%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP225_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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:36:56 AM UTC 2026
% Result : Theorem 58.50s 19.23s
% Output : Refutation 63.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1896
% Syntax : Number of formulae : 3794 (1476 unt; 0 typ; 0 def)
% Number of atoms : 9691 (4318 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 59809 (1110 ~; 254 |;1159 &;52909 @)
% ( 510 <=>;3867 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 316 ( 315 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 289 ( 286 usr; 100 con; 0-8 aty)
% Number of variables : 8047 ( 0 ^;7674 !; 261 ?;8047 :)
% ( 0 !>; 0 ?*; 0 @-; 112 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_Co1105491363547889651atural_type,type,
fun_Co1105491363547889651atural: $tType ).
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_o: $tType ).
thf(fun_fu5323616038969315652_int_o_type,type,
fun_fu5323616038969315652_int_o: $tType ).
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(fun_Pr7769407664385210434atural_type,type,
fun_Pr7769407664385210434atural: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(fun_Pr3592279944642289454ural_o_type,type,
fun_Pr3592279944642289454ural_o: $tType ).
thf(fun_li6914387844523535256_nat_o_type,type,
fun_li6914387844523535256_nat_o: $tType ).
thf(fun_Pr1263128411319240110enat_o_type,type,
fun_Pr1263128411319240110enat_o: $tType ).
thf(fun_fu1950632212952468284_rat_o_type,type,
fun_fu1950632212952468284_rat_o: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(fun_Pr1308109350235310159nt_int_type,type,
fun_Pr1308109350235310159nt_int: $tType ).
thf(fun_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_fu4306744791715064858_rat_o_type,type,
fun_fu4306744791715064858_rat_o: $tType ).
thf(fun_fu6699046866436802030_int_o_type,type,
fun_fu6699046866436802030_int_o: $tType ).
thf(fun_Pr8877776288780692068_nat_o_type,type,
fun_Pr8877776288780692068_nat_o: $tType ).
thf(fun_fu3064074204415222357nt_int_type,type,
fun_fu3064074204415222357nt_int: $tType ).
thf(fun_fu1098312133097393581at_rat_type,type,
fun_fu1098312133097393581at_rat: $tType ).
thf(fun_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_fu9045186299510176150at_o_o_type,type,
fun_fu9045186299510176150at_o_o: $tType ).
thf(fun_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(fun_fu6910828598506988974real_o_type,type,
fun_fu6910828598506988974real_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(produc5835291356934675326atural_type,type,
produc5835291356934675326atural: $tType ).
thf(fun_fu7677565902479959693_rat_o_type,type,
fun_fu7677565902479959693_rat_o: $tType ).
thf(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(fun_VE2573032740582156747_nat_o_type,type,
fun_VE2573032740582156747_nat_o: $tType ).
thf(fun_fu8391177546919232046_nat_o_type,type,
fun_fu8391177546919232046_nat_o: $tType ).
thf(fun_fu7503566767892366382_int_o_type,type,
fun_fu7503566767892366382_int_o: $tType ).
thf(fun_Pr2028404973800837934_nat_o_type,type,
fun_Pr2028404973800837934_nat_o: $tType ).
thf(fun_Pr9018117161326028078_int_o_type,type,
fun_Pr9018117161326028078_int_o: $tType ).
thf(fun_fu3711856879280950809l_real_type,type,
fun_fu3711856879280950809l_real: $tType ).
thf(fun_fu6579618355643354601at_rat_type,type,
fun_fu6579618355643354601at_rat: $tType ).
thf(fun_fu1400560744564786701nteger_type,type,
fun_fu1400560744564786701nteger: $tType ).
thf(fun_fu2034268335391280352ural_o_type,type,
fun_fu2034268335391280352ural_o: $tType ).
thf(fun_fu726873822431485118eger_o_type,type,
fun_fu726873822431485118eger_o: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_in2204242111582549184nt_int_type,type,
fun_in2204242111582549184nt_int: $tType ).
thf(fun_Co6597186368970283863nteger_type,type,
fun_Co6597186368970283863nteger: $tType ).
thf(fun_fu9090758901314268781nt_o_o_type,type,
fun_fu9090758901314268781nt_o_o: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_Pr2478283820680522243nt_int_type,type,
fun_Pr2478283820680522243nt_int: $tType ).
thf(fun_fu8643405727515436425nteger_type,type,
fun_fu8643405727515436425nteger: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_fu1590586450949517859at_nat_type,type,
fun_fu1590586450949517859at_nat: $tType ).
thf(fun_fu6924846375782198887atural_type,type,
fun_fu6924846375782198887atural: $tType ).
thf(fun_fu2499394402704830801nteger_type,type,
fun_fu2499394402704830801nteger: $tType ).
thf(fun_fu6921880696561781257nteger_type,type,
fun_fu6921880696561781257nteger: $tType ).
thf(fun_fu3628599891403802633nteger_type,type,
fun_fu3628599891403802633nteger: $tType ).
thf(fun_fu5956788528830221615omplex_type,type,
fun_fu5956788528830221615omplex: $tType ).
thf(fun_fu6196024946523381971eger_o_type,type,
fun_fu6196024946523381971eger_o: $tType ).
thf(fun_fu5589980185390252312t_real_type,type,
fun_fu5589980185390252312t_real: $tType ).
thf(fun_fu7075445697382584196_int_o_type,type,
fun_fu7075445697382584196_int_o: $tType ).
thf(fun_fu4413992040155564420at_nat_type,type,
fun_fu4413992040155564420at_nat: $tType ).
thf(fun_Co6813818151677833714atural_type,type,
fun_Co6813818151677833714atural: $tType ).
thf(fun_Co1981900195452921617nteger_type,type,
fun_Co1981900195452921617nteger: $tType ).
thf(fun_fu7981297689148232565al_o_o_type,type,
fun_fu7981297689148232565al_o_o: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(list_P5578671422887162913nteger_type,type,
list_P5578671422887162913nteger: $tType ).
thf(fun_fu7714627026455246123x_real_type,type,
fun_fu7714627026455246123x_real: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(fun_fu3380082687118895412nteger_type,type,
fun_fu3380082687118895412nteger: $tType ).
thf(fun_fu40286998686754419omplex_type,type,
fun_fu40286998686754419omplex: $tType ).
thf(fun_fu2990765671291504771ex_rat_type,type,
fun_fu2990765671291504771ex_rat: $tType ).
thf(fun_fu705315015666092147ex_nat_type,type,
fun_fu705315015666092147ex_nat: $tType ).
thf(fun_na6632006986671646835omplex_type,type,
fun_na6632006986671646835omplex: $tType ).
thf(fun_fu4846507671440591850_rat_o_type,type,
fun_fu4846507671440591850_rat_o: $tType ).
thf(fun_fu5908277796454533188_int_o_type,type,
fun_fu5908277796454533188_int_o: $tType ).
thf(fun_fu6714665071556184448_rat_o_type,type,
fun_fu6714665071556184448_rat_o: $tType ).
thf(fun_fu9201817095025044880_nat_o_type,type,
fun_fu9201817095025044880_nat_o: $tType ).
thf(fun_fu4208408993564413984_int_o_type,type,
fun_fu4208408993564413984_int_o: $tType ).
thf(fun_na927404270896789692_nat_o_type,type,
fun_na927404270896789692_nat_o: $tType ).
thf(fun_fu1622112948621879430al_o_o_type,type,
fun_fu1622112948621879430al_o_o: $tType ).
thf(fun_fu4168831735773172575er_o_o_type,type,
fun_fu4168831735773172575er_o_o: $tType ).
thf(fun_Pr4738963024209204295_int_o_type,type,
fun_Pr4738963024209204295_int_o: $tType ).
thf(fun_Pr7537129237977221859_rat_o_type,type,
fun_Pr7537129237977221859_rat_o: $tType ).
thf(fun_na3970208099681795815_nat_o_type,type,
fun_na3970208099681795815_nat_o: $tType ).
thf(fun_fu3077872570260440615l_real_type,type,
fun_fu3077872570260440615l_real: $tType ).
thf(fun_na7078387940644931716nteger_type,type,
fun_na7078387940644931716nteger: $tType ).
thf(fun_Co6226381647958292740nteger_type,type,
fun_Co6226381647958292740nteger: $tType ).
thf(fun_Co8521658056209057742er_num_type,type,
fun_Co8521658056209057742er_num: $tType ).
thf(fun_Co3583066429914935172er_nat_type,type,
fun_Co3583066429914935172er_nat: $tType ).
thf(fun_Co1092983284983208416er_int_type,type,
fun_Co1092983284983208416er_int: $tType ).
thf(fun_re8542384036533109323t_real_type,type,
fun_re8542384036533109323t_real: $tType ).
thf(fun_re4112884445705685835l_real_type,type,
fun_re4112884445705685835l_real: $tType ).
thf(list_P7037539587688870467BT_nat_type,type,
list_P7037539587688870467BT_nat: $tType ).
thf(list_P4547456442757143711BT_int_type,type,
list_P4547456442757143711BT_int: $tType ).
thf(produc8243902056947475879T_VEBT_type,type,
produc8243902056947475879T_VEBT: $tType ).
thf(fun_fu2598743018846156927al_rat_type,type,
fun_fu2598743018846156927al_rat: $tType ).
thf(fun_fu3214020956574444655al_nat_type,type,
fun_fu3214020956574444655al_nat: $tType ).
thf(fun_fu6899955116716589935t_real_type,type,
fun_fu6899955116716589935t_real: $tType ).
thf(fun_fu121957152452960295t_real_type,type,
fun_fu121957152452960295t_real: $tType ).
thf(fun_na5225841814499866095t_real_type,type,
fun_na5225841814499866095t_real: $tType ).
thf(fun_li1025265955262268170_nat_o_type,type,
fun_li1025265955262268170_nat_o: $tType ).
thf(produc7822875418678951345atural_type,type,
produc7822875418678951345atural: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(fun_fu6119738925743952495t_real_type,type,
fun_fu6119738925743952495t_real: $tType ).
thf(fun_na7718645245721260691t_real_type,type,
fun_na7718645245721260691t_real: $tType ).
thf(fun_VE2962686792283380846VEBT_o_type,type,
fun_VE2962686792283380846VEBT_o: $tType ).
thf(produc7272778201969148633d_enat_type,type,
produc7272778201969148633d_enat: $tType ).
thf(fun_fu8328862064278946247at_rat_type,type,
fun_fu8328862064278946247at_rat: $tType ).
thf(fun_fu7002938529518989751at_nat_type,type,
fun_fu7002938529518989751at_nat: $tType ).
thf(fun_fu8464300013002972271at_int_type,type,
fun_fu8464300013002972271at_int: $tType ).
thf(fun_fu8905809029841901679nt_nat_type,type,
fun_fu8905809029841901679nt_nat: $tType ).
thf(fun_fu1143798476471108391nt_int_type,type,
fun_fu1143798476471108391nt_int: $tType ).
thf(fun_na3244735409550470327at_nat_type,type,
fun_na3244735409550470327at_nat: $tType ).
thf(fun_na7654559027617327379at_int_type,type,
fun_na7654559027617327379at_int: $tType ).
thf(fun_fu2916398056546941156ural_o_type,type,
fun_fu2916398056546941156ural_o: $tType ).
thf(fun_fu1769128043447206010eger_o_type,type,
fun_fu1769128043447206010eger_o: $tType ).
thf(fun_Co7302518231560758906ural_o_type,type,
fun_Co7302518231560758906ural_o: $tType ).
thf(fun_Co2081214437782444048eger_o_type,type,
fun_Co2081214437782444048eger_o: $tType ).
thf(fun_fu7564235448449272366at_o_o_type,type,
fun_fu7564235448449272366at_o_o: $tType ).
thf(fun_fu6971708032831053102nt_o_o_type,type,
fun_fu6971708032831053102nt_o_o: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(fun_ra4503298312962071866nt_int_type,type,
fun_ra4503298312962071866nt_int: $tType ).
thf(fun_Pr2602117396471556196at_nat_type,type,
fun_Pr2602117396471556196at_nat: $tType ).
thf(fun_Pr7647638413817135296at_int_type,type,
fun_Pr7647638413817135296at_int: $tType ).
thf(fun_Pr1652463973008025892nt_rat_type,type,
fun_Pr1652463973008025892nt_rat: $tType ).
thf(fun_na1476630412504255114at_nat_type,type,
fun_na1476630412504255114at_nat: $tType ).
thf(fun_in4514472496968388910at_nat_type,type,
fun_in4514472496968388910at_nat: $tType ).
thf(fun_in4211310926729683942nt_int_type,type,
fun_in4211310926729683942nt_int: $tType ).
thf(fun_na819858167508000762st_nat_type,type,
fun_na819858167508000762st_nat: $tType ).
thf(fun_fu1771228864347509049real_o_type,type,
fun_fu1771228864347509049real_o: $tType ).
thf(fun_re8658731967611918585t_real_type,type,
fun_re8658731967611918585t_real: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(fun_nu2537414170016844299nteger_type,type,
fun_nu2537414170016844299nteger: $tType ).
thf(fun_na8135612474337863287nteger_type,type,
fun_na8135612474337863287nteger: $tType ).
thf(fun_na1591161823130732966omplex_type,type,
fun_na1591161823130732966omplex: $tType ).
thf(fun_co3258106519541737638omplex_type,type,
fun_co3258106519541737638omplex: $tType ).
thf(fun_na7928631014926962227_nat_o_type,type,
fun_na7928631014926962227_nat_o: $tType ).
thf(fun_in5570076352459579423_int_o_type,type,
fun_in5570076352459579423_int_o: $tType ).
thf(fun_Su884838341992399436at_nat_type,type,
fun_Su884838341992399436at_nat: $tType ).
thf(fun_na3635074868517587788at_nat_type,type,
fun_na3635074868517587788at_nat: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(fun_VE3165209603783583043T_VEBT_type,type,
fun_VE3165209603783583043T_VEBT: $tType ).
thf(fun_Pr4796943543331071514_nat_o_type,type,
fun_Pr4796943543331071514_nat_o: $tType ).
thf(fun_Pr3238374608701176162_int_o_type,type,
fun_Pr3238374608701176162_int_o: $tType ).
thf(fun_na7234455742697417626_nat_o_type,type,
fun_na7234455742697417626_nat_o: $tType ).
thf(fun_na6887940067898170868VEBT_o_type,type,
fun_na6887940067898170868VEBT_o: $tType ).
thf(fun_na1142814060743658952omplex_type,type,
fun_na1142814060743658952omplex: $tType ).
thf(fun_Co7398788559141407565atural_type,type,
fun_Co7398788559141407565atural: $tType ).
thf(fun_Co2940338738630218498nteger_type,type,
fun_Co2940338738630218498nteger: $tType ).
thf(fun_Co3734316457315071362atural_type,type,
fun_Co3734316457315071362atural: $tType ).
thf(fun_Co8499238673658658103nteger_type,type,
fun_Co8499238673658658103nteger: $tType ).
thf(fun_na8563630686737515764_nat_o_type,type,
fun_na8563630686737515764_nat_o: $tType ).
thf(fun_na2240068485812228818ural_o_type,type,
fun_na2240068485812228818ural_o: $tType ).
thf(fun_in4891666191172872833eger_o_type,type,
fun_in4891666191172872833eger_o: $tType ).
thf(fun_co1148497455491383662plex_o_type,type,
fun_co1148497455491383662plex_o: $tType ).
thf(fun_re7681423839302404990l_real_type,type,
fun_re7681423839302404990l_real: $tType ).
thf(set_Sum_sum_nat_nat_type,type,
set_Sum_sum_nat_nat: $tType ).
thf(fun_re4238438383274954274t_real_type,type,
fun_re4238438383274954274t_real: $tType ).
thf(fun_na6724076748692969250l_real_type,type,
fun_na6724076748692969250l_real: $tType ).
thf(list_P6285523579766656935_o_nat_type,type,
list_P6285523579766656935_o_nat: $tType ).
thf(list_P3795440434834930179_o_int_type,type,
list_P3795440434834930179_o_int: $tType ).
thf(produc334124729049499915VEBT_o_type,type,
produc334124729049499915VEBT_o: $tType ).
thf(produc2504756804600209347T_VEBT_type,type,
produc2504756804600209347T_VEBT: $tType ).
thf(fun_fun_nat_rat_real_type,type,
fun_fun_nat_rat_real: $tType ).
thf(fun_real_fun_nat_rat_type,type,
fun_real_fun_nat_rat: $tType ).
thf(fun_nat_fun_nat_real_type,type,
fun_nat_fun_nat_real: $tType ).
thf(fun_list_VEBT_VEBT_o_type,type,
fun_list_VEBT_VEBT_o: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(fun_rat_fun_rat_rat_type,type,
fun_rat_fun_rat_rat: $tType ).
thf(fun_rat_fun_nat_rat_type,type,
fun_rat_fun_nat_rat: $tType ).
thf(fun_num_fun_num_int_type,type,
fun_num_fun_num_int: $tType ).
thf(fun_nat_fun_rat_rat_type,type,
fun_nat_fun_rat_rat: $tType ).
thf(fun_nat_fun_nat_rat_type,type,
fun_nat_fun_nat_rat: $tType ).
thf(fun_nat_fun_nat_nat_type,type,
fun_nat_fun_nat_nat: $tType ).
thf(fun_nat_fun_nat_int_type,type,
fun_nat_fun_nat_int: $tType ).
thf(fun_nat_fun_int_int_type,type,
fun_nat_fun_int_int: $tType ).
thf(fun_int_fun_nat_int_type,type,
fun_int_fun_nat_int: $tType ).
thf(fun_int_fun_int_rat_type,type,
fun_int_fun_int_rat: $tType ).
thf(fun_int_fun_int_int_type,type,
fun_int_fun_int_int: $tType ).
thf(fun_co8153928105989009288nteger_type,type,
fun_co8153928105989009288nteger: $tType ).
thf(fun_na1554462459066888140plex_o_type,type,
fun_na1554462459066888140plex_o: $tType ).
thf(fun_num_option_num_type,type,
fun_num_option_num: $tType ).
thf(fun_list_nat_real_type,type,
fun_list_nat_real: $tType ).
thf(fun_fun_real_real_o_type,type,
fun_fun_real_real_o: $tType ).
thf(fun_real_fun_real_o_type,type,
fun_real_fun_real_o: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_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(fun_nat_list_nat_type,type,
fun_nat_list_nat: $tType ).
thf(fun_list_nat_nat_type,type,
fun_list_nat_nat: $tType ).
thf(fun_VEBT_VEBT_nat_type,type,
fun_VEBT_VEBT_nat: $tType ).
thf(fun_set_nat_nat_type,type,
fun_set_nat_nat: $tType ).
thf(fun_num_Code_integer_type,type,
fun_num_Code_integer: $tType ).
thf(fun_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_Code_natural_type,type,
fun_nat_Code_natural: $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_natural_nat_type,type,
fun_Code_natural_nat: $tType ).
thf(fun_Code_integer_num_type,type,
fun_Code_integer_num: $tType ).
thf(fun_Code_integer_nat_type,type,
fun_Code_integer_nat: $tType ).
thf(fun_Code_integer_int_type,type,
fun_Code_integer_int: $tType ).
thf(fun_fun_rat_rat_o_type,type,
fun_fun_rat_rat_o: $tType ).
thf(fun_fun_nat_rat_o_type,type,
fun_fun_nat_rat_o: $tType ).
thf(fun_fun_nat_nat_o_type,type,
fun_fun_nat_nat_o: $tType ).
thf(fun_fun_int_int_o_type,type,
fun_fun_int_int_o: $tType ).
thf(fun_rat_fun_rat_o_type,type,
fun_rat_fun_rat_o: $tType ).
thf(fun_Pr1792556611952799308t_real_type,type,
fun_Pr1792556611952799308t_real: $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_int_o_type,type,
fun_int_fun_int_o: $tType ).
thf(sum_sum_nat_nat_type,type,
sum_sum_nat_nat: $tType ).
thf(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(list_list_nat_type,type,
list_list_nat: $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(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_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_fun_real_o_o_type,type,
fun_fun_real_o_o: $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_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_Code_integer_type,type,
set_Code_integer: $tType ).
thf(fun_set_nat_o_type,type,
fun_set_nat_o: $tType ).
thf(fun_Code_natural_o_type,type,
fun_Code_natural_o: $tType ).
thf(fun_Code_integer_o_type,type,
fun_Code_integer_o: $tType ).
thf(fun_nat_fun_o_o_type,type,
fun_nat_fun_o_o: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(fun_char_nat_type,type,
fun_char_nat: $tType ).
thf(fun_real_real_type,type,
fun_real_real: $tType ).
thf(fun_nat_char_type,type,
fun_nat_char: $tType ).
thf(fun_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(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(filter_int_type,type,
filter_int: $tType ).
thf(fun_o_fun_o_o_type,type,
fun_o_fun_o_o: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(list_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_natural_type,type,
code_natural: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(fun_rat_o_type,type,
fun_rat_o: $tType ).
thf(fun_num_o_type,type,
fun_num_o: $tType ).
thf(fun_nat_o_type,type,
fun_nat_o: $tType ).
thf(fun_int_o_type,type,
fun_int_o: $tType ).
thf(fun_o_nat_type,type,
fun_o_nat: $tType ).
thf(fun_o_int_type,type,
fun_o_int: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(fun_o_o_type,type,
fun_o_o: $tType ).
thf(char_type,type,
char: $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_af_decl,type,
aTP_Lamm_af: fun_nat_fun_nat_o ).
thf(aTP_Lamm_ag_decl,type,
aTP_Lamm_ag: fun_nat_fun_nat_o ).
thf(aTP_Lamm_aj_decl,type,
aTP_Lamm_aj: fun_nat_nat ).
thf(aTP_Lamm_au_decl,type,
aTP_Lamm_au: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_az_decl,type,
aTP_Lamm_az: fun_complex_complex ).
thf(aTP_Lamm_bg_decl,type,
aTP_Lamm_bg: complex > fun_na1554462459066888140plex_o ).
thf(aTP_Lamm_bh_decl,type,
aTP_Lamm_bh: nat > fun_complex_o ).
thf(aTP_Lamm_cs_decl,type,
aTP_Lamm_cs: fun_nat_int > fun_nat_int ).
thf(aTP_Lamm_cy_decl,type,
aTP_Lamm_cy: fun_nat_rat > fun_nat_rat ).
thf(aTP_Lamm_dc_decl,type,
aTP_Lamm_dc: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_fm_decl,type,
aTP_Lamm_fm: nat > fun_complex_nat ).
thf(aTP_Lamm_hl_decl,type,
aTP_Lamm_hl: fun_nat_real > fun_nat_real ).
thf(aTP_Lamm_in_decl,type,
aTP_Lamm_in: fun_list_nat_nat > fun_list_nat_nat ).
thf(aTP_Lamm_iw_decl,type,
aTP_Lamm_iw: nat > fun_co1148497455491383662plex_o ).
thf(aTP_Lamm_je_decl,type,
aTP_Lamm_je: nat > fun_nat_complex ).
thf(aTP_Lamm_jf_decl,type,
aTP_Lamm_jf: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_jo_decl,type,
aTP_Lamm_jo: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_jz_decl,type,
aTP_Lamm_jz: fun_nat_o > fun_nat_fun_nat_o ).
thf(aTP_Lamm_ke_decl,type,
aTP_Lamm_ke: fun_nat_o ).
thf(aTP_Lamm_kf_decl,type,
aTP_Lamm_kf: fun_nat_o ).
thf(aTP_Lamm_ki_decl,type,
aTP_Lamm_ki: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_kj_decl,type,
aTP_Lamm_kj: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mb_decl,type,
aTP_Lamm_mb: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mf_decl,type,
aTP_Lamm_mf: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mh_decl,type,
aTP_Lamm_mh: fun_na6724076748692969250l_real ).
thf(aTP_Lamm_mi_decl,type,
aTP_Lamm_mi: fun_real_real > fun_na6724076748692969250l_real ).
thf(aTP_Lamm_mx_decl,type,
aTP_Lamm_mx: fun_na6724076748692969250l_real ).
thf(aTP_Lamm_nb_decl,type,
aTP_Lamm_nb: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_nf_decl,type,
aTP_Lamm_nf: real > fun_nat_real ).
thf(aTP_Lamm_nr_decl,type,
aTP_Lamm_nr: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_ob_decl,type,
aTP_Lamm_ob: nat > fun_nat_fun_nat_o ).
thf(aTP_Lamm_om_decl,type,
aTP_Lamm_om: fun_na1476630412504255114at_nat ).
thf(aTP_Lamm_ou_decl,type,
aTP_Lamm_ou: fun_nat_fun_nat_o ).
thf(aTP_Lamm_ov_decl,type,
aTP_Lamm_ov: nat > fun_nat_fun_nat_o ).
thf(aTP_Lamm_pe_decl,type,
aTP_Lamm_pe: fun_nat_fun_nat_o ).
thf(aTP_Lamm_pf_decl,type,
aTP_Lamm_pf: extended_enat > fun_nat_o ).
thf(aTP_Lamm_ps_decl,type,
aTP_Lamm_ps: nat > fun_nat_fun_nat_o ).
thf(bNF_re4705727531993890431at_o_o_decl,type,
bNF_re4705727531993890431at_o_o: fun_nat_fun_nat_o > fun_o_fun_o_o > fun_fu7564235448449272366at_o_o ).
thf(bNF_re1448341924010609215_nat_o_decl,type,
bNF_re1448341924010609215_nat_o: fun_nat_fun_nat_o > fun_fu7564235448449272366at_o_o > fun_nat_fun_nat_o > fun_nat_fun_nat_o > $o ).
thf(binomial_decl,type,
binomial: fun_nat_fun_nat_nat ).
thf(gbinomial_int_decl,type,
gbinomial_int: int > fun_nat_int ).
thf(gbinomial_nat_decl,type,
gbinomial_nat: fun_nat_fun_nat_nat ).
thf(gbinomial_rat_decl,type,
gbinomial_rat: rat > fun_nat_rat ).
thf(gbinomial_real_decl,type,
gbinomial_real: real > fun_nat_real ).
thf(bit_se727722235901077358nd_nat_decl,type,
bit_se727722235901077358nd_nat: fun_nat_fun_nat_nat ).
thf(bit_se8570568707652914677it_nat_decl,type,
bit_se8570568707652914677it_nat: fun_nat_fun_nat_nat ).
thf(bit_se2161824704523386999it_nat_decl,type,
bit_se2161824704523386999it_nat: fun_nat_fun_nat_nat ).
thf(bit_se2002935070580805687sk_nat_decl,type,
bit_se2002935070580805687sk_nat: fun_nat_nat ).
thf(bit_se1412395901928357646or_nat_decl,type,
bit_se1412395901928357646or_nat: fun_nat_fun_nat_nat ).
thf(bit_se547839408752420682it_nat_decl,type,
bit_se547839408752420682it_nat: fun_nat_fun_nat_nat ).
thf(bit_se2925701944663578781it_nat_decl,type,
bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).
thf(bit_se6528837805403552850or_nat_decl,type,
bit_se6528837805403552850or_nat: fun_nat_fun_nat_nat ).
thf(bit_se1146084159140164899it_int_decl,type,
bit_se1146084159140164899it_int: int > fun_nat_o ).
thf(bit_se1148574629649215175it_nat_decl,type,
bit_se1148574629649215175it_nat: fun_nat_fun_nat_o ).
thf(unique6322359934112328802ux_nat_decl,type,
unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
thf(unique5055182867167087721od_nat_decl,type,
unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
thf(unique5026877609467782581ep_nat_decl,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(euclid3398187327856392827nt_nat_decl,type,
euclid3398187327856392827nt_nat: fun_nat_nat ).
thf(extended_eSuc_decl,type,
extended_eSuc: extended_enat > extended_enat ).
thf(extended_enat2_decl,type,
extended_enat2: nat > extended_enat ).
thf(extended_case_enat_o_decl,type,
extended_case_enat_o: fun_nat_o > $o > extended_enat > $o ).
thf(comm_s4663373288045622133er_nat_decl,type,
comm_s4663373288045622133er_nat: fun_nat_fun_nat_nat ).
thf(comm_s4028243227959126397er_rat_decl,type,
comm_s4028243227959126397er_rat: rat > fun_nat_rat ).
