[152]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_3193_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq) ).
thf(1577,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)],[105]) ).
thf(1034,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/sandbox2/benchmark/theBenchmark.p',fact_54_list__update__overwrite) ).
thf(5989,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)],[1034]) ).
thf(675,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1703_div__0) ).
thf(4238,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)],[675]) ).
thf(1029,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/sandbox2/benchmark/theBenchmark.p',fact_1983_div__mult__mult1__if) ).
thf(5953,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)],[1029]) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',fact_226_add__leD2) ).
thf(2916,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)],[401]) ).
thf(732,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/sandbox2/benchmark/theBenchmark.p',fact_8758_fact__diff__Suc) ).
thf(4524,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)],[732]) ).
thf(620,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/sandbox2/benchmark/theBenchmark.p',fact_5175_power__minus__mult) ).
thf(3938,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)],[620]) ).
thf(429,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/sandbox2/benchmark/theBenchmark.p',fact_6904_of__nat__mono) ).
thf(3029,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)],[429]) ).
thf(646,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/sandbox2/benchmark/theBenchmark.p',fact_3346_mod__induct) ).
thf(4070,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)],[646]) ).
thf(662,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/sandbox2/benchmark/theBenchmark.p',fact_3272_mod__less) ).
thf(4151,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)],[662]) ).
thf(497,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/sandbox2/benchmark/theBenchmark.p',fact_3020_lift__Suc__mono__less__iff) ).
thf(3342,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)],[497]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_2561_nat__mult__le__cancel1) ).
thf(2269,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)],[253]) ).
thf(1128,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_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_in__children__def) ).
thf(6350,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_VEB2314620471664397097_nat_o ) @ 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_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_921_order_Ostrict__iff__order) ).
thf(2217,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)],[243]) ).
thf(596,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/sandbox2/benchmark/theBenchmark.p',fact_704_exists__least__iff) ).
thf(3803,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)],[596]) ).
thf(840,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/sandbox2/benchmark/theBenchmark.p',fact_3009_add__Suc) ).
thf(5108,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)],[840]) ).
thf(1090,axiom,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__min__Null__member) ).
thf(6208,plain,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',fact_568_dual__order_Oeq__iff) ).
thf(3043,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)],[433]) ).
thf(878,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_plus__nat_Oadd__0) ).
thf(5279,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)],[878]) ).
thf(923,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/sandbox2/benchmark/theBenchmark.p',fact_2910_even__odd__cases) ).
thf(5461,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)],[923]) ).
thf(346,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( 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 @ ( dvd_dvd_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/sandbox2/benchmark/theBenchmark.p',fact_3767_dvd__mod__iff) ).
thf(2703,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 ) )
=> ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( 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 @ ( dvd_dvd_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)],[346]) ).
thf(541,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/sandbox2/benchmark/theBenchmark.p',fact_3035_gr0__conv__Suc) ).
thf(3517,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)],[541]) ).
thf(695,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/sandbox2/benchmark/theBenchmark.p',fact_2990_All__less__Suc) ).
thf(4353,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)],[695]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_211_nat__less__le) ).
thf(2049,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)],[201]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_2354_times__div__less__eq__dividend) ).
thf(2373,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)],[272]) ).
thf(928,axiom,
! [A: fun_nat_o,B: fun_nat_o] :
( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
<=> ( C @ ( B @ aa_nat_o ) ) )
=> ( ( A @ collect_nat )
= ( B @ collect_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Collect__cong) ).
thf(5480,plain,
! [A: fun_nat_o,B: fun_nat_o] :
( ! [C: nat] :
( ( ( C @ ( B @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) ) )
=> ( ( A @ collect_nat )
= ( B @ collect_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(438,axiom,
! [A: nat] : ( zero_zero_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3766_gcd__nat_Oextremum) ).
thf(3084,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)],[438]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',fact_2767_power__le__one) ).
thf(2635,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)],[330]) ).
thf(738,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/sandbox2/benchmark/theBenchmark.p',fact_200_add__mono__thms__linordered__field_I2_J) ).
thf(4551,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)],[738]) ).
thf(780,axiom,
! [A: $o,B: $o,C: nat] :
~ ( C @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3327_VEBT__internal_Omembermima_Osimps_I1_J) ).
thf(4793,plain,
! [A: $o,B: $o,C: nat] :
~ ( C @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(830,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5072_minus__mod__eq__div__mult) ).
thf(5077,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(482,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/sandbox2/benchmark/theBenchmark.p',fact_1815_zero__power) ).
thf(3268,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)],[482]) ).
thf(772,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/sandbox2/benchmark/theBenchmark.p',fact_8131_choose__reduce__nat) ).
thf(4756,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)],[772]) ).
thf(986,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/sandbox2/benchmark/theBenchmark.p',fact_3046_one__is__add) ).
thf(5744,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)],[986]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',fact_495_ex__least__nat__le) ).
thf(1545,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)],[97]) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',fact_5131_nat__less__add__iff2) ).
thf(3463,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)],[524]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',fact_3115_max_OboundedE) ).
thf(1379,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)],[56]) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_168_add__mono__thms__linordered__semiring_I2_J) ).
thf(2169,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)],[230]) ).
thf(89,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_bot__nat__0_Oextremum) ).
thf(1514,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)],[89]) ).
thf(760,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/sandbox2/benchmark/theBenchmark.p',fact_3078_nat__induct__non__zero) ).
thf(4664,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)],[760]) ).
thf(366,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3705_dvd__mult) ).
thf(2767,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( times_times_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)],[366]) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',fact_4228_of__bool__less__iff) ).
thf(3734,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)],[587]) ).
thf(698,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1938_mult__1) ).
thf(4368,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)],[698]) ).
thf(806,axiom,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9179_triangle__0) ).
thf(4952,plain,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(1060,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_verit__sum__simplify) ).
thf(6098,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)],[1060]) ).
thf(983,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/sandbox2/benchmark/theBenchmark.p',fact_2974_diff__induct) ).
thf(5727,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)],[983]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',fact_3852_dvd__power__le) ).
thf(2794,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)],[372]) ).
thf(612,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/sandbox2/benchmark/theBenchmark.p',fact_2472_mult__strict__left__mono) ).
thf(3887,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)],[612]) ).
thf(507,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/sandbox2/benchmark/theBenchmark.p',fact_5128_div__geq) ).
thf(3393,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)],[507]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',fact_135_le__antisym) ).
thf(1373,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)],[54]) ).
thf(1069,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_comm__monoid__add__class_Oadd__0) ).
thf(6135,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)],[1069]) ).
thf(766,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/sandbox2/benchmark/theBenchmark.p',fact_212_less__add__eq__less) ).
thf(4724,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)],[766]) ).
thf(936,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/sandbox2/benchmark/theBenchmark.p',fact_301_add__cancel__right__right) ).
thf(5541,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)],[936]) ).
thf(852,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/sandbox2/benchmark/theBenchmark.p',fact_4604_left__diff__distrib_H) ).
thf(5156,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)],[852]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',fact_1690_power__mono__iff) ).
thf(1960,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)],[180]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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 ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3530_dvd__add__times__triv__left__iff) ).
thf(1183,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( 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 ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( 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 ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(782,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/sandbox2/benchmark/theBenchmark.p',fact_3931_is__unit__div__mult__cancel__right) ).
thf(4810,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)],[782]) ).
thf(1003,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/sandbox2/benchmark/theBenchmark.p',fact_3297_mod__by__Suc__0) ).
thf(5834,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)],[1003]) ).
thf(1057,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1907_mult__zero__right) ).
thf(6081,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)],[1057]) ).
thf(712,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/sandbox2/benchmark/theBenchmark.p',fact_410_zero__less__iff__neq__zero) ).
thf(4411,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)],[712]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',fact_208_less__or__eq__imp__le) ).
thf(2950,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)],[411]) ).
thf(667,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2231_nat__mult__1) ).
thf(4205,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)],[667]) ).
thf(1097,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/sandbox2/benchmark/theBenchmark.p',fact_48_add__right__cancel) ).
thf(6227,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)],[1097]) ).
thf(618,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/sandbox2/benchmark/theBenchmark.p',fact_204_add__mono__thms__linordered__field_I5_J) ).
thf(3934,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)],[618]) ).
thf(746,axiom,
! [A: $o,B: $o] :
( ( ( A @ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat ) )
<=> ( A
<=> B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4528_of__bool__eq__iff) ).
thf(4578,plain,
! [A: $o,B: $o] :
( ( ( ( B
=> A )
& ( A
=> B ) )
=> ( ( A @ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat ) ) )
& ( ( ( A @ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat ) )
=> ( ( B
=> A )
& ( A
=> B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(952,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ng @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10100_ATP_Olambda__537) ).
thf(5597,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ng @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(394,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/sandbox2/benchmark/theBenchmark.p',fact_7732_fold__atLeastAtMost__nat_Osimps) ).
thf(2893,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)],[394]) ).
thf(685,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_deg__not__0) ).
thf(4297,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_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)],[685]) ).
thf(892,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xx @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9630_ATP_Olambda__67) ).
thf(5333,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xx @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(458,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/sandbox2/benchmark/theBenchmark.p',fact_1293_verit__comp__simplify1_I3_J) ).
thf(3163,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)],[458]) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',fact_4282_le__add__diff__inverse) ).
thf(2650,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)],[334]) ).
thf(1009,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4098_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(5856,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)],[1009]) ).
thf(522,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_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_buildup__gives__valid) ).
thf(3453,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_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(293,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/sandbox2/benchmark/theBenchmark.p',fact_3025_lift__Suc__mono__le) ).
thf(2451,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)],[293]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3806_mult__unit__dvd__iff) ).
thf(1858,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( 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 @ ( 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)],[158]) ).
thf(1082,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/sandbox2/benchmark/theBenchmark.p',fact_9476_drop__upt) ).
thf(6187,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)],[1082]) ).
thf(1117,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_qw @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9795_ATP_Olambda__232) ).
thf(6300,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_qw @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(542,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/sandbox2/benchmark/theBenchmark.p',fact_2981_Nat_OlessE) ).
thf(3525,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)],[542]) ).
thf(159,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/sandbox2/benchmark/theBenchmark.p',fact_3197_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(1864,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)],[159]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',fact_3055_Suc__mult__le__cancel1) ).
thf(1828,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)],[153]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',fact_3390_nat__mod__eq__lemma) ).
thf(2925,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)],[403]) ).
thf(628,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/sandbox2/benchmark/theBenchmark.p',fact_3053_Suc__mult__less__cancel1) ).
thf(3973,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)],[628]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3691_dvdE) ).
thf(1383,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [C: nat] :
( B
!= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(250,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/sandbox2/benchmark/theBenchmark.p',fact_3764_gcd__nat_Oextremum__unique) ).
thf(2254,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)],[250]) ).
thf(123,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/sandbox2/benchmark/theBenchmark.p',fact_3045_le__imp__less__Suc) ).
thf(1677,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)],[123]) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',fact_206_less__mono__imp__le__mono) ).
thf(2540,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)],[311]) ).
thf(987,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_add__0) ).
thf(5761,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)],[987]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_2424_mult__right__mono) ).
thf(1581,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)],[106]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',fact_3940_dvd__power__iff) ).
thf(2777,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)],[368]) ).
thf(899,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ tl_nat )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9474_tl__upt) ).
thf(5360,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)],[899]) ).
thf(1024,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/sandbox2/benchmark/theBenchmark.p',fact_4717_diff__mult__distrib2) ).
thf(5929,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)],[1024]) ).
thf(764,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/sandbox2/benchmark/theBenchmark.p',fact_1792_power__not__zero) ).
thf(4718,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)],[764]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',fact_7082_pochhammer__nonneg) ).
thf(2367,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)],[270]) ).
thf(909,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/sandbox2/benchmark/theBenchmark.p',fact_4718_diff__mult__distrib) ).
thf(5401,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)],[909]) ).
thf(872,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3323_mod__add__right__eq) ).
thf(5246,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( plus_plus_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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3744_dvd__add__right__iff) ).
thf(1351,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 @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( plus_plus_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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',fact_4925_dvd__minus__self) ).
thf(2002,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)],[187]) ).
thf(247,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/sandbox2/benchmark/theBenchmark.p',fact_1409_pinf_I6_J) ).
thf(2242,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)],[247]) ).
thf(762,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/sandbox2/benchmark/theBenchmark.p',fact_2875_Euclidean__Division_Odiv__eq__0__iff) ).
thf(4701,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)],[762]) ).
thf(474,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/sandbox2/benchmark/theBenchmark.p',fact_218_add__less__mono) ).
thf(3226,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)],[474]) ).
thf(961,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/sandbox2/benchmark/theBenchmark.p',fact_2130_div__mult__self4) ).
thf(5629,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)],[961]) ).
thf(607,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/sandbox2/benchmark/theBenchmark.p',fact_9558_last__upt) ).
thf(3870,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)],[607]) ).
thf(999,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/sandbox2/benchmark/theBenchmark.p',fact_6807_of__nat__Suc) ).
thf(5819,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)],[999]) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',fact_1543_max__absorb1) ).
thf(2392,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)],[278]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',fact_148_le__iff__add) ).
thf(2718,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)],[349]) ).
thf(503,axiom,
( ( zero_zero_nat @ ( one_one_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2071_max__0__1_I2_J) ).
thf(3378,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)],[503]) ).
thf(944,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_member__valid__both__member__options) ).
thf(5572,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(414,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/sandbox2/benchmark/theBenchmark.p',fact_3038_Suc__le__eq) ).
thf(2964,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)],[414]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',fact_3951_power__dvd__imp__le) ).
thf(1796,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)],[145]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',fact_3039_dec__induct) ).
thf(3036,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)],[432]) ).
thf(696,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/sandbox2/benchmark/theBenchmark.p',fact_3050_less__add__Suc2) ).
thf(4364,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)],[696]) ).
thf(1095,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abd @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9714_ATP_Olambda__151) ).
thf(6221,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abd @ 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)],[1095]) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_3783_pinf_I9_J) ).
thf(1622,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(812,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/sandbox2/benchmark/theBenchmark.p',fact_2997_not__less__less__Suc__eq) ).
thf(4996,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)],[812]) ).
thf(883,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2302_combine__common__factor) ).
thf(5296,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(359,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/sandbox2/benchmark/theBenchmark.p',fact_617_linorder__linear) ).
thf(2750,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)],[359]) ).
thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_549_order__antisym) ).
thf(1405,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)],[62]) ).
thf(1091,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_kn @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10105_ATP_Olambda__542) ).
thf(6210,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_kn @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',fact_209_le__eq__less__or__eq) ).
thf(1696,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)],[127]) ).
thf(724,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/sandbox2/benchmark/theBenchmark.p',fact_3095_split__div_H) ).
thf(4483,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)],[724]) ).
thf(539,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7035_pochhammer__0) ).
thf(3510,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)],[539]) ).
thf(976,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_valid__tree__deg__neq__0) ).
thf(5695,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(1111,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/sandbox2/benchmark/theBenchmark.p',fact_2220_mult_Ocommute) ).
thf(6282,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)],[1111]) ).
thf(475,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/sandbox2/benchmark/theBenchmark.p',fact_2987_Ex__less__Suc) ).
thf(3229,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)],[475]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_4777_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(1206,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)],[22]) ).
thf(521,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/sandbox2/benchmark/theBenchmark.p',fact_3033_gr0__implies__Suc) ).
thf(3450,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)],[521]) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',fact_2500_mult__pos__pos) ).
thf(3301,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)],[486]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_2922_max_Oabsorb1) ).
thf(1153,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)],[7]) ).
thf(1011,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
<=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1521_Ball__set__replicate) ).
thf(5862,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(332,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/sandbox2/benchmark/theBenchmark.p',fact_4706_le__diff__iff) ).
thf(2641,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)],[332]) ).
thf(132,axiom,
! [A: nat,B: nat,C: 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 @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3818_div__mult__swap) ).
thf(1736,plain,
! [A: nat,B: nat,C: 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 @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(666,axiom,
! [A: $o,B: $o,C: nat] :
( ( C @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( C = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3356_VEBT__internal_Ovalid_H_Osimps_I1_J) ).
thf(4172,plain,
! [A: $o,B: $o,C: nat] :
( ( ( C = one_one_nat )
=> ( C @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(689,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_less__imp__neq) ).
thf(4323,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)],[689]) ).
thf(400,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( 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 ) )
<=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3830_div__unit__dvd__iff) ).
thf(2910,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( 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 ) )
=> ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(747,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/sandbox2/benchmark/theBenchmark.p',fact_3402_Suc__times__mod__eq) ).
thf(4589,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)],[747]) ).
thf(299,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_eq__imp__le) ).
thf(2473,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)],[299]) ).
thf(1040,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2979_old_Onat_Odistinct_I2_J) ).
thf(6015,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(584,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1262_subset__iff) ).
thf(3720,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) )
& ( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',fact_1394_minf_I8_J) ).
thf(3169,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)],[459]) ).
thf(1116,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/sandbox2/benchmark/theBenchmark.p',fact_119_add__mono__thms__linordered__semiring_I4_J) ).
thf(6296,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)],[1116]) ).
thf(723,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1933_mult_Oright__neutral) ).
thf(4480,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)],[723]) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',fact_3338_unique__euclidean__semiring__numeral__class_Opos__mod__bound) ).
thf(3265,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)],[481]) ).
thf(333,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( ( B != A )
& ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4041_gcd__nat_Oasym) ).
thf(2646,plain,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ~ ( ( B != A )
& ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(543,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2582_zero__less__one) ).
thf(3531,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)],[543]) ).
thf(920,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/sandbox2/benchmark/theBenchmark.p',fact_1892_mult__cancel__right) ).
thf(5443,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)],[920]) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',fact_227_add__leD1) ).
thf(2164,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)],[228]) ).
thf(1052,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/sandbox2/benchmark/theBenchmark.p',fact_4292_diff__add__zero) ).
thf(6064,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)],[1052]) ).
thf(1051,axiom,
! [A: set_VEBT_VEBT,B: vEBT_VEBT] :
( ( B @ ( A @ aTP_Lamm_a @ aa_VEBT_VEBT_o ) )
<=> ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9732_ATP_Olambda__169) ).
thf(6058,plain,
! [A: set_VEBT_VEBT,B: vEBT_VEBT] :
( ( ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( A @ aTP_Lamm_a @ aa_VEBT_VEBT_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_a @ aa_VEBT_VEBT_o ) )
=> ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4053_gcd__nat_Ostrict__implies__order) ).