thf(comm_s7457072308508201937r_real_decl,type,
comm_s7457072308508201937r_real: real > fun_nat_real ).
thf(semiri1408675320244567234ct_nat_decl,type,
semiri1408675320244567234ct_nat: fun_nat_nat ).
thf(at_top_nat_decl,type,
at_top_nat: filter_nat ).
thf(filterlim_nat_nat_decl,type,
filterlim_nat_nat: fun_nat_nat > filter_nat > filter_nat > $o ).
thf(finite_card_o_decl,type,
finite_card_o: set_o > nat ).
thf(finite_card_complex_decl,type,
finite_card_complex: set_complex > nat ).
thf(finite_card_int_decl,type,
finite_card_int: set_int > nat ).
thf(finite_card_list_nat_decl,type,
finite_card_list_nat: set_list_nat > nat ).
thf(finite_card_set_nat_decl,type,
finite_card_set_nat: set_set_nat > nat ).
thf(finite7802652506058667612T_VEBT_decl,type,
finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat ).
thf(finite3207457112153483333omplex_decl,type,
finite3207457112153483333omplex: set_complex > $o ).
thf(bij_betw_nat_complex_decl,type,
bij_betw_nat_complex: fun_nat_complex > set_nat > set_complex > $o ).
thf(inj_on_real_real_decl,type,
inj_on_real_real: fun_real_real > set_real > $o ).
thf(the_in5290026491893676941l_real_decl,type,
the_in5290026491893676941l_real: set_real > fun_real_real > fun_real_real ).
thf(fun_pair_leq_decl,type,
fun_pair_leq: set_Pr8693737435421807431at_nat ).
thf(fun_pair_less_decl,type,
fun_pair_less: set_Pr8693737435421807431at_nat ).
thf(gcd_gcd_nat_decl,type,
gcd_gcd_nat: fun_nat_fun_nat_nat ).
thf(gcd_lcm_nat_decl,type,
gcd_lcm_nat: fun_nat_fun_nat_nat ).
thf(gcd_nat_rel_decl,type,
gcd_nat_rel: fun_Pr2028404973800837934_nat_o ).
thf(abs_abs_real_decl,type,
abs_abs_real: fun_real_real ).
thf(comm_monoid_nat_decl,type,
comm_monoid_nat: fun_nat_fun_nat_nat > fun_nat_o ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: fun_nat_fun_nat_nat ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > fun_real_real ).
thf(minus_811609699411566653omplex_decl,type,
minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
thf(monoid_nat_decl,type,
monoid_nat: fun_nat_fun_nat_nat > fun_nat_o ).
thf(one_one_complex_decl,type,
one_one_complex: complex ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_rat_decl,type,
one_one_rat: rat ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(plus_p3455044024723400733d_enat_decl,type,
plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(plus_plus_num_decl,type,
plus_plus_num: num > fun_num_num ).
thf(sgn_sgn_real_decl,type,
sgn_sgn_real: fun_real_real ).
thf(times_times_nat_decl,type,
times_times_nat: fun_nat_fun_nat_nat ).
thf(uminus_uminus_real_decl,type,
uminus_uminus_real: fun_real_real ).
thf(zero_zero_complex_decl,type,
zero_zero_complex: complex ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_rat_decl,type,
zero_zero_rat: rat ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(groups7754918857620584856omplex_decl,type,
groups7754918857620584856omplex: fun_complex_complex > set_complex > complex ).
thf(groups5693394587270226106ex_nat_decl,type,
groups5693394587270226106ex_nat: fun_complex_nat > set_complex > nat ).
thf(groups4396056296759096172at_nat_decl,type,
groups4396056296759096172at_nat: fun_list_nat_nat > set_list_nat > nat ).
thf(groups861055069439313189ex_nat_decl,type,
groups861055069439313189ex_nat: fun_complex_nat > set_complex > nat ).
thf(groups9119017779487936845_o_nat_decl,type,
groups9119017779487936845_o_nat: fun_o_nat > nat > list_o > nat ).
thf(semila9081495762789891438tr_nat_decl,type,
semila9081495762789891438tr_nat: fun_nat_fun_nat_nat > fun_nat_o ).
thf(semila1623282765462674594er_nat_decl,type,
semila1623282765462674594er_nat: fun_nat_fun_nat_nat > nat > fun_nat_fun_nat_o > fun_nat_fun_nat_o > $o ).
thf(semila1248733672344298208er_nat_decl,type,
semila1248733672344298208er_nat: fun_nat_fun_nat_nat > fun_nat_fun_nat_o > fun_nat_fun_nat_o > $o ).
thf(append_nat_decl,type,
append_nat: list_nat > list_nat > list_nat ).
thf(count_list_VEBT_VEBT_decl,type,
count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
thf(last_nat_decl,type,
last_nat: fun_list_nat_nat ).
thf(cons_nat_decl,type,
cons_nat: nat > list_nat > list_nat ).
thf(nil_nat_decl,type,
nil_nat: list_nat ).
thf(hd_nat_decl,type,
hd_nat: fun_list_nat_nat ).
thf(map_nat_nat_decl,type,
map_nat_nat: fun_nat_nat > list_nat > list_nat ).
thf(set_o2_decl,type,
set_o2: list_o > set_o ).
thf(set_complex2_decl,type,
set_complex2: list_complex > set_complex ).
thf(set_int2_decl,type,
set_int2: list_int > set_int ).
thf(set_list_nat2_decl,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(set_nat2_decl,type,
set_nat2: list_nat > set_nat ).
thf(set_real2_decl,type,
set_real2: list_real > set_real ).
thf(set_set_nat2_decl,type,
set_set_nat2: list_set_nat > set_set_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(nth_o_decl,type,
nth_o: list_o > fun_nat_o ).
thf(nth_complex_decl,type,
nth_complex: list_complex > fun_nat_complex ).
thf(nth_int_decl,type,
nth_int: list_int > fun_nat_int ).
thf(nth_Product_prod_o_o_decl,type,
nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
thf(nth_Pr1649062631805364268_o_int_decl,type,
nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
thf(nth_Pr6777367263587873994T_VEBT_decl,type,
nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
thf(nth_Pr4606735188037164562VEBT_o_decl,type,
nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
thf(nth_Pr4953567300277697838T_VEBT_decl,type,
nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
thf(nth_real_decl,type,
nth_real: list_real > fun_nat_real ).
thf(nth_set_nat_decl,type,
nth_set_nat: list_set_nat > fun_nat_set_nat ).
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_int_decl,type,
product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
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_o_decl,type,
replicate_o: nat > $o > list_o ).
thf(replicate_complex_decl,type,
replicate_complex: nat > complex > list_complex ).
thf(replicate_int_decl,type,
replicate_int: nat > int > list_int ).
thf(replicate_real_decl,type,
replicate_real: nat > real > list_real ).
thf(replicate_set_nat_decl,type,
replicate_set_nat: nat > set_nat > list_set_nat ).
thf(replicate_VEBT_VEBT_decl,type,
replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(take_nat_decl,type,
take_nat: nat > list_nat > list_nat ).
thf(upt_decl,type,
upt: nat > nat > list_nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(case_nat_o_decl,type,
case_nat_o: $o > fun_nat_o > fun_nat_o ).
thf(semiri1314217659103216013at_int_decl,type,
semiri1314217659103216013at_int: fun_nat_int ).
thf(semiri1316708129612266289at_nat_decl,type,
semiri1316708129612266289at_nat: fun_nat_nat ).
thf(semiri681578069525770553at_rat_decl,type,
semiri681578069525770553at_rat: fun_nat_rat ).
thf(semiri5074537144036343181t_real_decl,type,
semiri5074537144036343181t_real: fun_nat_real ).
thf(size_size_list_o_decl,type,
size_size_list_o: list_o > nat ).
thf(size_s3451745648224563538omplex_decl,type,
size_s3451745648224563538omplex: list_complex > nat ).
thf(size_size_list_int_decl,type,
size_size_list_int: list_int > nat ).
thf(size_s3023201423986296836st_nat_decl,type,
size_s3023201423986296836st_nat: list_list_nat > nat ).
thf(size_size_list_real_decl,type,
size_size_list_real: list_real > nat ).
thf(size_s3254054031482475050et_nat_decl,type,
size_s3254054031482475050et_nat: list_set_nat > nat ).
thf(size_s6755466524823107622T_VEBT_decl,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(size_size_num_decl,type,
size_size_num: fun_num_nat ).
thf(size_size_char_decl,type,
size_size_char: char > nat ).
thf(nat_prod_decode_aux_decl,type,
nat_prod_decode_aux: nat > fun_na1476630412504255114at_nat ).
thf(nat_pr5047031295181774490ux_rel_decl,type,
nat_pr5047031295181774490ux_rel: fun_Pr2028404973800837934_nat_o ).
thf(root_decl,type,
root: fun_na6724076748692969250l_real ).
thf(nat_of_num_decl,type,
nat_of_num: fun_num_nat ).
thf(bit0_decl,type,
bit0: fun_num_num ).
thf(bit1_decl,type,
bit1: fun_num_num ).
thf(one_decl,type,
one: num ).
thf(size_num_decl,type,
size_num: fun_num_nat ).
thf(numera1916890842035813515d_enat_decl,type,
numera1916890842035813515d_enat: num > extended_enat ).
thf(numeral_numeral_nat_decl,type,
numeral_numeral_nat: fun_num_nat ).
thf(pred_numeral_decl,type,
pred_numeral: fun_num_nat ).
thf(some_P7363390416028606310at_nat_decl,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: nat ).
thf(bot_bot_fun_nat_o_decl,type,
bot_bot_fun_nat_o: fun_nat_o ).
thf(ord_Least_nat_decl,type,
ord_Least_nat: fun_nat_o > nat ).
thf(ord_le72135733267957522d_enat_decl,type,
ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: fun_nat_fun_nat_o ).
thf(ord_le2932123472753598470d_enat_decl,type,
ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: fun_nat_fun_nat_o ).
thf(ord_le211207098394363844omplex_decl,type,
ord_le211207098394363844omplex: set_complex > set_complex > $o ).
thf(ord_le6893508408891458716et_nat_decl,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(ord_le4337996190870823476T_VEBT_decl,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ord_max_nat_decl,type,
ord_max_nat: fun_nat_fun_nat_nat ).
thf(order_mono_nat_nat_decl,type,
order_mono_nat_nat: fun_nat_nat > $o ).
thf(order_5726023648592871131at_nat_decl,type,
order_5726023648592871131at_nat: fun_nat_nat > $o ).
thf(ordering_top_nat_decl,type,
ordering_top_nat: fun_nat_fun_nat_o > fun_nat_fun_nat_o > fun_nat_o ).
thf(top_top_set_real_decl,type,
top_top_set_real: set_real ).
thf(power_power_complex_decl,type,
power_power_complex: complex > fun_nat_complex ).
thf(power_power_int_decl,type,
power_power_int: int > fun_nat_int ).
thf(power_power_nat_decl,type,
power_power_nat: fun_nat_fun_nat_nat ).
thf(power_power_rat_decl,type,
power_power_rat: rat > fun_nat_rat ).
thf(power_power_real_decl,type,
power_power_real: real > fun_nat_real ).
thf(product_Pair_o_o_decl,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(product_Pair_o_int_decl,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(produc2982872950893828659T_VEBT_decl,type,
produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: nat > fun_na1476630412504255114at_nat ).
thf(produc6161850002892822231at_nat_decl,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(produc8721562602347293563VEBT_o_decl,type,
produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
thf(produc537772716801021591T_VEBT_decl,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(field_5140801741446780682s_real_decl,type,
field_5140801741446780682s_real: set_real ).
thf(real_V7735802525324610683m_real_decl,type,
real_V7735802525324610683m_real: fun_real_real ).
thf(algebr934650988132801477me_nat_decl,type,
algebr934650988132801477me_nat: fun_nat_fun_nat_o ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
thf(divide_divide_real_decl,type,
divide_divide_real: real > fun_real_real ).
thf(dvd_dvd_complex_decl,type,
dvd_dvd_complex: complex > fun_complex_o ).
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(unit_f2748546683901255202or_nat_decl,type,
unit_f2748546683901255202or_nat: fun_nat_nat ).
thf(zero_n2687167440665602831ol_nat_decl,type,
zero_n2687167440665602831ol_nat: fun_o_nat ).
thf(zero_n3304061248610475627l_real_decl,type,
zero_n3304061248610475627l_real: $o > real ).
thf(suminf_nat_decl,type,
suminf_nat: fun_nat_nat > nat ).
thf(summable_nat_decl,type,
summable_nat: fun_nat_nat > $o ).
thf(sums_nat_decl,type,
sums_nat: fun_nat_nat > fun_nat_o ).
thf(collect_complex_decl,type,
collect_complex: fun_complex_o > set_complex ).
thf(insert_complex_decl,type,
insert_complex: complex > set_complex > set_complex ).
thf(insert_int_decl,type,
insert_int: int > set_int > set_int ).
thf(insert_list_nat_decl,type,
insert_list_nat: list_nat > set_list_nat > set_list_nat ).
thf(insert_nat_decl,type,
insert_nat: nat > set_nat > set_nat ).
thf(insert_set_nat_decl,type,
insert_set_nat: set_nat > set_set_nat > set_set_nat ).
thf(set_fo2584398358068434914at_nat_decl,type,
set_fo2584398358068434914at_nat: fun_nat_fun_nat_nat > nat > fun_nat_fun_nat_nat ).
thf(set_ord_atMost_nat_decl,type,
set_ord_atMost_nat: fun_nat_set_nat ).
thf(set_ord_lessThan_nat_decl,type,
set_ord_lessThan_nat: fun_nat_set_nat ).
thf(char2_decl,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(size_char_decl,type,
size_char: char > nat ).
thf(exp_real_decl,type,
exp_real: fun_real_real ).
thf(transi6264000038957366511cl_nat_decl,type,
transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(vEBT_Leaf_decl,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
thf(vEBT_Node_decl,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_o ).
thf(vEBT_vebt_buildup_decl,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(accp_P4275260045618599050at_nat_decl,type,
accp_P4275260045618599050at_nat: fun_Pr2028404973800837934_nat_o > product_prod_nat_nat > $o ).
thf(less_than_decl,type,
less_than: set_Pr1261947904930325089at_nat ).
thf(pred_nat_decl,type,
pred_nat: set_Pr1261947904930325089at_nat ).
thf(aa_o_o_decl,type,
aa_o_o: fun_o_o > $o > $o ).
thf(aa_o_nat_decl,type,
aa_o_nat: fun_o_nat > $o > nat ).
thf(aa_o_fun_o_o_decl,type,
aa_o_fun_o_o: fun_o_fun_o_o > $o > fun_o_o ).
thf(aa_complex_o_decl,type,
aa_complex_o: fun_complex_o > complex > $o ).
thf(aa_complex_nat_decl,type,
aa_complex_nat: fun_complex_nat > complex > nat ).
thf(aa_com5808801942499186519plex_o_decl,type,
aa_com5808801942499186519plex_o: fun_co1148497455491383662plex_o > complex > fun_complex_o ).
thf(aa_int_o_decl,type,
aa_int_o: fun_int_o > int > $o ).
thf(aa_list_o_o_decl,type,
aa_list_o_o: fun_list_o_o > list_o > $o ).
thf(aa_list_int_o_decl,type,
aa_list_int_o: fun_list_int_o > list_int > $o ).
thf(aa_list_nat_nat_decl,type,
aa_list_nat_nat: fun_list_nat_nat > list_nat > nat ).
thf(aa_list_VEBT_VEBT_o_decl,type,
aa_list_VEBT_VEBT_o: fun_list_VEBT_VEBT_o > list_VEBT_VEBT > $o ).
thf(aa_nat_o_decl,type,
aa_nat_o: fun_nat_o > nat > $o ).
thf(aa_nat_complex_decl,type,
aa_nat_complex: fun_nat_complex > nat > complex ).
thf(aa_nat_int_decl,type,
aa_nat_int: fun_nat_int > nat > int ).
thf(aa_nat_nat_decl,type,
aa_nat_nat: fun_nat_nat > nat > nat ).
thf(aa_nat7603221163087113075at_nat_decl,type,
aa_nat7603221163087113075at_nat: fun_na1476630412504255114at_nat > nat > product_prod_nat_nat ).
thf(aa_nat_rat_decl,type,
aa_nat_rat: fun_nat_rat > nat > rat ).
thf(aa_nat_real_decl,type,
aa_nat_real: fun_nat_real > nat > real ).
thf(aa_nat_set_nat_decl,type,
aa_nat_set_nat: fun_nat_set_nat > nat > set_nat ).
thf(aa_nat_fun_o_o_decl,type,
aa_nat_fun_o_o: fun_nat_fun_o_o > nat > fun_o_o ).
thf(aa_nat_fun_complex_o_decl,type,
aa_nat_fun_complex_o: fun_na1554462459066888140plex_o > nat > fun_complex_o ).
thf(aa_nat_fun_int_o_decl,type,
aa_nat_fun_int_o: fun_nat_fun_int_o > nat > fun_int_o ).
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_real_real_decl,type,
aa_nat_fun_real_real: fun_na6724076748692969250l_real > nat > fun_real_real ).
thf(aa_nat1925708948643195573VEBT_o_decl,type,
aa_nat1925708948643195573VEBT_o: fun_na6887940067898170868VEBT_o > nat > fun_VEBT_VEBT_o ).
thf(aa_num_nat_decl,type,
aa_num_nat: fun_num_nat > num > nat ).
thf(aa_num_num_decl,type,
aa_num_num: fun_num_num > num > num ).
thf(aa_real_o_decl,type,
aa_real_o: fun_real_o > real > $o ).
thf(aa_real_real_decl,type,
aa_real_real: fun_real_real > real > real ).
thf(aa_set_nat_o_decl,type,
aa_set_nat_o: fun_set_nat_o > set_nat > $o ).
thf(aa_VEBT_VEBT_o_decl,type,
aa_VEBT_VEBT_o: fun_VEBT_VEBT_o > vEBT_VEBT > $o ).
thf(fequal_o_decl,type,
fequal_o: fun_o_fun_o_o ).
thf(fequal_nat_decl,type,
fequal_nat: fun_nat_fun_nat_o ).
thf(member_o_decl,type,
member_o: $o > set_o > $o ).
thf(member_complex_decl,type,
member_complex: complex > set_complex > $o ).
thf(member_int_decl,type,
member_int: int > set_int > $o ).
thf(member8440522571783428010at_nat_decl,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(member8206827879206165904at_nat_decl,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(member_set_nat_decl,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(member_VEBT_VEBT_decl,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(deg_decl,type,
deg: nat ).
thf(m_decl,type,
m: nat ).
thf(na_decl,type,
na: nat ).
thf(summary_decl,type,
summary: vEBT_VEBT ).
thf(723,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7174_choose__dvd) ).
thf(5136,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(513,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_1529_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(4169,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)],[513]) ).
thf(755,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_9318_upt__conv__Cons) ).
thf(5320,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)],[755]) ).
thf(441,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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_7919_Suc__0__xor__eq) ).
thf(3863,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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)],[441]) ).
thf(1086,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_1435_le__add2) ).
thf(6845,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)],[1086]) ).
thf(1025,axiom,
! [A: list_int,B: fun_int_o,C: int] :
( ! [D: nat] :
( ( A @ size_size_list_int @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) )
=> ( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C @ ( B @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6440_all__nth__imp__all__set) ).
thf(6566,plain,
! [A: list_int,B: fun_int_o,C: int] :
( ! [D: nat] :
( ( A @ size_size_list_int @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) )
=> ( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C @ ( B @ aa_int_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(1109,axiom,
! [A: nat,B: nat,C: nat] :
( ! [D: nat] :
( ~ ( D @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( D @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7831_bit__disjunctive__add__iff) ).
thf(6954,plain,
! [A: nat,B: nat,C: nat] :
( ! [D: nat] :
( ~ ( D @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( D @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( ( C @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(60,axiom,
! [A: real,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2753_minus__divide__divide) ).
thf(2163,plain,
! [A: real,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1462,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_3450_less__mult__imp__div__less) ).
thf(8607,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)],[1462]) ).
thf(1194,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6534_binomial__absorption) ).
thf(7375,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).
thf(72,axiom,
! [A: $o] :
( ( ( A @ zero_n3304061248610475627l_real )
= zero_zero_real )
<=> ~ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7451_of__bool__eq__0__iff) ).
thf(2199,plain,
! [A: $o] :
( ( ~ A
=> ( ( A @ zero_n3304061248610475627l_real )
= zero_zero_real ) )
& ( ( ( A @ zero_n3304061248610475627l_real )
= zero_zero_real )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1447,axiom,
one_one_nat = one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8978_one__natural_Orsp) ).
thf(8536,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447]) ).
thf(779,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6531_binomial__Suc__Suc__eq__times) ).
thf(5437,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(1466,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: vEBT_VEBT] :
( ! [D: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6437_all__nth__imp__all__set) ).
thf(8618,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: vEBT_VEBT] :
( ! [D: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466]) ).
thf(520,axiom,
! [A: nat] :
( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_of__nat__eq__0__iff) ).
thf(4201,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int ) )
& ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(1084,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9675_gcd__Suc__0) ).
thf(6836,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(1850,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_2163_order__less__imp__not__less) ).
thf(10647,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)],[1850]) ).
thf(765,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_6858_dvdI) ).
thf(5365,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)],[765]) ).
thf(1374,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_7139_dvd__fact) ).
thf(8186,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)],[1374]) ).
thf(1801,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_2300_dual__order_Ostrict__trans1) ).
thf(10410,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)],[1801]) ).
thf(1113,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_6973_unit__mult__right__cancel) ).
thf(6979,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)],[1113]) ).
thf(937,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_3091_zero__less__mult__pos) ).
thf(6167,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)],[937]) ).
thf(881,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_3898_power__le__imp__le__base) ).
thf(5918,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)],[881]) ).
thf(713,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_3729_power__decreasing__iff) ).
thf(5088,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)],[713]) ).
thf(1771,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_2189_minf_I8_J) ).
thf(10259,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)],[1771]) ).
thf(280,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_4029_power__diff__power__eq) ).
thf(3053,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)],[280]) ).
thf(111,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6737_neg__one__odd__power) ).
thf(2341,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(45,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_add_Oinverse__inverse) ).
thf(2109,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(51,axiom,
! [A: real,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6452_power__minus__Bit1) ).
thf(2131,plain,
! [A: real,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(1298,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_1036_Suc__diff__eq__diff__pred) ).
thf(7854,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)],[1298]) ).
thf(674,axiom,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_Leaf__0__not) ).
thf(4909,plain,
! [A: $o,B: $o] :
~ ( zero_zero_nat @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(746,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_6977_dvd__mult__imp__div) ).
thf(5260,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)],[746]) ).
thf(758,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_6588_div__dvd__div) ).
thf(5329,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)],[758]) ).
thf(1353,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6512_le__numeral__Suc) ).
thf(8097,plain,
! [A: num,B: nat] :
( ( ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).
thf(671,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) @ ( B @ ( abs_abs_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3121_nonzero__abs__divide) ).
thf(4899,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) @ ( B @ ( abs_abs_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(424,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_nat ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7238_mod2__eq__if) ).
thf(3798,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_nat ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1660,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_2215_leI) ).
thf(9516,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)],[1660]) ).
thf(407,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_zero__neq__one) ).
thf(3666,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(633,axiom,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( zero_zero_nat @ ( C @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8642_sum__nonpos) ).
thf(4729,plain,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( zero_zero_nat @ ( C @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(891,axiom,
! [A: list_o,B: fun_o_o,C: $o] :
( ! [D: nat] :
( ( A @ size_size_list_o @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) )
=> ( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C @ ( B @ aa_o_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6438_all__nth__imp__all__set) ).
thf(5950,plain,
! [A: list_o,B: fun_o_o,C: $o] :
( ! [D: nat] :
( ( A @ size_size_list_o @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) )
=> ( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C @ ( B @ aa_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(1693,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7837_bit__1__iff) ).
thf(9754,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693]) ).
thf(250,axiom,
! [A: nat] :
( ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ upt ) @ set_nat2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9306_atMost__upto) ).
thf(2921,plain,
! [A: nat] :
( ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ upt ) @ set_nat2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1865,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__Nat__Onat_T) ).
thf(10730,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865]) ).
thf(1260,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_7128_mod__greater__zero__iff__not__dvd) ).
thf(7660,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)],[1260]) ).
thf(1398,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_7071_unit__div__eq__0__iff) ).
thf(8283,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)],[1398]) ).
thf(3,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8995_or__nat__numerals_I1_J) ).
thf(1899,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(388,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8036_push__bit__of__0) ).
thf(3581,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(1147,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5004_power__zero__numeral) ).
thf(7143,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(1335,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_3473_Suc__div__le__mono) ).
thf(8030,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)],[1335]) ).
thf(1519,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_7689_product__nth) ).
thf(8843,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)],[1519]) ).
thf(16,axiom,
! [A: real] :
( ( field_5140801741446780682s_real @ ( A @ ( abs_abs_real @ aa_real_real ) @ member_real ) )
<=> ( field_5140801741446780682s_real @ ( A @ member_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9310_Rats__abs__iff) ).
thf(1982,plain,
! [A: real] :
( ( ( field_5140801741446780682s_real @ ( A @ member_real ) )
=> ( field_5140801741446780682s_real @ ( A @ ( abs_abs_real @ aa_real_real ) @ member_real ) ) )
& ( ( field_5140801741446780682s_real @ ( A @ ( abs_abs_real @ aa_real_real ) @ member_real ) )
=> ( field_5140801741446780682s_real @ ( A @ member_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(358,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5855_one__div__two__eq__zero) ).
thf(3449,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(1729,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_6904_gcd__nat_Onot__eq__extremum) ).
thf(10081,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)],[1729]) ).
thf(998,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9681_gcd__le2__nat) ).
thf(6448,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(899,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_1407_full__nat__induct) ).
thf(5999,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)],[899]) ).
thf(853,axiom,
aTP_Lamm_af @ ( aTP_Lamm_ag @ ( zero_zero_nat @ ( ord_max_nat @ semila1623282765462674594er_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9091_max__nat_Osemilattice__neutr__order__axioms) ).
thf(5778,plain,
aTP_Lamm_af @ ( aTP_Lamm_ag @ ( zero_zero_nat @ ( ord_max_nat @ semila1623282765462674594er_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(1785,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_2_less__nat__zero__code) ).
thf(10319,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)],[1785]) ).
thf(108,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7943_xor__numerals_I5_J) ).
thf(2331,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(846,axiom,
( ( one_one_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4252_fact__1) ).
thf(5733,plain,
( ( one_one_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(1472,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_26_nat__induct) ).
thf(8639,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)],[1472]) ).
thf(512,axiom,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3855_power__0) ).
thf(4166,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(1077,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_3829_zero__less__power) ).
thf(6808,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)],[1077]) ).
thf(83,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6150_power__minus1__odd) ).
thf(2250,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1523,axiom,
! [A: complex] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_complex @ aa_nat_complex ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3627_power__Suc0__right) ).
thf(8855,plain,
! [A: complex] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_complex @ aa_nat_complex ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523]) ).
thf(1560,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_1442_Nat_Odiff__diff__eq) ).
thf(9020,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)],[1560]) ).
thf(1191,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5003_power__zero__numeral) ).
thf(7358,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).
thf(1090,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_8511_intind) ).
thf(6868,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)],[1090]) ).
thf(1050,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_488_diff__less) ).
thf(6695,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)],[1050]) ).
thf(827,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_3452_div__less__iff__less__mult) ).
thf(5644,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)],[827]) ).
thf(1145,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_9358_tl__upt) ).
thf(7132,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)],[1145]) ).
thf(192,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5796_zero__eq__power2) ).
thf(2676,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1888,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ag @ 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_10273_ATP_Olambda__122) ).
thf(10837,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( aTP_Lamm_ag @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( aTP_Lamm_ag @ 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)],[1888]) ).
thf(47,axiom,
! [A: real] :
( ( A @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(2114,plain,
! [A: real] :
( ( A @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1151,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_6586_dvd__1__left) ).
thf(7182,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)],[1151]) ).
thf(1034,axiom,
! [A: nat,B: real] :
( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( @+[C: real] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( aTP_Lamm_mh @ aa_nat_fun_real_real ) @ ( top_top_set_real @ the_in5290026491893676941l_real ) @ aa_real_real ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9376_root__def) ).
thf(6602,plain,
! [A: nat,B: real] :
( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( @+[C: real] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( aTP_Lamm_mh @ aa_nat_fun_real_real ) @ ( top_top_set_real @ the_in5290026491893676941l_real ) @ aa_real_real ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1609,axiom,
zero_zero_nat @ ( aTP_Lamm_af @ ( aTP_Lamm_ag @ ordering_top_nat ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9790_bot__nat__0_Oordering__top__axioms) ).
thf(9241,plain,
zero_zero_nat @ ( aTP_Lamm_af @ ( aTP_Lamm_ag @ ordering_top_nat ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609]) ).
thf(677,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5888_not__mod__2__eq__0__eq__1) ).
thf(4931,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(481,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6086_power__odd__eq) ).
thf(4037,plain,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8040_push__bit__push__bit) ).
thf(2976,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(1781,axiom,
! [A: extended_enat,B: nat] :
( ( B @ extended_enat2 @ ( A @ ord_le72135733267957522d_enat ) )
=> ~ ! [C: nat] :
( ( A
= ( C @ extended_enat2 ) )
=> ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9870_less__enatE) ).
thf(10299,plain,
! [A: extended_enat,B: nat] :
( ( B @ extended_enat2 @ ( A @ ord_le72135733267957522d_enat ) )
=> ~ ! [C: nat] :
( ( A
= ( C @ extended_enat2 ) )
=> ~ ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781]) ).
thf(286,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_2443_div__by__0) ).
thf(3072,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)],[286]) ).
thf(48,axiom,
! [A: real] :
( ( ( A @ ( exp_real @ aa_real_real ) )
= one_one_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4257_exp__eq__one__iff) ).
thf(2117,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( exp_real @ aa_real_real ) )
= one_one_real ) )
& ( ( ( A @ ( exp_real @ aa_real_real ) )
= one_one_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ! [D: nat] :
~ ( D @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7897_bit__sum__mult__2__cases) ).
thf(2940,plain,
! [A: nat,B: nat,C: nat] :
( ! [D: nat] :
~ ( D @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) )
=> ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1312,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6522_Suc__times__binomial) ).
thf(7935,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).
thf(1136,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_6539_times__binomial__minus1__eq) ).
thf(7083,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)],[1136]) ).
thf(1106,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_4915_Suc__mod__mult__self2) ).
thf(6944,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)],[1106]) ).
thf(148,axiom,
! [A: real,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5900_Power_Oring__1__class_Opower__minus__even) ).
thf(2495,plain,
! [A: real,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1348,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_116_Suc__pred) ).
thf(8082,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)],[1348]) ).
thf(1063,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_1350_add__right__mono) ).
thf(6744,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)],[1063]) ).
thf(1094,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_1496_add__nonpos__eq__0__iff) ).
thf(6883,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)],[1094]) ).
thf(1254,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_6838_dvd__mult__left) ).
thf(7641,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)],[1254]) ).
thf(944,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6430_in__set__conv__nth) ).
thf(6199,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) ) )
& ( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_VEBT_VEBT ) )
= A )
& ( B @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(344,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3608_of__nat__power) ).
thf(3377,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(1000,axiom,
! [A: nat,B: real] :
( ( B @ ( A @ ( aTP_Lamm_mx @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10278_ATP_Olambda__127) ).
thf(6458,plain,
! [A: nat,B: real] :
( ( B @ ( A @ ( aTP_Lamm_mx @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(1564,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_1428_trans__le__add2) ).
thf(9045,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)],[1564]) ).
thf(1433,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_3098_mult__pos__neg2) ).
thf(8463,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)],[1433]) ).
thf(464,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
& ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6762_even__power) ).
thf(3959,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
& ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(1358,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_3496_n__less__m__mult__n) ).
thf(8118,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)],[1358]) ).
thf(1076,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_9023_max__nat_Oeq__neutr__iff) ).
thf(6798,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)],[1076]) ).
thf(291,axiom,
! [A: real] :
( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2563_divide__self__if) ).
thf(3098,plain,
! [A: real] :
( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(1859,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_2410_complete__interval) ).
thf(10705,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)],[1859]) ).
thf(1372,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_3539_nat__mult__less__cancel1) ).
thf(8169,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)],[1372]) ).
thf(739,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9726_gcd__nat_Oright__idem) ).
thf(5224,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(834,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3851_power__Suc2) ).
thf(5669,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1545,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9674_gcd__nat_Oabsorb1) ).
thf(8943,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545]) ).
thf(1283,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_6961_is__unit__mult__iff) ).
thf(7781,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)],[1283]) ).
thf(840,axiom,
! [A: nat,B: nat,C: product_prod_nat_nat] :
( ( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= C )
=> ( C
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9062_prod__decode__aux_Oelims) ).
thf(5691,plain,
! [A: nat,B: nat,C: product_prod_nat_nat] :
( ( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= C )
=> ( C
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(1587,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_3280_mult__left__le) ).
thf(9135,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)],[1587]) ).
thf(577,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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_7666_mask__nat__def) ).
thf(4487,plain,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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)],[577]) ).
thf(946,axiom,
! [A: nat] :
( ( zero_zero_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_of__nat__0__eq__iff) ).
thf(6214,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)],[946]) ).
thf(1556,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_1192_le__add__same__cancel1) ).
thf(9003,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)],[1556]) ).
thf(964,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4308_fact__nonzero) ).
thf(6295,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(792,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( gcd_lcm_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_9978_dvd__lcm__I2__nat) ).
thf(5501,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( gcd_lcm_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)],[792]) ).
thf(500,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_int__int__eq) ).
thf(4105,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(377,axiom,
! [A: nat,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se2925701944663578781it_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_7192_take__bit__Suc__bit0) ).
thf(3530,plain,
! [A: nat,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se2925701944663578781it_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)],[377]) ).
thf(636,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_6660_take__bit__0) ).
thf(4739,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)],[636]) ).
thf(1586,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_7012_dvd__eq__mod__eq__0) ).
thf(9127,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)],[1586]) ).
thf(67,axiom,
! [A: real,B: real] :
( ( B @ ( A @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2756_minus__divide__left) ).
thf(2184,plain,
! [A: real,B: real] :
( ( B @ ( A @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(200,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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 ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6805_take__bit__of__nat) ).
thf(2712,plain,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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 ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(1011,axiom,
! [A: fun_nat_nat,B: nat] :
( ( A @ summable_nat )
=> ( ! [C: nat] : ( C @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8467_suminf__pos2) ).
thf(6515,plain,
! [A: fun_nat_nat,B: nat] :
( ( A @ summable_nat )
=> ( ! [C: nat] : ( C @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(1555,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_4461_mod__self) ).
thf(9000,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)],[1555]) ).
thf(487,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7532_one__div__2__pow__eq) ).
thf(4058,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(17,axiom,
! [A: real] :
( ( A @ ( zero_zero_real @ minus_minus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_verit__minus__simplify_I3_J) ).
thf(1988,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ minus_minus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(686,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( binomial @ 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_6541_binomial__strict__mono) ).
thf(4980,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( binomial @ 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)],[686]) ).
thf(1092,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6662_take__bit__Suc__1) ).
thf(6877,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(271,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( 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_6159_ex__power__ivl2) ).
thf(3017,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( 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)],[271]) ).
thf(591,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_deg__deg__n) ).
thf(4543,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(961,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_269_add__gr__0) ).
thf(6278,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)],[961]) ).
thf(527,axiom,
! [A: nat,B: set_int,C: int] :
( ( 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 ) @ ( B @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_int ) @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8013_card__insert__le__m1) ).
thf(4234,plain,
! [A: nat,B: set_int,C: int] :
( ( 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 ) @ ( B @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_int ) @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(1776,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_2158_order__less__imp__not__eq2) ).
thf(10282,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)],[1776]) ).
thf(1493,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_1406_not__less__eq__eq) ).
thf(8733,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)],[1493]) ).
thf(296,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7953_and__nat__numerals_I4_J) ).
thf(3120,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1155,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_3446_nat__0__less__mult__iff) ).
thf(7203,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)],[1155]) ).
thf(1807,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zero__reorient) ).
thf(10433,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)],[1807]) ).
thf(1751,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_261_of__nat__less__iff) ).
thf(10181,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)],[1751]) ).
thf(1265,axiom,
! [A: extended_enat,B: nat] :
( ( ( A @ extended_eSuc )
= ( B @ extended_enat2 ) )
<=> ? [C: nat] :
( ( A
= ( C @ extended_enat2 ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9893_eSuc__enat__iff) ).
thf(7695,plain,
! [A: extended_enat,B: nat] :
( ( ? [C: nat] :
( ( A
= ( C @ extended_enat2 ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( A @ extended_eSuc )
= ( B @ extended_enat2 ) ) )
& ( ( ( A @ extended_eSuc )
= ( B @ extended_enat2 ) )
=> ? [C: nat] :
( ( A
= ( C @ extended_enat2 ) )
& ( B
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).
thf(29,axiom,
! [A: num,B: num] :
( ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6179_cong__exp__iff__simps_I2_J) ).
thf(2035,plain,
! [A: num,B: num] :
( ( ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(658,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_3414_div__mult__self4) ).
thf(4839,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)],[658]) ).
thf(459,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8051_push__bit__Suc) ).
thf(3942,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(1894,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9676_gcd__pos__nat) ).
thf(10869,plain,
! [A: nat,B: nat] :
( ( ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) )
=> ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B != zero_zero_nat )
| ( A != zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894]) ).
thf(1895,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_1927_minf_I7_J) ).
thf(10881,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)],[1895]) ).
thf(1795,axiom,
! [A: list_o,B: list_o] :
( ( A = B )
<=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_o @ aa_nat_o ) )
<=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6407_list__eq__iff__nth__eq) ).
thf(10358,plain,
! [A: list_o,B: list_o] :
( ( ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
& ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795]) ).
thf(1301,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_jo @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( 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_10254_ATP_Olambda__103) ).
thf(7873,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_jo @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( 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)],[1301]) ).
thf(1290,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_1554_Suc__leI) ).
thf(7824,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)],[1290]) ).
thf(925,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9727_gcd__nat_Oleft__idem) ).
thf(6127,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(1497,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9664_gcd__nat_Oleft__neutral) ).
thf(8747,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497]) ).
thf(1613,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_65_Nat_OlessE) ).
thf(9261,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)],[1613]) ).
thf(21,axiom,
! [A: real,B: nat] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3629_abs__power__minus) ).
thf(1999,plain,
! [A: real,B: nat] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(103,axiom,
! [A: nat,B: complex] :
( ( B @ ( A @ aTP_Lamm_fm @ aa_complex_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10537_ATP_Olambda__386) ).
thf(2316,plain,
! [A: nat,B: complex] :
( ( B @ ( A @ aTP_Lamm_fm @ aa_complex_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(357,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_4744_mod__mult__div__eq) ).
thf(3446,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)],[357]) ).
thf(1477,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_4508_mod__mult__self1__is__0) ).
thf(8667,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)],[1477]) ).
thf(1893,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_1419_less__mono__imp__le__mono) ).
thf(10864,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)],[1893]) ).
thf(919,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A
!= ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9691_gcd__nat_Ostrict__boundedE) ).
thf(6089,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
!= ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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 != C )
& ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(1702,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_59_Ex__less__Suc) ).
thf(9813,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)],[1702]) ).
thf(1060,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_7031_dvd__diffD1) ).
thf(6727,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)],[1060]) ).
thf(1739,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_2227_antisym__conv1) ).
thf(10138,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)],[1739]) ).
thf(1217,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 @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( gcd_gcd_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_9705_gcd__nat_Omono) ).
thf(7484,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 @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( gcd_gcd_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)],[1217]) ).
thf(1885,axiom,
ord_less_nat @ ( ord_less_nat @ ( fequal_o @ ( fequal_nat @ bNF_re4705727531993890431at_o_o ) @ ( fequal_nat @ bNF_re1448341924010609215_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9568_less__natural_Orsp) ).
thf(10827,plain,
ord_less_nat @ ( ord_less_nat @ ( fequal_o @ ( fequal_nat @ bNF_re4705727531993890431at_o_o ) @ ( fequal_nat @ bNF_re1448341924010609215_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885]) ).
thf(952,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_3459_Suc__mult__cancel1) ).
thf(6241,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)],[952]) ).
thf(352,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5927_mod2__gr__0) ).
thf(3414,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) ) )
& ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(691,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_3503_mult__eq__if) ).
thf(5005,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)],[691]) ).
thf(1117,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_1433_add__leD2) ).
thf(6996,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)],[1117]) ).
thf(1747,axiom,
! [A: set_nat,B: list_set_nat] :
( ( B @ set_set_nat2 @ ( A @ member_set_nat ) )
=> ( B @ size_s3254054031482475050et_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6298_length__pos__if__in__set) ).
thf(10170,plain,
! [A: set_nat,B: list_set_nat] :
( ( B @ set_set_nat2 @ ( A @ member_set_nat ) )
=> ( B @ size_s3254054031482475050et_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747]) ).
thf(1699,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_1996_less__imp__neq) ).
thf(9801,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)],[1699]) ).
thf(922,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_3241_mult__strict__mono_H) ).
thf(6117,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)],[922]) ).
thf(1475,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_3472_Euclidean__Division_Odiv__eq__0__iff) ).
thf(8650,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)],[1475]) ).
thf(12,axiom,
! [A: nat,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4303_real__root__minus) ).
thf(1954,plain,
! [A: nat,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1330,axiom,
! [A: $o] :
( ( one_one_nat @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7496_of__bool__less__one__iff) ).
thf(8012,plain,
! [A: $o] :
( ( ~ A
=> ( one_one_nat @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).
thf(1803,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_1422_le__eq__less__or__eq) ).
thf(10414,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)],[1803]) ).
thf(1664,axiom,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109__C3_Ohyps_C_I1_J) ).
thf(9540,plain,
m @ ( summary @ vEBT_invar_vebt @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664]) ).
thf(1159,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_3682_of__nat__power__less__of__nat__cancel__iff) ).
thf(7220,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)],[1159]) ).
thf(1651,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_6816_dvd__0__left) ).
thf(9481,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)],[1651]) ).
thf(1695,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_76_less__Suc__eq__0__disj) ).
thf(9774,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)],[1695]) ).
thf(321,axiom,
! [A: int] :
( ( zero_zero_nat @ ( A @ gbinomial_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3640_gbinomial__0_I1_J) ).
thf(3276,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ gbinomial_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(740,axiom,
! [A: list_real,B: nat,C: real] :
( ( ( A @ size_size_list_real )
= B )
=> ( ! [D: real] :
( ( A @ set_real2 @ ( D @ member_real ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8650_replicate__eqI) ).
thf(5227,plain,
! [A: list_real,B: nat,C: real] :
( ( ( A @ size_size_list_real )
= B )
=> ( ! [D: real] :
( ( A @ set_real2 @ ( D @ member_real ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(133,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( A @ ( B @ divide_divide_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2991_nonzero__minus__divide__divide) ).
thf(2432,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( A @ ( B @ divide_divide_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(163,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_4614_mod__add__eq) ).
thf(2548,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)],[163]) ).
thf(1514,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9669_gcd__1__nat) ).
thf(8816,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514]) ).
thf(1635,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3943_zero__power) ).
thf(9396,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635]) ).
thf(1451,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_list__decode_Ocases) ).
thf(8546,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451]) ).
thf(1825,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( B @ size_s6755466524823107622T_VEBT @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6299_length__pos__if__in__set) ).
thf(10530,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( B @ size_s6755466524823107622T_VEBT @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825]) ).
thf(157,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9015_Suc__0__or__eq) ).
thf(2531,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(645,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( size_size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6397_num_Osize_I6_J) ).
thf(4775,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( size_size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(1299,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_3430_div__less) ).
thf(7858,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)],[1299]) ).
thf(1643,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_7359_gcd__nat_Oeq__iff) ).
thf(9443,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)],[1643]) ).
thf(1295,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_3455_less__eq__div__iff__mult__less__eq) ).
thf(7839,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)],[1295]) ).
thf(485,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_4756_mod__div__decomp) ).
thf(4047,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)],[485]) ).
thf(1122,axiom,
zero_zero_nat @ ( aTP_Lamm_ou @ ( dvd_dvd_nat @ ordering_top_nat ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9789_gcd__nat_Oordering__top__axioms) ).
thf(7018,plain,
zero_zero_nat @ ( aTP_Lamm_ou @ ( dvd_dvd_nat @ ordering_top_nat ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(1805,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_less__irrefl__nat) ).
thf(10427,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805]) ).
thf(1315,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = one_one_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9769_coprime__common__divisor__nat) ).
thf(7944,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).
thf(745,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_1249_of__nat__le__0__iff) ).
thf(5252,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)],[745]) ).
thf(580,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6525_binomial__gbinomial) ).
thf(4496,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(886,axiom,
! [A: nat,B: list_complex] :
( ( B @ size_s3451745648224563538omplex @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_complex2 @ ( A @ ( B @ nth_complex @ aa_nat_complex ) @ member_complex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6416_nth__mem) ).
thf(5935,plain,
! [A: nat,B: list_complex] :
( ( B @ size_s3451745648224563538omplex @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_complex2 @ ( A @ ( B @ nth_complex @ aa_nat_complex ) @ member_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1221,axiom,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7970_not__bit__Suc__0__numeral) ).
thf(7499,plain,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).
thf(982,axiom,
! [A: num] :
~ ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5482_not__numeral__less__one) ).
thf(6381,plain,
! [A: num] :
~ ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(1274,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( one_one_nat @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8156_bit__iff__and__push__bit__not__eq__0) ).
thf(7734,plain,
! [A: nat,B: nat] :
( ( ( ( one_one_nat @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).
thf(1363,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_4315_fact__ge__zero) ).
thf(8133,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)],[1363]) ).
thf(624,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
<=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_deg1Leaf) ).
thf(4679,plain,
! [A: vEBT_VEBT] :
( ( ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) )
=> ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(1163,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_3252_mult__strict__mono) ).
thf(7235,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)],[1163]) ).
thf(786,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_1148_Suc__le__mono) ).
thf(5476,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)],[786]) ).
thf(1594,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_1476_add__decreasing2) ).
thf(9159,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)],[1594]) ).
thf(1096,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6664_take__bit__numeral__1) ).
thf(6904,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(1603,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_1962_pinf_I5_J) ).
thf(9195,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)],[1603]) ).
thf(845,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9663_gcd__nat_Oeq__neutr__iff) ).
thf(5723,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(1436,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_3705_power__mono__iff) ).
thf(8472,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)],[1436]) ).
thf(1683,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_1150_bot__nat__0_Oextremum) ).
thf(9708,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)],[1683]) ).
thf(1193,axiom,
! [A: complex,B: nat,C: complex] :
( ( C @ ( B @ replicate_complex ) @ set_complex2 @ ( A @ member_complex ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8559_in__set__replicate) ).
thf(7364,plain,
! [A: complex,B: nat,C: complex] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_complex ) @ set_complex2 @ ( A @ member_complex ) ) )
& ( ( C @ ( B @ replicate_complex ) @ set_complex2 @ ( A @ member_complex ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).
thf(1485,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_1359_add__mono) ).
thf(8705,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)],[1485]) ).
thf(1647,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_2011_ord__less__eq__trans) ).
thf(9465,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)],[1647]) ).
thf(967,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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_6797_of__nat__dvd__iff) ).
thf(6306,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( 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)],[967]) ).
thf(1591,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_6920_dvd__diff__nat) ).
thf(9148,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)],[1591]) ).
thf(445,axiom,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_plus__1__eq__Suc) ).
thf(3880,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(620,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_321_add_Ocommute) ).
thf(4665,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)],[620]) ).
thf(544,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) )
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
<=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3601_of__nat__eq__of__nat__power__cancel__iff) ).
thf(4322,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) )
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ) )
& ( ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) )
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(1325,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_1152_diff__diff__cancel) ).
thf(7993,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)],[1325]) ).
thf(761,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_1604_add__nonneg__pos) ).
thf(5342,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)],[761]) ).
thf(1198,axiom,
! [A: list_complex] : ( A @ size_s3451745648224563538omplex @ ( A @ set_complex2 @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6303_card__length) ).
thf(7390,plain,
! [A: list_complex] : ( A @ size_s3451745648224563538omplex @ ( A @ set_complex2 @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).
thf(554,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_6993_div__plus__div__distrib__dvd__left) ).
thf(4386,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)],[554]) ).
thf(1584,axiom,
! [A: num,B: nat] :
( ( B @ extended_enat2 @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) )
<=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9862_numeral__less__enat__iff) ).
thf(9116,plain,
! [A: num,B: nat] :
( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ extended_enat2 @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) ) )
& ( ( B @ extended_enat2 @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) )
=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584]) ).
thf(1220,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_3470_nat__mult__1) ).
thf(7496,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)],[1220]) ).
thf(1726,axiom,
! [A: nat,B: fun_na6887940067898170868VEBT_o] :
( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
<=> ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6402_Skolem__list__nth) ).
thf(10042,plain,
! [A: nat,B: fun_na6887940067898170868VEBT_o] :
( ( ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) )
=> ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: vEBT_VEBT] : ( D @ ( C @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
=> ? [C: list_VEBT_VEBT] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_VEBT_VEBT ) @ ( D @ ( B @ aa_nat1925708948643195573VEBT_o ) @ aa_VEBT_VEBT_o ) ) )
& ( ( C @ size_s6755466524823107622T_VEBT )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726]) ).
thf(404,axiom,
! [A: complex,B: nat,C: complex] :
( ( C @ ( B @ ( A @ aTP_Lamm_bg @ aa_nat_fun_complex_o ) @ aa_complex_o ) )
<=> ( ( B @ ( C @ power_power_complex @ aa_nat_complex ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10435_ATP_Olambda__284) ).
thf(3644,plain,
! [A: complex,B: nat,C: complex] :
( ( ( ( B @ ( C @ power_power_complex @ aa_nat_complex ) )
= A )
=> ( C @ ( B @ ( A @ aTP_Lamm_bg @ aa_nat_fun_complex_o ) @ aa_complex_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_bg @ aa_nat_fun_complex_o ) @ aa_complex_o ) )
=> ( ( B @ ( C @ power_power_complex @ aa_nat_complex ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1639,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_1420_le__neq__implies__less) ).
thf(9410,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)],[1639]) ).
thf(1114,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_4723_unique__euclidean__semiring__numeral__class_Opos__mod__sign) ).
thf(6987,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)],[1114]) ).
thf(1474,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9673_gcd__nat_Oabsorb2) ).
thf(8647,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474]) ).
thf(1509,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_2654_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(8785,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)],[1509]) ).
thf(1111,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_3465_le__cube) ).
thf(6968,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)],[1111]) ).
thf(727,axiom,
( m
= ( na @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__C3_Ohyps_C_I3_J) ).
thf(5160,plain,
( m
= ( na @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(717,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_3932_power__less__imp__less__exp) ).
thf(5108,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)],[717]) ).
thf(1165,axiom,
! [A: nat,B: complex] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ collect_complex @ ( aTP_Lamm_az @ groups7754918857620584856omplex ) )
= zero_zero_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8857_sum__nth__roots) ).
thf(7241,plain,
! [A: nat,B: complex] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ collect_complex @ ( aTP_Lamm_az @ groups7754918857620584856omplex ) )
= zero_zero_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(592,axiom,
! [A: num,B: num] :
( ( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6467_cong__exp__iff__simps_I7_J) ).
thf(4546,plain,
! [A: num,B: num] :
( ( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(1735,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_6499_binomial__eq__0__iff) ).
thf(10121,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)],[1735]) ).
thf(1777,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_40_not__less__eq) ).
thf(10286,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)],[1777]) ).
thf(778,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_1427_nat__le__iff__add) ).
thf(5429,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)],[778]) ).
thf(174,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_3552_nat__le__add__iff2) ).
thf(2603,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)],[174]) ).
thf(107,axiom,
! [A: real] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5807_power2__minus) ).
thf(2328,plain,
! [A: real] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1596,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6521_Suc__times__binomial__eq) ).
thf(9172,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596]) ).
thf(1175,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9702_gcd__nat_Oabsorb3) ).
thf(7277,plain,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).
thf(1310,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_489_one__is__add) ).
thf(7914,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)],[1310]) ).
thf(872,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_6979_dvd__div__mult2__eq) ).
thf(5883,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)],[872]) ).
thf(1016,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_1488_add__nonpos__nonpos) ).
thf(6538,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)],[1016]) ).
thf(298,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_351_diff__diff__eq) ).
thf(3131,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)],[298]) ).
thf(559,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_3518_div__add__self1) ).
thf(4415,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)],[559]) ).
thf(1714,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_9613_Least__eq__0) ).
thf(9988,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)],[1714]) ).
thf(524,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_4938_div__mod__decomp) ).
thf(4224,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)],[524]) ).
thf(386,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_3420_div__mult__self1) ).
thf(3574,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)],[386]) ).
thf(1190,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_7081_unit__eq__div2) ).
thf(7349,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)],[1190]) ).
thf(1862,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_63_Suc__lessE) ).
thf(10722,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)],[1862]) ).
thf(430,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3610_of__nat__power) ).
thf(3821,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( B @ extended_enat2 @ ( A @ extended_enat2 @ plus_p3455044024723400733d_enat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ extended_enat2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9859_plus__enat__simps_I1_J) ).
thf(2444,plain,
! [A: nat,B: nat] :
( ( B @ extended_enat2 @ ( A @ extended_enat2 @ plus_p3455044024723400733d_enat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ extended_enat2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(75,axiom,
! [A: nat] :
( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7255_minus__one__power__iff) ).
thf(2217,plain,
! [A: nat] :
( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B = one_one_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1281,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_6950_minf_I9_J) ).
thf(7771,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).
thf(1548,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_446_add__less__mono1) ).
thf(8951,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)],[1548]) ).
thf(302,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_147_add__cancel__left__right) ).
thf(3148,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)],[302]) ).
thf(1861,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_452_of__nat__less__0__iff) ).
thf(10719,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)],[1861]) ).
thf(646,axiom,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n3304061248610475627l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7523_sgn__of__nat) ).
thf(4778,plain,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ zero_n3304061248610475627l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(1384,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_1564_mono__nat__linear__lb) ).
thf(8214,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)],[1384]) ).
thf(381,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_1525_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(3542,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)],[381]) ).
thf(536,axiom,
! [A: real] :
( ( zero_zero_real
= ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2571_zero__eq__1__divide__iff) ).
thf(4275,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( zero_zero_real
= ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) ) ) )
& ( ( zero_zero_real
= ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) ) )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(921,axiom,
! [A: rat,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
!= zero_zero_rat )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
!= zero_zero_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4100_pochhammer__neq__0__mono) ).
thf(6113,plain,
! [A: rat,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
!= zero_zero_rat )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
!= zero_zero_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(166,axiom,
! [A: nat] :
( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= zero_zero_real )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_of__nat__eq__0__iff) ).
thf(2562,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= zero_zero_real )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1791,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_7347_dvd__antisym) ).
thf(10337,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)],[1791]) ).
thf(1675,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_7026_nat__dvd__not__less) ).
thf(9668,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)],[1675]) ).
thf(1043,axiom,
! [A: nat,B: complex,C: complex] :
( ( C @ ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ aa_complex_o ) )
<=> ( ( A @ ( C @ power_power_complex @ aa_nat_complex ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10434_ATP_Olambda__283) ).
thf(6662,plain,
! [A: nat,B: complex,C: complex] :
( ( ( ( A @ ( C @ power_power_complex @ aa_nat_complex ) )
= B )
=> ( C @ ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ aa_complex_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ aa_complex_o ) )
=> ( ( A @ ( C @ power_power_complex @ aa_nat_complex ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(1700,axiom,
! [A: nat,B: nat] :
( ( less_than @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9854_less__than__iff) ).
thf(9805,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( less_than @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) ) )
& ( ( less_than @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700]) ).
thf(842,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_9034_nat__mult__max__left) ).
thf(5706,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)],[842]) ).
thf(598,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_1572_le__diff__conv) ).