thf(2118,plain,
! [A: nat,B: nat] :
( ( ( A != B )
& ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_2679_mult__right__less__imp__less) ).
thf(2047,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)],[200]) ).
thf(941,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/sandbox2/benchmark/theBenchmark.p',fact_3008_nat__arith_Osuc1) ).
thf(5562,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)],[941]) ).
thf(914,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/sandbox2/benchmark/theBenchmark.p',fact_2968_vebt__buildup_Ocases) ).
thf(5416,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)],[914]) ).
thf(647,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/sandbox2/benchmark/theBenchmark.p',fact_365_add__gr__0) ).
thf(4076,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)],[647]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',fact_3922_dvd__mult__cancel) ).
thf(2737,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)],[354]) ).
thf(643,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/sandbox2/benchmark/theBenchmark.p',fact_2784_power__less__imp__less__exp) ).
thf(4059,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)],[643]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',fact_2394_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(1868,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)],[160]) ).
thf(763,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/sandbox2/benchmark/theBenchmark.p',fact_2917_Suc__less__eq) ).
thf(4712,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)],[763]) ).
thf(322,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat,E: nat] :
( ( A
= ( E @ ( D @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( E @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3701_dvd__productE) ).
thf(2601,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [D: nat,E: nat] :
( ( A
= ( E @ ( D @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( C @ ( E @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(1102,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/sandbox2/benchmark/theBenchmark.p',fact_18_nth__list__update__neq) ).
thf(6247,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)],[1102]) ).
thf(91,axiom,
! [A: nat] :
~ ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3003_Suc__n__not__le__n) ).
thf(1519,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)],[91]) ).
thf(255,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/sandbox2/benchmark/theBenchmark.p',fact_4919_le__diff__conv) ).
thf(2277,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)],[255]) ).
thf(876,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/sandbox2/benchmark/theBenchmark.p',fact_4713_Nat_Odiff__cancel) ).
thf(5266,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)],[876]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_433_bot__nat__0_Oextremum__unique) ).
thf(1487,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)],[85]) ).
thf(562,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/sandbox2/benchmark/theBenchmark.p',fact_2900_max_Oabsorb3) ).
thf(3610,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)],[562]) ).
thf(901,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/sandbox2/benchmark/theBenchmark.p',fact_3011_Suc__mult__cancel1) ).
thf(5366,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)],[901]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',fact_4781_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(1387,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)],[58]) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',fact_3926_mod__greater__zero__iff__not__dvd) ).
thf(1900,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)],[170]) ).
thf(719,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/sandbox2/benchmark/theBenchmark.p',fact_219_add__lessD1) ).
thf(4466,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)],[719]) ).
thf(1066,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5358_list__decode_Ocases) ).
thf(6124,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',fact_1013_order__less__imp__le) ).
thf(2805,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)],[376]) ).
thf(1123,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_cg @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10316_ATP_Olambda__753) ).
thf(6328,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_cg @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(821,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/sandbox2/benchmark/theBenchmark.p',fact_2265_power__gt1__lemma) ).
thf(5044,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)],[821]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_4927_dvd__diffD1) ).
thf(1174,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)],[12]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_544_ord__le__eq__trans) ).
thf(1502,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)],[87]) ).
thf(1030,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/sandbox2/benchmark/theBenchmark.p',fact_2136_div__mult__self1) ).
thf(5956,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)],[1030]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',fact_229_le__add1) ).
thf(1824,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)],[151]) ).
thf(682,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/sandbox2/benchmark/theBenchmark.p',fact_274_not__gr__zero) ).
thf(4284,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)],[682]) ).
thf(1129,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/sandbox2/benchmark/theBenchmark.p',fact_3548_length__product) ).
thf(6356,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)],[1129]) ).
thf(838,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8117_binomial__n__0) ).
thf(5102,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)],[838]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',fact_3886_unity__coeff__ex) ).
thf(2986,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)],[418]) ).
thf(1080,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( bot_bo4779999733149731012_nat_o @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( bot_bo1642239108664514429BT_nat @ ( B @ ( A @ produc738532404422230701BT_nat ) @ member373505688050248522BT_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5138_bot__empty__eq2) ).
thf(6178,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( bot_bo1642239108664514429BT_nat @ ( B @ ( A @ produc738532404422230701BT_nat ) @ member373505688050248522BT_nat ) )
=> ( B @ ( A @ ( bot_bo4779999733149731012_nat_o @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bot_bo4779999733149731012_nat_o @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( bot_bo1642239108664514429BT_nat @ ( B @ ( A @ produc738532404422230701BT_nat ) @ member373505688050248522BT_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(285,axiom,
! [A: nat,B: nat,C: 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 ) )
= C )
<=> ( B
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3908_unit__eq__div1) ).
thf(2414,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( 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)],[285]) ).
thf(787,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/sandbox2/benchmark/theBenchmark.p',fact_496_less__imp__add__positive) ).
thf(4836,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)],[787]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',fact_2142_nat__mult__le__cancel__disj) ).
thf(2132,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)],[221]) ).
thf(393,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/sandbox2/benchmark/theBenchmark.p',fact_4772_diff__add) ).
thf(2890,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)],[393]) ).
thf(664,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/sandbox2/benchmark/theBenchmark.p',fact_5122_power__diff) ).
thf(4160,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)],[664]) ).
thf(759,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/sandbox2/benchmark/theBenchmark.p',fact_2261_power__less__power__Suc) ).
thf(4661,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)],[759]) ).
thf(966,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/sandbox2/benchmark/theBenchmark.p',fact_3010_add__Suc__shift) ).
thf(5655,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)],[966]) ).
thf(924,axiom,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1598_replicate__length__same) ).
thf(5465,plain,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',fact_3881_unit__dvdE) ).
thf(2477,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)],[300]) ).
thf(609,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/sandbox2/benchmark/theBenchmark.p',fact_697_dual__order_Oasym) ).
thf(3877,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)],[609]) ).
thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_39_add__le__cancel__right) ).
thf(2200,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)],[239]) ).
thf(967,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3301_Suc__mod__mult__self4) ).
thf(5658,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(242,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3808_dvd__mult__unit__iff_H) ).
thf(2211,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_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 @ ( 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 @ ( 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)],[242]) ).
thf(592,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/sandbox2/benchmark/theBenchmark.p',fact_2996_strict__inc__induct) ).
thf(3763,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)],[592]) ).
thf(891,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5076_minus__mult__div__eq__mod) ).
thf(5330,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(639,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/sandbox2/benchmark/theBenchmark.p',fact_1485_max__nat_Oneutr__eq__iff) ).
thf(4027,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)],[639]) ).
thf(335,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 ) )
=> ( ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3498_div__dvd__div) ).
thf(2653,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 @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(483,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/sandbox2/benchmark/theBenchmark.p',fact_5079_nat__diff__split) ).
thf(3271,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)],[483]) ).
thf(684,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/sandbox2/benchmark/theBenchmark.p',fact_833_order__less__imp__not__less) ).
thf(4295,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)],[684]) ).
thf(1118,axiom,
! [A: list_VEBT_VEBT,B: nat] :
( ( B @ ( A @ nth_VEBT_VEBT ) @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_list__update__id) ).
thf(6303,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)],[1118]) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',fact_2167_power__increasing__iff) ).
thf(3191,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)],[466]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_3799_dvd__div__eq__0__iff) ).
thf(1938,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)],[175]) ).
thf(681,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/sandbox2/benchmark/theBenchmark.p',fact_8135_binomial__addition__formula) ).
thf(4280,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)],[681]) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_5084_nat__le__add__iff1) ).
thf(1602,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)],[110]) ).
thf(565,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_order_Ostrict__implies__not__eq) ).
thf(3618,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)],[565]) ).
thf(811,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/sandbox2/benchmark/theBenchmark.p',fact_743_order__less__asym) ).
thf(4994,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)],[811]) ).
thf(535,axiom,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3059_plus__1__eq__Suc) ).
thf(3499,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(703,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/sandbox2/benchmark/theBenchmark.p',fact_671_order_Oasym) ).
thf(4385,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)],[703]) ).
thf(178,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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3752_dvd__add) ).
thf(1951,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 @ ( plus_plus_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)],[178]) ).
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/sandbox2/benchmark/theBenchmark.p',fact_4600_right__diff__distrib_H) ).
thf(5779,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(690,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/sandbox2/benchmark/theBenchmark.p',fact_427_not__gr0) ).
thf(4327,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)],[690]) ).
thf(819,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( aTP_Lamm_acz @ map_nat_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9505_map__decr__upt) ).
thf(5038,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( aTP_Lamm_acz @ map_nat_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',fact_4934_le__mod__geq) ).
thf(3144,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)],[454]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_435_le__0__eq) ).
thf(1159,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)],[9]) ).
thf(709,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/sandbox2/benchmark/theBenchmark.p',fact_2351_nat__mult__max__left) ).
thf(4402,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)],[709]) ).
thf(545,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/sandbox2/benchmark/theBenchmark.p',fact_2936_less__Suc0) ).
thf(3535,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)],[545]) ).
thf(803,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/sandbox2/benchmark/theBenchmark.p',fact_5689_take__bit__of__Suc__0) ).
thf(4942,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)],[803]) ).
thf(861,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/sandbox2/benchmark/theBenchmark.p',fact_437_add__eq__self__zero) ).
thf(5201,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)],[861]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',fact_460_add__decreasing2) ).
thf(1210,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)],[23]) ).
thf(942,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3377_mod__div__decomp) ).
thf(5566,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_3562_pow__divides__pow__iff) ).
thf(2327,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)],[264]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',fact_3151_max_OcoboundedI2) ).
thf(1634,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)],[117]) ).
thf(1026,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/sandbox2/benchmark/theBenchmark.p',fact_2243_nat__mult__eq__cancel__disj) ).
thf(5936,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)],[1026]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',fact_1538_max__absorb2) ).
thf(3033,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)],[431]) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',fact_3057_Suc__div__le__mono) ).
thf(1740,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)],[133]) ).
thf(274,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/sandbox2/benchmark/theBenchmark.p',fact_3001_Suc__le__D) ).
thf(2377,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)],[274]) ).
thf(729,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_not__less0) ).
thf(4512,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)],[729]) ).
thf(471,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2225_mult_Ocomm__neutral) ).
thf(3218,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)],[471]) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',fact_3859_nat__dvd__not__less) ).
thf(2692,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)],[344]) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',fact_156_add__left__mono) ).
thf(2726,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)],[350]) ).
thf(671,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/sandbox2/benchmark/theBenchmark.p',fact_2485_zero__less__mult__pos2) ).
thf(4227,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)],[671]) ).
thf(797,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/sandbox2/benchmark/theBenchmark.p',fact_446_list__eq__iff__nth__eq) ).
thf(4883,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)],[797]) ).
thf(573,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/sandbox2/benchmark/theBenchmark.p',fact_7155_pochhammer__product) ).
thf(3650,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)],[573]) ).
thf(614,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/sandbox2/benchmark/theBenchmark.p',fact_2644_less__eq__div__iff__mult__less__eq) ).
thf(3916,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)],[614]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_237_add__le__less__mono) ).
thf(1402,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)],[61]) ).
thf(586,axiom,
! [A: fun_nat_o] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( A @ ord_Least_nat )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9542_Least__eq__0) ).
thf(3731,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)],[586]) ).
thf(655,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/sandbox2/benchmark/theBenchmark.p',fact_3387_div__less__mono) ).
thf(4123,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)],[655]) ).
thf(886,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
!= ( B @ size_size_list_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_size__neq__size__imp__neq) ).
thf(5313,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)],[886]) ).
thf(1055,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9177_triangle__Suc) ).
thf(6075,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(857,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/sandbox2/benchmark/theBenchmark.p',fact_2941_power__Suc__0) ).
thf(5189,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)],[857]) ).
thf(960,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/sandbox2/benchmark/theBenchmark.p',fact_2939_div__by__Suc__0) ).
thf(5626,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)],[960]) ).
thf(581,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/sandbox2/benchmark/theBenchmark.p',fact_353_less__add__same__cancel1) ).
thf(3699,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)],[581]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_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 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3532_dvd__div__mult__self) ).
thf(2300,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_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 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(980,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/sandbox2/benchmark/theBenchmark.p',fact_5743_exists__least__lemma) ).
thf(5714,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)],[980]) ).
thf(808,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/sandbox2/benchmark/theBenchmark.p',fact_1611_pinf_I2_J) ).
thf(4957,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)],[808]) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',fact_857_add__pos__nonneg) ).
thf(2157,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)],[226]) ).
thf(956,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_cg @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9514_sort__upt) ).
thf(5609,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_cg @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(866,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/sandbox2/benchmark/theBenchmark.p',fact_2348_add__mult__distrib) ).
thf(5221,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)],[866]) ).
thf(479,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/sandbox2/benchmark/theBenchmark.p',fact_2462_mult__strict__right__mono) ).
thf(3254,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)],[479]) ).
thf(1061,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_sv @ 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/sandbox2/benchmark/theBenchmark.p',fact_9704_ATP_Olambda__141) ).
thf(6101,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_sv @ 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)],[1061]) ).
thf(958,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/sandbox2/benchmark/theBenchmark.p',fact_2270_mult__right__cancel) ).
thf(5615,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)],[958]) ).
thf(382,axiom,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4042_gcd__nat_Orefl) ).
thf(2841,plain,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(1085,axiom,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= summary ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_A_061_Asummary_092_060close_062) ).
thf(6195,plain,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= summary ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(1043,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/sandbox2/benchmark/theBenchmark.p',fact_3340_mod__eq__self__iff__div__eq__0) ).
thf(6028,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)],[1043]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_3838_mod__eq__0__iff__dvd) ).
thf(2359,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)],[269]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',fact_3040_inc__induct) ).
thf(2973,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)],[416]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',fact_3000_le__SucI) ).
thf(2709,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)],[347]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_221_trans__le__add2) ).
thf(1227,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)],[27]) ).
thf(1098,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/sandbox2/benchmark/theBenchmark.p',fact_3553_length__product) ).
thf(6235,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)],[1098]) ).
thf(789,axiom,
! [A: $o,B: $o] :
( ( ( B
& A )
@ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4556_of__bool__conj) ).
thf(4845,plain,
! [A: $o,B: $o] :
( ( ( B
& A )
@ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(569,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/sandbox2/benchmark/theBenchmark.p',fact_2489_zero__less__mult__pos) ).
thf(3632,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)],[569]) ).
thf(650,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/sandbox2/benchmark/theBenchmark.p',fact_1478_replicate__eq__replicate) ).
thf(4095,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)],[650]) ).
thf(998,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/sandbox2/benchmark/theBenchmark.p',fact_2275_mult__left__cancel) ).
thf(5811,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)],[998]) ).
thf(589,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/sandbox2/benchmark/theBenchmark.p',fact_3950_dvd__mult__cancel1) ).
thf(3746,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)],[589]) ).
thf(1067,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/sandbox2/benchmark/theBenchmark.p',fact_4161_add__diff__cancel__left_H) ).
thf(6128,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)],[1067]) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',fact_2447_mult__mono_H) ).
thf(2638,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)],[331]) ).
thf(1094,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/sandbox2/benchmark/theBenchmark.p',fact_2229_mult_Oleft__commute) ).
thf(6218,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)],[1094]) ).
thf(425,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/sandbox2/benchmark/theBenchmark.p',fact_2686_mult__strict__mono) ).
thf(3018,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)],[425]) ).
thf(798,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/sandbox2/benchmark/theBenchmark.p',fact_7087_pochhammer__0__left) ).
thf(4898,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)],[798]) ).
thf(731,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/sandbox2/benchmark/theBenchmark.p',fact_3943_dvd__power) ).
thf(4518,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)],[731]) ).
thf(615,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/sandbox2/benchmark/theBenchmark.p',fact_484_add__neg__neg) ).
thf(3922,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)],[615]) ).
thf(380,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/sandbox2/benchmark/theBenchmark.p',fact_3840_dvd__eq__mod__eq__0) ).
thf(2830,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)],[380]) ).
thf(69,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_le0) ).
thf(1424,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)],[69]) ).
thf(107,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/sandbox2/benchmark/theBenchmark.p',fact_3005_full__nat__induct) ).
thf(1584,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)],[107]) ).
thf(641,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/sandbox2/benchmark/theBenchmark.p',fact_2986_less__SucI) ).
thf(4049,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)],[641]) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',fact_927_order_Ostrict__trans1) ).
thf(1329,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)],[44]) ).
thf(593,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1270_subset__eq) ).
thf(3775,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) )
& ( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',fact_2562_div__less__iff__less__mult) ).
thf(3311,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)],[489]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',fact_3795_minf_I10_J) ).
thf(3143,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1079,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/sandbox2/benchmark/theBenchmark.p',fact_90_add_Oassoc) ).
thf(6175,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)],[1079]) ).
thf(809,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/sandbox2/benchmark/theBenchmark.p',fact_687_antisym__conv3) ).
thf(4983,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)],[809]) ).
thf(1022,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2294_crossproduct__noteq) ).
thf(5915,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( C != D )
& ( A != B ) ) )
& ( ( ( C != D )
& ( A != B ) )
=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(831,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_acy @ 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/sandbox2/benchmark/theBenchmark.p',fact_9504_map__add__upt) ).
thf(5080,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_acy @ 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)],[831]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( dvd_dvd_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/sandbox2/benchmark/theBenchmark.p',fact_4043_gcd__nat_Otrans) ).
thf(1292,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( dvd_dvd_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)],[38]) ).
thf(566,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/sandbox2/benchmark/theBenchmark.p',fact_2594_mult__less__mono2) ).
thf(3622,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)],[566]) ).
thf(1035,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_add_Ocomm__neutral) ).
thf(5992,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)],[1035]) ).
thf(995,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_zero__reorient) ).
thf(5791,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)],[995]) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',fact_2989_not__less__eq) ).
thf(3714,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)],[583]) ).
thf(1132,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/sandbox2/benchmark/theBenchmark.p',fact_68_add__right__imp__eq) ).
thf(6363,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)],[1132]) ).
thf(585,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/sandbox2/benchmark/theBenchmark.p',fact_2994_less__trans__Suc) ).