thf(4568,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)],[598]) ).
thf(642,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_4037_power__eq__if) ).
thf(4766,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)],[642]) ).
thf(945,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_6638_dvd__add__times__triv__left__iff) ).
thf(6208,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)],[945]) ).
thf(863,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_492_less__iff__Suc__add) ).
thf(5836,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)],[863]) ).
thf(209,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7158_odd__even__add) ).
thf(2745,plain,
! [A: nat,B: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(1499,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6518_choose__one) ).
thf(8753,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499]) ).
thf(530,axiom,
! [A: nat,B: int,C: fun_int_o] :
( ? [D: int] :
( ( D @ ( C @ aa_int_o ) )
& ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) ) )
<=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8557_Bex__set__replicate) ).
thf(4243,plain,
! [A: nat,B: int,C: fun_int_o] :
( ( ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_int_o ) ) )
=> ? [D: int] :
( ( D @ ( C @ aa_int_o ) )
& ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) ) ) )
& ( ? [D: int] :
( ( D @ ( C @ aa_int_o ) )
& ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) ) )
=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_int_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(926,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_3439_div__mult__mult2) ).
thf(6130,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)],[926]) ).
thf(902,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_4465_bits__mod__0) ).
thf(6010,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)],[902]) ).
thf(1359,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_6865_dvd__unit__imp__unit) ).
thf(8121,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)],[1359]) ).
thf(910,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_1432_le__Suc__ex) ).
thf(6049,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)],[910]) ).
thf(62,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( pred_numeral @ aa_num_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6509_pred__numeral__simps_I3_J) ).
thf(2169,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( pred_numeral @ aa_num_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1891,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_88_nat__less__induct) ).
thf(10850,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)],[1891]) ).
thf(1029,axiom,
! [A: fun_nat_nat] :
( ! [B: nat] :
( ( B @ ( A @ aa_nat_nat ) )
= zero_zero_nat )
=> ( zero_zero_nat @ ( A @ sums_nat @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8597_sums__0) ).
thf(6579,plain,
! [A: fun_nat_nat] :
( ! [B: nat] :
( ( B @ ( A @ aa_nat_nat ) )
= zero_zero_nat )
=> ( zero_zero_nat @ ( A @ sums_nat @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(288,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6756_even__succ__div__2) ).
thf(3084,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1832,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_2006_ord__eq__less__trans) ).
thf(10570,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)],[1832]) ).
thf(553,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5814_div2__Suc__Suc) ).
thf(4383,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(555,axiom,
! [A: nat] :
( ( one_one_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_of__nat__1__eq__iff) ).
thf(4390,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ) )
& ( ( one_one_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(1369,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_3497_n__less__n__mult__m) ).
thf(8161,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)],[1369]) ).
thf(916,axiom,
! [A: nat] :
( ( one_one_nat
= ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_of__nat__1__eq__iff) ).
thf(6071,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)],[916]) ).
thf(1536,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_1484_add__nonneg__nonneg) ).
thf(8907,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)],[1536]) ).
thf(343,axiom,
! [A: real,B: nat] :
( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( B = zero_zero_nat )
| ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5656_power__eq__1__iff) ).
thf(3374,plain,
! [A: real,B: nat] :
( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( B = zero_zero_nat )
| ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(347,axiom,
! [A: rat] :
( ( zero_zero_nat @ ( A @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3853_power__0) ).
thf(3385,plain,
! [A: rat] :
( ( zero_zero_nat @ ( A @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1268,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_4157_pochhammer__product_H) ).
thf(7711,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)],[1268]) ).
thf(1827,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ ( hd_nat @ aa_list_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9357_hd__upt) ).
thf(10534,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ ( hd_nat @ aa_list_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827]) ).
thf(737,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_2642_mult_Oleft__commute) ).
thf(5214,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)],[737]) ).
thf(550,axiom,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( ! [C: nat,D: $o] :
( ( C @ ( A @ aa_nat_o ) )
=> ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7575_bits__induct) ).
thf(4353,plain,
! [A: fun_nat_o,B: nat] :
( ! [C: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( ! [C: nat,D: $o] :
( ( C @ ( A @ aa_nat_o ) )
=> ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(1047,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_1409_transitive__stepwise__le) ).
thf(6681,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)],[1047]) ).
thf(1515,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_6959_dvd__div__eq__0__iff) ).
thf(8819,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)],[1515]) ).
thf(932,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_2646_mult_Ocommute) ).
thf(6149,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)],[932]) ).
thf(1897,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( A @ ( aTP_Lamm_kf @ ( $false @ case_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8972_nat_Odisc__eq__case_I2_J) ).
thf(10891,plain,
! [A: nat] :
( ( ( A @ ( aTP_Lamm_kf @ ( $false @ case_nat_o ) @ aa_nat_o ) )
=> ( A != zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( A @ ( aTP_Lamm_kf @ ( $false @ case_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897]) ).
thf(981,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_3224_mult__right__le__imp__le) ).
thf(6379,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)],[981]) ).
thf(1455,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_130_of__nat__eq__iff) ).
thf(8571,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)],[1455]) ).
thf(1489,axiom,
! [A: real,B: nat,C: real] :
( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= ( B @ ( C @ power_power_real @ aa_nat_real ) ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( C @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5547_power__eq__imp__eq__norm) ).
thf(8717,plain,
! [A: real,B: nat,C: real] :
( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= ( B @ ( C @ power_power_real @ aa_nat_real ) ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( C @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489]) ).
thf(735,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_495_less__natE) ).
thf(5193,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)],[735]) ).
thf(817,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_443_add__less__mono) ).
thf(5604,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)],[817]) ).
thf(1460,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Zero__neq__Suc) ).
thf(8600,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460]) ).
thf(771,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_rat @ gbinomial_rat @ aa_nat_rat ) )
= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3633_gbinomial__0_I2_J) ).
thf(5397,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_rat @ gbinomial_rat @ aa_nat_rat ) )
= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(822,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ aTP_Lamm_bh @ collect_complex @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8131_card__roots__unity) ).
thf(5622,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ aTP_Lamm_bh @ collect_complex @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(756,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_3902_power__inject__base) ).
thf(5323,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)],[756]) ).
thf(676,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3591_power__one) ).
thf(4928,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(310,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6515_diff__numeral__Suc) ).
thf(3216,plain,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(977,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_7153_is__unit__div__mult__cancel__right) ).
thf(6365,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)],[977]) ).
thf(623,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_3416_div__mult__self3) ).
thf(4675,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)],[623]) ).
thf(365,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6699_even__add) ).
thf(3470,plain,
! [A: nat,B: nat] :
( ( ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(1102,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_1401_le__SucE) ).
thf(6923,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)],[1102]) ).
thf(329,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3596_of__nat__power__eq__of__nat__cancel__iff) ).
thf(3312,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_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 ) )
= ( C @ ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(1465,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_4913_Suc__mod__mult__self4) ).
thf(8615,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)],[1465]) ).
thf(865,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_448_trans__less__add2) ).
thf(5851,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)],[865]) ).
thf(1273,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_1408_nat__induct__at__least) ).
thf(7728,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)],[1273]) ).
thf(1450,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_4932_mod__le__divisor) ).
thf(8543,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)],[1450]) ).
thf(1233,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_pe @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B
= ( A @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10272_ATP_Olambda__121) ).
thf(7560,plain,
! [A: nat,B: nat] :
( ( ( B
= ( A @ ( suc @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( aTP_Lamm_pe @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( aTP_Lamm_pe @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
= ( A @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).
thf(270,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6377_div__Suc__eq__div__add3) ).
thf(3014,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(204,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_353_diff__add__inverse) ).
thf(2730,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)],[204]) ).
thf(1416,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_6850_dvd__productE) ).
thf(8384,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)],[1416]) ).
thf(1709,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_10_gr__implies__not0) ).
thf(9869,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)],[1709]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9020_or__nat__unfold) ).
thf(2520,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(506,axiom,
! [A: real] :
( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4902_sgn__zero__iff) ).
thf(4141,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(433,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_4937_mod__mult2__eq) ).
thf(3835,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)],[433]) ).
thf(414,axiom,
! [A: nat,B: int,C: fun_int_o] :
( ! [D: int] :
( ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( C @ aa_int_o ) ) )
<=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8554_Ball__set__replicate) ).
thf(3708,plain,
! [A: nat,B: int,C: fun_int_o] :
( ( ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_int_o ) ) )
=> ! [D: int] :
( ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( C @ aa_int_o ) ) ) )
& ( ! [D: int] :
( ( B @ ( A @ replicate_int ) @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( C @ aa_int_o ) ) )
=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_int_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(709,axiom,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( bit_se2925701944663578781it_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_7309_take__bit__numeral__bit1) ).
thf(5076,plain,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( bit_se2925701944663578781it_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)],[709]) ).
thf(1361,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( gcd_gcd_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 ) )
=> ~ ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9700_gcd__nat_OboundedE) ).
thf(8126,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( gcd_gcd_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 ) )
=> ~ ( C @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).
thf(384,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_3529_nat__less__add__iff2) ).
thf(3557,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)],[384]) ).
thf(1319,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_int @ gbinomial_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3635_gbinomial__0_I2_J) ).
thf(7965,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_int @ gbinomial_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).
thf(1252,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9998_unit__factor__simps_I2_J) ).
thf(7633,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).
thf(1778,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_2088_order__less__trans) ).
thf(10292,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)],[1778]) ).
thf(313,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( 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_6760_odd__succ__div__two) ).
thf(3231,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( 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)],[313]) ).
thf(125,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7325_fact__code) ).
thf(2388,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1211,axiom,
! [A: list_o,B: fun_o_o,C: nat] :
( ! [D: $o] :
( ( A @ set_o2 @ ( D @ member_o ) )
=> ( D @ ( B @ aa_o_o ) ) )
=> ( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6339_inthall) ).
thf(7464,plain,
! [A: list_o,B: fun_o_o,C: nat] :
( ! [D: $o] :
( ( A @ set_o2 @ ( D @ member_o ) )
=> ( D @ ( B @ aa_o_o ) ) )
=> ( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).
thf(442,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_3553_nat__diff__add__eq1) ).
thf(3866,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)],[442]) ).
thf(1160,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_4528_bits__mod__div__trivial) ).
thf(7226,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)],[1160]) ).
thf(1824,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_2272_order_Ostrict__trans2) ).
thf(10527,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)],[1824]) ).
thf(229,axiom,
! [A: fun_nat_real,B: nat] :
( ( B @ ( A @ aTP_Lamm_hl @ aa_nat_real ) )
= ( @+[C: real] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_real ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10178_ATP_Olambda__27) ).
thf(2829,plain,
! [A: fun_nat_real,B: nat] :
( ( B @ ( A @ aTP_Lamm_hl @ aa_nat_real ) )
= ( @+[C: real] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_real ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1620,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_deg__not__0) ).
thf(9304,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620]) ).
thf(1376,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9767_coprime__Suc__0__left) ).
thf(8190,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).
thf(1869,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_747_less__one) ).
thf(10746,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)],[1869]) ).
thf(1704,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_74_lift__Suc__mono__less) ).
thf(9832,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)],[1704]) ).
thf(1323,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_556_Suc__diff__1) ).
thf(7986,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)],[1323]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8056_even__push__bit__iff) ).
thf(2777,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != zero_zero_nat ) )
=> ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(65,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5945_zero__power2) ).
thf(2178,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(837,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_3110_mult__neg__pos) ).
thf(5682,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)],[837]) ).
thf(1356,axiom,
! [A: nat,B: num] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) )
<=> ( A
= ( B @ ( pred_numeral @ aa_num_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6504_Suc__eq__numeral) ).
thf(8109,plain,
! [A: nat,B: num] :
( ( ( A
= ( B @ ( pred_numeral @ aa_num_nat ) ) )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) ) )
& ( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) )
=> ( A
= ( B @ ( pred_numeral @ aa_num_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).
thf(1821,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_2266_order_Ostrict__trans1) ).
thf(10519,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)],[1821]) ).
thf(80,axiom,
! [A: list_o,B: nat] :
( ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_n2687167440665602831ol_nat @ groups9119017779487936845_o_nat ) ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ nth_o @ aa_nat_o ) )
& ( A @ size_size_list_o @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8024_bit__horner__sum__bit__iff) ).
thf(2237,plain,
! [A: list_o,B: nat] :
( ( ( ( B @ ( A @ nth_o @ aa_nat_o ) )
& ( A @ size_size_list_o @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_n2687167440665602831ol_nat @ groups9119017779487936845_o_nat ) ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_n2687167440665602831ol_nat @ groups9119017779487936845_o_nat ) ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ nth_o @ aa_nat_o ) )
& ( A @ size_size_list_o @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1418,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_4926_mod__geq) ).
thf(8394,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)],[1418]) ).
thf(177,axiom,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6088_nat__bit__induct) ).
thf(2616,plain,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1172,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7118_fact__fact__dvd__fact) ).
thf(7268,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).
thf(1219,axiom,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( B @ ( A @ power_power_int @ aa_nat_int ) )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3749_power__not__zero) ).
thf(7492,plain,
! [A: int,B: nat] :
( ( A != zero_zero_int )
=> ( ( B @ ( A @ power_power_int @ aa_nat_int ) )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).
thf(465,axiom,
( ( zero_zero_real @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5136_norm__zero) ).
thf(3966,plain,
( ( zero_zero_real @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(1334,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_1018_zero__less__two) ).
thf(8029,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)],[1334]) ).
thf(1624,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_2312_dual__order_Ostrict__iff__not) ).
thf(9336,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)],[1624]) ).
thf(949,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_6535_binomial__fact__lemma) ).
thf(6227,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)],[949]) ).
thf(514,axiom,
( ( one_one_real @ ( sgn_sgn_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4485_sgn__1) ).
thf(4173,plain,
( ( one_one_real @ ( sgn_sgn_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(672,axiom,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8085_push__bit__of__nat) ).
thf(4903,plain,
! [A: nat,B: nat] :
( ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(564,axiom,
( ( zero_zero_real @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4482_sgn__0) ).
thf(4443,plain,
( ( zero_zero_real @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_nat__int__comparison_I1_J) ).
thf(3075,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(1653,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_2288_dual__order_Oorder__iff__strict) ).
thf(9490,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)],[1653]) ).
thf(1044,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_3437_div__mult__mult1) ).
thf(6670,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)],[1044]) ).
thf(1206,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_7120_nat__mult__dvd__cancel1) ).
thf(7423,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)],[1206]) ).
thf(868,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_of__nat__eq__1__iff) ).
thf(5861,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)],[868]) ).
thf(1843,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_1932_minf_I5_J) ).
thf(10623,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)],[1843]) ).
thf(1166,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_6654_dvd__imp__mod__0) ).
thf(7245,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)],[1166]) ).
thf(416,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_2827_left__diff__distrib_H) ).
thf(3724,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)],[416]) ).
thf(245,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_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 ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7829_of__nat__and__eq) ).
thf(2893,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_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 ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1042,axiom,
! [A: list_complex,B: fun_complex_o,C: complex] :
( ! [D: nat] :
( ( A @ size_s3451745648224563538omplex @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_complex @ aa_nat_complex ) @ ( B @ aa_complex_o ) ) )
=> ( ( A @ set_complex2 @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6434_all__nth__imp__all__set) ).
thf(6657,plain,
! [A: list_complex,B: fun_complex_o,C: complex] :
( ! [D: nat] :
( ( A @ size_s3451745648224563538omplex @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_complex @ aa_nat_complex ) @ ( B @ aa_complex_o ) ) )
=> ( ( A @ set_complex2 @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(634,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2441_div__by__0) ).
thf(4733,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(1368,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_1431_add__le__mono) ).
thf(8158,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)],[1368]) ).
thf(412,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_4626_mod__add__right__eq) ).
thf(3702,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)],[412]) ).
thf(470,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5803_bits__one__mod__two__eq__one) ).
thf(3983,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(1542,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_6981_div__div__eq__right) ).
thf(8929,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)],[1542]) ).
thf(1701,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4323_fact__gt__zero) ).
thf(9811,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701]) ).
thf(1296,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_4912_mod__by__Suc__0) ).
thf(7845,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)],[1296]) ).
thf(486,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_543_add__0__iff) ).
thf(4050,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)],[486]) ).
thf(940,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_12_old_Onat_Oinject) ).
thf(6176,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)],[940]) ).
thf(1871,axiom,
zero_zero_nat @ ( aTP_Lamm_aj @ sums_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8542_sums__zero) ).
thf(10757,plain,
zero_zero_nat @ ( aTP_Lamm_aj @ sums_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871]) ).
thf(1343,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9686_gcd__red__nat) ).
thf(8065,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).
thf(631,axiom,
( ( one_one_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_of__nat__1) ).
thf(4724,plain,
( ( one_one_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(401,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_4780_minus__div__mult__eq__mod) ).
thf(3621,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)],[401]) ).
thf(1110,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
!= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_of__nat__neq__0) ).
thf(6964,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
!= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(803,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7634_of__nat__mask__eq) ).
thf(5541,plain,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(698,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_3551_nat__le__add__iff1) ).
thf(5032,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)],[698]) ).
thf(1121,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_414_add__strict__mono) ).
thf(7015,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)],[1121]) ).
thf(828,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_6822_dvd__triv__right) ).
thf(5650,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)],[828]) ).
thf(339,axiom,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2549_div__self) ).
thf(3357,plain,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(1641,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_1982_pinf_I1_J) ).
thf(9415,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)],[1641]) ).
thf(857,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_3441_one__eq__mult__iff) ).
thf(5805,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)],[857]) ).
thf(1023,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_1405_Suc__n__not__le__n) ).
thf(6559,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)],[1023]) ).
thf(1631,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_2083_order__less__asym_H) ).
thf(9388,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)],[1631]) ).
thf(851,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_7164_dvd__power__iff) ).
thf(5761,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)],[851]) ).
thf(511,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( modulo_modulo_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_6173_mult__exp__mod__exp__eq) ).
thf(4162,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( modulo_modulo_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)],[511]) ).
thf(1307,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3620_power__0__Suc) ).
thf(7899,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).
thf(1024,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_406_add__mono__thms__linordered__field_I2_J) ).
thf(6562,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)],[1024]) ).
thf(1422,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4226_of__nat__fact) ).
thf(8411,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422]) ).
thf(1622,axiom,
zero_zero_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8974_zero__natural_Orsp) ).
thf(9309,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622]) ).
thf(884,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_4540_mod__mult__self2) ).
thf(5929,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)],[884]) ).
thf(1287,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_nat_OdiscI) ).
thf(7807,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).
thf(1007,axiom,
! [A: nat,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6423_list__ball__nth) ).
thf(6498,plain,
! [A: nat,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( A @ ( B @ nth_VEBT_VEBT ) @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(730,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_4907_mod__less) ).
thf(5169,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)],[730]) ).
thf(43,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ minus_minus_real @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__zero) ).
thf(2103,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ minus_minus_real @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1428,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_2765_mult__left__cancel) ).
thf(8443,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)],[1428]) ).
thf(443,axiom,
! [A: list_VEBT_VEBT,B: nat,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( B @ ( D @ vEBT_invar_vebt @ aa_nat_o ) ) )
=> ( ( ( A @ size_s6755466524823107622T_VEBT )
= ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6271_set__n__deg__not__0) ).
thf(3870,plain,
! [A: list_VEBT_VEBT,B: nat,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( B @ ( D @ vEBT_invar_vebt @ aa_nat_o ) ) )
=> ( ( ( A @ size_s6755466524823107622T_VEBT )
= ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(391,axiom,
( ( one_one_nat @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_of__nat__1) ).
thf(3588,plain,
( ( one_one_nat @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(202,axiom,
! [A: real] :
( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4610_sgn__eq__0__iff) ).
thf(2718,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1203,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_3443_div__mult__self__is__m) ).
thf(7408,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)],[1203]) ).
thf(151,axiom,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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_7959_xor__numerals_I4_J) ).
thf(2508,plain,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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)],[151]) ).
thf(1711,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_7352_gcd__nat_Oorder__iff__strict) ).
thf(9875,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)],[1711]) ).
thf(848,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_3997_one__less__power) ).
thf(5738,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)],[848]) ).
thf(1880,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_2153_order__less__imp__not__eq) ).
thf(10799,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)],[1880]) ).
thf(1808,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_1947_minf_I2_J) ).
thf(10442,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)],[1808]) ).
thf(1740,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_1805_le__refl) ).
thf(10145,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)],[1740]) ).
thf(480,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5963_Suc__double__not__eq__double) ).
thf(4033,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(1311,axiom,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ? [B: nat] : ( B @ ( A @ 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_8464_suminf__pos__iff) ).
thf(7931,plain,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ? [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [B: nat] : ( B @ ( A @ 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)],[1311]) ).
thf(91,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( C @ ( B @ divide_divide_real @ aa_real_real ) @ ( C @ ( A @ divide_divide_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2748_diff__divide__distrib) ).
thf(2281,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) )
= ( C @ ( B @ divide_divide_real @ aa_real_real ) @ ( C @ ( A @ divide_divide_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(239,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6712_even__Suc__div__two) ).
thf(2861,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1505,axiom,
! [A: num] :
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6208_cong__exp__iff__simps_I1_J) ).
thf(8774,plain,
! [A: num] :
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505]) ).
thf(715,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_6634_dvd__add__times__triv__right__iff) ).
thf(5096,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)],[715]) ).
thf(1062,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_4949_Suc__times__mod__eq) ).
thf(6740,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)],[1062]) ).
thf(766,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9704_gcd__nat_OorderE) ).
thf(5370,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(1120,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_3433_mult__cancel1) ).
thf(7004,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)],[1120]) ).
thf(1691,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_2254_order_Oorder__iff__strict) ).
thf(9743,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)],[1691]) ).
thf(1420,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_3488_mult__eq__self__implies__10) ).
thf(8406,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)],[1420]) ).
thf(1107,axiom,
! [A: nat,B: list_int,C: fun_int_o] :
( ( B @ size_size_list_int @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: int] :
( ( B @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( C @ aa_int_o ) ) )
=> ( A @ ( B @ nth_int @ aa_nat_int ) @ ( C @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6426_list__ball__nth) ).
thf(6947,plain,
! [A: nat,B: list_int,C: fun_int_o] :
( ( B @ size_size_list_int @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: int] :
( ( B @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( C @ aa_int_o ) ) )
=> ( A @ ( B @ nth_int @ aa_nat_int ) @ ( C @ aa_int_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(1365,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ unique6322359934112328802ux_nat )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7685_divides__aux__eq) ).
thf(8141,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ unique6322359934112328802ux_nat ) )
& ( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ unique6322359934112328802ux_nat )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).
thf(852,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_3486_Suc__mult__le__cancel1) ).
thf(5772,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)],[852]) ).
thf(427,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5904_not__mod2__eq__Suc__0__eq__0) ).
thf(3808,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(156,axiom,
! [A: real,B: real] :
( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_neg__equal__iff__equal) ).
thf(2523,plain,
! [A: real,B: real] :
( ( ( A = B )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(121,axiom,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( B @ ( C @ ( A @ minus_minus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_diff__right__commute) ).
thf(2371,plain,
! [A: real,B: real,C: real] :
( ( C @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( B @ ( C @ ( A @ minus_minus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(264,axiom,
( ( zero_zero_nat @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_of__nat__0) ).
thf(2979,plain,
( ( zero_zero_nat @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(743,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_3087_zero__less__mult__pos2) ).
thf(5246,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)],[743]) ).
thf(1774,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3946_zero__power) ).
thf(10273,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774]) ).
thf(1877,axiom,
! [A: $o,B: list_o] :
( ( B @ set_o2 @ ( A @ member_o ) )
=> ( B @ size_size_list_o @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6300_length__pos__if__in__set) ).
thf(10784,plain,
! [A: $o,B: list_o] :
( ( B @ set_o2 @ ( A @ member_o ) )
=> ( B @ size_size_list_o @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877]) ).
thf(53,axiom,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_minus__diff__eq) ).
thf(2137,plain,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(875,axiom,
( ( aTP_Lamm_aj @ suminf_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8308_suminf__zero) ).
thf(5897,plain,
( ( aTP_Lamm_aj @ suminf_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(1069,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_6830_mult__dvd__mono) ).
thf(6772,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)],[1069]) ).
thf(1053,axiom,
! [A: int] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_int @ aa_nat_int ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3624_power__Suc0__right) ).
thf(6702,plain,
! [A: int] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_int @ aa_nat_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(655,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6381_mod__Suc__eq__mod__add3) ).
thf(4825,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(1482,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_4916_Suc__mod__mult__self1) ).
thf(8691,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)],[1482]) ).
thf(482,axiom,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5966_numerals_I1_J) ).
thf(4040,plain,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(22,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6742_neg__one__even__power) ).
thf(2002,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1052,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_1000_less__add__one) ).
thf(6700,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)],[1052]) ).
thf(1432,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
thf(8459,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432]) ).
thf(225,axiom,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4447_sgn__sgn) ).
thf(2809,plain,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1732,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_1421_less__or__eq__imp__le) ).
thf(10106,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)],[1732]) ).
thf(180,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_4736_div__mult1__eq) ).
thf(2639,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)],[180]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8148_flip__bit__eq__xor) ).
thf(2154,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(860,axiom,
! [A: list_VEBT_VEBT] : ( A @ size_s6755466524823107622T_VEBT @ ( A @ set_VEBT_VEBT2 @ finite7802652506058667612T_VEBT @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6306_card__length) ).
thf(5824,plain,
! [A: list_VEBT_VEBT] : ( A @ size_s6755466524823107622T_VEBT @ ( A @ set_VEBT_VEBT2 @ finite7802652506058667612T_VEBT @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(603,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_of__nat__eq__iff) ).
thf(4588,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ) )
& ( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(1561,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_3480_div__greater__zero__iff) ).
thf(9024,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)],[1561]) ).
thf(1073,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9958_lcm__proj1__if__dvd__nat) ).
thf(6787,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(1414,axiom,
! [A: $o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A
=> B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7450_of__bool__less__eq__iff) ).
thf(8362,plain,
! [A: $o,B: $o] :
( ( ( A
=> B )
=> ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A
=> B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414]) ).
thf(573,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_1533_le__add__diff) ).
thf(4475,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)],[573]) ).
thf(244,axiom,
! [A: complex] :
( ( one_one_complex = A )
<=> ( A = one_one_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_one__reorient) ).
thf(2884,plain,
! [A: complex] :
( ( ( A = one_one_complex )
=> ( one_one_complex = A ) )
& ( ( one_one_complex = A )
=> ( A = one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(576,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ divide_divide_real @ aa_real_real ) @ ( exp_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( exp_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4411_exp__divide__power__eq) ).
thf(4483,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ divide_divide_real @ aa_real_real ) @ ( exp_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( exp_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(1183,axiom,
! [A: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat )
<=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7467_of__bool__eq__1__iff) ).
thf(7305,plain,
! [A: $o] :
( ( A
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).
thf(372,axiom,
! [A: vEBT_VEBT] :
( ! [B: option4927543243414619207at_nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
!= ( E @ ( D @ ( C @ ( B @ vEBT_Node ) ) ) ) )
=> ~ ! [B: $o,C: $o] :
( A
!= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_VEBT_Oexhaust) ).
thf(3510,plain,
! [A: vEBT_VEBT] :
( ! [B: option4927543243414619207at_nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
!= ( E @ ( D @ ( C @ ( B @ vEBT_Node ) ) ) ) )
=> ~ ! [B: $o,C: $o] :
( A
!= ( C @ ( B @ vEBT_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(841,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_3537_nat__mult__eq__cancel__disj) ).
thf(5695,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)],[841]) ).
thf(1495,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_3245_mult__right__less__imp__less) ).
thf(8742,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)],[1495]) ).
thf(627,axiom,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7171_div2__even__ext__nat) ).
thf(4700,plain,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(1259,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_1303_lift__Suc__mono__le) ).
thf(7657,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)],[1259]) ).
thf(693,axiom,
! [A: num] :
( ( A @ ( pred_numeral @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6533_pred__numeral__def) ).
thf(5012,plain,
! [A: num] :
( ( A @ ( pred_numeral @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(1150,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_3910_power__gt1__lemma) ).
thf(7179,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)],[1150]) ).
thf(1124,axiom,
! [A: real,B: nat,C: nat] :
( ( A != zero_zero_real )
=> ( ( 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_real @ aa_nat_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( C @ ( A @ power_power_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4000_power__diff) ).
thf(7022,plain,
! [A: real,B: nat,C: nat] :
( ( A != zero_zero_real )
=> ( ( 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_real @ aa_nat_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( C @ ( A @ power_power_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(1272,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_3053_mult__mono) ).
thf(7725,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)],[1272]) ).
thf(781,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_7056_unit__dvdE) ).
thf(5443,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)],[781]) ).
thf(1158,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_6876_dvd__add) ).
thf(7217,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)],[1158]) ).
thf(894,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_3482_div__eq__dividend__iff) ).
thf(5968,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)],[894]) ).
thf(1557,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_3940_power__increasing) ).
thf(9009,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)],[1557]) ).
thf(1847,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 @ ( gcd_lcm_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_9986_lcm__pos__nat) ).
thf(10639,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 @ ( gcd_lcm_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)],[1847]) ).
thf(1597,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4801_fact__mod) ).
thf(9175,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597]) ).
thf(720,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9683_gcd__diff2__nat) ).
thf(5122,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(1758,axiom,
! [A: complex,B: list_complex] :
( ( B @ set_complex2 @ ( A @ member_complex ) )
=> ( B @ size_s3451745648224563538omplex @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6296_length__pos__if__in__set) ).
thf(10216,plain,
! [A: complex,B: list_complex] :
( ( B @ set_complex2 @ ( A @ member_complex ) )
=> ( B @ size_s3451745648224563538omplex @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758]) ).
thf(1565,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9709_gcd__nat_Osimps) ).
thf(9048,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565]) ).
thf(1360,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_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 ) @ ( binomial @ 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_6532_binomial__absorb__comp) ).
thf(8123,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_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 ) @ ( binomial @ 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)],[1360]) ).
thf(1766,axiom,
! [A: num] : ( A @ ( nat_of_num @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10010_nat__of__num__pos) ).
thf(10243,plain,
! [A: num] : ( A @ ( nat_of_num @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766]) ).
thf(1686,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ou @ 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_10202_ATP_Olambda__51) ).
thf(9720,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( aTP_Lamm_ou @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( aTP_Lamm_ou @ 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)],[1686]) ).
thf(1169,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4917_mod__Suc__Suc__eq) ).
thf(7254,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).
thf(269,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_add_Oassoc) ).
thf(3011,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1228,axiom,
! [A: $o,B: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) )
<=> ( A
<=> B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7545_of__bool__eq__iff) ).
thf(7535,plain,
! [A: $o,B: $o] :
( ( ( ( B
=> A )
& ( A
=> B ) )
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) )
=> ( ( B
=> A )
& ( A
=> B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).
thf(439,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8088_of__nat__push__bit) ).
thf(3857,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( B @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(726,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_2465_mult__1) ).
thf(5157,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)],[726]) ).
thf(523,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8038_push__bit__eq__0__iff) ).
thf(4216,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(248,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_2801_distrib__left) ).
thf(2910,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)],[248]) ).
thf(1380,axiom,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_invar__vebt_Ointros_I1_J) ).
thf(8201,plain,
! [A: $o,B: $o] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ vEBT_Leaf ) @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).
thf(613,axiom,
~ ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7156_odd__one) ).
thf(4629,plain,
~ ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(142,axiom,
! [A: complex] : ( A @ ( one_one_complex @ dvd_dvd_complex @ aa_complex_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6869_one__dvd) ).
thf(2473,plain,
! [A: complex] : ( A @ ( one_one_complex @ dvd_dvd_complex @ aa_complex_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(1339,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_1552_of__nat__0__le__iff) ).
thf(8046,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)],[1339]) ).
thf(1402,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_4438_fact__diff__Suc) ).
thf(8302,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)],[1402]) ).
thf(168,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_1528_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(2574,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)],[168]) ).
thf(415,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_1176_Nat_Oadd__diff__assoc) ).
thf(3720,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)],[415]) ).
thf(774,axiom,
! [A: fun_real_real,B: nat,C: real] :
( ( C @ ( B @ ( A @ aTP_Lamm_mi @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( C @ ( A @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10474_ATP_Olambda__323) ).
thf(5411,plain,
! [A: fun_real_real,B: nat,C: real] :
( ( C @ ( B @ ( A @ aTP_Lamm_mi @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( C @ ( A @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(1817,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_8_not__less0) ).
thf(10506,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)],[1817]) ).
thf(1706,axiom,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_o @ aa_nat_o ) )
<=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6399_nth__equalityI) ).
thf(9836,plain,
! [A: list_o,B: list_o] :
( ( ( A @ size_size_list_o )
= ( B @ size_size_list_o ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( A @ nth_o @ aa_nat_o ) )
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706]) ).
thf(914,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_old_Onat_Odistinct_I2_J) ).
thf(6064,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(912,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_3471_nat__mult__1__right) ).
thf(6058,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)],[912]) ).
thf(725,axiom,
! [A: list_int,B: list_int] :
( ( A = B )
<=> ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_int @ aa_nat_int ) )
= ( C @ ( B @ nth_int @ aa_nat_int ) ) ) )
& ( ( A @ size_size_list_int )
= ( B @ size_size_list_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6409_list__eq__iff__nth__eq) ).
thf(5142,plain,
! [A: list_int,B: list_int] :
( ( ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_int @ aa_nat_int ) )
= ( C @ ( B @ nth_int @ aa_nat_int ) ) ) )
& ( ( A @ size_size_list_int )
= ( B @ size_size_list_int ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_int @ aa_nat_int ) )
= ( C @ ( B @ nth_int @ aa_nat_int ) ) ) )
& ( ( A @ size_size_list_int )
= ( B @ size_size_list_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(594,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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_5944_zero__power2) ).
thf(4557,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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)],[594]) ).
thf(1419,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_one__reorient) ).
thf(8397,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)],[1419]) ).
thf(1123,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_6842_dvd__mult2) ).
thf(7019,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)],[1123]) ).
thf(1224,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_1608_add__neg__nonpos) ).
thf(7518,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)],[1224]) ).
thf(1026,axiom,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7839_bit__numeral__simps_I1_J) ).
thf(6571,plain,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(1770,axiom,
zero_zero_nat @ ( gcd_gcd_nat @ semila9081495762789891438tr_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9915_gcd__nat_Osemilattice__neutr__axioms) ).
thf(10258,plain,
zero_zero_nat @ ( gcd_gcd_nat @ semila9081495762789891438tr_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770]) ).
thf(1887,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_69_lift__Suc__mono__less__iff) ).
thf(10831,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)],[1887]) ).
thf(1611,axiom,
! [A: nat,B: nat] :
( ( pred_nat @ transi6264000038957366511cl_nat @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9913_less__eq) ).
thf(9252,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( pred_nat @ transi6264000038957366511cl_nat @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) ) )
& ( ( pred_nat @ transi6264000038957366511cl_nat @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ member8440522571783428010at_nat ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611]) ).
thf(100,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( one @ unique5055182867167087721od_nat ) )
= ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7739_divmod__algorithm__code_I3_J) ).
thf(2307,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( one @ unique5055182867167087721od_nat ) )
= ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1392,axiom,
! [A: int,B: list_int] :
( ( B @ set_int2 @ ( A @ member_int ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_int @ aa_nat_int ) )
= A )
& ( B @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6433_in__set__conv__nth) ).
thf(8250,plain,
! [A: int,B: list_int] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_int @ aa_nat_int ) )
= A )
& ( B @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_int2 @ ( A @ member_int ) ) )
& ( ( B @ set_int2 @ ( A @ member_int ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_int @ aa_nat_int ) )
= A )
& ( B @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).
thf(38,axiom,
! [A: num] :
( one
!= ( A @ ( bit0 @ aa_num_num ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5932_verit__eq__simplify_I10_J) ).
thf(2083,plain,
! [A: num] :
( one
!= ( A @ ( bit0 @ aa_num_num ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(541,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_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_6565_even__succ__mod__exp) ).
thf(4312,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_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)],[541]) ).
thf(1563,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_7030_less__eq__dvd__minus) ).
thf(9041,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)],[1563]) ).
thf(759,axiom,
! [A: extended_enat,B: extended_enat] :
( ( B @ ( A @ ord_le72135733267957522d_enat ) )
<=> ( A @ ( $false @ ( B @ aTP_Lamm_pf @ extended_case_enat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9804_less__enat__def) ).
thf(5334,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( A @ ( $false @ ( B @ aTP_Lamm_pf @ extended_case_enat_o ) ) )
=> ( B @ ( A @ ord_le72135733267957522d_enat ) ) )
& ( ( B @ ( A @ ord_le72135733267957522d_enat ) )
=> ( A @ ( $false @ ( B @ aTP_Lamm_pf @ extended_case_enat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(123,axiom,
! [A: nat] :
( ( A @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7922_xor__self__eq) ).
thf(2382,plain,
! [A: nat] :
( ( A @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(1411,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5508_one__plus__numeral__commute) ).
thf(8343,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).
thf(1692,axiom,
zero_zero_nat @ ( gcd_gcd_nat @ comm_monoid_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10000_gcd__nat_Ocomm__monoid__axioms) ).
thf(9753,plain,
zero_zero_nat @ ( gcd_gcd_nat @ comm_monoid_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692]) ).
thf(973,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_224_add__less__same__cancel2) ).
thf(6343,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)],[973]) ).
thf(1035,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_9025_max__nat_Oneutr__eq__iff) ).
thf(6605,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)],[1035]) ).
thf(1161,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_3460_mult__0) ).
thf(7229,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)],[1161]) ).
thf(1562,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_1492_add__nonneg__eq__0__iff) ).
thf(9031,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)],[1562]) ).
thf(1889,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_62_Suc__lessI) ).
thf(10843,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)],[1889]) ).
thf(1115,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_2773_divisors__zero) ).
thf(6990,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)],[1115]) ).
thf(399,axiom,
! [A: real] :
( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4605_sgn__0__0) ).
thf(3610,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(548,axiom,
! [A: nat] :
( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6747_even__of__nat) ).
thf(4344,plain,
! [A: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(581,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5731_pow__sum) ).
thf(4499,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(428,axiom,
( ( zero_zero_real @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1742_abs__0) ).
thf(3816,plain,
( ( zero_zero_real @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(1195,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_1021_nat__induct__non__zero) ).
thf(7378,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)],[1195]) ).
thf(172,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6768_odd__two__times__div__two__nat) ).
thf(2589,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(418,axiom,
! [A: nat,B: set_complex] :
( ( B @ ( A @ aTP_Lamm_fm @ groups5693394587270226106ex_nat ) )
= ( A @ ( B @ finite_card_complex @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8574_sum__constant) ).
thf(3735,plain,
! [A: nat,B: set_complex] :
( ( B @ ( A @ aTP_Lamm_fm @ groups5693394587270226106ex_nat ) )
= ( A @ ( B @ finite_card_complex @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(570,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_3502_div__geq) ).
thf(4466,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)],[570]) ).
thf(924,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( gcd_gcd_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 ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9707_gcd__mult__distrib__nat) ).
thf(6124,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( gcd_gcd_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 ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(1383,axiom,
! [A: nat,B: nat,C: num] :
( ( C @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( numeral_numeral_nat @ aa_num_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_5063_distrib__right__numeral) ).
thf(8211,plain,
! [A: nat,B: nat,C: num] :
( ( C @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( numeral_numeral_nat @ aa_num_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)],[1383]) ).
thf(1619,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_7356_gcd__nat_Ostrict__trans) ).
thf(9296,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)],[1619]) ).
thf(917,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( gcd_gcd_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_9672_gcd__nat_Obounded__iff) ).
thf(6079,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( 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 ) ) )
=> ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( gcd_gcd_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)],[917]) ).
thf(432,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6778_semiring__parity__class_Oeven__mask__iff) ).
thf(3827,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(1662,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_80_Ex__less__Suc2) ).
thf(9522,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)],[1662]) ).
thf(1324,axiom,
! [A: rat,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= zero_zero_rat )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= zero_zero_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4102_pochhammer__eq__0__mono) ).
thf(7989,plain,
! [A: rat,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= zero_zero_rat )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= zero_zero_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).
thf(205,axiom,
! [A: nat] :
( ( A @ ( one_one_complex @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3592_power__one) ).
thf(2733,plain,
! [A: nat] :
( ( A @ ( one_one_complex @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(467,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( 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_6158_ex__power__ivl1) ).
thf(3972,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( 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)],[467]) ).
thf(1020,axiom,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7637_prod__decode__aux_Ocases) ).
thf(6550,plain,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(1351,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_2677_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq) ).
thf(8091,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)],[1351]) ).
thf(1571,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(9075,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)],[1571]) ).
thf(690,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_4740_mult__div__mod__eq) ).
thf(5002,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)],[690]) ).
thf(1761,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_6799_dvd__trans) ).
thf(10229,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)],[1761]) ).
thf(1500,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_449_less__add__eq__less) ).
thf(8756,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)],[1500]) ).
thf(1531,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_3485_mult__less__mono2) ).
thf(8888,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)],[1531]) ).
thf(667,axiom,
! [A: nat] :
( ( one_one_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_of__nat__1__eq__iff) ).
thf(4878,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( ( one_one_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(272,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_395_add_Ocomm__neutral) ).
thf(3022,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)],[272]) ).
thf(858,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_6965_mult__unit__dvd__iff) ).
thf(5815,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)],[858]) ).
thf(1491,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_6987_dvd__div__unit__iff) ).
thf(8724,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)],[1491]) ).
thf(1537,axiom,
! [A: nat,B: nat] : ( B @ ( B @ ( A @ ( gcd_gcd_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_9696_gcd__nat_Ocobounded2) ).
thf(8910,plain,
! [A: nat,B: nat] : ( B @ ( B @ ( A @ ( gcd_gcd_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)],[1537]) ).
thf(285,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_4473_mod__add__self1) ).
thf(3069,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)],[285]) ).
thf(1452,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_7079_unit__eq__div1) ).
thf(8550,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)],[1452]) ).
thf(342,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ upt ) )
= nil_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9298_upt__0) ).
thf(3371,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ upt ) )
= nil_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(1731,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_1942_minf_I3_J) ).
thf(10102,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)],[1731]) ).
thf(567,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7874_bit__Suc) ).
thf(4449,plain,
! [A: nat,B: nat] :
( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(299,axiom,
( ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6459_numeral__3__eq__3) ).
thf(3134,plain,
( ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(579,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9330_upt__Suc) ).
thf(4493,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(712,axiom,
! [A: complex] :
( ( one_one_nat @ ( A @ power_power_complex @ aa_nat_complex ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3614_power__one__right) ).
thf(5085,plain,
! [A: complex] :
( ( one_one_nat @ ( A @ power_power_complex @ aa_nat_complex ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(28,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8108_numeral__code_I2_J) ).
thf(2032,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(716,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_1188_add__le__same__cancel2) ).
thf(5102,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)],[716]) ).
thf(654,axiom,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8632_sum__nonneg) ).
thf(4821,plain,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(1488,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_1592_add__strict__increasing) ).
thf(8714,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)],[1488]) ).
thf(373,axiom,
( ( one_one_nat @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_of__nat__1) ).
thf(3514,plain,
( ( one_one_nat @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(478,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_1174_Nat_Odiff__diff__right) ).
thf(4021,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)],[478]) ).
thf(1689,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_2038_linorder__less__wlog) ).
thf(9734,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)],[1689]) ).
thf(484,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_3469_diff__mult__distrib2) ).
thf(4044,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)],[484]) ).
thf(1716,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_2034_exists__least__iff) ).
thf(9993,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)],[1716]) ).
thf(324,axiom,
! [A: nat,B: complex] :
( ( B @ ( A @ aTP_Lamm_bh @ aa_complex_o ) )
<=> ( ( A @ ( B @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10208_ATP_Olambda__57) ).
thf(3286,plain,
! [A: nat,B: complex] :
( ( ( ( A @ ( B @ power_power_complex @ aa_nat_complex ) )
= one_one_complex )
=> ( B @ ( A @ aTP_Lamm_bh @ aa_complex_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_bh @ aa_complex_o ) )
=> ( ( A @ ( B @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1038,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_3442_mult__eq__1__iff) ).
thf(6620,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)],[1038]) ).
thf(1030,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9701_gcd__nat_Oabsorb4) ).
thf(6582,plain,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(1317,axiom,
! [A: list_set_nat,B: fun_set_nat_o,C: set_nat] :
( ! [D: nat] :
( ( A @ size_s3254054031482475050et_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_set_nat @ aa_nat_set_nat ) @ ( B @ aa_set_nat_o ) ) )
=> ( ( A @ set_set_nat2 @ ( C @ member_set_nat ) )
=> ( C @ ( B @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6436_all__nth__imp__all__set) ).
thf(7957,plain,
! [A: list_set_nat,B: fun_set_nat_o,C: set_nat] :
( ! [D: nat] :
( ( A @ size_s3254054031482475050et_nat @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_set_nat @ aa_nat_set_nat ) @ ( B @ aa_set_nat_o ) ) )
=> ( ( A @ set_set_nat2 @ ( C @ member_set_nat ) )
=> ( C @ ( B @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).
thf(1467,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_1503_add__mono__thms__linordered__field_I4_J) ).
thf(8623,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)],[1467]) ).
thf(1644,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_87_infinite__descent) ).
thf(9455,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)],[1644]) ).
thf(1308,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_6963_dvd__mult__unit__iff) ).
thf(7902,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)],[1308]) ).
thf(854,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_490_add__is__1) ).
thf(5779,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)],[854]) ).
thf(175,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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6254_divmod__digit__1_I1_J) ).
thf(2609,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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(679,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( C @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) ) )
<=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3598_of__nat__power__eq__of__nat__cancel__iff) ).
thf(4942,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( C @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) ) ) )
& ( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( C @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) ) )
=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(1242,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_1441_diff__le__mono) ).
thf(7591,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)],[1242]) ).
thf(350,axiom,
! [A: real] :
( ( zero_zero_nat @ ( A @ gbinomial_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3637_gbinomial__0_I1_J) ).
thf(3408,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ gbinomial_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1577,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_3003_mult__nonneg__nonpos2) ).
thf(9095,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)],[1577]) ).
thf(323,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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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_6216_divmod__digit__1_I2_J) ).
thf(3282,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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[323]) ).
thf(461,axiom,
( ( one_one_real @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1747_abs__1) ).
thf(3948,plain,
( ( one_one_real @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(1140,axiom,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( A @ suminf_nat )
= zero_zero_nat )
<=> ! [B: nat] :
( ( B @ ( A @ aa_nat_nat ) )
= zero_zero_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8432_suminf__eq__zero__iff) ).
thf(7097,plain,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ! [B: nat] :
( ( B @ ( A @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( A @ suminf_nat )
= zero_zero_nat ) )
& ( ( ( A @ suminf_nat )
= zero_zero_nat )
=> ! [B: nat] :
( ( B @ ( A @ aa_nat_nat ) )
= zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(539,axiom,
! [A: int] :
( ( one_one_int = A )
<=> ( A = one_one_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_one__reorient) ).
thf(4295,plain,
! [A: int] :
( ( ( A = one_one_int )
=> ( one_one_int = A ) )
& ( ( one_one_int = A )
=> ( A = one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(1773,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_2048_not__less__iff__gr__or__eq) ).
thf(10263,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)],[1773]) ).
thf(966,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_2438_mult__zero__left) ).
thf(6303,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)],[966]) ).
thf(1583,axiom,
! [A: nat] :
( ( A @ ( euclid3398187327856392827nt_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9799_division__segment__nat__def) ).
thf(9113,plain,
! [A: nat] :
( ( A @ ( euclid3398187327856392827nt_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583]) ).
thf(861,axiom,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3750_power__not__zero) ).
thf(5826,plain,
! [A: real,B: nat] :
( ( A != zero_zero_real )
=> ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(1103,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9971_lcm__nat__def) ).
thf(6926,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(141,axiom,
! [A: real,B: real] :
( ( A = B )
<=> ( ( B @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_eq__iff__diff__eq__0) ).
thf(2464,plain,
! [A: real,B: real] :
( ( ( ( B @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(214,axiom,
( ( one_one_real @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5142_norm__one) ).
thf(2758,plain,
( ( one_one_real @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(469,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ minus_minus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4943_field__char__0__class_Oof__nat__div) ).
thf(3980,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ minus_minus_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(887,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3621_power__0__Suc) ).
thf(5937,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(400,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2451_division__ring__divide__zero) ).
thf(3618,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(1539,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_1434_add__leD1) ).
thf(8920,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)],[1539]) ).
thf(1449,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_445_not__add__less2) ).
thf(8540,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)],[1449]) ).
thf(1510,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( A @ ( C @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= B )
& ( B @ ( A @ ( C @ ( gcd_gcd_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_9688_gcd__nat_Ostrict__coboundedI2) ).
thf(8788,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( A @ ( C @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= B )
& ( B @ ( A @ ( C @ ( gcd_gcd_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)],[1510]) ).
thf(1340,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_3463_mult__le__mono) ).
thf(8048,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)],[1340]) ).
thf(179,axiom,
! [A: real,B: real,C: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( B @ ( C @ divide_divide_real @ aa_real_real ) ) )
<=> ( ( A = C )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2454_divide__cancel__right) ).
thf(2628,plain,
! [A: real,B: real,C: real] :
( ( ( ( A = C )
| ( B = zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( B @ ( C @ divide_divide_real @ aa_real_real ) ) ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( B @ ( C @ divide_divide_real @ aa_real_real ) ) )
=> ( ( A = C )
| ( B = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1415,axiom,
! [A: $o,B: $o] :
( ( ( B
& A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7542_of__bool__conj) ).
thf(8371,plain,
! [A: $o,B: $o] :
( ( ( B
& A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415]) ).
thf(1231,axiom,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7967_not__bit__Suc__0__Suc) ).
thf(7555,plain,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).
thf(608,axiom,
! [A: real,B: real,C: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( C @ ( A @ divide_divide_real @ aa_real_real ) ) )
<=> ( ( B = C )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2457_divide__cancel__left) ).
thf(4608,plain,
! [A: real,B: real,C: real] :
( ( ( ( B = C )
| ( A = zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( C @ ( A @ divide_divide_real @ aa_real_real ) ) ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( C @ ( A @ divide_divide_real @ aa_real_real ) ) )
=> ( ( B = C )
| ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1814,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_1704_order__le__imp__less__or__eq) ).
thf(10490,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)],[1814]) ).
thf(1349,axiom,
! [A: nat] :
( ( A @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= ( @+[B: complex] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_complex ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_complex ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3916_power__0__left) ).
thf(8085,plain,
! [A: nat] :
( ( A @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= ( @+[B: complex] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_complex ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).
thf(144,axiom,
! [A: num,B: num] :
( ( A @ ( bit0 @ aa_num_num ) )
!= ( B @ ( bit1 @ aa_num_num ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6392_verit__eq__simplify_I14_J) ).
thf(2477,plain,
! [A: num,B: num] :
( ( A @ ( bit0 @ aa_num_num ) )
!= ( B @ ( bit1 @ aa_num_num ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1672,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_7115_dvd__imp__le) ).
thf(9658,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)],[1672]) ).
thf(1131,axiom,
! [A: nat] :
( ( A @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9728_gcd__nat_Oidem) ).
thf(7063,plain,
! [A: nat] :
( ( A @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1441,axiom,
( ( one @ ( nat_of_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10017_nat__of__num_Osimps_I1_J) ).
thf(8503,plain,
( ( one @ ( nat_of_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441]) ).
thf(992,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_3011_mult__nonneg__nonpos) ).
thf(6427,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)],[992]) ).
thf(509,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [B: nat] :
( A
!= ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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_7234_oddE) ).
thf(4155,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ! [B: nat] :
( A
!= ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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)],[509]) ).
thf(997,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_4936_nat__mod__eq__lemma) ).
thf(6445,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)],[997]) ).
thf(1676,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_1325_zero__le) ).
thf(9671,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)],[1676]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_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_6469_Suc__div__eq__add3__div) ).
thf(2826,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_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)],[228]) ).
thf(1185,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( D @ ( 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 ) ) )
<=> ( ( D = B )
& ( A = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9764_coprime__crossproduct__nat) ).
thf(7314,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( D = B )
& ( A = C ) )
=> ( ( D @ ( 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 ) ) ) )
& ( ( ( D @ ( 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 ) ) )
=> ( ( D = B )
& ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).
thf(1208,axiom,
! [A: nat,B: nat,C: nat] :
( ( ! [D: nat] :
( ( ( D @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( 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 @ ( 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 @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9977_lcm__unique__nat) ).
thf(7432,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B
= ( C @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ! [D: nat] :
( ( ( D @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( 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 @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( ! [D: nat] :
( ( ( D @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( 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 @ ( 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 @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).
thf(336,axiom,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6119_numeral__One) ).
thf(3349,plain,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(839,axiom,
aTP_Lamm_ou @ ( dvd_dvd_nat @ ( zero_zero_nat @ ( gcd_gcd_nat @ semila1623282765462674594er_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9716_gcd__nat_Osemilattice__neutr__order__axioms) ).
thf(5690,plain,
aTP_Lamm_ou @ ( dvd_dvd_nat @ ( zero_zero_nat @ ( gcd_gcd_nat @ semila1623282765462674594er_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(1615,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_95_gr__implies__not__zero) ).
thf(9277,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)],[1615]) ).
thf(1022,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_3432_mult__0__right) ).
thf(6556,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)],[1022]) ).
thf(387,axiom,
! [A: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6089_square__norm__one) ).
thf(3578,plain,
! [A: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(1192,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_3462_mult__le__mono1) ).
thf(7361,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)],[1192]) ).
thf(696,axiom,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT,F: nat] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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_7608_mi__ma__2__deg) ).
thf(5021,plain,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT,F: nat] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( 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)],[696]) ).
thf(1055,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_4928_le__mod__geq) ).
thf(6708,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)],[1055]) ).
thf(1835,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_94_zero__less__iff__neq__zero) ).
thf(10583,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)],[1835]) ).
thf(444,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_214_diff__Suc__Suc) ).
thf(3877,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)],[444]) ).
thf(807,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_of__nat__neq__0) ).
thf(5551,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
!= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(699,axiom,
! [A: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
<=> ( ( A @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6008_abs__square__eq__1) ).
thf(5038,plain,
! [A: real] :
( ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= one_one_real )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( A @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(274,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7947_and__nat__numerals_I1_J) ).
thf(3028,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(279,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_213_Suc__diff__diff) ).
thf(3050,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)],[279]) ).
thf(987,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_6580_dvd__add__triv__left__iff) ).
thf(6402,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)],[987]) ).
thf(1763,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_2194_minf_I6_J) ).
thf(10235,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)],[1763]) ).
thf(958,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Zero__not__Suc) ).
thf(6267,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(112,axiom,
( one_one_real
!= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_one__neq__neg__one) ).
thf(2344,plain,
( one_one_real
!= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(102,axiom,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( ( A != zero_zero_real ) @ zero_n3304061248610475627l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7512_sgn__abs) ).
thf(2313,plain,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( ( A != zero_zero_real ) @ zero_n3304061248610475627l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(867,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_418_add__strict__left__mono) ).
thf(5858,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)],[867]) ).
thf(147,axiom,
! [A: real] :
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ divide_divide_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2583_divide__minus1) ).
thf(2492,plain,
! [A: real] :
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ divide_divide_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(417,axiom,
! [A: real] :
( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_abs__eq__0) ).
thf(3727,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(1572,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_444_not__add__less1) ).
thf(9080,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)],[1572]) ).
thf(46,axiom,
( ( one_one_real @ ( one_one_real @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_diff__numeral__special_I9_J) ).
thf(2112,plain,
( ( one_one_real @ ( one_one_real @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(494,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_1569_Nat_Odiff__add__assoc2) ).
thf(4080,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)],[494]) ).
thf(1279,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_3256_mult__left__less__imp__less) ).
thf(7767,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)],[1279]) ).
thf(1443,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4341_pochhammer__fact) ).
thf(8518,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443]) ).
thf(1834,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_1411_bot__nat__0_Oextremum__uniqueI) ).