thf(3728,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)],[585]) ).
thf(705,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/sandbox2/benchmark/theBenchmark.p',fact_2982_Suc__lessD) ).
thf(4389,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)],[705]) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',fact_4349_zero__less__of__bool__iff) ).
thf(3596,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)],[558]) ).
thf(737,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/sandbox2/benchmark/theBenchmark.p',fact_4351_zero__less__diff) ).
thf(4545,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)],[737]) ).
thf(875,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4105_zero__diff) ).
thf(5263,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)],[875]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_641_linorder__le__cases) ).
thf(1414,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)],[65]) ).
thf(246,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3715_dvd__mult__left) ).
thf(2240,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1076,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_valid__member__both__member__options) ).
thf(6164,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(324,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/sandbox2/benchmark/theBenchmark.p',fact_3765_gcd__nat_Oextremum__strict) ).
thf(2613,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)],[324]) ).
thf(1025,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2976_old_Onat_Oexhaust) ).
thf(5932,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(148,axiom,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2566_not__one__le__zero) ).
thf(1810,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)],[148]) ).
thf(791,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2237_nat__mult__1__right) ).
thf(4861,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)],[791]) ).
thf(215,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3822_dvd__div__mult2__eq) ).
thf(2108,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( 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)],[215]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',fact_3848_power__le__dvd) ).
thf(2038,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)],[196]) ).
thf(577,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/sandbox2/benchmark/theBenchmark.p',fact_180_add__less__imp__less__left) ).
thf(3671,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)],[577]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3711_dvd__mult2) ).
thf(2085,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( times_times_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)],[208]) ).
thf(549,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/sandbox2/benchmark/theBenchmark.p',fact_1559_nat__add__max__left) ).
thf(3555,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)],[549]) ).
thf(783,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/sandbox2/benchmark/theBenchmark.p',fact_3049_less__add__Suc1) ).
thf(4814,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)],[783]) ).
thf(904,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/sandbox2/benchmark/theBenchmark.p',fact_2927_power__0__Suc) ).
thf(5387,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)],[904]) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',fact_1336_bounded__Max__nat) ).
thf(1744,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)],[135]) ).
thf(734,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_neq__if__length__neq) ).
thf(4530,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)],[734]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_4709_diff__le__self) ).
thf(1419,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)],[67]) ).
thf(476,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/sandbox2/benchmark/theBenchmark.p',fact_1631_pinf_I7_J) ).
thf(3242,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)],[476]) ).
thf(1027,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/sandbox2/benchmark/theBenchmark.p',fact_4365_diff__Suc__1) ).
thf(5947,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)],[1027]) ).
thf(902,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_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/sandbox2/benchmark/theBenchmark.p',fact_6946_mod__mult2__eq_H) ).
thf(5374,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri1316708129612266289at_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)],[902]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( B @ ( dvd_dvd_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/sandbox2/benchmark/theBenchmark.p',fact_4044_gcd__nat_Oeq__iff) ).
thf(1530,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( 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 ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( dvd_dvd_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)],[95]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',fact_1002_linorder__not__le) ).
thf(2465,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)],[297]) ).
thf(506,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/sandbox2/benchmark/theBenchmark.p',fact_692_linorder__cases) ).
thf(3390,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)],[506]) ).
thf(825,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/sandbox2/benchmark/theBenchmark.p',fact_2563_nat__mult__div__cancel1) ).
thf(5058,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)],[825]) ).
thf(654,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/sandbox2/benchmark/theBenchmark.p',fact_188_add__strict__left__mono) ).
thf(4120,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)],[654]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',fact_2451_mult__mono) ).
thf(1874,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)],[162]) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',fact_4352_diff__is__0__eq_H) ).
thf(1599,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)],[109]) ).
thf(954,axiom,
! [A: vEBT_VEBT] :
( ( A @ vEBT_VEBT_set_vebt )
= ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3462_set__vebt_H__def) ).
thf(5603,plain,
! [A: vEBT_VEBT] :
( ( A @ vEBT_VEBT_set_vebt )
= ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(887,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/sandbox2/benchmark/theBenchmark.p',fact_2314_comm__semiring__class_Odistrib) ).
thf(5317,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)],[887]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_3923_bezout__add__strong__nat) ).
thf(1263,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)],[34]) ).
thf(530,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2639_power__0) ).
thf(3486,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)],[530]) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',fact_973_dual__order_Ostrict__iff__not) ).
thf(2125,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)],[220]) ).
thf(574,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/sandbox2/benchmark/theBenchmark.p',fact_357_less__add__same__cancel2) ).
thf(3654,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)],[574]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',fact_366_list__update__beyond) ).
thf(1478,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)],[82]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: 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 ) )
=> ( ( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( E @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
=> ? [F: nat,G: nat] :
( ( ( ( F @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( G @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( F @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( G @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( C @ ( B @ ( plus_plus_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 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3863_bezout__lemma__nat) ).
thf(1249,plain,
! [A: nat,B: nat,C: nat,D: nat,E: 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 ) )
=> ( ( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( E @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
=> ? [F: nat,G: nat] :
( ( ( ( F @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( G @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( F @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( G @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( C @ ( B @ ( plus_plus_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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',fact_839_list__update__same__conv) ).
thf(3354,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)],[500]) ).
thf(1124,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/sandbox2/benchmark/theBenchmark.p',fact_76_add_Oleft__commute) ).
thf(6331,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)],[1124]) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',fact_3910_unit__imp__mod__eq__0) ).
thf(2153,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)],[225]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',fact_2846_power__le__imp__le__exp) ).
thf(2900,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)],[397]) ).
thf(964,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/sandbox2/benchmark/theBenchmark.p',fact_1111_add__0__iff) ).
thf(5639,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)],[964]) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',fact_2992_less__antisym) ).
thf(3743,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)],[588]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_4776_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(1192,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)],[19]) ).
thf(677,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/sandbox2/benchmark/theBenchmark.p',fact_3348_mod__less__divisor) ).
thf(4244,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)],[677]) ).
thf(591,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/sandbox2/benchmark/theBenchmark.p',fact_5690_take__bit__of__1) ).
thf(3760,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)],[591]) ).
thf(626,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/sandbox2/benchmark/theBenchmark.p',fact_192_add__strict__mono) ).
thf(3967,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)],[626]) ).
thf(512,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/sandbox2/benchmark/theBenchmark.p',fact_184_add__strict__right__mono) ).
thf(3409,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)],[512]) ).
thf(443,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/sandbox2/benchmark/theBenchmark.p',fact_583_antisym) ).
thf(3109,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)],[443]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_151_add__right__mono) ).
thf(1979,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)],[183]) ).
thf(222,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2574_zero__less__one__class_Ozero__le__one) ).
thf(2140,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)],[222]) ).
thf(1096,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/sandbox2/benchmark/theBenchmark.p',fact_80_add_Ocommute) ).
thf(6224,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)],[1096]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',fact_865_add__strict__increasing2) ).
thf(2370,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)],[271]) ).
thf(470,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/sandbox2/benchmark/theBenchmark.p',fact_217_not__add__less1) ).
thf(3215,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)],[470]) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',fact_1412_complete__interval) ).
thf(3147,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)],[455]) ).
thf(661,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/sandbox2/benchmark/theBenchmark.p',fact_2850_self__le__power) ).
thf(4148,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)],[661]) ).
thf(369,axiom,
! [A: nat] :
~ ( ( A != A )
& ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4045_gcd__nat_Oirrefl) ).
thf(2788,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(885,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/sandbox2/benchmark/theBenchmark.p',fact_3279_mod__mult__self2__is__0) ).
thf(5310,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)],[885]) ).
thf(4624,plain,
zero_zero_nat != one_one_nat,
inference(polarity_switch,[status(thm)],[4623]) ).
thf(4625,plain,
zero_zero_nat != one_one_nat,
inference(lifteq,[status(thm)],[4624]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_876_leI) ).
thf(2043,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)],[198]) ).
thf(461,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3898_is__unit__div__mult2__eq) ).
thf(3173,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( 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 ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( C @ ( 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)],[461]) ).
thf(358,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/sandbox2/benchmark/theBenchmark.p',fact_3067_power__le__imp__le__base) ).
thf(2748,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)],[358]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',fact_967_dual__order_Ostrict__trans2) ).
thf(2402,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)],[281]) ).
thf(289,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/sandbox2/benchmark/theBenchmark.p',fact_472_add__nonpos__nonpos) ).
thf(2440,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)],[289]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',fact_4711_diff__le__mono2) ).
thf(2408,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)],[283]) ).
thf(873,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/sandbox2/benchmark/theBenchmark.p',fact_3056_mult__Suc) ).
thf(5249,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)],[873]) ).
thf(744,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/sandbox2/benchmark/theBenchmark.p',fact_4410_Suc__pred) ).
thf(4572,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)],[744]) ).
thf(31,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3814_unit__mult__right__cancel) ).
thf(1241,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( 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)],[31]) ).
thf(979,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4209_diff__self__eq__0) ).
thf(5711,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)],[979]) ).
thf(1002,axiom,
m @ ( summary @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__C1_C) ).
thf(5833,plain,
m @ ( summary @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',fact_985_dual__order_Ostrict__implies__order) ).
thf(1563,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)],[101]) ).
thf(1054,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_list__ball__nth) ).
thf(6070,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(1110,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_th @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9807_ATP_Olambda__244) ).
thf(6279,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_th @ 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)],[1110]) ).
thf(1016,axiom,
! [A: vEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1515_in__set__replicate) ).
thf(5887,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 @ aa_set_VEBT_VEBT_o ) ) )
& ( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(168,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3824_dvd__mult__imp__div) ).
thf(1895,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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 @ ( C @ ( divide_divide_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)],[168]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4054_gcd__nat_Ostrict__implies__not__eq) ).
thf(1167,plain,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(932,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/sandbox2/benchmark/theBenchmark.p',fact_1956_mult__is__0) ).
thf(5513,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)],[932]) ).
thf(860,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/sandbox2/benchmark/theBenchmark.p',fact_4714_diff__cancel2) ).
thf(5198,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)],[860]) ).
thf(1020,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/sandbox2/benchmark/theBenchmark.p',fact_2919_add__Suc__right) ).
thf(5909,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)],[1020]) ).
thf(605,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/sandbox2/benchmark/theBenchmark.p',fact_1558_nat__add__max__right) ).
thf(3841,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)],[605]) ).
thf(1120,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_both__member__options__def) ).
thf(6311,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',fact_4780_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(2617,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)],[325]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',fact_6883_of__nat__0__le__iff) ).
thf(2423,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)],[286]) ).
thf(308,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5671_take__bit__of__0) ).
thf(2529,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)],[308]) ).
thf(575,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_not__less__zero) ).
thf(3660,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)],[575]) ).
thf(890,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/sandbox2/benchmark/theBenchmark.p',fact_2093_nat__mult__div__cancel__disj) ).
thf(5327,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)],[890]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',fact_2876_div__greater__zero__iff) ).
thf(2677,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)],[340]) ).
thf(795,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/sandbox2/benchmark/theBenchmark.p',fact_8115_binomial__eq__0__iff) ).
thf(4872,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)],[795]) ).
thf(997,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_valid__0__not) ).
thf(5808,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(613,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/sandbox2/benchmark/theBenchmark.p',fact_1641_minf_I2_J) ).
thf(3890,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)],[613]) ).
thf(532,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/sandbox2/benchmark/theBenchmark.p',fact_6924_of__nat__max) ).
thf(3491,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)],[532]) ).
thf(1058,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/sandbox2/benchmark/theBenchmark.p',fact_3277_mod__mult__self1__is__0) ).
thf(6084,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)],[1058]) ).
thf(631,axiom,
~ ( zero_zero_nat @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2578_not__one__less__zero) ).
thf(3985,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)],[631]) ).
thf(1031,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1594_replicate__eqI) ).
thf(5960,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 @ aa_set_VEBT_VEBT_o ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(836,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/sandbox2/benchmark/theBenchmark.p',fact_2008_nonzero__mult__div__cancel__right) ).
thf(5095,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)],[836]) ).
thf(1049,axiom,
! [A: nat] :
? [B: list_o] :
( ( B @ size_size_list_o )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_Ex__list__of__length) ).
thf(6052,plain,
! [A: nat] :
? [B: list_o] :
( ( B @ size_size_list_o )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(718,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/sandbox2/benchmark/theBenchmark.p',fact_3036_Ex__less__Suc2) ).
thf(4453,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)],[718]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_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 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3558_unit__div__mult__self) ).
thf(2121,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_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 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(1084,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/sandbox2/benchmark/theBenchmark.p',fact_2207_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(6192,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)],[1084]) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_335_le__add__same__cancel2) ).
thf(1278,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)],[36]) ).
thf(171,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 ) )
=> ( ( ( A @ ( B @ ( 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 = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3754_dvd__div__eq__iff) ).
thf(1906,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 ) )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( 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 = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',fact_4363_Nat_Oadd__diff__assoc2) ).
thf(1135,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)],[3]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',fact_861_add__strict__increasing) ).
thf(2729,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)],[351]) ).
thf(982,axiom,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3385_invar__vebt_Ointros_I1_J) ).
thf(5722,plain,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(933,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2970_Zero__not__Suc) ).
thf(5524,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( one_one_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3738_unit__imp__dvd) ).
thf(1754,plain,
! [A: nat,B: nat] :
( ( one_one_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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(701,axiom,
~ ( zero_zero_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_less__numeral__extra_I3_J) ).
thf(4380,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)],[701]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',fact_142_add__le__imp__le__right) ).
thf(2275,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)],[254]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_2999_le__SucE) ).
thf(2033,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)],[194]) ).
thf(1032,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/sandbox2/benchmark/theBenchmark.p',fact_3047_add__is__1) ).
thf(5969,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)],[1032]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',fact_2067_power__inject__exp) ).
thf(3257,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)],[480]) ).
thf(561,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/sandbox2/benchmark/theBenchmark.p',fact_2646_dividend__less__div__times) ).
thf(3607,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)],[561]) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',fact_2251_mult__le__one) ).
thf(2570,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)],[316]) ).
thf(716,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_subset__code_I1_J) ).
thf(4438,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) )
& ( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(707,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/sandbox2/benchmark/theBenchmark.p',fact_753_order__less__asym_H) ).
thf(4393,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)],[707]) ).
thf(1038,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/sandbox2/benchmark/theBenchmark.p',fact_1897_mult__cancel__left) ).
thf(6001,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)],[1038]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',fact_247_mono__nat__linear__lb) ).
thf(2028,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)],[193]) ).
thf(502,axiom,
! [A: nat,B: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ size_s6755466524823107622T_VEBT )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1479_length__replicate) ).
thf(3375,plain,
! [A: nat,B: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ size_s6755466524823107622T_VEBT )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(965,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2913_nat_Oinject) ).
thf(5647,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)],[965]) ).
thf(637,axiom,
! [A: $o] :
( ( ( A @ zero_n2687167440665602831ol_nat )
= one_one_nat )
<=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4233_of__bool__eq__1__iff) ).
thf(4017,plain,
! [A: $o] :
( ( A
=> ( ( A @ zero_n2687167440665602831ol_nat )
= one_one_nat ) )
& ( ( ( A @ zero_n2687167440665602831ol_nat )
= one_one_nat )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(977,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/sandbox2/benchmark/theBenchmark.p',fact_3285_bits__mod__div__trivial) ).
thf(5698,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)],[977]) ).
thf(415,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/sandbox2/benchmark/theBenchmark.p',fact_4708_diff__le__mono) ).
thf(2970,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)],[415]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',fact_979_order_Ostrict__implies__order) ).
thf(2789,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)],[370]) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',fact_5087_nat__diff__add__eq2) ).
thf(2525,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)],[307]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3902_unit__div__commute) ).
thf(2188,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(526,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/sandbox2/benchmark/theBenchmark.p',fact_349_add__less__same__cancel2) ).
thf(3472,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)],[526]) ).
thf(622,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_size__neq__size__imp__neq) ).
thf(3945,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)],[622]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',fact_5083_nat__eq__add__iff2) ).
thf(2514,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)],[305]) ).
thf(957,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3371_mod__mult__div__eq) ).
thf(5612,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(837,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3260_mod__0) ).
thf(5099,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)],[837]) ).
thf(1127,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_adf @ aa_nat_o ) )
<=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9748_ATP_Olambda__185) ).
thf(6344,plain,
! [A: fun_nat_o,B: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_adf @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_adf @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(560,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/sandbox2/benchmark/theBenchmark.p',fact_125_linorder__neqE__nat) ).
thf(3604,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)],[560]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',fact_2143_mult__le__cancel2) ).
thf(2695,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)],[345]) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',fact_3166_max_Ostrict__order__iff) ).
thf(4000,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)],[635]) ).
thf(465,axiom,
! [A: nat,B: nat,C: 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3816_dvd__div__mult) ).
thf(3187,plain,
! [A: nat,B: nat,C: 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(616,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/sandbox2/benchmark/theBenchmark.p',fact_4703_diff__less__mono2) ).
thf(3925,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)],[616]) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',fact_5706_take__bit__tightened) ).
thf(2938,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)],[407]) ).
thf(926,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/sandbox2/benchmark/theBenchmark.p',fact_3552_length__product) ).
thf(5474,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)],[926]) ).
thf(537,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1953_div__by__1) ).
thf(3504,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(907,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/sandbox2/benchmark/theBenchmark.p',fact_2931_power__Suc0__right) ).
thf(5395,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)],[907]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',fact_2634_one__le__power) ).
thf(2791,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)],[371]) ).
thf(439,axiom,
! [A: nat,B: nat,C: nat] :
( ( 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 ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3526_dvd__add__times__triv__right__iff) ).
thf(3086,plain,
! [A: nat,B: nat,C: 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 @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 @ ( plus_plus_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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',fact_8698_fact__ge__self) ).
thf(1752,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)],[136]) ).
thf(1041,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/sandbox2/benchmark/theBenchmark.p',fact_2973_zero__induct) ).
thf(6019,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)],[1041]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( B != C )
& ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4047_gcd__nat_Ostrict__trans) ).
thf(1965,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( B != C )
& ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(473,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/sandbox2/benchmark/theBenchmark.p',fact_3079_power__gt__expt) ).
thf(3223,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)],[473]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_456_add__increasing) ).
thf(1139,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)],[4]) ).
thf(656,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/sandbox2/benchmark/theBenchmark.p',fact_4917_less__diff__conv) ).
thf(4127,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)],[656]) ).
thf(1010,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3304_Suc__mod__mult__self1) ).
thf(5859,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(594,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/sandbox2/benchmark/theBenchmark.p',fact_8118_binomial__eq__0) ).
thf(3783,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)],[594]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',fact_4040_dvd__antisym) ).
thf(2166,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)],[229]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',fact_849_add__nonneg__pos) ).
thf(1897,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)],[169]) ).
thf(679,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/sandbox2/benchmark/theBenchmark.p',fact_1646_minf_I3_J) ).
thf(4273,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)],[679]) ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( 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 ) @ ( A @ ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3834_div__plus__div__distrib__dvd__right) ).
thf(1464,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( C @ ( 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 ) @ ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(552,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/sandbox2/benchmark/theBenchmark.p',fact_2352_nat__mult__max__right) ).
thf(3568,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)],[552]) ).
thf(939,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3266_bits__mod__0) ).
thf(5556,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)],[939]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',fact_2413_mult__nonneg__nonneg) ).
thf(3023,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)],[427]) ).
thf(740,axiom,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ zero_n2687167440665602831ol_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6784_of__nat__of__bool) ).
thf(4558,plain,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ zero_n2687167440665602831ol_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',fact_3123_max_Oorder__iff) ).
thf(1669,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)],[122]) ).
thf(900,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3302_Suc__mod__mult__self3) ).
thf(5363,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(258,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/sandbox2/benchmark/theBenchmark.p',fact_888_antisym__conv1) ).
thf(2293,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)],[258]) ).
thf(925,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/sandbox2/benchmark/theBenchmark.p',fact_4157_add__diff__cancel__left) ).
thf(5471,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)],[925]) ).
thf(879,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/sandbox2/benchmark/theBenchmark.p',fact_2522_add__scale__eq__noteq) ).
thf(5282,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)],[879]) ).
thf(576,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3257_deg1Leaf) ).
thf(3663,plain,
! [A: vEBT_VEBT] :
( ( ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) )
=> ( one_one_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(669,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/sandbox2/benchmark/theBenchmark.p',fact_213_trans__less__add2) ).
thf(4218,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)],[669]) ).
thf(406,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3522_unit__prod) ).
thf(2935,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( dvd_dvd_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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(785,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/sandbox2/benchmark/theBenchmark.p',fact_1961_nat__mult__eq__1__iff) ).
thf(4822,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)],[785]) ).
thf(496,axiom,
! [A: nat] :
? [B: nat] : ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_gt__ex) ).
thf(3340,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)],[496]) ).
thf(833,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/sandbox2/benchmark/theBenchmark.p',fact_2242_mult__eq__self__implies__10) ).
thf(5086,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)],[833]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',fact_2343_mult__le__mono1) ).
thf(1332,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)],[45]) ).
thf(774,axiom,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_Ex__list__of__length) ).
thf(4764,plain,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',fact_3043_less__Suc__eq__le) ).
thf(3123,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)],[446]) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',fact_3894_dvd__div__eq__mult) ).
thf(2425,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)],[287]) ).
thf(514,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_dual__order_Ostrict__implies__not__eq) ).
thf(3416,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)],[514]) ).
thf(1125,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_valid__eq2) ).
thf(6334,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',fact_3347_gcd__nat__induct) ).
thf(3304,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)],[487]) ).
thf(917,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3262_mod__by__0) ).
thf(5432,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)],[917]) ).
thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_2877_div__le__mono2) ).
thf(1224,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)],[26]) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',fact_1802_zero__le__power) ).
thf(2573,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)],[317]) ).
thf(946,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/sandbox2/benchmark/theBenchmark.p',fact_3058_Suc__eq__plus1__left) ).
thf(5578,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)],[946]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',fact_1821_power__eq__iff__eq__base) ).
thf(2319,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)],[263]) ).
thf(544,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/sandbox2/benchmark/theBenchmark.p',fact_2504_mult__pos__neg) ).
thf(3532,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)],[544]) ).
thf(1048,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/sandbox2/benchmark/theBenchmark.p',fact_2132_div__mult__self3) ).
thf(6048,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)],[1048]) ).
thf(1072,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/sandbox2/benchmark/theBenchmark.p',fact_1958_mult__cancel1) ).
thf(6144,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)],[1072]) ).
thf(1042,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2964_n__not__Suc__n) ).
thf(6024,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(779,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_less__zeroE) ).
thf(4790,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)],[779]) ).
thf(828,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2591_power__add) ).
thf(5071,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(692,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/sandbox2/benchmark/theBenchmark.p',fact_2983_Suc__lessE) ).
thf(4337,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)],[692]) ).
thf(863,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_7128_pochhammer__product_H) ).
thf(5212,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( 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)],[863]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_2842_power__decreasing) ).
thf(1408,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)],[63]) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',fact_3325_mod__less__eq__dividend) ).
thf(2151,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)],[224]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',fact_4773_le__add__diff) ).
thf(2383,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)],[276]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_2908_max_Oabsorb2) ).
thf(1574,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)],[104]) ).
thf(1093,axiom,
na = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C8_C) ).
thf(6216,plain,
na = m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(6217,plain,
na = m,
inference(lifteq,[status(thm)],[6216]) ).
thf(1086,axiom,
~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
thf(6197,plain,
~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(824,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_order__less__imp__not__eq2) ).
thf(5054,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)],[824]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',fact_146_add__le__imp__le__left) ).
thf(3138,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)],[451]) ).
thf(974,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3268_mod__add__self1) ).
thf(5689,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',fact_24_nat__add__left__cancel__less) ).
thf(3384,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)],[505]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_4926_dvd__diffD) ).
thf(1349,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)],[50]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',fact_4411_diff__Suc__diff__eq1) ).
thf(2097,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)],[212]) ).
thf(1008,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/sandbox2/benchmark/theBenchmark.p',fact_4715_diff__add__inverse) ).
thf(5853,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)],[1008]) ).
thf(929,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/sandbox2/benchmark/theBenchmark.p',fact_2938_mult__eq__1__iff) ).
thf(5491,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)],[929]) ).
thf(1018,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2977_nat_OdiscI) ).
thf(5901,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',fact_8763_binomial__altdef__nat) ).
thf(3106,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)],[442]) ).
thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_6932_of__nat__diff) ).
thf(1542,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)],[96]) ).
thf(911,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/sandbox2/benchmark/theBenchmark.p',fact_2310_distrib__left) ).
thf(5407,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)],[911]) ).
thf(409,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_zero__le) ).
thf(2945,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)],[409]) ).
thf(467,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/sandbox2/benchmark/theBenchmark.p',fact_4920_Nat_Ole__diff__conv2) ).
thf(3197,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)],[467]) ).
thf(663,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/sandbox2/benchmark/theBenchmark.p',fact_2349_nat__mult__less__cancel1) ).
thf(4154,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)],[663]) ).
thf(1081,axiom,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ~ ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__C5_C) ).
thf(6184,plain,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ~ ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',fact_991_order__le__less) ).
thf(3066,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)],[436]) ).
thf(395,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3538_unit__div__1__unit) ).
thf(2896,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( one_one_nat @ ( divide_divide_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)],[395]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_207_le__neq__implies__less) ).
thf(1571,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)],[103]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_845_add__neg__nonpos) ).
thf(1376,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)],[55]) ).
thf(728,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/sandbox2/benchmark/theBenchmark.p',fact_4704_less__imp__diff__less) ).
thf(4509,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)],[728]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_4784_add__le__imp__le__diff) ).
thf(1439,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)],[72]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_3119_max_OboundedI) ).
thf(2197,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)],[238]) ).
thf(722,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/sandbox2/benchmark/theBenchmark.p',fact_4467_Suc__diff__1) ).
thf(4477,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)],[722]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',fact_4412_diff__Suc__diff__eq2) ).
thf(2065,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)],[203]) ).
thf(842,axiom,
! [A: set_VEBT_VEBT,B: vEBT_VEBT] :
( ( B @ ( A @ aTP_Lamm_eo @ aa_VEBT_VEBT_o ) )
<=> ~ ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9773_ATP_Olambda__210) ).
thf(5114,plain,
! [A: set_VEBT_VEBT,B: vEBT_VEBT] :
( ( ~ ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( A @ aTP_Lamm_eo @ aa_VEBT_VEBT_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_eo @ aa_VEBT_VEBT_o ) )
=> ~ ( A @ ( B @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_8754_dvd__fact) ).
thf(2025,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)],[192]) ).
thf(356,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/sandbox2/benchmark/theBenchmark.p',fact_4364_Nat_Odiff__diff__right) ).
thf(2742,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)],[356]) ).
thf(713,axiom,
! [A: $o] :
( ( A @ zero_n2687167440665602831ol_nat )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4748_of__bool__def) ).
thf(4420,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)],[713]) ).
thf(266,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( 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 != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4049_gcd__nat_Ostrict__trans2) ).
thf(2343,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( 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 != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(743,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3258_deg__1__Leaf) ).
thf(4569,plain,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(216,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_4908_dvd__minus__mod) ).
thf(2111,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[216]) ).
thf(855,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/sandbox2/benchmark/theBenchmark.p',fact_9544_Least__Suc2) ).
thf(5175,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)],[855]) ).
thf(768,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/sandbox2/benchmark/theBenchmark.p',fact_3051_less__iff__Suc__add) ).
thf(4731,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)],[768]) ).
thf(919,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/sandbox2/benchmark/theBenchmark.p',fact_2134_div__mult__self2) ).
thf(5439,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)],[919]) ).
thf(668,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/sandbox2/benchmark/theBenchmark.p',fact_2988_less__Suc__eq) ).
thf(4208,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)],[668]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_894_antisym__conv2) ).
thf(1556,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)],[100]) ).
thf(249,axiom,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8655_fact__Suc__0) ).
thf(2252,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',fact_35_add__le__cancel__left) ).
thf(2553,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)],[313]) ).
thf(912,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_Nat_Oadd__0__right) ).
thf(5410,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)],[912]) ).
thf(1059,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/sandbox2/benchmark/theBenchmark.p',fact_2942_nat__power__eq__Suc__0__iff) ).
thf(6087,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)],[1059]) ).
thf(715,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/sandbox2/benchmark/theBenchmark.p',fact_310_bot__nat__0_Onot__eq__extremum) ).
thf(4430,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)],[715]) ).
thf(948,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/sandbox2/benchmark/theBenchmark.p',fact_4207_Suc__diff__diff) ).
thf(5584,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)],[948]) ).
thf(818,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/sandbox2/benchmark/theBenchmark.p',fact_818_linorder__less__linear) ).
thf(5035,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)],[818]) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',fact_2345_le__square) ).
thf(1877,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)],[163]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',fact_1548_max__def) ).
thf(3133,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)],[449]) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',fact_563_linorder__wlog) ).
thf(3055,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)],[434]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',fact_468_add__nonneg__nonneg) ).
thf(2446,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)],[291]) ).
thf(680,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/sandbox2/benchmark/theBenchmark.p',fact_758_order__less__trans) ).
thf(4277,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)],[680]) ).
thf(362,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/sandbox2/benchmark/theBenchmark.p',fact_3842_mod__0__imp__dvd) ).
thf(2757,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)],[362]) ).
thf(906,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/sandbox2/benchmark/theBenchmark.p',fact_6758_of__nat__add) ).
thf(5392,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)],[906]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4055_gcd__nat_Onot__eq__order__implies__strict) ).
thf(1838,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_230_add__leE) ).
thf(1325,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)],[43]) ).
thf(1121,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/sandbox2/benchmark/theBenchmark.p',fact_2216_mult_Oassoc) ).
thf(6319,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)],[1121]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',fact_2031_div__self) ).
thf(3298,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)],[485]) ).
thf(756,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/sandbox2/benchmark/theBenchmark.p',fact_2637_div__less__dividend) ).
thf(4652,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)],[756]) ).
thf(556,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/sandbox2/benchmark/theBenchmark.p',fact_718_not__less__iff__gr__or__eq) ).
thf(3583,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)],[556]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_134_nat__le__linear) ).
thf(1344,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)],[48]) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).
thf(2928,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)],[404]) ).
thf(14,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( 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 ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3540_unit__div__1__div__1) ).
thf(1177,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( 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 ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(810,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_order__less__imp__not__eq) ).
thf(4990,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)],[810]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_3135_le__max__iff__disj) ).
thf(1688,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)],[126]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',fact_2650_mult__less__le__imp__less) ).
thf(1171,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)],[11]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',fact_3684_dvd__0__left) ).
thf(1396,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)],[59]) ).
thf(990,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2971_Zero__neq__Suc) ).
thf(5775,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(673,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/sandbox2/benchmark/theBenchmark.p',fact_2645_dividend__less__times__div) ).
thf(4232,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)],[673]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',fact_2342_mult__le__mono2) ).
thf(2620,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)],[326]) ).
thf(700,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/sandbox2/benchmark/theBenchmark.p',fact_2091_nat__0__less__mult__iff) ).
thf(4373,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)],[700]) ).
thf(1113,axiom,
! [A: vEBT_VEBT] :
( ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C11_C) ).
thf(6288,plain,
! [A: vEBT_VEBT] :
( ( na @ ( mi @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(456,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3731_dvd__triv__right) ).
thf(3159,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( times_times_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)],[456]) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',fact_3787_pinf_I10_J) ).
thf(1176,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(945,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8116_binomial__Suc__Suc) ).
thf(5575,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',fact_559_order__trans) ).
thf(2797,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)],[373]) ).
thf(213,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( dvd_dvd_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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3723_mult__dvd__mono) ).
thf(2101,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( dvd_dvd_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 ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(645,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/sandbox2/benchmark/theBenchmark.p',fact_5078_diff__Suc__less) ).
thf(4067,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)],[645]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_23_nat__add__left__cancel__le) ).
thf(1973,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)],[182]) ).
thf(204,axiom,
! [A: nat] : ( A @ ( one_one_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3736_one__dvd) ).
thf(2069,plain,
! [A: nat] : ( A @ ( one_one_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(367,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/sandbox2/benchmark/theBenchmark.p',fact_2946_one__le__mult__iff) ).
thf(2770,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)],[367]) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',fact_3048_less__natE) ).
thf(4832,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)],[786]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_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/sandbox2/benchmark/theBenchmark.p',fact_3812_unit__mult__left__cancel) ).
thf(1213,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_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)],[24]) ).
thf(604,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/sandbox2/benchmark/theBenchmark.p',fact_3076_n__less__m__mult__n) ).
thf(3838,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)],[604]) ).
thf(903,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/sandbox2/benchmark/theBenchmark.p',fact_304_zero__eq__add__iff__both__eq__0) ).
thf(5377,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)],[903]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',fact_210_less__imp__le__nat) ).
thf(2765,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)],[365]) ).
thf(516,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/sandbox2/benchmark/theBenchmark.p',fact_2387_power__Suc__less) ).
thf(3423,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)],[516]) ).
thf(865,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_set__update__subsetI) ).
thf(5218,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',fact_5082_nat__eq__add__iff1) ).
thf(2244,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)],[248]) ).
thf(360,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/sandbox2/benchmark/theBenchmark.p',fact_225_le__Suc__ex) ).
thf(2752,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)],[360]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',fact_3762_gcd__nat_Oextremum__uniqueI) ).
thf(2022,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)],[191]) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',fact_2759_zero__less__two) ).
thf(3310,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)],[488]) ).
thf(1007,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_size__neq__size__imp__neq) ).
thf(5849,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)],[1007]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_3500_nat__mult__dvd__cancel__disj) ).
thf(1726,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)],[131]) ).
thf(807,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/sandbox2/benchmark/theBenchmark.p',fact_2895_max_Oabsorb4) ).
thf(4954,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)],[807]) ).
thf(970,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2912_old_Onat_Oinject) ).
thf(5667,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)],[970]) ).
thf(884,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2298_crossproduct__eq) ).
thf(5299,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_3037_Suc__leI) ).
thf(2303,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)],[260]) ).
thf(1115,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aba @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9722_ATP_Olambda__159) ).
thf(6293,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_aba @ 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)],[1115]) ).
thf(725,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1711_div__by__0) ).
thf(4497,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)],[725]) ).
thf(752,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/sandbox2/benchmark/theBenchmark.p',fact_1616_pinf_I3_J) ).
thf(4626,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)],[752]) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',fact_4788_add__le__add__imp__diff__le) ).
thf(2999,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)],[421]) ).
thf(498,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3054_One__nat__def) ).
thf(3348,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(834,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/sandbox2/benchmark/theBenchmark.p',fact_2285_divisors__zero) ).
thf(5089,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)],[834]) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',fact_6801_of__nat__le__0__iff) ).
thf(2506,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)],[304]) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',fact_2559_div__add__self1) ).
thf(3380,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)],[504]) ).
thf(648,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/sandbox2/benchmark/theBenchmark.p',fact_2995_less__Suc__induct) ).
thf(4084,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)],[648]) ).
thf(968,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/sandbox2/benchmark/theBenchmark.p',fact_4716_diff__add__inverse2) ).
thf(5661,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)],[968]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_8719_fact__less__mono__nat) ).
thf(1948,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)],[177]) ).
thf(658,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/sandbox2/benchmark/theBenchmark.p',fact_2890_max__less__iff__conj) ).
thf(4136,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)],[658]) ).
thf(934,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/sandbox2/benchmark/theBenchmark.p',fact_303_add__eq__0__iff__both__eq__0) ).
thf(5528,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)],[934]) ).
thf(817,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/sandbox2/benchmark/theBenchmark.p',fact_1728_nat__zero__less__power__iff) ).
thf(5025,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)],[817]) ).
thf(457,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/sandbox2/benchmark/theBenchmark.p',fact_2690_mult__left__less__imp__less) ).
thf(3161,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)],[457]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',fact_961_dual__order_Ostrict__trans1) ).
thf(2503,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)],[303]) ).
thf(329,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( plus_plus_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3490_dvd__add__triv__right__iff) ).
thf(2629,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( B @ ( plus_plus_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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1063,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8113_binomial__1) ).
thf(6115,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)],[1063]) ).
thf(765,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/sandbox2/benchmark/theBenchmark.p',fact_6897_of__nat__less__imp__less) ).
thf(4722,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)],[765]) ).