thf(10580,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)],[1834]) ).
thf(796,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_1341_add__le__imp__le__right) ).
thf(5515,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)],[796]) ).
thf(394,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8054_push__bit__of__Suc__0) ).
thf(3595,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(1263,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_1515_add__less__le__mono) ).
thf(7686,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)],[1263]) ).
thf(542,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_2797_comm__semiring__class_Odistrib) ).
thf(4316,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)],[542]) ).
thf(750,axiom,
( ( zero_zero_nat @ vEBT_vebt_buildup )
= ( $false @ ( $false @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_vebt__buildup_Osimps_I1_J) ).
thf(5285,plain,
( ( zero_zero_nat @ vEBT_vebt_buildup )
= ( $false @ ( $false @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(1367,axiom,
! [A: nat] :
( ( A @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= ( @+[B: int] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_int ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3913_power__0__left) ).
thf(8155,plain,
! [A: nat] :
( ( A @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= ( @+[B: int] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_int ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).
thf(1388,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_One__nat__def) ).
thf(8238,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).
thf(1687,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_6_gr0I) ).
thf(9730,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)],[1687]) ).
thf(621,axiom,
! [A: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7663_mask__nat__less__exp) ).
thf(4668,plain,
! [A: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(1461,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_3993_self__le__power) ).
thf(8604,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)],[1461]) ).
thf(199,axiom,
! [A: num,B: nat] :
( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( B @ ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6125_Suc__nat__number__of__add) ).
thf(2709,plain,
! [A: num,B: nat] :
( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( B @ ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(648,axiom,
! [A: fun_complex_nat,B: set_complex] :
( ( ( B @ ( A @ groups5693394587270226106ex_nat ) )
!= zero_zero_nat )
=> ~ ! [C: complex] :
( ( B @ ( C @ member_complex ) )
=> ( ( C @ ( A @ aa_complex_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8606_sum_Onot__neutral__contains__not__neutral) ).
thf(4789,plain,
! [A: fun_complex_nat,B: set_complex] :
( ( ( B @ ( A @ groups5693394587270226106ex_nat ) )
!= zero_zero_nat )
=> ~ ! [C: complex] :
( ( B @ ( C @ member_complex ) )
=> ( ( C @ ( A @ aa_complex_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(1790,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_6907_gcd__nat_Oextremum) ).
thf(10335,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)],[1790]) ).
thf(1429,axiom,
! [A: list_o] : ( A @ size_size_list_o @ ( A @ set_o2 @ finite_card_o @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6307_card__length) ).
thf(8451,plain,
! [A: list_o] : ( A @ size_size_list_o @ ( A @ set_o2 @ finite_card_o @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429]) ).
thf(203,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_3751_power__not__zero) ).
thf(2726,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)],[203]) ).
thf(315,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_373_nat__diff__split__asm) ).
thf(3237,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)],[315]) ).
thf(791,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_4935_mod__eq__nat2E) ).
thf(5497,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)],[791]) ).
thf(466,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_1530_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(3968,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)],[466]) ).
thf(1413,axiom,
! [A: num,B: nat,C: nat] :
( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5235_numeral__power__eq__of__nat__cancel__iff) ).
thf(8354,plain,
! [A: num,B: nat,C: nat] :
( ( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
=> ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).
thf(866,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_6985_dvd__div__mult) ).
thf(5854,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)],[866]) ).
thf(1189,axiom,
! [A: fun_nat_nat,B: nat] :
( ( A @ order_5726023648592871131at_nat )
=> ( B @ ( A @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9806_strict__mono__imp__increasing) ).
thf(7346,plain,
! [A: fun_nat_nat,B: nat] :
( ( A @ order_5726023648592871131at_nat )
=> ( B @ ( A @ aa_nat_nat ) @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).
thf(1483,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_1444_eq__diff__iff) ).
thf(8694,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)],[1483]) ).
thf(364,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_3467_add__mult__distrib2) ).
thf(3467,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)],[364]) ).
thf(98,axiom,
! [A: real,B: real] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_minus__diff__commute) ).
thf(2300,plain,
! [A: real,B: real] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(149,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_rat @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5946_one__power2) ).
thf(2498,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_rat @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1177,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9671_gcd__proj1__if__dvd__nat) ).
thf(7281,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).
thf(1344,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_3541_nat__mult__div__cancel1) ).
thf(8068,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)],[1344]) ).
thf(58,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7674_num_Osize__gen_I2_J) ).
thf(2157,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(231,axiom,
( ( zero_zero_nat @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9997_unit__factor__simps_I1_J) ).
thf(2840,plain,
( ( zero_zero_nat @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(316,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_4391_fact__div__fact__le__pow) ).
thf(3254,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)],[316]) ).
thf(42,axiom,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( ( A != zero_zero_real ) @ zero_n3304061248610475627l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7517_idom__abs__sgn__class_Oabs__sgn) ).
thf(2100,plain,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( ( A != zero_zero_real ) @ zero_n3304061248610475627l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(920,axiom,
! [A: list_o,B: $o] :
( ! [C: $o] :
( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C
<=> B ) )
=> ( ( B @ ( A @ size_size_list_o @ replicate_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8657_replicate__length__same) ).
thf(6101,plain,
! [A: list_o,B: $o] :
( ! [C: $o] :
( ( A @ set_o2 @ ( C @ member_o ) )
=> ( ( B
=> C )
& ( C
=> B ) ) )
=> ( ( B @ ( A @ size_size_list_o @ replicate_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(1590,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_3945_zero__power) ).
thf(9145,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)],[1590]) ).
thf(255,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10020_nat__of__num__code_I3_J) ).
thf(2946,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1779,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_1413_less__eq__nat_Osimps_I1_J) ).
thf(10295,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)],[1779]) ).
thf(1318,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_4453_mod__0) ).
thf(7962,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)],[1318]) ).
thf(684,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_354_diff__add__inverse2) ).
thf(4974,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)],[684]) ).
thf(1627,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_86_linorder__neqE__nat) ).
thf(9355,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)],[1627]) ).
thf(1329,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_1037_Suc__pred_H) ).
thf(8009,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)],[1329]) ).
thf(1454,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_7068_dvd__div__eq__mult) ).
thf(8562,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)],[1454]) ).
thf(762,axiom,
! [A: nat,B: extended_enat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ extended_enat2 @ ord_le2932123472753598470d_enat ) )
<=> ( B @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9872_Suc__ile__eq) ).
thf(5345,plain,
! [A: nat,B: extended_enat] :
( ( ( B @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) )
=> ( B @ ( A @ ( suc @ aa_nat_nat ) @ extended_enat2 @ ord_le2932123472753598470d_enat ) ) )
& ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ extended_enat2 @ ord_le2932123472753598470d_enat ) )
=> ( B @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(1802,axiom,
zero_zero_nat @ ( ord_max_nat @ comm_monoid_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10001_max__nat_Ocomm__monoid__axioms) ).
thf(10413,plain,
zero_zero_nat @ ( ord_max_nat @ comm_monoid_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802]) ).
thf(980,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_7083_div__mult__unit2) ).
thf(6375,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)],[980]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_mb @ 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_10279_ATP_Olambda__128) ).
thf(2359,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_mb @ 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)],[117]) ).
thf(262,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_4752_div__mult__mod__eq) ).
thf(2973,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)],[262]) ).
thf(1423,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_3435_nat__1__eq__mult__iff) ).
thf(8414,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)],[1423]) ).
thf(1712,axiom,
! [A: $o,B: $o,C: $o,D: $o,E: $o,F: $o,G: $o,H: $o] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ char2 ) ) ) ) ) ) ) @ size_size_char )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9908_char_Osize_I2_J) ).
thf(9889,plain,
! [A: $o,B: $o,C: $o,D: $o,E: $o,F: $o,G: $o,H: $o] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ char2 ) ) ) ) ) ) ) @ size_size_char )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712]) ).
thf(195,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7387_take__bit__nat__eq__self) ).
thf(2692,plain,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1849,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_61_less__SucE) ).
thf(10644,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)],[1849]) ).
thf(1853,axiom,
! [A: nat,B: fun_nat_fun_o_o] :
( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: $o] : ( D @ ( C @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) )
<=> ? [C: list_o] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_o @ aa_nat_o ) @ ( D @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) )
& ( ( C @ size_size_list_o )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6403_Skolem__list__nth) ).
thf(10661,plain,
! [A: nat,B: fun_nat_fun_o_o] :
( ( ? [C: list_o] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_o @ aa_nat_o ) @ ( D @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) )
& ( ( C @ size_size_list_o )
= A ) )
=> ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: $o] : ( D @ ( C @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: $o] : ( D @ ( C @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) )
=> ? [C: list_o] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_o @ aa_nat_o ) @ ( D @ ( B @ aa_nat_fun_o_o ) @ aa_o_o ) ) )
& ( ( C @ size_size_list_o )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853]) ).
thf(525,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_3520_div__add__self2) ).
thf(4227,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)],[525]) ).
thf(896,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 @ ( gcd_gcd_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_9699_gcd__nat_OboundedI) ).
thf(5978,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 @ ( gcd_gcd_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)],[896]) ).
thf(238,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6003_less__2__cases) ).
thf(2858,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1806,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_35_less__trans__Suc) ).
thf(10430,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)],[1806]) ).
thf(497,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) @ ( B @ ( real_V7735802525324610683m_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5545_nonzero__norm__divide) ).
thf(4095,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) @ ( B @ ( real_V7735802525324610683m_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(767,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_6630_unit__prod) ).
thf(5373,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)],[767]) ).
thf(1874,axiom,
! [A: fun_list_int_o,B: list_int] :
( ! [C: list_int] :
( ! [D: list_int] :
( ( C @ size_size_list_int @ ( D @ size_size_list_int @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_int_o ) ) )
=> ( C @ ( A @ aa_list_int_o ) ) )
=> ( B @ ( A @ aa_list_int_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6294_length__induct) ).
thf(10771,plain,
! [A: fun_list_int_o,B: list_int] :
( ! [C: list_int] :
( ! [D: list_int] :
( ( C @ size_size_list_int @ ( D @ size_size_list_int @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_int_o ) ) )
=> ( C @ ( A @ aa_list_int_o ) ) )
=> ( B @ ( A @ aa_list_int_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874]) ).
thf(1366,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_7168_dvd__power) ).
thf(8149,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)],[1366]) ).
thf(1425,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ power_power_real @ aa_nat_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( abs_abs_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4382_root__abs__power) ).
thf(8429,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ power_power_real @ aa_nat_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( abs_abs_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_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_6752_even__diff__nat) ).
thf(3087,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( 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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_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)],[289]) ).
thf(282,axiom,
! [A: rat] :
( ( zero_zero_nat @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4075_pochhammer__0) ).
thf(3060,plain,
! [A: rat] :
( ( zero_zero_nat @ ( A @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1357,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_6954_minf_I10_J) ).
thf(8117,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).
thf(965,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_old_Onat_Oexhaust) ).
thf(6299,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(862,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_6967_dvd__mult__unit__iff_H) ).
thf(5830,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)],[862]) ).
thf(729,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_1308_lift__Suc__antimono__le) ).
thf(5166,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)],[729]) ).
thf(1012,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_3276_mult__le__one) ).
thf(6518,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)],[1012]) ).
thf(454,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_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_7289_take__bit__Suc) ).
thf(3922,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_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)],[454]) ).
thf(1331,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_deg__SUcn__Node) ).
thf(8017,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).
thf(1058,axiom,
! [A: complex,B: nat] :
( ( A != zero_zero_complex )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aTP_Lamm_bg @ aa_nat_fun_complex_o ) @ collect_complex @ finite_card_complex )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8125_card__nth__roots) ).
thf(6720,plain,
! [A: complex,B: nat] :
( ( A != zero_zero_complex )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ aTP_Lamm_bg @ aa_nat_fun_complex_o ) @ collect_complex @ finite_card_complex )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(1481,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_nat_Odistinct_I1_J) ).
thf(8687,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_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 ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7962_of__nat__xor__eq) ).
thf(2196,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_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 ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1412,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_11_nat_Oinject) ).
thf(8346,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)],[1412]) ).
thf(1059,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_2851_mult__of__nat__commute) ).
thf(6724,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)],[1059]) ).
thf(139,axiom,
( ( one @ ( size_size_num @ aa_num_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6461_num_Osize_I4_J) ).
thf(2460,plain,
( ( one @ ( size_size_num @ aa_num_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(222,axiom,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6014_nat__induct2) ).
thf(2798,plain,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ( one_one_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1138,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_3825_zero__le__power) ).
thf(7091,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)],[1138]) ).
thf(1601,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 @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7520_take__bit__of__Suc__0) ).
thf(9186,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 @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601]) ).
thf(1251,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_7032_dvd__diffD) ).
thf(7631,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)],[1251]) ).
thf(687,axiom,
! [A: num,B: nat,C: nat] :
( ( C @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( A @ unique5026877609467782581ep_nat ) )
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7676_divmod__step__eq) ).
thf(4983,plain,
! [A: num,B: nat,C: nat] :
( ( C @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( A @ unique5026877609467782581ep_nat ) )
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( C @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(1657,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_2352_order__less__imp__le) ).
thf(9508,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)],[1657]) ).
thf(437,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6059_exp__add__not__zero__imp__right) ).
thf(3846,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1130,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_512_Euclid__induct) ).
thf(7054,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)],[1130]) ).
thf(1210,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_2430_mult__eq__0__iff) ).
thf(7453,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)],[1210]) ).
thf(1270,axiom,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5462_zero__le__numeral) ).
thf(7717,plain,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).
thf(1250,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_494_less__add__Suc1) ).
thf(7629,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)],[1250]) ).
thf(644,axiom,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5660_norm__sgn) ).
thf(4772,plain,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(308,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_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_6378_Suc__div__eq__add3__div__numeral) ).
thf(3210,plain,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_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)],[308]) ).
thf(630,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7259_central__binomial__odd) ).
thf(4721,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(1797,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_1709_linorder__le__less__linear) ).
thf(10391,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)],[1797]) ).
thf(37,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5779_Suc__numeral) ).
thf(2080,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1459,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6511_less__Suc__numeral) ).
thf(8594,plain,
! [A: nat,B: num] :
( ( ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459]) ).
thf(805,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_6942_pinf_I9_J) ).
thf(5547,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(936,axiom,
! [A: fun_list_nat_nat,B: list_nat] :
( ( B @ ( A @ aTP_Lamm_in @ aa_list_nat_nat ) )
= ( B @ ( A @ aa_list_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10380_ATP_Olambda__229) ).
thf(6164,plain,
! [A: fun_list_nat_nat,B: list_nat] :
( ( B @ ( A @ aTP_Lamm_in @ aa_list_nat_nat ) )
= ( B @ ( A @ aa_list_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(176,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3859_gbinomial__of__nat__symmetric) ).
thf(2613,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1039,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_3434_mult__cancel2) ).
thf(6630,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)],[1039]) ).
thf(8,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10014_nat__of__num_Osimps_I2_J) ).
thf(1937,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(885,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_6640_dvd__mult__div__cancel) ).
thf(5932,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)],[885]) ).
thf(1067,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_270_zero__less__diff) ).
thf(6763,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)],[1067]) ).
thf(663,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_162_add__0) ).
thf(4861,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)],[663]) ).
thf(63,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4491_idom__abs__sgn__class_Osgn__minus) ).
thf(2172,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(617,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_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_6749_odd__Suc__minus__one) ).
thf(4648,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_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)],[617]) ).
thf(1550,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_3483_Suc__mult__less__cancel1) ).
thf(8968,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)],[1550]) ).
thf(1618,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_7355_gcd__nat_Ostrict__trans1) ).
thf(9288,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)],[1618]) ).
thf(831,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_6913_dvd__mod__imp__dvd) ).
thf(5662,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)],[831]) ).
thf(164,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( @+[D: nat] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one_one_nat @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_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_6559_binomial__code) ).
thf(2551,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( @+[D: nat] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one_one_nat @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ set_fo2584398358068434914at_nat ) @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_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)],[164]) ).
thf(1237,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_2470_mult_Oright__neutral) ).
thf(7577,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)],[1237]) ).
thf(1417,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_3444_div__mult__self1__is__m) ).
thf(8390,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)],[1417]) ).
thf(1745,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_113_of__nat__0__less__iff) ).
thf(10163,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)],[1745]) ).
thf(665,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_286_group__cancel_Oadd2) ).
thf(4867,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)],[665]) ).
thf(1765,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_2058_order_Ostrict__implies__not__eq) ).
thf(10239,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)],[1765]) ).
thf(189,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_368_add__diff__inverse__nat) ).
thf(2666,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)],[189]) ).
thf(878,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_3019_split__mult__neg__le) ).
thf(5905,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)],[878]) ).
thf(1017,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_6530_choose__mult) ).
thf(6541,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)],[1017]) ).
thf(1321,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_1156_add__le__cancel__right) ).
thf(7976,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)],[1321]) ).
thf(960,axiom,
! [A: num] :
~ ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5466_not__numeral__le__zero) ).
thf(6275,plain,
! [A: num] :
~ ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(652,axiom,
! [A: num,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6457_cong__exp__iff__simps_I3_J) ).
thf(4814,plain,
! [A: num,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1633,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__not__refl) ).
thf(9392,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633]) ).
thf(610,axiom,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3854_power__0) ).
thf(4621,plain,
! [A: int] :
( ( zero_zero_nat @ ( A @ power_power_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(959,axiom,
! [A: num] :
( ( A @ ( nat_of_num @ aa_num_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10011_nat__of__num__neq__0) ).
thf(6271,plain,
! [A: num] :
( ( A @ ( nat_of_num @ aa_num_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1226,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_3049_mult__mono_H) ).
thf(7523,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)],[1226]) ).
thf(1813,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_4312_fact__less__mono__nat) ).
thf(10487,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)],[1813]) ).
thf(325,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6793_even__succ__div__exp) ).
thf(3294,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(635,axiom,
! [A: nat,B: nat,C: fun_int_o,D: int] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_int_o ) )
=> ( A @ ( D @ ( B @ replicate_int ) @ nth_int @ aa_nat_int ) @ ( C @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8510_intind) ).
thf(4736,plain,
! [A: nat,B: nat,C: fun_int_o,D: int] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( D @ ( C @ aa_int_o ) )
=> ( A @ ( D @ ( B @ replicate_int ) @ nth_int @ aa_nat_int ) @ ( C @ aa_int_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1659,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_6903_gcd__nat_Oextremum__uniqueI) ).
thf(9513,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)],[1659]) ).
thf(769,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
<=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9959_lcm__proj2__iff__nat) ).
thf(5387,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) )
& ( ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1387,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_7177_dvd__mult__cancel1) ).
thf(8230,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)],[1387]) ).
thf(1667,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_25_diff__induct) ).
thf(9645,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)],[1667]) ).
thf(1833,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_1563_ex__least__nat__le) ).
thf(10575,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)],[1833]) ).
thf(1558,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_9022_max__Suc__Suc) ).
thf(9012,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)],[1558]) ).
thf(1831,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_41_less__Suc__eq) ).
thf(10560,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)],[1831]) ).
thf(584,axiom,
! [A: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) )
=> ~ ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7242_parity__cases) ).
thf(4508,plain,
! [A: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) )
=> ~ ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(233,axiom,
( ( one @ ( nat_of_num @ aa_num_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10013_nat__of__num__code_I1_J) ).
thf(2845,plain,
( ( one @ ( nat_of_num @ aa_num_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(825,axiom,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4424_fact__num__eq__if) ).
thf(5639,plain,
! [A: nat] :
( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(1722,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_60_less__SucI) ).
thf(10026,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)],[1722]) ).
thf(1400,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_1436_le__add1) ).
thf(8294,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)],[1400]) ).
thf(170,axiom,
! [A: complex,B: fun_complex_o] :
( ( B @ collect_complex @ ( A @ member_complex ) )
<=> ( A @ ( B @ aa_complex_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mem__Collect__eq) ).
thf(2581,plain,
! [A: complex,B: fun_complex_o] :
( ( ( A @ ( B @ aa_complex_o ) )
=> ( B @ collect_complex @ ( A @ member_complex ) ) )
& ( ( B @ collect_complex @ ( A @ member_complex ) )
=> ( A @ ( B @ aa_complex_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(528,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_4760_cancel__div__mod__rules_I1_J) ).
thf(4237,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)],[528]) ).
thf(590,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5820_one__plus__numeral) ).
thf(4540,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(526,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
=> ~ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7313_odd__mod__4__div__2) ).
thf(4231,plain,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
=> ~ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1144,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_7122_bezout__add__strong__nat) ).
thf(7123,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)],[1144]) ).
thf(1768,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_7025_dvd__pos__nat) ).
thf(10252,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)],[1768]) ).
thf(1569,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_3890_power__less__imp__less__base) ).
thf(9068,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)],[1569]) ).
thf(974,axiom,
( aTP_Lamm_aj
= ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8062_lambda__zero) ).
thf(6349,plain,
( aTP_Lamm_aj
= ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(890,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_dc @ 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_10357_ATP_Olambda__206) ).
thf(5947,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_dc @ 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)],[890]) ).
thf(660,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6061_exp__add__not__zero__imp__left) ).
thf(4846,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(1479,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_lcm_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_9953_lcm__0__iff__nat) ).
thf(8673,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( gcd_lcm_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)],[1479]) ).
thf(927,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_4134_pochhammer__Suc) ).
thf(6134,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)],[927]) ).
thf(1316,axiom,
! [A: real,B: list_real] :
( ( B @ set_real2 @ ( A @ member_real ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_real @ aa_nat_real ) )
= A )
& ( B @ size_size_list_real @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6428_in__set__conv__nth) ).
thf(7948,plain,
! [A: real,B: list_real] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_real @ aa_nat_real ) )
= A )
& ( B @ size_size_list_real @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_real2 @ ( A @ member_real ) ) )
& ( ( B @ set_real2 @ ( A @ member_real ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_real @ aa_nat_real ) )
= A )
& ( B @ size_size_list_real @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).
thf(253,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( ( A @ ( B @ divide_divide_real @ aa_real_real ) )
= one_one_real )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2986_right__inverse__eq) ).
thf(2932,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( ( B = A )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) )
= one_one_real ) )
& ( ( ( A @ ( B @ divide_divide_real @ aa_real_real ) )
= one_one_real )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(49,axiom,
! [A: real,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6100_power__minus__Bit0) ).
thf(2125,plain,
! [A: real,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1385,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= zero_zero_real )
<=> ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4270_real__root__eq__0__iff) ).
thf(8219,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = zero_zero_real )
=> ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= zero_zero_real )
=> ( B = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).
thf(1427,axiom,
zero_zero_int = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8975_zero__integer_Orsp) ).
thf(8442,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427]) ).
thf(1257,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_4516_mod__by__1) ).
thf(7651,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)],[1257]) ).
thf(1345,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_4905_verit__le__mono__div) ).
thf(8072,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)],[1345]) ).
thf(159,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6460_Suc3__eq__add__3) ).
thf(2536,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1532,axiom,
! [A: fun_nat_rat,B: nat] :
( ( B @ ( A @ aTP_Lamm_cy @ aa_nat_rat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10302_ATP_Olambda__151) ).
thf(8891,plain,
! [A: fun_nat_rat,B: nat] :
( ( B @ ( A @ aTP_Lamm_cy @ aa_nat_rat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532]) ).
thf(338,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_3468_diff__mult__distrib) ).
thf(3354,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)],[338]) ).
thf(490,axiom,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1722_abs__abs) ).
thf(4068,plain,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(994,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_1507_add__mono__thms__linordered__field_I3_J) ).
thf(6433,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)],[994]) ).
thf(1838,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_6906_gcd__nat_Oextremum__strict) ).
thf(10603,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)],[1838]) ).
thf(1240,axiom,
! [A: nat,B: list_o] :
( ( B @ size_size_list_o @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_o2 @ ( A @ ( B @ nth_o @ aa_nat_o ) @ member_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6420_nth__mem) ).
thf(7587,plain,
! [A: nat,B: list_o] :
( ( B @ size_size_list_o @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_o2 @ ( A @ ( B @ nth_o @ aa_nat_o ) @ member_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).
thf(236,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_deg__1__Leafy) ).
thf(2851,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( B = one_one_nat )
=> ? [C: $o,D: $o] :
( A
= ( D @ ( C @ vEBT_Leaf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1004,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9682_gcd__diff1__nat) ).
thf(6475,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(1645,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_929_less__numeral__extra_I4_J) ).
thf(9461,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)],[1645]) ).
thf(10,axiom,
( ( one_one_nat @ ( suc @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5813_Suc__1) ).
thf(1947,plain,
( ( one_one_nat @ ( suc @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1534,axiom,
! [A: list_complex,B: set_complex] :
( ( B @ ( A @ set_complex2 @ ord_le211207098394363844omplex ) )
<=> ! [C: complex] :
( ( A @ set_complex2 @ ( C @ member_complex ) )
=> ( B @ ( C @ member_complex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2165_subset__code_I1_J) ).
thf(8896,plain,
! [A: list_complex,B: set_complex] :
( ( ! [C: complex] :
( ( A @ set_complex2 @ ( C @ member_complex ) )
=> ( B @ ( C @ member_complex ) ) )
=> ( B @ ( A @ set_complex2 @ ord_le211207098394363844omplex ) ) )
& ( ( B @ ( A @ set_complex2 @ ord_le211207098394363844omplex ) )
=> ! [C: complex] :
( ( A @ set_complex2 @ ( C @ member_complex ) )
=> ( B @ ( C @ member_complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534]) ).
thf(1247,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_3129_less__1__mult) ).
thf(7614,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)],[1247]) ).
thf(900,axiom,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7835_not__bit__1__Suc) ).
thf(6005,plain,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( one_one_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(295,axiom,
! [A: set_complex,B: fun_complex_nat,C: nat,D: nat] :
( ! [E: complex] :
( ( A @ ( E @ member_complex ) )
=> ( ( C @ ( E @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( E @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( ( D @ ( A @ finite_card_complex @ ( 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 ) )
=> ( D @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8306_prod__le__power) ).
thf(3115,plain,
! [A: set_complex,B: fun_complex_nat,C: nat,D: nat] :
( ! [E: complex] :
( ( A @ ( E @ member_complex ) )
=> ( ( C @ ( E @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( E @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( ( D @ ( A @ finite_card_complex @ ( 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 ) )
=> ( D @ ( C @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(738,axiom,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7571_of__bool__def) ).
thf(5217,plain,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(504,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6526_binomial__gbinomial) ).
thf(4135,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(1072,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ upt ) @ ( B @ take_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9294_take__upt) ).
thf(6784,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ upt ) @ ( B @ take_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(508,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_136_add_Oright__neutral) ).
thf(4152,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)],[508]) ).
thf(532,axiom,
! [A: num,B: num] :
( ( ( A @ ( bit1 @ aa_num_num ) )
= ( B @ ( bit1 @ aa_num_num ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6342_verit__eq__simplify_I9_J) ).
thf(4259,plain,
! [A: num,B: num] :
( ( ( A = B )
=> ( ( A @ ( bit1 @ aa_num_num ) )
= ( B @ ( bit1 @ aa_num_num ) ) ) )
& ( ( ( A @ ( bit1 @ aa_num_num ) )
= ( B @ ( bit1 @ aa_num_num ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(1291,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9666_gcd__nat_Oright__neutral) ).
thf(7826,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).
thf(933,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_436_less__imp__diff__less) ).
thf(6152,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)],[933]) ).
thf(626,axiom,
! [A: real,B: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real )
<=> ( ( B = A )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2565_divide__eq__eq__1) ).
thf(4689,plain,
! [A: real,B: real] :
( ( ( ( B = A )
& ( B != zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real )
=> ( ( B = A )
& ( B != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(697,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ bit_se1146084159140164899it_int @ aa_nat_o ) )
<=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7825_bit__of__nat__iff__bit) ).
thf(5026,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ bit_se1146084159140164899it_int @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(54,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7951_xor__nat__numerals_I3_J) ).
thf(2140,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( binomial @ 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_6543_binomial__less__binomial__Suc) ).
thf(2756,plain,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( binomial @ 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)],[213]) ).
thf(360,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8133_push__bit__take__bit) ).