thf(813,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/sandbox2/benchmark/theBenchmark.p',fact_6831_of__nat__power__less__of__nat__cancel__iff) ).
thf(5003,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)],[813]) ).
thf(553,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/sandbox2/benchmark/theBenchmark.p',fact_2140_power__strict__increasing__iff) ).
thf(3571,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)],[553]) ).
thf(1088,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/sandbox2/benchmark/theBenchmark.p',fact_123_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(6202,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)],[1088]) ).
thf(918,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
!= ( B @ size_s6755466524823107622T_VEBT ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_neq__if__length__neq) ).
thf(5435,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)],[918]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',fact_3143_max_Oabsorb__iff2) ).
thf(1626,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)],[116]) ).
thf(423,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/sandbox2/benchmark/theBenchmark.p',fact_3147_max_OcoboundedI1) ).
thf(3009,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)],[423]) ).
thf(710,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/sandbox2/benchmark/theBenchmark.p',fact_2774_power__0__left) ).
thf(4405,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)],[710]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',fact_241_add__mono__thms__linordered__field_I3_J) ).
thf(3031,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)],[430]) ).
thf(935,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3383_div__mult1__eq) ).
thf(5538,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(949,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/sandbox2/benchmark/theBenchmark.p',fact_317_length__list__update) ).
thf(5587,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)],[949]) ).
thf(619,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/sandbox2/benchmark/theBenchmark.p',fact_176_add__less__imp__less__right) ).
thf(3936,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)],[619]) ).
thf(799,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/sandbox2/benchmark/theBenchmark.p',fact_2145_div__mult__self__is__m) ).
thf(4901,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)],[799]) ).
thf(1014,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3317_mod__add__eq) ).
thf(5881,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1109,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_buildup__nothing__in__leaf) ).
thf(6276,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',fact_997_order__less__le) ).
thf(2665,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)],[338]) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',fact_8122_zero__less__binomial) ).
thf(2471,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)],[298]) ).
thf(993,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_cg @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9086_diff__Suc) ).
thf(5785,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_cg @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(683,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/sandbox2/benchmark/theBenchmark.p',fact_3052_less__imp__Suc__add) ).
thf(4292,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)],[683]) ).
thf(292,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/sandbox2/benchmark/theBenchmark.p',fact_8731_fact__ge__zero) ).
thf(2449,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)],[292]) ).
thf(972,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ 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 ) @ ( B @ ( A @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_7102_pochhammer__Suc) ).
thf(5678,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ 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 ) @ ( B @ ( A @ ( 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)],[972]) ).
thf(742,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/sandbox2/benchmark/theBenchmark.p',fact_1808_nat__power__less__imp__less) ).
thf(4566,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)],[742]) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',fact_5709_take__bit__nat__less__eq__self) ).
thf(2684,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)],[341]) ).
thf(523,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/sandbox2/benchmark/theBenchmark.p',fact_2350_nat__mult__eq__cancel1) ).
thf(3455,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)],[523]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_5086_nat__diff__add__eq1) ).
thf(1472,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)],[80]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_3912_is__unit__power__iff) ).
thf(2333,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)],[265]) ).
thf(6,axiom,
! [A: nat,B: nat,C: 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 ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3828_unit__div__cancel) ).
thf(1145,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( 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 = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(652,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/sandbox2/benchmark/theBenchmark.p',fact_370_nth__list__update__eq) ).
thf(4113,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)],[652]) ).
thf(822,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/sandbox2/benchmark/theBenchmark.p',fact_5126_Suc__diff__eq__diff__pred) ).
thf(5047,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)],[822]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_270_nat__descend__induct) ).
thf(1798,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)],[146]) ).
thf(1000,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2328_mult__0) ).
thf(5822,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)],[1000]) ).
thf(538,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/sandbox2/benchmark/theBenchmark.p',fact_3087_power__Suc__less__one) ).
thf(3507,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)],[538]) ).
thf(792,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/sandbox2/benchmark/theBenchmark.p',fact_2609_add__mono1) ).
thf(4864,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)],[792]) ).
thf(444,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3906_unit__eq__div2) ).
thf(3112,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( B
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(236,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/sandbox2/benchmark/theBenchmark.p',fact_909_not__le__imp__less) ).
thf(2192,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)],[236]) ).
thf(469,axiom,
one_one_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2586_less__numeral__extra_I1_J) ).
thf(3214,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)],[469]) ).
thf(590,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/sandbox2/benchmark/theBenchmark.p',fact_490_canonically__ordered__monoid__add__class_OlessE) ).
thf(3754,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)],[590]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',fact_3520_dvd__times__right__cancel__iff) ).
thf(1647,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)],[119]) ).
thf(755,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/sandbox2/benchmark/theBenchmark.p',fact_132_nat__neq__iff) ).
thf(4641,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)],[755]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',fact_525_nle__le) ).
thf(1780,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)],[142]) ).
thf(753,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_os @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7252_pochhammer__code) ).
thf(4630,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_os @ 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)],[753]) ).
thf(343,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/sandbox2/benchmark/theBenchmark.p',fact_3030_lift__Suc__antimono__le) ).
thf(2689,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)],[343]) ).
thf(1039,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_sz @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10097_ATP_Olambda__534) ).
thf(6012,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_sz @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[1039]) ).
thf(758,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8260_gbinomial__0_I1_J) ).
thf(4658,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)],[758]) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',fact_2247_mult__left__le) ).
thf(2942,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)],[408]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',fact_3238_div__positive) ).
thf(2567,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)],[315]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_2872_div__le__mono) ).
thf(1845,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)],[156]) ).
thf(1131,axiom,
( na
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o )
@ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__C12_C) ).
thf(6362,plain,
( na
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o )
@ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_3103_max_Omono) ).
thf(1516,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)],[90]) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',fact_8761_binomial__fact__lemma) ).
thf(2863,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)],[386]) ).
thf(1099,axiom,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( zero_zero_nat @ ( A @ ( aTP_Lamm_na @ semiri8422978514062236437ux_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7016_of__nat__code) ).
thf(6238,plain,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( zero_zero_nat @ ( A @ ( aTP_Lamm_na @ semiri8422978514062236437ux_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(337,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3904_div__mult__unit2) ).
thf(2661,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( 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)],[337]) ).
thf(844,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2980_nat_Odistinct_I1_J) ).
thf(5125,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',fact_224_add__le__mono) ).
thf(1611,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)],[112]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_8697_fact__mono__nat) ).
thf(2375,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)],[273]) ).
thf(841,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/sandbox2/benchmark/theBenchmark.p',fact_4165_add__diff__cancel__right) ).
thf(5111,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)],[841]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_853_add__nonpos__neg) ).
thf(1156,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)],[8]) ).
thf(802,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1282_in__mono) ).
thf(4939,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(697,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/sandbox2/benchmark/theBenchmark.p',fact_2613_less__add__one) ).
thf(4366,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)],[697]) ).
thf(602,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/sandbox2/benchmark/theBenchmark.p',fact_493_pos__add__strict) ).
thf(3833,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)],[602]) ).
thf(735,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/sandbox2/benchmark/theBenchmark.p',fact_311_neq0__conv) ).
thf(4534,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)],[735]) ).
thf(352,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 ) )
=> ( ( A @ ( C @ ( B @ ( 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 ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3542_div__add) ).
thf(2732,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 ) )
=> ( ( A @ ( C @ ( B @ ( 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 ) @ ( 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)],[352]) ).
thf(829,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/sandbox2/benchmark/theBenchmark.p',fact_4169_add__diff__cancel__right_H) ).
thf(5074,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)],[829]) ).
thf(447,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/sandbox2/benchmark/theBenchmark.p',fact_137_le__trans) ).
thf(3129,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)],[447]) ).
thf(623,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/sandbox2/benchmark/theBenchmark.p',fact_2090_mult__less__cancel2) ).
thf(3949,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)],[623]) ).
thf(595,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/sandbox2/benchmark/theBenchmark.p',fact_5080_nat__diff__split__asm) ).
thf(3786,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)],[595]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',fact_331_le__add__same__cancel1) ).
thf(2386,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)],[277]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_2401_mult__nonneg__nonpos2) ).
thf(1230,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)],[28]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_4928_less__eq__dvd__minus) ).
thf(2160,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)],[227]) ).
thf(748,axiom,
! [A: $o,B: $o] :
( ( ( B
| A )
@ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4240_of__bool__or__iff) ).
thf(4593,plain,
! [A: $o,B: $o] :
( ( ( B
| A )
@ zero_n2687167440665602831ol_nat )
= ( B @ zero_n2687167440665602831ol_nat @ ( A @ zero_n2687167440665602831ol_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',fact_1404_pinf_I8_J) ).
thf(2888,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)],[392]) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',fact_3107_max_OorderE) ).
thf(2882,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)],[390]) ).
thf(815,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/sandbox2/benchmark/theBenchmark.p',fact_4356_of__bool__less__one__iff) ).
thf(5018,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)],[815]) ).
thf(478,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6777_of__nat__eq__1__iff) ).
thf(3246,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)],[478]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',fact_480_add__nonpos__eq__0__iff) ).
thf(1637,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)],[118]) ).
thf(1021,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_acz @ 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/sandbox2/benchmark/theBenchmark.p',fact_9565_ATP_Olambda__2) ).
thf(5912,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_acz @ 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)],[1021]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',fact_4722_dvd__diff__nat) ).
thf(3026,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)],[428]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat,E: nat] :
( ( C @ ( E @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A
= ( E @ ( D @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3707_division__decomp) ).
thf(1235,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: nat,E: nat] :
( ( C @ ( E @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( D @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A
= ( E @ ( D @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(601,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/sandbox2/benchmark/theBenchmark.p',fact_676_ord__eq__less__trans) ).
thf(3828,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)],[601]) ).
thf(493,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/sandbox2/benchmark/theBenchmark.p',fact_2993_Suc__less__SucD) ).
thf(3329,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)],[493]) ).
thf(653,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/sandbox2/benchmark/theBenchmark.p',fact_214_trans__less__add1) ).
thf(4117,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)],[653]) ).
thf(665,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/sandbox2/benchmark/theBenchmark.p',fact_2092_less__one) ).
thf(4164,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)],[665]) ).
thf(869,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( 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/sandbox2/benchmark/theBenchmark.p',fact_265_inthall) ).
thf(5235,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( 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)],[869]) ).
thf(989,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3351_nat__mod__eq__iff) ).
thf(5767,plain,
! [A: nat,B: nat,C: nat] :
( ( ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(210,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3727_dvd__mult__right) ).
thf(2092,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( 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)],[210]) ).
thf(649,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/sandbox2/benchmark/theBenchmark.p',fact_2780_power__strict__increasing) ).
thf(4092,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)],[649]) ).
thf(800,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/sandbox2/benchmark/theBenchmark.p',fact_216_not__add__less2) ).
thf(4905,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)],[800]) ).
thf(1101,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/sandbox2/benchmark/theBenchmark.p',fact_4537_diff__right__commute) ).
thf(6244,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)],[1101]) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',fact_2788_power__increasing) ).
thf(1790,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)],[143]) ).
thf(915,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( 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/sandbox2/benchmark/theBenchmark.p',fact_519_all__set__conv__all__nth) ).
thf(5420,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 @ aa_set_VEBT_VEBT_o ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( 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)],[915]) ).
thf(1044,axiom,
! [A: nat] :
( ( suc @ ( A @ compow_fun_nat_nat ) )
= ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9145_Suc__funpow) ).
thf(6036,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)],[1044]) ).
thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_4922_Nat_Odiff__add__assoc2) ).
thf(2454,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)],[294]) ).
thf(660,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/sandbox2/benchmark/theBenchmark.p',fact_3083_power__Suc__le__self) ).
thf(4145,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)],[660]) ).
thf(599,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/sandbox2/benchmark/theBenchmark.p',fact_1552_max__add__distrib__right) ).
thf(3823,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)],[599]) ).
thf(1036,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_na @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9569_ATP_Olambda__6) ).
thf(5995,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_na @ 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)],[1036]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_3139_max_Oabsorb__iff1) ).
thf(1317,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)],[42]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_4743_of__bool__less__eq__one) ).
thf(1763,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)],[139]) ).
thf(676,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1487_max__0L) ).
thf(4241,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)],[676]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',fact_4362_Nat_Oadd__diff__assoc) ).
thf(2903,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)],[398]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3699_dvd__def) ).
thf(2545,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_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 ) )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(321,axiom,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8639_fact__0) ).
thf(2599,plain,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',fact_3004_not__less__eq__eq) ).
thf(1679,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)],[124]) ).
thf(513,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/sandbox2/benchmark/theBenchmark.p',fact_1524_nth__replicate) ).
thf(3412,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)],[513]) ).
thf(551,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/sandbox2/benchmark/theBenchmark.p',fact_2144_div__mult__self1__is__m) ).
thf(3564,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)],[551]) ).
thf(856,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/sandbox2/benchmark/theBenchmark.p',fact_3345_mod__Suc) ).
thf(5186,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)],[856]) ).
thf(826,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/sandbox2/benchmark/theBenchmark.p',fact_5130_nat__less__add__iff1) ).
thf(5062,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)],[826]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',fact_554_order_Otrans) ).
thf(2411,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)],[284]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',fact_3896_unit__div__eq__0__iff) ).
thf(1766,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)],[140]) ).
thf(971,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3293_mod__mult__self2) ).
thf(5675,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',fact_2455_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(4133,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)],[657]) ).
thf(674,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/sandbox2/benchmark/theBenchmark.p',fact_813_order__less__imp__triv) ).
thf(4235,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)],[674]) ).
thf(693,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1928_bits__div__0) ).
thf(4342,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)],[693]) ).
thf(832,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_add_Oright__neutral) ).
thf(5083,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)],[832]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_2675_mult__strict__mono_H) ).
thf(2266,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)],[252]) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',fact_1483_max__nat_Oeq__neutr__iff) ).
thf(3288,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)],[484]) ).
thf(339,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( modulo_modulo_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 @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3769_dvd__mod__imp__dvd) ).
thf(2675,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( modulo_modulo_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 @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(849,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/sandbox2/benchmark/theBenchmark.p',fact_4647_add__implies__diff) ).
thf(5147,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)],[849]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',fact_434_bot__nat__0_Oextremum__uniqueI) ).
thf(2838,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)],[381]) ).
thf(627,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/sandbox2/benchmark/theBenchmark.p',fact_4933_mod__geq) ).
thf(3970,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)],[627]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',fact_3074_ex__least__nat__less) ).
thf(2113,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)],[217]) ).
thf(1037,axiom,
! [A: nat] :
? [B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_Ex__list__of__length) ).
thf(5998,plain,
! [A: nat] :
? [B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(870,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/sandbox2/benchmark/theBenchmark.p',fact_8255_gbinomial__0_I2_J) ).
thf(5240,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)],[870]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_933_order_Ostrict__trans2) ).
thf(1221,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)],[25]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_5088_mod__eq__dvd__iff__nat) ).
thf(1284,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)],[37]) ).
thf(931,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/sandbox2/benchmark/theBenchmark.p',fact_1107_Euclid__induct) ).
thf(5504,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)],[931]) ).
thf(383,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( 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 @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3820_div__div__eq__right) ).
thf(2843,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( 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 @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',fact_8760_fact__div__fact__le__pow) ).
thf(1485,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)],[84]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',fact_646_order__antisym__conv) ).
thf(2711,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)],[348]) ).
thf(1092,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ aTP_Lamm_aao @ aa_nat_fun_set_nat_o ) @ collect_set_nat @ finite_card_set_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9087_binomial__def) ).
thf(6213,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ aTP_Lamm_aao @ aa_nat_fun_set_nat_o ) @ collect_set_nat @ finite_card_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',fact_529_le__cases3) ).
thf(2579,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)],[319]) ).
thf(962,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4210_diff__0__eq__0) ).
thf(5633,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)],[962]) ).
thf(659,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/sandbox2/benchmark/theBenchmark.p',fact_2916_Suc__mono) ).
thf(4143,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)],[659]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( 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 ) )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4050_gcd__nat_Ostrict__iff__not) ).
thf(1427,plain,
! [A: nat,B: nat] :
( ( ( ~ ( A @ ( B @ ( 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 )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( ( A != B )
& ( 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 ) )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',fact_9489_upt__conv__Cons__Cons) ).
thf(2807,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)],[377]) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_323_add__le__same__cancel1) ).
thf(1272,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)],[35]) ).
thf(363,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/sandbox2/benchmark/theBenchmark.p',fact_3063_power__inject__base) ).
thf(2760,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)],[363]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',fact_3389_mod__eq__nat2E) ).
thf(2458,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)],[295]) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',fact_5708_take__bit__tightened__less__eq__nat) ).
thf(2626,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)],[328]) ).
thf(749,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/sandbox2/benchmark/theBenchmark.p',fact_3933_is__unit__div__mult__cancel__left) ).
thf(4606,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)],[749]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_4921_Nat_Odiff__add__assoc) ).
thf(2088,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)],[209]) ).
thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_1798_power__mono) ).
thf(1553,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)],[99]) ).
thf(520,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2212_comm__monoid__mult__class_Omult__1) ).
thf(3447,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)],[520]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_160_add__mono) ).
thf(2194,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)],[237]) ).
thf(617,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/sandbox2/benchmark/theBenchmark.p',fact_345_add__less__same__cancel1) ).
thf(3928,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)],[617]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',fact_2662_mult__left__le__imp__le) ).
thf(2209,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)],[241]) ).
thf(567,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__refl2) ).
thf(3625,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)],[567]) ).
thf(557,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/sandbox2/benchmark/theBenchmark.p',fact_4918_add__diff__inverse__nat) ).
thf(3593,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)],[557]) ).
thf(68,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 ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3534_dvd__mult__div__cancel) ).
thf(1421,plain,
! [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 ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_3888_dvd__div__div__eq__mult) ).
thf(2013,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)],[189]) ).
thf(509,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/sandbox2/benchmark/theBenchmark.p',fact_808_order__less__not__sym) ).
thf(3400,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)],[509]) ).
thf(527,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_bot__nat__0_Oextremum__strict) ).
thf(3478,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)],[527]) ).
thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_4710_le__diff__iff_H) ).
thf(1459,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)],[76]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_3349_mod__Suc__le__divisor) ).
thf(2045,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)],[199]) ).
thf(440,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/sandbox2/benchmark/theBenchmark.p',fact_3481_dvd__0__left__iff) ).
thf(3092,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)],[440]) ).
thf(804,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/sandbox2/benchmark/theBenchmark.p',fact_8132_times__binomial__minus1__eq) ).
thf(4945,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)],[804]) ).