thf(3454,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(1727,axiom,
! [A: nat] :
( ( A != bot_bot_nat )
<=> ( A @ ( bot_bot_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7640_bot_Onot__eq__extremum) ).
thf(10058,plain,
! [A: nat] :
( ( ( A @ ( bot_bot_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A != bot_bot_nat ) )
& ( ( A != bot_bot_nat )
=> ( A @ ( bot_bot_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727]) ).
thf(402,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_369_less__diff__conv) ).
thf(3624,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)],[402]) ).
thf(1554,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_2422_mult__cancel__right) ).
thf(8989,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)],[1554]) ).
thf(1347,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_486_diff__less__Suc) ).
thf(8080,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)],[1347]) ).
thf(1823,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_4662_unique__euclidean__semiring__numeral__class_Opos__mod__bound) ).
thf(10524,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)],[1823]) ).
thf(210,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_9037_nat__minus__add__max) ).
thf(2748,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)],[210]) ).
thf(120,axiom,
! [A: real,B: real] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( B @ minus_minus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5952_power2__commute) ).
thf(2368,plain,
! [A: real,B: real] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ minus_minus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( B @ minus_minus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1816,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_97_gr__zeroI) ).
thf(10503,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)],[1816]) ).
thf(1486,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_752_diff__Suc__1) ).
thf(8708,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)],[1486]) ).
thf(431,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_199_add__diff__cancel__left_H) ).
thf(3824,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)],[431]) ).
thf(1520,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_of__nat__neq__0) ).
thf(8846,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520]) ).
thf(1511,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_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_7561_split__of__bool__asm) ).
thf(8796,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 @ aa_o_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_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)],[1511]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
!= ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8019_xor__nat__rec) ).
thf(1991,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
!= ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_6169_divmod__digit__0_I1_J) ).
thf(2788,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[219]) ).
thf(804,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_6502_binomial__n__0) ).
thf(5544,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)],[804]) ).
thf(754,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_6610_nat__mult__dvd__cancel__disj) ).
thf(5310,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)],[754]) ).
thf(1446,axiom,
! [A: $o,B: $o] :
( ( B @ ( A @ ( fequal_o @ aa_o_fun_o_o ) @ aa_o_o ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001_Eo_T) ).
thf(8527,plain,
! [A: $o,B: $o] :
( ( B @ ( A @ ( fequal_o @ aa_o_fun_o_o ) @ aa_o_o ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446]) ).
thf(252,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_1571_Nat_Ole__diff__conv2) ).
thf(2926,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)],[252]) ).
thf(616,axiom,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( C @ ( B @ cons_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9316_list__encode_Ocases) ).
thf(4644,plain,
! [A: list_nat] :
( ( A != nil_nat )
=> ~ ! [B: nat,C: list_nat] :
( A
!= ( C @ ( B @ cons_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> @+[C: $o] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7899_bit__rec) ).
thf(3225,plain,
! [A: nat,B: nat] :
( ( @+[C: $o] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) )
=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> @+[C: $o] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(1494,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_3454_div__nat__eqI) ).
thf(8739,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)],[1494]) ).
thf(162,axiom,
( ( one @ ( pred_numeral @ aa_num_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6501_pred__numeral__simps_I1_J) ).
thf(2546,plain,
( ( one @ ( pred_numeral @ aa_num_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(385,axiom,
! [A: real,B: real] :
( ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) )
<=> ( ( B = A )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2567_eq__divide__eq__1) ).
thf(3563,plain,
! [A: real,B: real] :
( ( ( ( B = A )
& ( B != zero_zero_real ) )
=> ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) ) )
& ( ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) )
=> ( ( B = A )
& ( B != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(1391,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_2787_comm__monoid__mult__class_Omult__1) ).
thf(8247,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)],[1391]) ).
thf(30,axiom,
! [A: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
<=> ( ( A
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5999_power2__eq__1__iff) ).
thf(2043,plain,
! [A: real] :
( ( ( ( A
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = one_one_real ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= one_one_real )
=> ( ( A
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(322,axiom,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_deg__1__Leaf) ).
thf(3279,plain,
! [A: vEBT_VEBT] :
( ( one_one_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ? [B: $o,C: $o] :
( A
= ( C @ ( B @ vEBT_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(390,axiom,
zero_zero_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7147_even__zero) ).
thf(3587,plain,
zero_zero_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1527,axiom,
! [A: nat] :
( ( A @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = one_one_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9999_unit__factor__nat__def) ).
thf(8871,plain,
! [A: nat] :
( ( A @ ( unit_f2748546683901255202or_nat @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = one_one_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527]) ).
thf(1453,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_796_of__nat__Suc) ).
thf(8559,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)],[1453]) ).
thf(32,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7949_xor__nat__numerals_I1_J) ).
thf(2057,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(327,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_3535_bits__div__by__0) ).
thf(3306,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)],[327]) ).
thf(1397,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_4045_power__minus__mult) ).
thf(8279,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)],[1397]) ).
thf(1580,axiom,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real @ aa_nat_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3612_power__one__right) ).
thf(9104,plain,
! [A: real] :
( ( one_one_nat @ ( A @ power_power_real @ aa_nat_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580]) ).
thf(1327,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_442_add__lessD1) ).
thf(8004,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)],[1327]) ).
thf(673,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_4748_mod__div__mult__eq) ).
thf(4906,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)],[673]) ).
thf(1463,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_zero__neq__one) ).
thf(8609,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463]) ).
thf(1214,axiom,
! [A: nat,B: list_VEBT_VEBT,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_VEBT_VEBT_o ) @ nth_Pr4606735188037164562VEBT_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc8721562602347293563VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7690_product__nth) ).
thf(7476,plain,
! [A: nat,B: list_VEBT_VEBT,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_s6755466524823107622T_VEBT @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_VEBT_VEBT_o ) @ nth_Pr4606735188037164562VEBT_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ produc8721562602347293563VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).
thf(1697,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_64_Suc__lessD) ).
thf(9793,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)],[1697]) ).
thf(1314,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_3936_power__strict__increasing) ).
thf(7941,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)],[1314]) ).
thf(182,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7773_and__zero__eq) ).
thf(2645,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(353,axiom,
! [A: nat] :
( ( zero_zero_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_of__nat__0__eq__iff) ).
thf(3422,plain,
! [A: nat] :
( ( ( zero_zero_nat = A )
=> ( zero_zero_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( ( zero_zero_int
= ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(1180,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_1404_le__Suc__eq) ).
thf(7289,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)],[1180]) ).
thf(879,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_1511_add__le__less__mono) ).
thf(5909,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)],[879]) ).
thf(435,axiom,
( ( zero_zero_nat @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_of__nat__0) ).
thf(3841,plain,
( ( zero_zero_nat @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1753,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_986_zero__less__one) ).
thf(10190,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)],[1753]) ).
thf(474,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_atMost_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8882_atMost__Suc) ).
thf(4004,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_atMost_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(20,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4899_Real__Vector__Spaces_Osgn__minus) ).
thf(1996,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(410,axiom,
! [A: nat,B: fun_nat_fun_int_o] :
( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: int] : ( D @ ( C @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) )
<=> ? [C: list_int] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_int @ aa_nat_int ) @ ( D @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) )
& ( ( C @ size_size_list_int )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6405_Skolem__list__nth) ).
thf(3675,plain,
! [A: nat,B: fun_nat_fun_int_o] :
( ( ? [C: list_int] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_int @ aa_nat_int ) @ ( D @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) )
& ( ( C @ size_size_list_int )
= A ) )
=> ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: int] : ( D @ ( C @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) ) )
& ( ! [C: nat] :
( ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ? [D: int] : ( D @ ( C @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) )
=> ? [C: list_int] :
( ! [D: nat] :
( ( A @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ nth_int @ aa_nat_int ) @ ( D @ ( B @ aa_nat_fun_int_o ) @ aa_int_o ) ) )
& ( ( C @ size_size_list_int )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(1133,axiom,
! [A: nat] :
( ( A @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9725_gcd__idem__nat) ).
thf(7074,plain,
! [A: nat] :
( ( A @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(689,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8145_bit__push__bit__iff__nat) ).
thf(4995,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(1014,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_7064_dvd__div__iff__mult) ).
thf(6524,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)],[1014]) ).
thf(1101,axiom,
aTP_Lamm_aj @ summable_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8374_summable__zero) ).
thf(6922,plain,
aTP_Lamm_aj @ summable_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(503,axiom,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( 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_6133_divmod__digit__0_I2_J) ).
thf(4131,plain,
! [A: nat,B: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( 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)],[503]) ).
thf(794,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_4070_power__Suc__0) ).
thf(5508,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)],[794]) ).
thf(701,axiom,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( 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 ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5973_power2__eq__imp__eq) ).
thf(5048,plain,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( 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 ) )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(600,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_3533_bits__div__0) ).
thf(4577,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)],[600]) ).
thf(1668,axiom,
zero_zero_nat @ ( ord_max_nat @ monoid_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9934_max__nat_Omonoid__axioms) ).
thf(9650,plain,
zero_zero_nat @ ( ord_max_nat @ monoid_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668]) ).
thf(605,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7948_and__nat__numerals_I3_J) ).
thf(4599,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(772,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_4930_nat__mod__eq__iff) ).
thf(5400,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)],[772]) ).
thf(815,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_4659_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend) ).
thf(5598,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)],[815]) ).
thf(1581,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_not0__implies__Suc) ).
thf(9107,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581]) ).
thf(1652,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_1333_verit__comp__simplify1_I3_J) ).
thf(9484,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)],[1652]) ).
thf(1836,axiom,
! [A: $o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B
& ~ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7462_of__bool__less__iff) ).
thf(10592,plain,
! [A: $o,B: $o] :
( ( ( B
& ~ A )
=> ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B
& ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836]) ).
thf(1855,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_2027_dual__order_Oasym) ).
thf(10683,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)],[1855]) ).
thf(1370,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_4524_mod__div__trivial) ).
thf(8164,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)],[1370]) ).
thf(1858,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_1423_less__imp__le__nat) ).
thf(10703,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)],[1858]) ).
thf(571,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3606_of__nat__power) ).
thf(4470,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(1839,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_5_bot__nat__0_Oextremum__strict) ).
thf(10607,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)],[1839]) ).
thf(95,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5960_numeral__2__eq__2) ).
thf(2292,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1749,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_2022_linorder__cases) ).
thf(10175,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)],[1749]) ).
thf(907,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_2996_ordered__comm__semiring__class_Ocomm__mult__left__mono) ).
thf(6026,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)],[907]) ).
thf(666,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_3528_nat__less__add__iff1) ).
thf(4872,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)],[666]) ).
thf(126,axiom,
! [A: fun_real_o,B: $o] :
( ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) )
<=> ( ( ~ B
=> ( zero_zero_real @ ( A @ aa_real_o ) ) )
& ( B
=> ( one_one_real @ ( A @ aa_real_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7563_split__of__bool) ).
thf(2391,plain,
! [A: fun_real_o,B: $o] :
( ( ( ( ~ B
=> ( zero_zero_real @ ( A @ aa_real_o ) ) )
& ( B
=> ( one_one_real @ ( A @ aa_real_o ) ) ) )
=> ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) ) )
& ( ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) )
=> ( ( ~ B
=> ( zero_zero_real @ ( A @ aa_real_o ) ) )
& ( B
=> ( one_one_real @ ( A @ aa_real_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1501,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_4119_pochhammer__0__left) ).
thf(8760,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)],[1501]) ).
thf(1607,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ps @ 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_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_10421_ATP_Olambda__270) ).
thf(9231,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( 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 ) )
& ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_ps @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_ps @ 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_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)],[1607]) ).
thf(1352,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_4353_fact__ge__Suc__0__nat) ).
thf(8095,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)],[1352]) ).
thf(84,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_verit__minus__simplify_I4_J) ).
thf(2253,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(724,axiom,
! [A: complex,B: nat] :
( ( A != zero_zero_complex )
=> ( ( B @ ( A @ power_power_complex @ aa_nat_complex ) )
!= zero_zero_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3752_power__not__zero) ).
thf(5138,plain,
! [A: complex,B: nat] :
( ( A != zero_zero_complex )
=> ( ( B @ ( A @ power_power_complex @ aa_nat_complex ) )
!= zero_zero_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(1036,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_430_add__less__imp__less__right) ).
thf(6615,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)],[1036]) ).
thf(278,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_7041_take__bit__eq__0__iff) ).
thf(3042,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[278]) ).
thf(1655,axiom,
! [A: nat,B: complex] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ collect_complex @ finite3207457112153483333omplex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8913_finite__nth__roots) ).
thf(9502,plain,
! [A: nat,B: complex] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_iw @ aa_com5808801942499186519plex_o ) @ collect_complex @ finite3207457112153483333omplex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655]) ).
thf(1378,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_om @ aa_nat7603221163087113075at_nat ) )
= ( zero_zero_nat @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10162_ATP_Olambda__11) ).
thf(8195,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_om @ aa_nat7603221163087113075at_nat ) )
= ( zero_zero_nat @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).
thf(782,axiom,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7477_of__nat__of__bool) ).
thf(5451,plain,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(398,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7307_even__mod__4__div__2) ).
thf(3607,plain,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(1724,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_2341_linorder__not__le) ).
thf(10030,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)],[1724]) ).
thf(367,axiom,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) )
=> ( ( B @ ( zero_zero_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_5969_power2__le__imp__le) ).
thf(3491,plain,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) )
=> ( ( B @ ( zero_zero_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)],[367]) ).
thf(1275,axiom,
! [A: list_real,B: fun_real_o,C: nat] :
( ! [D: real] :
( ( A @ set_real2 @ ( D @ member_real ) )
=> ( D @ ( B @ aa_real_o ) ) )
=> ( ( A @ size_size_list_real @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_real @ aa_nat_real ) @ ( B @ aa_real_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6336_inthall) ).
thf(7742,plain,
! [A: list_real,B: fun_real_o,C: nat] :
( ! [D: real] :
( ( A @ set_real2 @ ( D @ member_real ) )
=> ( D @ ( B @ aa_real_o ) ) )
=> ( ( A @ size_size_list_real @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_real @ aa_nat_real ) @ ( B @ aa_real_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).
thf(558,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_170_zero__diff) ).
thf(4412,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)],[558]) ).
thf(167,axiom,
! [A: nat,B: nat,C: int] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ replicate_int ) @ nth_int @ aa_nat_int ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8566_nth__replicate) ).
thf(2570,plain,
! [A: nat,B: nat,C: int] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ replicate_int ) @ nth_int @ aa_nat_int ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(531,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_336_add__right__imp__eq) ).
thf(4256,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)],[531]) ).
thf(1585,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_432_zero__induct__lemma) ).
thf(9122,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)],[1585]) ).
thf(471,axiom,
! [A: nat] :
( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= one_one_rat )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_of__nat__eq__1__iff) ).
thf(3985,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= one_one_rat ) )
& ( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= one_one_rat )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(1277,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_4071_nat__power__eq__Suc__0__iff) ).
thf(7753,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)],[1277]) ).
thf(1599,axiom,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5478_one__le__numeral) ).
thf(9181,plain,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599]) ).
thf(596,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 ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ minus_minus_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1632_of__nat__diff) ).
thf(4562,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 ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ minus_minus_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(319,axiom,
! [A: real,B: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real )
<=> ( ( B = zero_zero_real )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2460_divide__eq__0__iff) ).
thf(3262,plain,
! [A: real,B: real] :
( ( ( ( B = zero_zero_real )
| ( A = zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= zero_zero_real )
=> ( ( B = zero_zero_real )
| ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(1458,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ~ ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ( A @ ( B @ count_list_VEBT_VEBT ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4959_count__notin) ).
thf(8591,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ~ ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ( A @ ( B @ count_list_VEBT_VEBT ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458]) ).
thf(1788,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_7358_gcd__nat_Oirrefl) ).
thf(10327,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788]) ).
thf(1504,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_3074_mult__strict__left__mono) ).
thf(8771,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)],[1504]) ).
thf(1002,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_7121_dvd__mult__cancel) ).
thf(6469,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)],[1002]) ).
thf(419,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_344_diff__right__commute) ).
thf(3738,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)],[419]) ).
thf(1253,axiom,
! [A: list_real,B: fun_real_o,C: real] :
( ! [D: nat] :
( ( A @ size_size_list_real @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_real @ aa_nat_real ) @ ( B @ aa_real_o ) ) )
=> ( ( A @ set_real2 @ ( C @ member_real ) )
=> ( C @ ( B @ aa_real_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6435_all__nth__imp__all__set) ).
thf(7636,plain,
! [A: list_real,B: fun_real_o,C: real] :
( ! [D: nat] :
( ( A @ size_size_list_real @ ( D @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ nth_real @ aa_nat_real ) @ ( B @ aa_real_o ) ) )
=> ( ( A @ set_real2 @ ( C @ member_real ) )
=> ( C @ ( B @ aa_real_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).
thf(1170,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_3540_nat__mult__eq__cancel1) ).
thf(7257,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)],[1170]) ).
thf(1844,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_2138_order__less__not__sym) ).
thf(10625,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)],[1844]) ).
thf(1528,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_nb @ 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_10276_ATP_Olambda__125) ).
thf(8874,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_nb @ 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)],[1528]) ).
thf(911,axiom,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8656_replicate__length__same) ).
thf(6052,plain,
! [A: list_VEBT_VEBT,B: vEBT_VEBT] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_s6755466524823107622T_VEBT @ replicate_VEBT_VEBT ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(334,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5989_mult__2__right) ).
thf(3343,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1439,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9770_coprime__diff__one__right__nat) ).
thf(8495,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439]) ).
thf(1293,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9667_gcd__0__nat) ).
thf(7833,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).
thf(370,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7534_take__bit__of__exp) ).
thf(3504,plain,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(1649,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_32_not__less__less__Suc__eq) ).
thf(9471,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)],[1649]) ).
thf(819,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9680_gcd__le1__nat) ).
thf(5612,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(450,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7206_odd__iff__mod__2__eq__one) ).
thf(3900,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(392,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_177_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(3590,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)],[392]) ).
thf(397,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 ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7136_real__of__nat__div) ).
thf(3604,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 ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(856,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_4921_mod__induct) ).
thf(5799,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)],[856]) ).
thf(196,axiom,
! [A: rat] :
( ( one_one_rat = A )
<=> ( A = one_one_rat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_one__reorient) ).
thf(2695,plain,
! [A: rat] :
( ( ( A = one_one_rat )
=> ( one_one_rat = A ) )
& ( ( one_one_rat = A )
=> ( A = one_one_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(379,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( modulo_modulo_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 @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7538_one__mod__2__pow__eq) ).
thf(3536,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( modulo_modulo_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 @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(929,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
!= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_of__nat__neq__0) ).
thf(6140,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
!= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(1246,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_6540_binomial__altdef__nat) ).
thf(7611,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)],[1246]) ).
thf(420,axiom,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
<=> ( ( B
<=> D )
& ( A
<=> C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_VEBT_Oinject_I2_J) ).
thf(3741,plain,
! [A: $o,B: $o,C: $o,D: $o] :
( ( ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) )
=> ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) ) )
& ( ( ( B @ ( A @ vEBT_Leaf ) )
= ( D @ ( C @ vEBT_Leaf ) ) )
=> ( ( D
=> B )
& ( B
=> D )
& ( C
=> A )
& ( A
=> C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(619,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_216_diff__self__eq__0) ).
thf(4662,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)],[619]) ).
thf(783,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_1562_le__imp__less__Suc) ).
thf(5456,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)],[783]) ).
thf(1179,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_1400_Suc__leD) ).
thf(7287,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)],[1179]) ).
thf(1269,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8881_lessThan__Suc__atMost) ).
thf(7714,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_atMost_nat @ aa_nat_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).
thf(1320,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_7016_mod__eq__0__iff__dvd) ).
thf(7968,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)],[1320]) ).
thf(1313,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9670_gcd__proj2__if__dvd__nat) ).
thf(7938,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).
thf(1755,axiom,
! [A: rat,B: nat] :
( ( ( B @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3670_power__eq__0__iff) ).
thf(10194,plain,
! [A: rat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_rat ) )
=> ( ( B @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ) )
& ( ( ( B @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_rat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755]) ).
thf(261,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5984_mult__2) ).
thf(2970,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1762,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_2376_order__less__le__trans) ).
thf(10232,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)],[1762]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7223_even__flip__bit__iff) ).
thf(1916,plain,
! [A: nat,B: nat] :
( ( ~ ( ( ( A = zero_zero_nat )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) )
=> ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( ( A = zero_zero_nat )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1393,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_1337_le__numeral__extra_I4_J) ).
thf(8259,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)],[1393]) ).
thf(314,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_1534_diff__add) ).
thf(3234,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)],[314]) ).
thf(455,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) )
= ( C @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
<=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3600_of__nat__eq__of__nat__power__cancel__iff) ).
thf(3925,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) )
= ( C @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( ( ( B @ ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) )
= ( C @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(1589,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_3981_power__le__imp__le__exp) ).
thf(9142,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)],[1589]) ).
thf(1037,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9703_gcd__nat_OorderI) ).
thf(6617,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(537,axiom,
! [A: real] :
( ( one_one_real = A )
<=> ( A = one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_one__reorient) ).
thf(4283,plain,
! [A: real] :
( ( ( A = one_one_real )
=> ( one_one_real = A ) )
& ( ( one_one_real = A )
=> ( A = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(493,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_3531_bits__div__by__1) ).
thf(4077,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)],[493]) ).
thf(1009,axiom,
! [A: real] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3625_power__Suc0__right) ).
thf(6510,plain,
! [A: real] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(770,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_kf @ aa_nat_o ) )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10568_ATP_Olambda__417) ).
thf(5395,plain,
! [A: nat] : ( A @ ( aTP_Lamm_kf @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(968,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_4866_unique__euclidean__semiring__numeral__class_Omod__mult2__eq) ).
thf(6312,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)],[968]) ).
thf(375,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5811_add__2__eq__Suc) ).
thf(3519,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(705,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_6813_take__bit__add) ).
thf(5065,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)],[705]) ).
thf(864,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_3448_one__le__mult__iff) ).
thf(5844,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)],[864]) ).
thf(510,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7956_and__Suc__0__eq) ).
thf(4159,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(1688,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_1460_linordered__nonzero__semiring__class_Ozero__le__one) ).
thf(9733,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)],[1688]) ).
thf(265,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
<=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_VEBT_Oinject_I1_J) ).
thf(2981,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1218,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_24_zero__induct) ).
thf(7487,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)],[1218]) ).
thf(1593,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_1363_add__mono__thms__linordered__semiring_I1_J) ).
thf(9157,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)],[1593]) ).
thf(1487,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_kj @ 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_10332_ATP_Olambda__181) ).
thf(8711,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_kj @ 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)],[1487]) ).
thf(888,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_491_less__imp__Suc__add) ).
thf(5940,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)],[888]) ).
thf(460,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9329_upt__Suc__append) ).
thf(3945,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ upt ) )
= ( nil_nat @ ( B @ cons_nat ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(1512,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_1352_less__eqE) ).
thf(8809,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)],[1512]) ).
thf(25,axiom,
( ( zero_zero_real @ ( exp_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4239_exp__zero) ).
thf(2016,plain,
( ( zero_zero_real @ ( exp_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(153,axiom,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( exp_real @ aa_real_real ) )
= ( B @ ( exp_real @ aa_real_real ) @ ( A @ ( exp_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4334_exp__diff) ).
thf(2514,plain,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( exp_real @ aa_real_real ) )
= ( B @ ( exp_real @ aa_real_real ) @ ( A @ ( exp_real @ aa_real_real ) @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1533,axiom,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4263_fact__Suc__0) ).
thf(8894,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533]) ).
thf(1480,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8868_lessThan__Suc) ).
thf(8684,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480]) ).
thf(607,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_329_add__left__imp__eq) ).
thf(4605,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)],[607]) ).
thf(1506,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_422_add__strict__right__mono) ).
thf(8777,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)],[1506]) ).
thf(1602,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_181_add__less__cancel__left) ).
thf(9189,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)],[1602]) ).
thf(224,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8017_and__nat__rec) ).
thf(2806,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(1409,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_6991_unit__div__cancel) ).
thf(8332,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)],[1409]) ).
thf(1371,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_1402_le__SucI) ).
thf(8167,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)],[1371]) ).
thf(905,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_6544_binomial__addition__formula) ).
thf(6019,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)],[905]) ).
thf(1213,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_7151_is__unit__div__mult__cancel__left) ).
thf(7472,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)],[1213]) ).
thf(850,axiom,
! [A: complex,B: list_complex] :
( ( B @ set_complex2 @ ( A @ member_complex ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_complex @ aa_nat_complex ) )
= A )
& ( B @ size_s3451745648224563538omplex @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6427_in__set__conv__nth) ).
thf(5752,plain,
! [A: complex,B: list_complex] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_complex @ aa_nat_complex ) )
= A )
& ( B @ size_s3451745648224563538omplex @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_complex2 @ ( A @ member_complex ) ) )
& ( ( B @ set_complex2 @ ( A @ member_complex ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_complex @ aa_nat_complex ) )
= A )
& ( B @ size_s3451745648224563538omplex @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(641,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7202_even__iff__mod__2__eq__zero) ).
thf(4758,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(643,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_4776_minus__mod__eq__div__mult) ).
thf(4769,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)],[643]) ).
thf(1289,axiom,
! [A: list_set_nat,B: nat,C: set_nat] :
( ( ( A @ size_s3254054031482475050et_nat )
= B )
=> ( ! [D: set_nat] :
( ( A @ set_set_nat2 @ ( D @ member_set_nat ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_set_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8651_replicate__eqI) ).
thf(7815,plain,
! [A: list_set_nat,B: nat,C: set_nat] :
( ( ( A @ size_s3254054031482475050et_nat )
= B )
=> ( ! [D: set_nat] :
( ( A @ set_set_nat2 @ ( D @ member_set_nat ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).
thf(1054,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_3479_div__le__mono2) ).
thf(6705,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)],[1054]) ).
thf(52,axiom,
! [A: real,B: real] :
( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
!= ( B @ ( sgn_sgn_real @ aa_real_real ) ) )
=> ( ( ( B @ ( sgn_sgn_real @ aa_real_real ) )
!= zero_zero_real )
=> ( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
!= zero_zero_real )
=> ( ( B @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4675_sgn__not__eq__imp) ).
thf(2134,plain,
! [A: real,B: real] :
( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
!= ( B @ ( sgn_sgn_real @ aa_real_real ) ) )
=> ( ( ( B @ ( sgn_sgn_real @ aa_real_real ) )
!= zero_zero_real )
=> ( ( ( A @ ( sgn_sgn_real @ aa_real_real ) )
!= zero_zero_real )
=> ( ( B @ ( sgn_sgn_real @ aa_real_real ) )
= ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(583,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_4671_div__add1__eq) ).
thf(4505,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)],[583]) ).
thf(259,axiom,
! [A: nat] :
( ( one_one_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_of__nat__1__eq__iff) ).
thf(2959,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ) )
& ( ( one_one_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(309,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9320_upt__rec) ).
thf(3213,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ cons_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1503,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_6975_div__mult__div__if__dvd) ).
thf(8767,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)],[1503]) ).
thf(1896,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_0_bot__nat__0_Onot__eq__extremum) ).
thf(10883,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)],[1896]) ).
thf(811,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= one_one_real )
<=> ( B = one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4273_real__root__eq__1__iff) ).
thf(5567,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = one_one_real )
=> ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= one_one_real ) )
& ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= one_one_real )
=> ( B = one_one_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(1173,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_7087_unit__div__mult__swap) ).
thf(7270,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)],[1173]) ).
thf(1142,axiom,
! [A: num,B: num] :
( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4969_numeral__eq__iff) ).
thf(7109,plain,
! [A: num,B: num] :
( ( ( A = B )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) ) )
& ( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(333,axiom,
! [A: complex] :
( ( zero_zero_nat @ ( A @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3857_power__0) ).
thf(3340,plain,
! [A: complex] :
( ( zero_zero_nat @ ( A @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1342,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_481_canonically__ordered__monoid__add__class_OlessE) ).
thf(8059,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)],[1342]) ).
thf(1440,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_6508_zero__less__binomial__iff) ).
thf(8497,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)],[1440]) ).
thf(970,axiom,
! [A: nat] :
( ( A @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6495_binomial__n__n) ).