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 @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_223_add__le__mono1) ).
thf(1180,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)],[15]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',fact_4046_gcd__nat_Oantisym) ).
thf(1685,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)],[125]) ).
thf(391,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/sandbox2/benchmark/theBenchmark.p',fact_452_add__decreasing) ).
thf(2885,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)],[391]) ).
thf(460,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_less__eq__nat_Osimps_I1_J) ).
thf(3171,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)],[460]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',fact_3388_mod__eq__nat1E) ).
thf(2960,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)],[413]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_4778_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(2078,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)],[206]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_8124_choose__mult) ).
thf(1834,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)],[154]) ).
thf(420,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_le__refl) ).
thf(2997,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)],[420]) ).
thf(17,axiom,
ma @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C4_Ohyps_C_I7_J) ).
thf(1189,plain,
ma @ ( mi @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(491,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/sandbox2/benchmark/theBenchmark.p',fact_713_order_Ostrict__trans) ).
thf(3320,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)],[491]) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',fact_949_dual__order_Oorder__iff__strict) ).
thf(2305,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)],[261]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',fact_2904_max_Obounded__iff) ).
thf(2071,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)],[205]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',fact_1019_order__le__neq__trans) ).
thf(2658,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)],[336]) ).
thf(827,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/sandbox2/benchmark/theBenchmark.p',fact_2925_max__Suc__Suc) ).
thf(5068,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)],[827]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',fact_3844_le__imp__power__dvd) ).
thf(2907,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)],[399]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_4214_of__bool__less__eq__iff) ).
thf(1590,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)],[108]) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',fact_2409_mult__nonneg__nonpos) ).
thf(2443,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)],[290]) ).
thf(563,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1484_max__nat_Oleft__neutral) ).
thf(3613,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)],[563]) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',fact_4914_less__diff__iff) ).
thf(2594,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)],[320]) ).
thf(1122,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_fd @ aa_nat_o ) )
<=> ~ ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9814_ATP_Olambda__251) ).
thf(6322,plain,
! [A: fun_nat_o,B: nat] :
( ( ~ ( B @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_fd @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_fd @ aa_nat_o ) )
=> ~ ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(529,axiom,
( ( one_one_nat @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2075_max__0__1_I1_J) ).
thf(3484,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)],[529]) ).
thf(385,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/sandbox2/benchmark/theBenchmark.p',fact_273_le__zero__eq) ).
thf(2855,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)],[385]) ).
thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_578_dual__order_Otrans) ).
thf(2290,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)],[257]) ).
thf(720,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/sandbox2/benchmark/theBenchmark.p',fact_6827_of__nat__0__less__iff) ).
thf(4468,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)],[720]) ).
thf(896,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/sandbox2/benchmark/theBenchmark.p',fact_2347_add__mult__distrib2) ).
thf(5351,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)],[896]) ).
thf(736,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_order__less__irrefl) ).
thf(4542,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(633,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 @ aa_set_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_set__update__memI) ).
thf(3991,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 @ aa_set_VEBT_VEBT_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(733,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/sandbox2/benchmark/theBenchmark.p',fact_2984_Suc__lessI) ).
thf(4527,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)],[733]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',fact_4775_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(2262,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)],[251]) ).
thf(953,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/sandbox2/benchmark/theBenchmark.p',fact_4924_diff__Suc__eq__diff__pred) ).
thf(5600,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)],[953]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( one_one_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 ) )
<=> ( ( one_one_nat @ ( B @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3802_is__unit__mult__iff) ).
thf(2283,plain,
! [A: nat,B: nat] :
( ( ( ( one_one_nat @ ( B @ ( 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 ) ) )
=> ( one_one_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 ) ) )
& ( ( one_one_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 ) )
=> ( ( one_one_nat @ ( B @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(781,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3259_deg__1__Leafy) ).
thf(4806,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_2355_div__times__less__eq__dividend) ).
thf(1476,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)],[81]) ).
thf(309,axiom,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3630_dvd__refl) ).
thf(2532,plain,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(996,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/sandbox2/benchmark/theBenchmark.p',fact_286_add__cancel__left__left) ).
thf(5800,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)],[996]) ).
thf(846,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/sandbox2/benchmark/theBenchmark.p',fact_1997_nonzero__mult__div__cancel__left) ).
thf(5132,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)],[846]) ).
thf(536,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/sandbox2/benchmark/theBenchmark.p',fact_2854_one__less__power) ).
thf(3501,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)],[536]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',fact_8112_zero__less__binomial__iff) ).
thf(3003,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)],[422]) ).
thf(871,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3369_mult__div__mod__eq) ).
thf(5243,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',fact_7731_fold__atLeastAtMost__nat_Oelims) ).
thf(1523,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)],[93]) ).
thf(494,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/sandbox2/benchmark/theBenchmark.p',fact_6745_of__nat__less__iff) ).
thf(3331,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)],[494]) ).
thf(450,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/sandbox2/benchmark/theBenchmark.p',fact_871_leD) ).
thf(3136,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)],[450]) ).
thf(463,axiom,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( 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 ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3560_unit__mult__div__div) ).
thf(3181,plain,
! [A: nat,B: nat] :
( ( one_one_nat @ ( A @ ( 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 ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(854,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 @ aa_set_VEBT_VEBT_o ) ) )
<=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1518_Bex__set__replicate) ).
thf(5162,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 @ aa_set_VEBT_VEBT_o ) ) ) )
& ( ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_4923_Nat_Ole__imp__diff__is__add) ).
thf(1308,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)],[41]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_4779_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(1706,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)],[128]) ).
thf(937,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/sandbox2/benchmark/theBenchmark.p',fact_1985_div__mult__mult2) ).
thf(5549,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)],[937]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',fact_3361_unique__euclidean__semiring__numeral__class_Opos__mod__sign) ).
thf(2183,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)],[233]) ).
thf(195,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1226_verit__comp__simplify1_I2_J) ).
thf(2036,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)],[195]) ).
thf(262,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( 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 @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3760_div__div__div__same) ).
thf(2315,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( 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 @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(355,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( dvd_dvd_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/sandbox2/benchmark/theBenchmark.p',fact_3632_dvd__trans) ).
thf(2739,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( dvd_dvd_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)],[355]) ).
thf(893,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/sandbox2/benchmark/theBenchmark.p',fact_291_add__cancel__left__right) ).
thf(5336,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)],[893]) ).
thf(412,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/sandbox2/benchmark/theBenchmark.p',fact_4707_Nat_Odiff__diff__eq) ).
thf(2956,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)],[412]) ).
thf(1105,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_valid__eq) ).
thf(6257,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',fact_3111_max_OorderI) ).
thf(2399,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)],[280]) ).
thf(197,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__refl) ).
thf(2041,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)],[197]) ).
thf(534,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/sandbox2/benchmark/theBenchmark.p',fact_2353_less__mult__imp__div__less) ).
thf(3497,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)],[534]) ).
thf(610,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/sandbox2/benchmark/theBenchmark.p',fact_409_gr__implies__not__zero) ).
thf(3879,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)],[610]) ).
thf(1114,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_acy @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9724_ATP_Olambda__161) ).
thf(6290,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_acy @ 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)],[1114]) ).
thf(606,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/sandbox2/benchmark/theBenchmark.p',fact_1606_pinf_I1_J) ).
thf(3844,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)],[606]) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',fact_3032_less__Suc__eq__0__disj) ).
thf(3430,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)],[518]) ).
thf(1064,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3295_mod__mult__self1) ).
thf(6118,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(975,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3283_bits__mod__by__1) ).
thf(5692,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)],[975]) ).
thf(686,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/sandbox2/benchmark/theBenchmark.p',fact_5165_power__diff__power__eq) ).
thf(4299,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)],[686]) ).
thf(1047,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/sandbox2/benchmark/theBenchmark.p',fact_4212_diff__diff__left) ).
thf(6045,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)],[1047]) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',fact_4913_Suc__diff__le) ).
thf(2462,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)],[296]) ).
thf(1004,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 @ aa_set_VEBT_VEBT_o ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_all__nth__imp__all__set) ).
thf(5837,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 @ aa_set_VEBT_VEBT_o ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(816,axiom,
( aTP_Lamm_cg
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3671_lambda__one) ).
thf(5023,plain,
( aTP_Lamm_cg
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(704,axiom,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2915_lessI) ).
thf(4387,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)],[704]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',fact_3080_nat__one__le__power) ).
thf(2576,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)],[318]) ).
thf(848,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3281_mod__by__1) ).
thf(5144,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)],[848]) ).
thf(121,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/sandbox2/benchmark/theBenchmark.p',fact_220_nat__le__iff__add) ).
thf(1661,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)],[121]) ).
thf(950,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xw @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9631_ATP_Olambda__68) ).
thf(5590,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xw @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(717,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/sandbox2/benchmark/theBenchmark.p',fact_708_linorder__less__wlog) ).
thf(4446,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)],[717]) ).
thf(794,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/sandbox2/benchmark/theBenchmark.p',fact_3015_lift__Suc__mono__less) ).
thf(4869,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)],[794]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',fact_4915_diff__less__mono) ).
thf(2623,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)],[327]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3695_dvdI) ).
thf(1994,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',fact_1556_max__add__distrib__left) ).
thf(3552,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)],[548]) ).
thf(880,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/sandbox2/benchmark/theBenchmark.p',fact_8114_binomial__0__Suc) ).
thf(5287,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)],[880]) ).
thf(515,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7097_pochhammer__rec) ).
thf(3420,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( comm_s4663373288045622133er_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)],[515]) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',fact_3892_div__dvd__iff__mult) ).
thf(1614,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)],[113]) ).
thf(796,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/sandbox2/benchmark/theBenchmark.p',fact_3090_div__nat__eqI) ).
thf(4880,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)],[796]) ).
thf(898,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/sandbox2/benchmark/theBenchmark.p',fact_9503_map__Suc__upt) ).
thf(5357,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)],[898]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_2918_Suc__le__mono) ).
thf(1774,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)],[141]) ).
thf(814,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2235_one__reorient) ).
thf(5009,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)],[814]) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',fact_2991_Suc__less__eq2) ).
thf(3705,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)],[582]) ).
thf(845,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1912_mult__zero__left) ).
thf(5129,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)],[845]) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',fact_327_add__le__same__cancel2) ).
thf(2534,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)],[310]) ).
thf(1068,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2972_Suc__neq__Zero) ).
thf(6131,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(632,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/sandbox2/benchmark/theBenchmark.p',fact_196_add__mono__thms__linordered__field_I1_J) ).
thf(3987,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)],[632]) ).
thf(988,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4702_minus__nat_Odiff__0) ).
thf(5764,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)],[988]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_5085_nat__le__add__iff2) ).
thf(1757,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)],[138]) ).
thf(579,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/sandbox2/benchmark/theBenchmark.p',fact_1806_zero__less__power) ).
thf(3690,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)],[579]) ).
thf(908,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8123_Suc__times__binomial__add) ).
thf(5398,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(1,conjecture,
? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1133,plain,
~ ? [A: nat] : ( A @ ( na @ ( mi @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(823,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/sandbox2/benchmark/theBenchmark.p',fact_407_gr__zeroI) ).
thf(5051,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)],[823]) ).
thf(784,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/sandbox2/benchmark/theBenchmark.p',fact_31_add__less__cancel__right) ).
thf(4816,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)],[784]) ).
thf(1050,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/sandbox2/benchmark/theBenchmark.p',fact_6875_mult__of__nat__commute) ).
thf(6055,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)],[1050]) ).
thf(761,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/sandbox2/benchmark/theBenchmark.p',fact_2647_split__div) ).
thf(4670,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)],[761]) ).
thf(955,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/sandbox2/benchmark/theBenchmark.p',fact_4651_diff__diff__eq) ).
thf(5606,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)],[955]) ).
thf(559,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/sandbox2/benchmark/theBenchmark.p',fact_3077_n__less__n__mult__m) ).
thf(3601,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)],[559]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_3042_le__less__Suc__eq) ).
thf(2233,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)],[245]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',fact_464_add__increasing2) ).
thf(2522,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)],[306]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',fact_6842_of__nat__power__le__of__nat__cancel__iff) ).
thf(3100,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)],[441]) ).
thf(378,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( 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 ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_3836_div__plus__div__distrib__dvd__left) ).
thf(2815,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ ( 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 ) @ ( 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)],[378]) ).
thf(353,axiom,
zero_zero_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1288_le__numeral__extra_I3_J) ).
thf(2736,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)],[353]) ).
thf(778,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/sandbox2/benchmark/theBenchmark.p',fact_723_dual__order_Ostrict__trans) ).
thf(4787,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)],[778]) ).
thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_5133_dvd__minus__add) ).
thf(1303,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)],[40]) ).
thf(788,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/sandbox2/benchmark/theBenchmark.p',fact_3400_unique__euclidean__semiring__numeral__class_Omod__mult2__eq) ).
thf(4841,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)],[788]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_1221_verit__la__disequality) ).
thf(1527,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)],[94]) ).
thf(1015,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/sandbox2/benchmark/theBenchmark.p',fact_3350_mod__eq__0D) ).
thf(5884,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)],[1015]) ).
thf(495,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/sandbox2/benchmark/theBenchmark.p',fact_4911_Suc__diff__Suc) ).
thf(3337,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)],[495]) ).
thf(927,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_xy @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9954_ATP_Olambda__391) ).
thf(5477,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_xy @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(448,axiom,
one_one_nat @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2331_le__numeral__extra_I4_J) ).
thf(3132,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)],[448]) ).
thf(468,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/sandbox2/benchmark/theBenchmark.p',fact_748_linorder__neq__iff) ).
thf(3203,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)],[468]) ).
thf(1023,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/sandbox2/benchmark/theBenchmark.p',fact_4935_nat__minus__add__max) ).
thf(5926,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)],[1023]) ).
thf(435,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( D @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3826_div__mult__div__if__dvd) ).
thf(3062,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( D @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(525,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1277_subsetD) ).
thf(3469,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT] :
( ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(820,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/sandbox2/benchmark/theBenchmark.p',fact_2240_less__1__mult) ).
thf(5041,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)],[820]) ).
thf(234,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3719_dvd__triv__left) ).
thf(2186,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( times_times_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)],[234]) ).
thf(462,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8695_fact__nonzero) ).
thf(3177,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(913,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2244_left__add__mult__distrib) ).
thf(5413,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(985,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3303_Suc__mod__mult__self2) ).
thf(5741,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B != C )
& ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4048_gcd__nat_Ostrict__trans1) ).
thf(1710,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B != C )
& ( C @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',fact_127_nat__less__induct) ).
thf(3323,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)],[492]) ).
thf(864,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/sandbox2/benchmark/theBenchmark.p',fact_4916_diff__add__0) ).
thf(5215,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)],[864]) ).
thf(889,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5074_minus__mod__eq__mult__div) ).
thf(5324,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(940,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/sandbox2/benchmark/theBenchmark.p',fact_4701_diffs0__imp__equal) ).
thf(5559,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)],[940]) ).
thf(630,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/sandbox2/benchmark/theBenchmark.p',fact_4932_mod__if) ).
thf(3982,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)],[630]) ).
thf(3819,plain,
( ( ~ $false
=> ( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ) )
& ( ( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat )
=> ~ $false ) ),
inference(instance,[status(thm)],[3816]) ).
thf(3820,plain,
( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ),
inference(simp,[status(thm)],[3819]) ).
thf(3822,plain,
( ( $false @ zero_n2687167440665602831ol_nat )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[3820]) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',fact_3386_mod__le__divisor) ).
thf(2800,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)],[374]) ).
thf(624,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/sandbox2/benchmark/theBenchmark.p',fact_5170_power__eq__if) ).
thf(3956,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)],[624]) ).
thf(687,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/sandbox2/benchmark/theBenchmark.p',fact_6847_of__nat__zero__less__power__iff) ).
thf(4303,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)],[687]) ).
thf(642,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/sandbox2/benchmark/theBenchmark.p',fact_3156_less__max__iff__disj) ).
thf(4051,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)],[642]) ).
thf(853,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5070_minus__div__mult__eq__mod) ).
thf(5159,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_904_less__le__not__le) ).
thf(1495,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)],[86]) ).
thf(910,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/sandbox2/benchmark/theBenchmark.p',fact_3549_length__product) ).
thf(5404,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)],[910]) ).
thf(835,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3373_mod__div__mult__eq) ).
thf(5092,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(550,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/sandbox2/benchmark/theBenchmark.p',fact_438_nth__equalityI) ).
thf(3558,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)],[550]) ).
thf(881,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3381_cancel__div__mod__rules_I2_J) ).
thf(5290,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(714,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/sandbox2/benchmark/theBenchmark.p',fact_3071_power__gt1) ).
thf(4427,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)],[714]) ).
thf(721,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/sandbox2/benchmark/theBenchmark.p',fact_426_gr0I) ).
thf(4474,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)],[721]) ).
thf(839,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3270_mod__add__self2) ).
thf(5105,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(357,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/sandbox2/benchmark/theBenchmark.p',fact_2346_le__cube) ).
thf(2746,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)],[357]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',fact_3041_Suc__le__lessD) ).
thf(1335,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)],[46]) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',fact_3413_verit__le__mono__div) ).
thf(4024,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)],[638]) ).
thf(517,axiom,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_subsetI) ).
thf(3426,plain,
! [A: set_VEBT_VEBT,B: set_VEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ ( C @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ ord_le4337996190870823476T_VEBT @ aa_set_VEBT_VEBT_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',fact_153_less__eqE) ).
thf(1891,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)],[167]) ).
thf(578,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/sandbox2/benchmark/theBenchmark.p',fact_3935_is__unitE) ).
thf(3673,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)],[578]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',fact_4286_le__add__diff__inverse2) ).
thf(1346,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)],[49]) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_8121_binomial__le__pow) ).
thf(1742,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)],[134]) ).
thf(1107,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/sandbox2/benchmark/theBenchmark.p',fact_4700_zero__induct__lemma) ).
thf(6269,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)],[1107]) ).
thf(268,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3494_dvd__add__triv__left__iff) ).
thf(2353,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( plus_plus_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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(477,axiom,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6767_of__nat__1) ).
thf(3244,plain,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1083,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_valid__eq1) ).
thf(6190,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(501,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/sandbox2/benchmark/theBenchmark.p',fact_4753_split__of__bool) ).
thf(3362,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)],[501]) ).
thf(862,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/sandbox2/benchmark/theBenchmark.p',fact_296_add__cancel__right__left) ).
thf(5204,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)],[862]) ).
thf(33,axiom,
~ ( one_one_nat @ ( zero_zero_nat @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3779_not__is__unit__0) ).
thf(1261,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)],[33]) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',fact_6835_of__nat__less__of__nat__power__cancel__iff) ).
thf(3543,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)],[546]) ).
thf(850,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2978_old_Onat_Odistinct_I1_J) ).
thf(5151,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(947,axiom,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8163_of__nat__id) ).
thf(5581,plain,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(531,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/sandbox2/benchmark/theBenchmark.p',fact_1656_minf_I5_J) ).
thf(3489,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)],[531]) ).
thf(973,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/sandbox2/benchmark/theBenchmark.p',fact_2290_mult__not__zero) ).
thf(5681,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)],[973]) ).
thf(897,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/sandbox2/benchmark/theBenchmark.p',fact_3287_mod__div__trivial) ).
thf(5354,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)],[897]) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',fact_5687_take__bit__of__1__eq__0__iff) ).
thf(3076,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)],[437]) ).
thf(694,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/sandbox2/benchmark/theBenchmark.p',fact_2636_div__eq__dividend__iff) ).
thf(4345,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)],[694]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_3676_max__def__raw) ).
thf(1399,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)],[60]) ).
thf(894,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/sandbox2/benchmark/theBenchmark.p',fact_1987_div__mult__mult1) ).
thf(5344,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)],[894]) ).
thf(1073,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2965_Suc__inject) ).
thf(6155,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)],[1073]) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',fact_1082_linorder__le__less__linear) ).
thf(2803,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)],[375]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',fact_3518_dvd__times__left__cancel__iff) ).
thf(2847,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)],[384]) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',fact_1812_power__less__imp__less__base) ).
thf(2898,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)],[396]) ).
thf(702,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/sandbox2/benchmark/theBenchmark.p',fact_5125_Suc__pred_H) ).
thf(4382,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)],[702]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',fact_3002_le__Suc__eq) ).
thf(2485,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)],[301]) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_222_trans__le__add1) ).
thf(1550,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)],[98]) ).
thf(1089,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_buildup__nothing__in__min__max) ).
thf(6205,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',fact_534_order__class_Oorder__eq__iff) ).
thf(1357,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)],[52]) ).
thf(727,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/sandbox2/benchmark/theBenchmark.p',fact_4798_linordered__semidom__class_Oadd__diff__inverse) ).
thf(4506,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)],[727]) ).
thf(959,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mg @ 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/sandbox2/benchmark/theBenchmark.p',fact_10080_ATP_Olambda__517) ).
thf(5623,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mg @ 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)],[959]) ).
thf(672,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1486_max__nat_Oright__neutral) ).
thf(4229,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)],[672]) ).
thf(1062,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/sandbox2/benchmark/theBenchmark.p',fact_1902_mult__eq__0__iff) ).
thf(6104,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)],[1062]) ).
thf(708,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/sandbox2/benchmark/theBenchmark.p',fact_2089_nat__mult__less__cancel__disj) ).
thf(4395,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)],[708]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3740_dvd__unit__imp__unit) ).
thf(1885,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(597,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/sandbox2/benchmark/theBenchmark.p',fact_5178_le__div__geq) ).
thf(3812,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)],[597]) ).
thf(533,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1238_verit__comp__simplify1_I1_J) ).
thf(3494,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(670,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/sandbox2/benchmark/theBenchmark.p',fact_2203_power__decreasing__iff) ).
thf(4221,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)],[670]) ).
thf(1006,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/sandbox2/benchmark/theBenchmark.p',fact_139_list__update__swap) ).
thf(5845,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)],[1006]) ).
thf(691,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( B @ size_s6755466524823107622T_VEBT @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_length__pos__if__in__set) ).
thf(4335,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT @ aa_set_VEBT_VEBT_o ) )
=> ( 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)],[691]) ).
thf(851,axiom,
zero_zero_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9550_zero__natural_Orsp) ).
thf(5155,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(555,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/sandbox2/benchmark/theBenchmark.p',fact_1877_div__less) ).
thf(3580,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)],[555]) ).
thf(1033,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_min__Null__member) ).
thf(5986,plain,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1074,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6893_of__nat__neq__0) ).
thf(6158,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(176,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/sandbox2/benchmark/theBenchmark.p',fact_2405_mult__nonpos__nonneg) ).
thf(1945,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)],[176]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',fact_6748_of__nat__le__iff) ).
thf(1565,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)],[102]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',fact_2431_mult__left__mono) ).
thf(2866,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)],[387]) ).
thf(994,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/sandbox2/benchmark/theBenchmark.p',fact_3060_Suc__eq__plus1) ).
thf(5788,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)],[994]) ).
thf(66,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5677_take__bit__0) ).
thf(1416,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)],[66]) ).
thf(801,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/sandbox2/benchmark/theBenchmark.p',fact_3399_split__mod) ).
thf(4908,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)],[801]) ).
thf(571,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/sandbox2/benchmark/theBenchmark.p',fact_3034_All__less__Suc2) ).
thf(3637,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)],[571]) ).
thf(882,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_os @ 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/sandbox2/benchmark/theBenchmark.p',fact_9765_ATP_Olambda__202) ).
thf(5293,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_os @ 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)],[882]) ).
thf(417,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( 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 @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3804_dvd__mult__unit__iff) ).
thf(2980,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 ) @ ( B @ ( 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)],[417]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',fact_3044_less__eq__Suc__le) ).
thf(2177,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)],[232]) ).
thf(1053,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1957_mult__0__right) ).
thf(6067,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)],[1053]) ).
thf(757,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/sandbox2/benchmark/theBenchmark.p',fact_3440_product__nth) ).
thf(4655,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)],[757]) ).
thf(389,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( 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 = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3757_dvd__div__eq__cancel) ).
thf(2879,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( B @ ( 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 = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(922,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3375_div__mult__mod__eq) ).
thf(5458,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(739,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/sandbox2/benchmark/theBenchmark.p',fact_1423_intind) ).
thf(4555,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)],[739]) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',fact_2654_mult__le__less__imp__less) ).
thf(2206,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)],[240]) ).
thf(777,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/sandbox2/benchmark/theBenchmark.p',fact_738_linorder__neqE) ).
thf(4784,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)],[777]) ).
thf(805,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/sandbox2/benchmark/theBenchmark.p',fact_2838_power__strict__decreasing) ).
thf(4949,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)],[805]) ).
thf(775,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/sandbox2/benchmark/theBenchmark.p',fact_3949_dvd__mult__cancel2) ).
thf(4767,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)],[775]) ).
thf(511,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/sandbox2/benchmark/theBenchmark.p',fact_2557_div__add__self2) ).
thf(3405,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)],[511]) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_476_add__nonneg__eq__0__iff) ).
thf(1848,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)],[157]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_1007_linorder__not__less) ).
thf(2059,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)],[202]) ).
thf(943,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/sandbox2/benchmark/theBenchmark.p',fact_4366_Suc__0__mod__eq) ).
thf(5569,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)],[943]) ).
thf(771,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/sandbox2/benchmark/theBenchmark.p',fact_3161_max_Ostrict__boundedE) ).
thf(4752,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)],[771]) ).
thf(770,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/sandbox2/benchmark/theBenchmark.p',fact_1693_power__eq__0__iff) ).
thf(4742,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)],[770]) ).
thf(688,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/sandbox2/benchmark/theBenchmark.p',fact_1960_nat__1__eq__mult__iff) ).
thf(4313,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)],[688]) ).
thf(1104,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abz @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9721_ATP_Olambda__158) ).
thf(6254,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_abz @ 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)],[1104]) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',fact_374_set__swap) ).
thf(3443,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)],[519]) ).
thf(969,axiom,
! [A: fun_nat_o] :
( ( A @ aTP_Lamm_fd @ collect_nat )
= ( A @ collect_nat @ uminus5710092332889474511et_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5588_Collect__neg__eq) ).
thf(5664,plain,
! [A: fun_nat_o] :
( ( A @ aTP_Lamm_fd @ collect_nat )
= ( A @ collect_nat @ uminus5710092332889474511et_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',fact_3127_max_Ocobounded1) ).
thf(2351,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)],[267]) ).
thf(1071,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_lv @ 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/sandbox2/benchmark/theBenchmark.p',fact_10091_ATP_Olambda__528) ).
thf(6141,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_lv @ 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)],[1071]) ).
thf(984,axiom,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3256_Leaf__0__not) ).
thf(5732,plain,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(419,axiom,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3900_unit__div__mult__swap) ).
thf(2993,plain,
! [A: nat,B: nat,C: nat] :
( ( one_one_nat @ ( A @ ( 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 @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_164_add__mono__thms__linordered__semiring_I1_J) ).
thf(1204,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)],[21]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',fact_915_order_Oorder__iff__strict) ).
thf(1449,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)],[75]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_3195_discrete) ).
thf(1812,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)],[149]) ).
thf(790,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__irrefl__nat) ).
thf(4858,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
<=> ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4052_gcd__nat_Ostrict__iff__order) ).
thf(1468,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(7201,plain,
$false,
inference(e,[status(thm)],[3021,3873,3883,5593,5136,4062,5950,5320,3979,1982,6042,1879,1337,1718,2094,1411,6167,1469,1369,1190,5390,6285,3397,2559,6121,6172,6263,4728,1818,1295,4037,1924,2104,5718,6162,2495,5878,3012,5224,1142,2380,5348,5501,5454,3185,5898,3317,4500,1522,4515,2395,5842,3549,1443,1808,6199,4391,2947,3959,1793,3402,4623,4408,1655,4739,3648,4110,1999,2933,2141,2434,3826,4247,3577,5120,1426,1608,4633,2607,2686,4575,5906,3942,4011,6359,2918,5701,3616,1233,3693,6078,6241,3121,3481,5782,6336,1954,5636,1507,5192,2763,2227,2010,2082,3140,5874,4760,4610,2405,1887,1196,6138,3836,3629,3350,5227,3634,5252,6251,3994,1914,4371,1441,2020,3513,5195,5825,1921,2173,6306,2819,5269,1623,1482,4775,2869,5553,3221,5429,4866,4563,6039,6274,2755,1871,3821,1826,1577,5989,4238,5953,2916,4524,3938,3029,4070,4151,3342,2269,6350,2217,3803,5108,6208,3043,5279,5461,2703,3517,4353,2049,2373,5480,3084,2635,4551,4793,5077,3268,4756,5744,1545,3463,1379,2169,1514,4664,2767,3734,4368,4952,6098,5727,2794,3887,3393,1373,6135,4724,5541,5156,1960,1183,4810,5834,6081,4411,2950,4205,6227,3934,4578,5597,2893,4297,5333,3163,2650,5856,3453,2451,1858,6187,6300,3525,1864,1828,2925,3973,1383,2254,1677,2540,5761,1581,2777,5360,5929,4718,2367,5401,5246,1351,2002,2242,4701,3226,5629,3870,5819,2392,2718,3378,5572,2964,1796,3036,4364,6221,1622,4996,5296,2750,1405,6210,1696,4483,3510,5695,6282,3229,1206,3450,3301,1153,5862,2641,1736,4172,4323,2910,4589,2473,6015,3720,3169,6296,4480,3265,2646,3531,5443,2164,6064,6058,2118,2047,5562,5416,4076,2737,4059,1868,4712,2601,6247,1519,2277,5266,1487,3610,5366,1387,1900,4466,6124,2805,6328,5044,1174,1502,5956,1824,4284,3816,6356,5102,2986,6178,2414,4836,2132,2890,4160,4661,5655,5465,2477,3877,2200,5658,2211,3763,5330,4027,2653,3271,4295,6303,3191,1938,4280,1602,3618,4994,3499,4385,1951,5779,4327,5038,3144,1159,4402,3535,4942,5201,1210,5566,2327,1634,5936,3033,1740,2377,4512,3218,2692,2726,4227,4883,3650,3916,1402,3731,4123,5313,6075,5189,5626,3699,2300,5714,4957,2157,5609,5221,3254,6101,5615,2841,6195,6028,2359,2973,2709,1227,6235,4845,3632,4095,5811,3746,6128,2638,6218,3018,4898,4518,3922,2830,1424,1584,4049,1329,3775,3311,3143,6175,4983,5915,5080,1292,3622,5992,5791,3714,6363,3728,4389,3596,4545,5263,1414,2240,6164,2613,5932,1810,4861,2108,2038,3671,2085,3555,4814,5387,1744,4530,1419,3242,5947,5374,1530,2465,3390,5058,4120,1874,1599,5603,5317,1263,3486,2125,3654,1478,1249,3354,6331,2153,2900,5639,3743,1192,4244,3760,3967,3409,3109,1979,2140,6224,2370,3215,3147,4148,2788,5310,4625,2043,3173,2748,2402,2440,2408,5249,4572,1241,5711,5833,1563,6070,6279,5887,1895,1167,5513,5198,5909,3841,6311,2617,2423,2529,3660,5327,2677,4872,5808,3890,3491,6084,3985,5960,5095,6052,4453,2121,6192,1278,1906,1135,2729,5722,5524,1754,4380,2275,2033,5969,3257,3607,2570,4438,4393,6001,2028,3375,5647,4017,5698,2970,2789,2525,2188,3472,3945,2514,5612,5099,6344,3604,2695,4000,3187,3925,2938,5474,3504,5395,2791,3086,1752,6019,1965,3223,1139,4127,5859,3783,2166,1897,4273,1464,3568,5556,3023,4558,1669,5363,2293,5471,5282,3663,4218,2935,4822,3340,5086,1332,4764,3123,2425,3416,6334,3304,5432,1224,2573,5578,2319,3532,6048,6144,6024,4790,5071,4337,5212,1408,2151,2383,1574,6217,6197,5054,3138,5689,3384,1349,2097,5853,5491,5901,3106,1542,5407,2945,3197,4154,6184,3066,2896,1571,1376,4509,1439,2197,4477,2065,6216,5114,2025,2742,4420,2343,4569,2111,5175,4731,5439,4208,1556,2252,2553,5410,6087,4430,5584,5035,1877,3133,3055,2446,4277,2757,5392,1838,1325,6319,3298,4652,3583,1344,2928,1177,4990,1688,1171,1396,5775,4232,2620,4373,6288,3159,1176,5575,2797,2101,4067,1973,2069,2770,4832,1213,3838,5377,2765,3423,5218,2244,2752,2022,3310,5849,1726,4954,5667,5299,2303,6293,4497,4626,2999,3348,5089,2506,3380,4084,5661,1948,4136,5528,5025,3161,2503,2629,6115,4722,5003,3571,6202,5435,1626,3009,4405,3031,5538,5587,3936,4901,5881,6276,2665,2471,5785,4292,2449,5678,4566,2684,3455,1472,2333,1145,4113,5047,1798,5822,3507,4864,3112,2192,3214,3754,1647,4641,1780,4630,2689,6012,4658,2942,2567,1845,6362,1516,2863,6238,2661,5125,1611,2375,5111,1156,4939,4366,3833,4534,2732,5074,3129,3949,3786,2386,1230,2160,4593,2888,2882,5018,3246,1637,5912,3026,1235,3828,3329,4117,4164,5235,5767,2092,4092,4905,6244,1790,5420,6036,2454,4145,3823,5995,1317,1763,4241,2903,2545,2599,1679,3412,3564,5186,5062,2411,1766,5675,4133,4235,4342,5083,2266,3288,2675,5147,2838,3970,2113,5998,5240,1221,1284,5504,2843,1485,2711,6213,2579,5633,4143,1427,2807,1272,2760,2458,2626,4606,2088,1553,3447,2194,3928,2209,3625,3593,1421,2013,3400,3478,1459,2045,3092,4945,1180,1685,2885,3171,2960,2078,1834,2997,1189,3320,2305,2071,2658,5068,2907,1590,2443,3613,2594,6322,3484,2855,2290,4468,5351,4542,3991,4527,2262,5600,2283,4806,1476,2532,5800,5132,3501,3003,5243,1523,3331,3136,3181,5162,1308,1706,5549,2183,2036,2315,2739,5336,2956,6257,2399,2041,3497,3879,6290,3844,3430,6118,5692,4299,6045,2462,5837,5023,4387,2576,5144,1661,5590,4446,4869,2623,1994,3552,5287,3420,1614,4880,5357,1774,5009,3705,5129,2534,6131,3987,5764,1757,3690,5398,1133,5051,4816,6055,4670,5606,3601,2233,2522,3100,2815,2736,4787,1303,4841,1527,5884,3337,5477,3132,3203,5926,3062,3469,5041,2186,3177,5413,5741,1710,3323,5215,5324,5559,3982,3822,2800,3956,4303,4051,5159,1495,5404,5092,3558,5290,4427,4474,5105,2746,1335,4024,3426,1891,3673,1346,1742,6269,2353,3244,6190,3362,5204,1261,3543,5151,5581,3489,5681,5354,3076,4345,1399,5344,6155,2803,2847,2898,4382,2485,1550,6205,1357,4506,5623,4229,6104,4395,1885,3812,3494,4221,5845,4335,5155,3580,5986,6158,1945,1565,2866,5788,1416,4908,3637,5293,2980,2177,6067,4655,2879,5458,4555,2206,4784,4949,4767,3405,1848,2059,5569,4752,4742,4313,6254,3443,5664,2351,6141,5732,2993,1204,1449,1812,4858,1468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.42 % Computer : n026.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 18:24:54 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.70/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 8.50/2.53 % [INFO] Parsing done (1785ms).
% 8.50/2.55 % [INFO] Running in sequential loop mode.
% 10.03/2.93 % [INFO] eprover registered as external prover.
% 10.03/2.94 % [INFO] Scanning for conjecture ...
% 13.78/4.02 % [INFO] Found a conjecture (or negated_conjecture) and 10343 axioms. Running axiom selection ...
% 17.15/5.45 % [INFO] Axiom selection finished. Selected 1130 axioms (removed 9213 axioms).
% 19.66/6.08 % [INFO] Problem is typed first-order (TPTP TFF).
% 20.10/6.13 % [INFO] Type checking passed.
% 20.10/6.14 % [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 ...
% 50.66/16.58 % External prover 'e' found a proof!
% 50.66/16.59 % [INFO] Killing All external provers ...
% 50.66/16.59 % Time passed: 16075ms (effective reasoning time: 14029ms)
% 50.66/16.59 % 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)>
% 50.82/16.61 % Axioms used in derivation (1130): fact_64_set__update__subsetI, fact_857_add__pos__nonneg, fact_539_ord__eq__le__trans, fact_813_order__less__imp__triv, fact_3079_power__gt__expt, fact_3050_less__add__Suc2, fact_3383_div__mult1__eq, fact_8697_fact__mono__nat, fact_3902_unit__div__commute, fact_8122_zero__less__binomial, fact_849_add__nonneg__pos, fact_213_trans__less__add2, fact_3036_Ex__less__Suc2, fact_134_nat__le__linear, fact_3356_VEBT__internal_Ovalid_H_Osimps_I1_J, fact_5083_nat__eq__add__iff2, fact_48_add__right__cancel, fact_2285_divisors__zero, fact_3848_power__le__dvd, fact_3052_less__imp__Suc__add, fact_2919_add__Suc__right, fact_24_nat__add__left__cancel__less, fact_54_list__update__overwrite, fact_499_nth__mem, fact_6893_of__nat__neq__0, fact_2351_nat__mult__max__left, fact_5122_power__diff, fact_8117_binomial__n__0, fact_6875_mult__of__nat__commute, fact_3025_lift__Suc__mono__le, fact_1806_zero__less__power, fact_2854_one__less__power, fact_414_comm__monoid__add__class_Oadd__0, fact_4364_Nat_Odiff__diff__right, fact_568_dual__order_Oeq__iff, fact_135_le__antisym, fact_9514_sort__upt, fact_1850_power__strict__mono, fact_125_linorder__neqE__nat, fact_380_neq__if__length__neq, fact_274_not__gr__zero, fact_3038_Suc__le__eq, fact_3049_less__add__Suc1, fact_5131_nat__less__add__iff2, fact_5358_list__decode_Ocases, fact_3032_less__Suc__eq__0__disj, fact_2347_add__mult__distrib2, fact_4775_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_3765_gcd__nat_Oextremum__strict, fact_5081_less__diff__conv2, fact_408_not__less__zero, fact_1957_mult__0__right, fact_2496_mult__pos__neg2, fact_460_add__decreasing2, fact_2946_one__le__mult__iff, fact_2346_le__cube, fact_8639_fact__0, fact_3544_dvd__imp__mod__0, fact_3151_max_OcoboundedI2, fact_2998_Suc__leD, fact_4923_Nat_Ole__imp__diff__is__add, fact_4715_diff__add__inverse, fact_544_ord__le__eq__trans, fact_8__C0_C, fact_718_not__less__iff__gr__or__eq, fact_3894_dvd__div__eq__mult, fact_3058_Suc__eq__plus1__left, fact_2890_max__less__iff__conj, fact_687_antisym__conv3, fact_4046_gcd__nat_Oantisym, fact_949_dual__order_Oorder__iff__strict, fact_833_order__less__imp__not__less, fact_3387_div__less__mono, fact_2500_mult__pos__pos, fact_6758_of__nat__add, fact_4528_of__bool__eq__iff, fact_1651_minf_I4_J, fact_68_add__right__imp__eq, fact_3347_gcd__nat__induct, fact_2908_max_Oabsorb2, fact_7732_fold__atLeastAtMost__nat_Osimps, fact_2983_Suc__lessE, fact_4913_Suc__diff__le, fact_5677_take__bit__0, fact_4534_diff__commute, fact_313_bot__nat__0_Oextremum, fact_4774_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_3043_less__Suc__eq__le, fact_3760_div__div__div__same, fact_3143_max_Oabsorb__iff2, fact_1902_mult__eq__0__iff, fact_2451_mult__mono, fact_915_order_Oorder__iff__strict, fact_9732_ATP_Olambda__169, fact_3736_one__dvd, fact_1987_div__mult__mult1, fact_9807_ATP_Olambda__244, fact_503_list__ball__nth, fact_2093_nat__mult__div__cancel__disj, fact_226_add__leD2, fact_2984_Suc__lessI, fact_3279_mod__mult__self2__is__0, fact_3949_dvd__mult__cancel2, fact_146_add__le__imp__le__left, fact_704_exists__least__iff, fact_3388_mod__eq__nat1E, fact_1997_nonzero__mult__div__cancel__left, fact_4212_diff__diff__left, fact_1711_div__by__0, fact_9714_ATP_Olambda__151, fact_9895_ATP_Olambda__332, fact_3193_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_2212_comm__monoid__mult__class_Omult__1, fact_10100_ATP_Olambda__537, fact_2220_mult_Ocommute, fact_252_valid__eq, fact_2987_Ex__less__Suc, fact_3345_mod__Suc, fact_3386_mod__le__divisor, fact_5079_nat__diff__split, fact_3518_dvd__times__left__cancel__iff, fact_1611_pinf_I2_J, fact_991_order__le__less, fact_3542_div__add, fact_3481_dvd__0__left__iff, fact_4798_linordered__semidom__class_Oadd__diff__inverse, fact_2913_nat_Oinject, fact_6784_of__nat__of__bool, fact_1825_power__eq__imp__eq__base, fact_1621_pinf_I4_J, fact_613_order__eq__refl, fact_4169_add__diff__cancel__right_H, fact_2340_less__numeral__extra_I4_J, fact_18_nth__list__update__neq, fact_4__C12_C, fact_4929_bezout1__nat, fact_4772_diff__add, fact_573_dual__order_Oantisym, fact_9544_Least__Suc2, fact_2992_less__antisym, fact_3816_dvd__div__mult, fact_3048_less__natE, fact_4043_gcd__nat_Otrans, fact_3054_One__nat__def, fact_2394_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_8113_binomial__1, fact_4467_Suc__diff__1, fact_8120_choose__mult__lemma, fact_3892_div__dvd__iff__mult, fact_3795_minf_I10_J, fact_2971_Zero__neq__Suc, fact_3912_is__unit__power__iff, fact_1_False, fact_278_add_Oright__neutral, fact_248_buildup__gives__valid, fact_3020_lift__Suc__mono__less__iff, fact_490_canonically__ordered__monoid__add__class_OlessE, fact_2994_less__trans__Suc, fact_4352_diff__is__0__eq_H, fact_2995_less__Suc__induct, fact_2895_max_Oabsorb4, fact_216_not__add__less2, fact_845_add__neg__nonpos, fact_3067_power__le__imp__le__base, fact_3161_max_Ostrict__boundedE, fact_676_ord__eq__less__trans, fact_2872_div__le__mono, fact_3900_unit__div__mult__swap, fact_4933_mod__geq, fact_2876_div__greater__zero__iff, fact_4912_diff__less, fact_4228_of__bool__less__iff, fact_2654_mult__le__less__imp__less, fact_9558_last__upt, fact_2142_nat__mult__le__cancel__disj, fact_583_antisym, fact_10091_ATP_Olambda__528, fact_4286_le__add__diff__inverse2, fact_3779_not__is__unit__0, fact_4753_split__of__bool, fact_2508_mult__neg__pos, fact_464_add__increasing2, fact_1409_pinf_I6_J, fact_3632_dvd__trans, fact_5129_add__eq__if, fact_3908_unit__eq__div1, fact_5708_take__bit__tightened__less__eq__nat, fact_3343_div__add1__eq, fact_9630_ATP_Olambda__67, fact_1598_replicate__length__same, fact_2354_times__div__less__eq__dividend, fact_4214_of__bool__less__eq__iff, fact_563_linorder__wlog, fact_230_add__leE, fact_44_min__Null__member, fact_1960_nat__1__eq__mult__iff, fact_5088_mod__eq__dvd__iff__nat, fact_2089_nat__mult__less__cancel__disj, fact_5689_take__bit__of__Suc__0, fact_3711_dvd__mult2, fact_365_add__gr__0, fact_249_set__vebt__set__vebt_H__valid, fact_6901_less__imp__of__nat__less, fact_2980_nat_Odistinct_I1_J, fact_2343_mult__le__mono1, fact_115_group__cancel_Oadd1, fact_2650_mult__less__le__imp__less, fact_733_dual__order_Ostrict__implies__not__eq, fact_3553_length__product, fact_3922_dvd__mult__cancel, fact_2647_split__div, fact_2225_mult_Ocomm__neutral, fact_1956_mult__is__0, fact_2850_self__le__power, fact_1812_power__less__imp__less__base, fact_1007_linorder__not__less, fact_3319_mod__add__cong, fact_4743_of__bool__less__eq__one, fact_3783_pinf_I9_J, fact_370_nth__list__update__eq, fact_4702_minus__nat_Odiff__0, fact_9748_ATP_Olambda__185, fact_3881_unit__dvdE, fact_23_nat__add__left__cancel__le, fact_6924_of__nat__max, fact_2265_power__gt1__lemma, fact_9550_zero__natural_Orsp, fact_9505_map__decr__upt, fact_5588_Collect__neg__eq, fact_9489_upt__conv__Cons__Cons, fact_1959_mult__cancel2, fact_4353_diff__is__0__eq, fact_4781_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_8753_fact__ge__Suc__0__nat, fact_1815_zero__power, fact_2993_Suc__less__SucD, fact_646_order__antisym__conv, fact_2143_mult__le__cancel2, fact_3536_unit__div, fact_2582_zero__less__one, fact_979_order_Ostrict__implies__order, fact_3719_dvd__triv__left, fact_3302_Suc__mod__mult__self3, fact_8118_binomial__eq__0, fact_272_valid__tree__deg__neq__0, fact_296_add__cancel__right__left, fact_3262_mod__by__0, fact_4050_gcd__nat_Ostrict__iff__not, fact_1606_pinf_I1_J, fact_1641_minf_I2_J, fact_72_add__left__imp__eq, fact_2979_old_Onat_Odistinct_I2_J, fact_107_Collect__cong, fact_291_add__cancel__left__right, fact_8131_choose__reduce__nat, fact_3051_less__iff__Suc__add, fact_681_ord__less__eq__trans, fact_4600_right__diff__distrib_H, fact_27_add__less__cancel__left, fact_207_le__neq__implies__less, fact_164_add__mono__thms__linordered__semiring_I1_J, fact_6_in__children__def, fact_4556_of__bool__conj, fact_5128_div__geq, fact_3752_dvd__add, fact_9495_upt__eq__Cons__conv, fact_8124_choose__mult, fact_3896_unit__div__eq__0__iff, fact_2229_mult_Oleft__commute, fact_4920_Nat_Ole__diff__conv2, fact_1082_linorder__le__less__linear, fact_136_eq__imp__le, fact_2310_distrib__left, fact_1636_minf_I1_J, fact_2472_mult__strict__left__mono, fact_2578_not__one__less__zero, fact_3822_dvd__div__mult2__eq, fact_353_less__add__same__cancel1, fact_692_linorder__cases, fact_3039_dec__induct, fact_3950_dvd__mult__cancel1, fact_5130_nat__less__add__iff1, fact_3814_unit__mult__right__cancel, fact_3156_less__max__iff__disj, fact_3906_unit__eq__div2, fact_1399_minf_I6_J, fact_480_add__nonpos__eq__0__iff, fact_534_order__class_Oorder__eq__iff, fact_2067_power__inject__exp, fact_5175_power__minus__mult, fact_208_less__or__eq__imp__le, fact_2613_less__add__one, fact_3840_dvd__eq__mod__eq__0, fact_488_add__pos__pos, fact_7102_pochhammer__Suc, fact_4045_gcd__nat_Oirrefl, fact_1025_order__neq__le__trans, fact_4706_le__diff__iff, fact_5138_bot__empty__eq2, fact_433_bot__nat__0_Oextremum__unique, fact_427_not__gr0, fact_3490_dvd__add__triv__right__iff, fact_366_list__update__beyond, fact_3176_max_Ostrict__coboundedI2, fact_876_leI, fact_4365_diff__Suc__1, fact_8132_times__binomial__minus1__eq, fact_2203_power__decreasing__iff, fact_3530_dvd__add__times__triv__left__iff, fact_4773_le__add__diff, fact_8114_binomial__0__Suc, fact_2247_mult__left__le, fact_210_less__imp__le__nat, fact_748_linorder__neq__iff, fact_2842_power__decreasing, fact_8760_fact__div__fact__le__pow, fact_1703_div__0, fact_3001_Suc__le__D, fact_2280_no__zero__divisors, fact_1594_replicate__eqI, fact_1288_le__numeral__extra_I3_J, fact_4927_dvd__diffD1, fact_3011_Suc__mult__cancel1, fact_4411_diff__Suc__diff__eq1, fact_241_add__mono__thms__linordered__field_I3_J, fact_468_add__nonneg__nonneg, fact_3526_dvd__add__times__triv__right__iff, fact_3257_deg1Leaf, fact_41_valid__member__both__member__options, fact_2941_power__Suc__0, fact_3500_nat__mult__dvd__cancel__disj, fact_985_dual__order_Ostrict__implies__order, fact_273_le__zero__eq, fact_2387_power__Suc__less, fact_4713_Nat_Odiff__cancel, fact_3291_mod__mult__self3, fact_271_valid__0__not, fact_3119_max_OboundedI, fact_3808_dvd__mult__unit__iff_H, fact_3534_dvd__mult__div__cancel, fact_2561_nat__mult__le__cancel1, fact_4777_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_3057_Suc__div__le__mono, fact_1484_max__nat_Oleft__neutral, fact_3522_unit__prod, fact_3281_mod__by__1, fact_2522_add__scale__eq__noteq, fact_316_Nat_Oadd__0__right, fact_3919_dvd__imp__le, fact_955_dual__order_Ostrict__iff__order, fact_4240_of__bool__or__iff, fact_2916_Suc__mono, fact_5704_take__bit__add, fact_5671_take__bit__of__0, fact_3560_unit__mult__div__div, fact_9569_ATP_Olambda__6, fact_2976_old_Onat_Oexhaust, fact_3083_power__Suc__le__self, fact_3348_mod__less__divisor, 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fact_3787_pinf_I10_J, fact_7252_pochhammer__code, fact_349_add__less__same__cancel2, fact_3943_dvd__power, fact_4748_of__bool__def, fact_6807_of__nat__Suc, fact_2925_max__Suc__Suc, fact_221_trans__le__add2, fact_2644_less__eq__div__iff__mult__less__eq, fact_3723_mult__dvd__mono, fact_4351_zero__less__diff, fact_2636_div__eq__dividend__iff, fact_1088_order__le__imp__less__or__eq, fact_1558_nat__add__max__right, fact_3824_dvd__mult__imp__div, fact_1037_order__less__le__trans, fact_2658_mult__right__le__imp__le, fact_2904_max_Obounded__iff, fact_3842_mod__0__imp__dvd, fact_3910_unit__imp__mod__eq__0, fact_80_add_Ocommute, fact_3287_mod__div__trivial, fact_728_order_Ostrict__implies__not__eq, fact_973_dual__order_Ostrict__iff__not, fact_9177_triangle__Suc, fact_2413_mult__nonneg__nonneg, fact_7035_pochhammer__0, fact_6801_of__nat__le__0__iff, fact_2132_div__mult__self3, fact_431_infinite__descent0, fact_2424_mult__right__mono, fact_2767_power__le__one, fact_1031_order__le__less__trans, fact_3__C8_C, fact_3103_max_Omono, fact_2991_Suc__less__eq2, fact_3055_Suc__mult__le__cancel1, fact_2981_Nat_OlessE, fact_2134_div__mult__self2, fact_758_order__less__trans, fact_52_add__left__cancel, fact_3769_dvd__mod__imp__dvd, fact_1336_bounded__Max__nat, fact_588_Orderings_Oorder__eq__iff, fact_4707_Nat_Odiff__diff__eq, fact_3075_one__less__mult, fact_2970_Zero__not__Suc, fact_3395_mod__mult2__eq, fact_3715_dvd__mult__left, fact_314_le0, fact_2594_mult__less__mono2, fact_697_dual__order_Oasym, fact_2939_div__by__Suc__0, fact_3402_Suc__times__mod__eq, fact_4776_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_119_add__mono__thms__linordered__semiring_I4_J, fact_4049_gcd__nat_Ostrict__trans2, fact_137_le__trans, fact_2996_strict__inc__induct, fact_3004_not__less__eq__eq, fact_218_add__less__mono, fact_4710_le__diff__iff_H, fact_2989_not__less__eq, fact_2566_not__one__le__zero, fact_495_ex__least__nat__le, fact_9477_length__upt, fact_641_linorder__le__cases, fact_3063_power__inject__base, fact_708_linorder__less__wlog, fact_2646_dividend__less__div__times, fact_3139_max_Oabsorb__iff1, fact_3864_bezout__add__nat, fact_1985_div__mult__mult2, fact_6827_of__nat__0__less__iff, fact_153_less__eqE, fact_3888_dvd__div__div__eq__mult, fact_3379_cancel__div__mod__rules_I1_J, fact_2008_nonzero__mult__div__cancel__right, fact_1270_subset__eq, fact_3671_lambda__one, fact_148_le__iff__add, fact_2235_one__reorient, fact_317_length__list__update, fact_5170_power__eq__if, fact_223_add__le__mono1, fact_2637_div__less__dividend, fact_2774_power__0__left, fact_3757_dvd__div__eq__cancel, fact_3828_unit__div__cancel, fact_6748_of__nat__le__iff, fact_1912_mult__zero__left, fact_8761_binomial__fact__lemma, fact_2290_mult__not__zero, fact_853_add__nonpos__neg, fact_4053_gcd__nat_Ostrict__implies__order, fact_3791_minf_I9_J, fact_3836_div__plus__div__distrib__dvd__left, fact_434_bot__nat__0_Oextremum__uniqueI, fact_9795_ATP_Olambda__232, fact_2634_one__le__power, 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% 50.82/16.61 % No. of inferences in proof: 2273
% 50.82/16.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16075 ms resp. 14029 ms w/o parsing
% 53.30/17.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.30/17.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------