thf(6334,plain,
! [A: nat] :
( ( A @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(979,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( pred_numeral @ aa_num_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6527_numeral__eq__Suc) ).
thf(6372,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( pred_numeral @ aa_num_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(1867,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_4096_pochhammer__pos) ).
thf(10741,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)],[1867]) ).
thf(589,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3607_of__nat__power) ).
thf(4537,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(1406,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_1555_Suc__le__eq) ).
thf(8318,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)],[1406]) ).
thf(1666,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_1800_Nat_Oex__has__greatest__nat) ).
thf(9638,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)],[1666]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9017_or__nat__rec) ).
thf(2220,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( plus_plus_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1798,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_7348_gcd__nat_Onot__eq__order__implies__strict) ).
thf(10393,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)],[1798]) ).
thf(1386,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 ) )
=> ( fun_pair_less @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9785_pair__lessI2) ).
thf(8227,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 ) )
=> ( fun_pair_less @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).
thf(1264,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_1561_less__eq__Suc__le) ).
thf(7689,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)],[1264]) ).
thf(1015,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_1184_add__le__same__cancel1) ).
thf(6532,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)],[1015]) ).
thf(498,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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_6773_odd__two__times__div__two__succ) ).
thf(4099,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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)],[498]) ).
thf(1271,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_1560_less__Suc__eq__le) ).
thf(7719,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)],[1271]) ).
thf(1679,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_77_gr0__implies__Suc) ).
thf(9687,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)],[1679]) ).
thf(507,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7954_and__nat__numerals_I2_J) ).
thf(4149,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(1529,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9694_gcd__nat_Oabsorb__iff2) ).
thf(8877,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( 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 @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529]) ).
thf(749,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5002_power__zero__numeral) ).
thf(5282,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(1598,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_4920_mod__Suc) ).
thf(9178,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)],[1598]) ).
thf(1041,axiom,
! [A: list_set_nat,B: set_set_nat] :
( ( B @ ( A @ set_set_nat2 @ ord_le6893508408891458716et_nat ) )
<=> ! [C: set_nat] :
( ( A @ set_set_nat2 @ ( C @ member_set_nat ) )
=> ( B @ ( C @ member_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2167_subset__code_I1_J) ).
thf(6649,plain,
! [A: list_set_nat,B: set_set_nat] :
( ( ! [C: set_nat] :
( ( A @ set_set_nat2 @ ( C @ member_set_nat ) )
=> ( B @ ( C @ member_set_nat ) ) )
=> ( B @ ( A @ set_set_nat2 @ ord_le6893508408891458716et_nat ) ) )
& ( ( B @ ( A @ set_set_nat2 @ ord_le6893508408891458716et_nat ) )
=> ! [C: set_nat] :
( ( A @ set_set_nat2 @ ( C @ member_set_nat ) )
=> ( B @ ( C @ member_set_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1139,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_1596_add__pos__nonneg) ).
thf(7094,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)],[1139]) ).
thf(297,axiom,
! [A: real] :
( ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5138_norm__eq__zero) ).
thf(3123,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1864,axiom,
! [A: list_list_nat] : ( A @ size_s3023201423986296836st_nat @ ( A @ set_list_nat2 @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6304_card__length) ).
thf(10728,plain,
! [A: list_list_nat] : ( A @ size_s3023201423986296836st_nat @ ( A @ set_list_nat2 @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864]) ).
thf(212,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6711_odd__Suc__div__two) ).
thf(2753,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(1815,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_2260_order_Ostrict__iff__order) ).
thf(10493,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)],[1815]) ).
thf(61,axiom,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5422_norm__minus__commute) ).
thf(2166,plain,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(802,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_3228_mult__left__le__imp__le) ).
thf(5539,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)],[802]) ).
thf(847,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_jf @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10286_ATP_Olambda__135) ).
thf(5735,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_jf @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1721,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_6576_dvd__0__right) ).
thf(10024,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)],[1721]) ).
thf(535,axiom,
( ( one_one_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_int__ops_I2_J) ).
thf(4273,plain,
( ( one_one_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(1445,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_4129_pochhammer__rec_H) ).
thf(8524,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)],[1445]) ).
thf(1575,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_475_add__neg__neg) ).
thf(9089,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)],[1575]) ).
thf(1612,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_1802_le__antisym) ).
thf(9258,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)],[1612]) ).
thf(104,axiom,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1823_abs__minus__commute) ).
thf(2319,plain,
! [A: real,B: real] :
( ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( B @ minus_minus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(563,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
| ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7893_even__bit__succ__iff) ).
thf(4433,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( B = zero_zero_nat )
| ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
| ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(904,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_2782_mult_Ocomm__neutral) ).
thf(6016,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)],[904]) ).
thf(1390,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_3894_power__le__one) ).
thf(8244,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)],[1390]) ).
thf(1216,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9424_mult__nat__left__at__top) ).
thf(7482,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).
thf(1705,axiom,
zero_zero_nat @ ( gcd_gcd_nat @ monoid_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9933_gcd__nat_Omonoid__axioms) ).
thf(9835,plain,
zero_zero_nat @ ( gcd_gcd_nat @ monoid_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705]) ).
thf(1632,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_6938_not__is__unit__0) ).
thf(9390,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)],[1632]) ).
thf(1005,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_3989_power__eq__imp__eq__base) ).
thf(6478,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)],[1005]) ).
thf(707,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_1519_add__le__imp__le__diff) ).
thf(5071,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)],[707]) ).
thf(1396,axiom,
! [A: nat,B: list_o,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_o ) @ nth_Product_prod_o_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ product_Pair_o_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7694_product__nth) ).
thf(8276,plain,
! [A: nat,B: list_o,C: list_o] :
( ( C @ size_size_list_o @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_o ) @ nth_Product_prod_o_o ) )
= ( C @ size_size_list_o @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_o @ aa_nat_o ) @ ( C @ size_size_list_o @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ product_Pair_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).
thf(824,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_7176_dvd__mult__cancel2) ).
thf(5631,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)],[824]) ).
thf(92,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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_8022_one__xor__eq) ).
thf(2284,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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)],[92]) ).
thf(82,axiom,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ groups861055069439313189ex_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8354_prod__ge__1) ).
thf(2246,plain,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( C @ ( B @ aa_complex_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ groups861055069439313189ex_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(972,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_9027_max__0L) ).
thf(6340,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)],[972]) ).
thf(1222,axiom,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) )
<=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8558_Bex__set__replicate) ).
thf(7502,plain,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) ) )
& ( ? [D: vEBT_VEBT] :
( ( D @ ( C @ aa_VEBT_VEBT_o ) )
& ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) ) )
=> ( ( A != zero_zero_nat )
& ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).
thf(820,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9771_coprime__diff__one__left__nat) ).
thf(5616,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(913,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_4925_mod__eq__0D) ).
thf(6061,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)],[913]) ).
thf(1031,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_7085_unit__div__commute) ).
thf(6585,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)],[1031]) ).
thf(1229,axiom,
! [A: nat,B: num,C: nat] :
( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5334_of__nat__le__numeral__power__cancel__iff) ).
thf(7546,plain,
! [A: nat,B: num,C: nat] :
( ( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[1229]) ).
thf(930,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_1403_Suc__le__D) ).
thf(6144,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)],[930]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3745_of__nat__gbinomial) ).
thf(3101,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ gbinomial_rat @ aa_nat_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1205,axiom,
! [A: num,B: nat] :
( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( ( A @ ( pred_numeral @ aa_num_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6503_eq__numeral__Suc) ).
thf(7415,plain,
! [A: num,B: nat] :
( ( ( ( A @ ( pred_numeral @ aa_num_nat ) )
= B )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( ( A @ ( pred_numeral @ aa_num_nat ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).
thf(1826,axiom,
( ( zero_zero_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) )
= bot_bot_fun_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7775_bit__0__eq) ).
thf(10532,plain,
( ( zero_zero_nat @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) )
= bot_bot_fun_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826]) ).
thf(1780,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_467_of__nat__less__imp__less) ).
thf(10297,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)],[1780]) ).
thf(1350,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_4536_mod__mult__self3) ).
thf(8088,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)],[1350]) ).
thf(1243,axiom,
! [A: $o,B: $o] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_o @ aa_o_fun_o_o ) @ aa_o_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001_Eo_T) ).
thf(7594,plain,
! [A: $o,B: $o] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_o @ aa_o_fun_o_o ) @ aa_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).
thf(473,axiom,
! [A: num] :
( ( one_one_nat
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) )
<=> ( one = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5742_one__eq__numeral__iff) ).
thf(3996,plain,
! [A: num] :
( ( ( one = A )
=> ( one_one_nat
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) ) )
& ( ( one_one_nat
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) )
=> ( one = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_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_6326_flip__bit__Suc) ).
thf(2151,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_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)],[56]) ).
thf(181,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7803_and__numerals_I1_J) ).
thf(2642,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1255,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_3668_power__strict__increasing__iff) ).
thf(7643,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)],[1255]) ).
thf(1100,axiom,
! [A: nat,B: list_real] :
( ( B @ size_size_list_real @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_real2 @ ( A @ ( B @ nth_real @ aa_nat_real ) @ member_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6417_nth__mem) ).
thf(6920,plain,
! [A: nat,B: list_real] :
( ( B @ size_size_list_real @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_real2 @ ( A @ ( B @ nth_real @ aa_nat_real ) @ member_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(74,axiom,
! [A: real,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_minus__diff__minus) ).
thf(2214,plain,
! [A: real,B: real] :
( ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= ( B @ ( A @ minus_minus_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(742,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_402_add__mono__thms__linordered__field_I5_J) ).
thf(5244,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)],[742]) ).
thf(1134,axiom,
! [A: real] :
( ( A @ ( zero_zero_nat @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4254_root__0) ).
thf(7077,plain,
! [A: real] :
( ( A @ ( zero_zero_nat @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(129,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9016_or__Suc__0__eq) ).
thf(2415,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(277,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_1239_diff__Suc__diff__eq2) ).
thf(3038,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)],[277]) ).
thf(1756,axiom,
! [A: complex,B: nat] :
( ( ( B @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_complex ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3674_power__eq__0__iff) ).
thf(10204,plain,
! [A: complex,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_complex ) )
=> ( ( B @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ) )
& ( ( ( B @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756]) ).
thf(1364,axiom,
! [A: list_int,B: int] :
( ! [C: int] :
( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_size_list_int @ replicate_int ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8659_replicate__length__same) ).
thf(8135,plain,
! [A: list_int,B: int] :
( ! [C: int] :
( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C = B ) )
=> ( ( B @ ( A @ size_size_list_int @ replicate_int ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).
thf(382,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_266_of__nat__add) ).
thf(3551,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)],[382]) ).
thf(1728,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_6406_list__eq__iff__nth__eq) ).
thf(10066,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)],[1728]) ).
thf(1001,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_2761_mult__right__cancel) ).
thf(6461,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)],[1001]) ).
thf(1854,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_2013_less__induct) ).
thf(10677,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)],[1854]) ).
thf(931,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_4924_mod__Suc__le__divisor) ).
thf(6147,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)],[931]) ).
thf(217,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8994_or__nat__numerals_I4_J) ).
thf(2774,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(656,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_9032_nat__add__max__right) ).
thf(4828,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)],[656]) ).
thf(943,axiom,
( ( $true @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7472_of__bool__eq_I2_J) ).
thf(6197,plain,
( ( $true @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(1245,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( abs_abs_real @ aa_real_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4356_real__root__abs) ).
thf(7607,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( abs_abs_real @ aa_real_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).
thf(1796,axiom,
! [A: fun_list_o_o,B: list_o] :
( ! [C: list_o] :
( ! [D: list_o] :
( ( C @ size_size_list_o @ ( D @ size_size_list_o @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_o_o ) ) )
=> ( C @ ( A @ aa_list_o_o ) ) )
=> ( B @ ( A @ aa_list_o_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6292_length__induct) ).
thf(10385,plain,
! [A: fun_list_o_o,B: list_o] :
( ! [C: list_o] :
( ! [D: list_o] :
( ( C @ size_size_list_o @ ( D @ size_size_list_o @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_o_o ) ) )
=> ( C @ ( A @ aa_list_o_o ) ) )
=> ( B @ ( A @ aa_list_o_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796]) ).
thf(789,axiom,
! [A: nat,B: list_o,C: list_int] :
( ( C @ size_size_list_int @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_int ) @ nth_Pr1649062631805364268_o_int ) )
= ( C @ size_size_list_int @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_int @ aa_nat_int ) @ ( C @ size_size_list_int @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ product_Pair_o_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7696_product__nth) ).
thf(5491,plain,
! [A: nat,B: list_o,C: list_int] :
( ( C @ size_size_list_int @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_int ) @ nth_Pr1649062631805364268_o_int ) )
= ( C @ size_size_list_int @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_int @ aa_nat_int ) @ ( C @ size_size_list_int @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ product_Pair_o_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(871,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_479_add__pos__pos) ).
thf(5880,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)],[871]) ).
thf(1083,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_100_exists__least__lemma) ).
thf(6832,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)],[1083]) ).
thf(703,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_438_add__Suc) ).
thf(5054,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)],[703]) ).
thf(1187,axiom,
! [A: list_complex,B: nat,C: complex] :
( ( ( A @ size_s3451745648224563538omplex )
= B )
=> ( ! [D: complex] :
( ( A @ set_complex2 @ ( D @ member_complex ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_complex ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8649_replicate__eqI) ).
thf(7330,plain,
! [A: list_complex,B: nat,C: complex] :
( ( ( A @ size_s3451745648224563538omplex )
= B )
=> ( ! [D: complex] :
( ( A @ set_complex2 @ ( D @ member_complex ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_complex ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).
thf(190,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_274_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2669,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)],[190]) ).
thf(1119,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_3965_power__Suc__le__self) ).
thf(7001,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)],[1119]) ).
thf(682,axiom,
! [A: real,B: nat] :
( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
<=> ? [C: nat] :
( ( A
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4148_pochhammer__eq__0__iff) ).
thf(4958,plain,
! [A: real,B: nat] :
( ( ? [C: nat] :
( ( A
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
=> ? [C: nat] :
( ( A
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(1171,axiom,
! [A: fun_nat_int,B: nat] :
( ( B @ ( A @ aTP_Lamm_cs @ aa_nat_int ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10304_ATP_Olambda__153) ).
thf(7265,plain,
! [A: fun_nat_int,B: nat] :
( ( B @ ( A @ aTP_Lamm_cs @ aa_nat_int ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).
thf(522,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_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_6448_numeral__Bit1) ).
thf(4213,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_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)],[522]) ).
thf(1559,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_3125_add__scale__eq__noteq) ).
thf(9015,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)],[1559]) ).
thf(1553,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_1567_diff__less__mono) ).
thf(8986,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)],[1553]) ).
thf(801,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2168_subset__code_I1_J) ).
thf(5531,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) )
=> ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) )
& ( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( B @ ( C @ member_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(963,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_6844_division__decomp) ).
thf(6289,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)],[963]) ).
thf(1438,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_3673_power__eq__0__iff) ).
thf(8485,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)],[1438]) ).
thf(1544,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_3677_of__nat__less__of__nat__power__cancel__iff) ).
thf(8937,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)],[1544]) ).
thf(1249,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_6500_binomial__Suc__Suc) ).
thf(7626,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)],[1249]) ).
thf(301,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_210_add__is__0) ).
thf(3138,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)],[301]) ).
thf(941,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_1556_dec__induct) ).
thf(6184,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)],[941]) ).
thf(284,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_2831_right__diff__distrib_H) ).
thf(3066,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)],[284]) ).
thf(246,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7811_bit__0) ).
thf(2896,plain,
! [A: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( zero_zero_nat @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(15,axiom,
! [A: fun_real_o,B: $o] :
( ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) )
<=> ~ ( ( ~ ( zero_zero_real @ ( A @ aa_real_o ) )
& ~ B )
| ( ~ ( one_one_real @ ( A @ aa_real_o ) )
& B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7558_split__of__bool__asm) ).
thf(1969,plain,
! [A: fun_real_o,B: $o] :
( ( ~ ( ( ~ ( zero_zero_real @ ( A @ aa_real_o ) )
& ~ B )
| ( ~ ( one_one_real @ ( A @ aa_real_o ) )
& B ) )
=> ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) ) )
& ( ( B @ zero_n3304061248610475627l_real @ ( A @ aa_real_o ) )
=> ~ ( ( ~ ( zero_zero_real @ ( A @ aa_real_o ) )
& ~ B )
| ( ~ ( one_one_real @ ( A @ aa_real_o ) )
& B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1164,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_3102_mult__pos__pos) ).
thf(7238,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)],[1164]) ).
thf(66,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_7198_fold__atLeastAtMost__nat_Oelims) ).
thf(2180,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)],[66]) ).
thf(311,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6677_even__Suc) ).
thf(3219,plain,
! [A: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(208,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_391_comm__monoid__add__class_Oadd__0) ).
thf(2742,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)],[208]) ).
thf(178,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7771_zero__and__eq) ).
thf(2625,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1552,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_4457_mod__by__0) ).
thf(8983,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)],[1552]) ).
thf(1182,axiom,
! [A: nat] :
( ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( zero_zero_nat @ upt ) @ set_nat2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9302_atLeast__upt) ).
thf(7302,plain,
! [A: nat] :
( ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) )
= ( A @ ( zero_zero_nat @ upt ) @ set_nat2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).
thf(1305,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_6672_unit__mult__div__div) ).
thf(7892,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)],[1305]) ).
thf(1498,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( gcd_lcm_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_9979_dvd__lcm__I1__nat) ).
thf(8750,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( gcd_lcm_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)],[1498]) ).
thf(366,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_9317_upt__conv__Cons__Cons) ).
thf(3483,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)],[366]) ).
thf(1068,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_6648_unit__div__1__div__1) ).
thf(6769,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)],[1068]) ).
thf(795,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_4934_mod__eq__nat1E) ).
thf(5511,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)],[795]) ).
thf(1516,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_7060_unity__coeff__ex) ).
thf(8826,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)],[1516]) ).
thf(1377,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_6867_unit__imp__dvd) ).
thf(8192,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)],[1377]) ).
thf(27,axiom,
! [A: $o] :
( ( ( A @ zero_n3304061248610475627l_real )
= one_one_real )
<=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7464_of__bool__eq__1__iff) ).
thf(2025,plain,
! [A: $o] :
( ( A
=> ( ( A @ zero_n3304061248610475627l_real )
= one_one_real ) )
& ( ( ( A @ zero_n3304061248610475627l_real )
= one_one_real )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1842,axiom,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7361_gcd__nat_Orefl) ).
thf(10621,plain,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842]) ).
thf(226,axiom,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3590_power__one) ).
thf(2812,plain,
! [A: nat] :
( ( A @ ( one_one_real @ power_power_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(882,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_6834_dvd__triv__left) ).
thf(5920,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)],[882]) ).
thf(565,axiom,
one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5961_pos2) ).
thf(4445,plain,
one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(874,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_9026_max__nat_Oright__neutral) ).
thf(5894,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)],[874]) ).
thf(711,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_1565_Suc__diff__le) ).
thf(5082,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)],[711]) ).
thf(1354,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_1006_Suc__eq__plus1) ).
thf(8103,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)],[1354]) ).
thf(1476,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_220_add__less__same__cancel1) ).
thf(8661,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)],[1476]) ).
thf(732,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_1347_le__iff__add) ).
thf(5175,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)],[732]) ).
thf(489,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_1531_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(4064,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)],[489]) ).
thf(653,axiom,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7838_bit__numeral__simps_I1_J) ).
thf(4818,plain,
! [A: num] :
~ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(1718,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ aTP_Lamm_bh @ collect_complex @ finite_card_complex )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8126_card__roots__unity__eq) ).
thf(10005,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ aTP_Lamm_bh @ collect_complex @ finite_card_complex )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718]) ).
thf(304,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8993_or__nat__numerals_I2_J) ).
thf(3165,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(517,axiom,
! [A: nat] :
( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_of__nat__eq__1__iff) ).
thf(4181,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int ) )
& ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= one_one_int )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(546,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_278_add__mono__thms__linordered__semiring_I4_J) ).
thf(4332,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)],[546]) ).
thf(1551,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= B )
=> ( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8652_replicate__eqI) ).
thf(8974,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( A @ size_s6755466524823107622T_VEBT )
= B )
=> ( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551]) ).
thf(276,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 ) )
=> ( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( 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_6213_mod__double__modulus) ).
thf(3034,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 ) )
=> ( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
| ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( 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)],[276]) ).
thf(468,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_3538_left__add__mult__distrib) ).
thf(3977,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)],[468]) ).
thf(1064,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3846_power__Suc) ).
thf(6747,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(1258,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_2434_mult__zero__right) ).
thf(7654,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)],[1258]) ).
thf(661,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_143_add__cancel__left__left) ).
thf(4850,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)],[661]) ).
thf(267,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_367_diff__add__0) ).
thf(3006,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)],[267]) ).
thf(359,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_1229_le__add__diff__inverse2) ).
thf(3451,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)],[359]) ).
thf(830,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7826_bit__of__nat__iff__bit) ).
thf(5656,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(326,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_155_add__cancel__right__right) ).
thf(3298,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)],[326]) ).
thf(1236,axiom,
! [A: nat] : ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9765_coprime__Suc__left__nat) ).
thf(7575,plain,
! [A: nat] : ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).
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_3436_nat__mult__eq__1__iff) ).
thf(5466,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(1508,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_3033_mult__left__mono) ).
thf(8782,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)],[1508]) ).
thf(1336,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_3530_nat__mult__div__cancel__disj) ).
thf(8032,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)],[1336]) ).
thf(161,axiom,
! [A: num] :
( one
!= ( A @ ( bit1 @ aa_num_num ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6393_verit__eq__simplify_I12_J) ).
thf(2542,plain,
! [A: num] :
( one
!= ( A @ ( bit1 @ aa_num_num ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1748,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_1292_verit__la__disequality) ).
thf(10172,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)],[1748]) ).
thf(1087,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_9614_Least__Suc2) ).
thf(6847,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)],[1087]) ).
thf(632,axiom,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2560_divide__self) ).
thf(4726,plain,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(188,axiom,
( ( one_one_real @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1819_abs__one) ).
thf(2664,plain,
( ( one_one_real @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(1209,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_3481_div__less__dividend) ).
thf(7450,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)],[1209]) ).
thf(1579,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_1468_add__decreasing) ).
thf(9101,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)],[1579]) ).
thf(1132,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9695_gcd__nat_Oabsorb__iff1) ).
thf(7066,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( 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 @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(1410,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_447_trans__less__add1) ).
thf(8340,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)],[1410]) ).
thf(232,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_539_verit__sum__simplify) ).
thf(2842,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)],[232]) ).
thf(448,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_3418_div__mult__self2) ).
thf(3893,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)],[448]) ).
thf(593,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_4469_mod__add__self2) ).
thf(4554,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)],[593]) ).
thf(1379,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_aj @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10551_ATP_Olambda__400) ).
thf(8198,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_aj @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).
thf(169,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6473_mod__exhaust__less__4) ).
thf(2578,plain,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
| ( ( one @ ( bit0 @ aa_num_num ) @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(114,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7952_xor__nat__numerals_I4_J) ).
thf(2350,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1650,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2032_dual__order_Oirrefl) ).
thf(9478,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650]) ).
thf(582,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4088_pochhammer__of__nat) ).
thf(4502,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(1212,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_497_diff__Suc__less) ).
thf(7469,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)],[1212]) ).
thf(675,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_158_zero__eq__add__iff__both__eq__0) ).
thf(4918,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)],[675]) ).
thf(1881,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_37_less__antisym) ).
thf(10803,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)],[1881]) ).
thf(1399,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_3906_power__less__power__Suc) ).
thf(8291,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)],[1399]) ).
thf(380,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5825_numeral__plus__one) ).
thf(3539,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(130,axiom,
! [A: num,B: num] :
( ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( B @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10015_nat__of__num__add) ).
thf(2418,plain,
! [A: num,B: num] :
( ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( B @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(1032,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_7035_bezout__lemma__nat) ).
thf(6589,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)],[1032]) ).
thf(216,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_6995_div__plus__div__distrib__dvd__right) ).
thf(2770,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)],[216]) ).
thf(1710,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_1989_gt__ex) ).
thf(9873,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)],[1710]) ).
thf(35,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5919_power__minus1__even) ).
thf(2075,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1741,axiom,
! [A: num] :
~ ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5474_not__numeral__less__zero) ).
thf(10147,plain,
! [A: num] :
~ ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741]) ).
thf(955,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_3833_one__le__power) ).
thf(6255,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)],[955]) ).
thf(1522,axiom,
! [A: list_int] : ( A @ size_size_list_int @ ( A @ set_int2 @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6309_card__length) ).
thf(8853,plain,
! [A: list_int] : ( A @ size_size_list_int @ ( A @ set_int2 @ finite_card_int @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522]) ).
thf(760,axiom,
nat_of_num = numeral_numeral_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10008_nat__of__num__numeral) ).
thf(5340,plain,
nat_of_num = numeral_numeral_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(704,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( C @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) ) )
<=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3595_of__nat__power__eq__of__nat__cancel__iff) ).
thf(5057,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( C @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) ) ) )
& ( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( C @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ power_power_real @ aa_nat_real ) ) )
=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(135,axiom,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ zero_n3304061248610475627l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7473_of__nat__of__bool) ).
thf(2439,plain,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( A @ zero_n3304061248610475627l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1244,axiom,
! [A: list_int,B: list_int] :
( ( ( A @ size_size_list_int )
!= ( B @ size_size_list_int ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6289_size__neq__size__imp__neq) ).
thf(7603,plain,
! [A: list_int,B: list_int] :
( ( ( A @ size_size_list_int )
!= ( B @ size_size_list_int ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).
thf(1027,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_3484_mult__less__mono1) ).
thf(6574,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)],[1027]) ).
thf(1078,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_3461_mult__le__mono2) ).
thf(6811,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)],[1078]) ).
thf(119,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7939_xor__numerals_I1_J) ).
thf(2365,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1431,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_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_5005_power__zero__numeral) ).
thf(8456,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_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)],[1431]) ).
thf(1048,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_232_less__add__same__cancel2) ).
thf(6687,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)],[1048]) ).
thf(1457,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_6642_dvd__div__mult__self) ).
thf(8588,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)],[1457]) ).
thf(434,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5815_add__self__div__2) ).
thf(3838,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(1215,axiom,
! [A: nat,B: list_o,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_VEBT_VEBT ) @ nth_Pr6777367263587873994T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ produc2982872950893828659T_VEBT ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7693_product__nth) ).
thf(7479,plain,
! [A: nat,B: list_o,C: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( B @ size_size_list_o @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( B @ product_o_VEBT_VEBT ) @ nth_Pr6777367263587873994T_VEBT ) )
= ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ nth_VEBT_VEBT ) @ ( C @ size_s6755466524823107622T_VEBT @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_o @ aa_nat_o ) @ produc2982872950893828659T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).
thf(1097,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_3697_power__strict__decreasing__iff) ).
thf(6907,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)],[1097]) ).
thf(736,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_7149_is__unitE) ).
thf(5197,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)],[736]) ).
thf(714,axiom,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9766_coprime__Suc__right__nat) ).
thf(5094,plain,
! [A: nat] : ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(145,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7924_xor_Oleft__neutral) ).
thf(2481,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1404,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_6854_dvd__def) ).
thf(8308,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)],[1404]) ).
thf(1830,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_2078_linorder__neq__iff) ).
thf(10549,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)],[1830]) ).
thf(1690,axiom,
! [A: int,B: list_int] :
( ( B @ set_int2 @ ( A @ member_int ) )
=> ( B @ size_size_list_int @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6302_length__pos__if__in__set) ).
thf(9741,plain,
! [A: int,B: list_int] :
( ( B @ set_int2 @ ( A @ member_int ) )
=> ( B @ size_size_list_int @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690]) ).
thf(787,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_6895_dvd__div__eq__cancel) ).
thf(5482,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)],[787]) ).
thf(1630,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_2243_less__le__not__le) ).
thf(9381,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)],[1630]) ).
thf(744,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_3198_unique__euclidean__semiring__numeral__class_Odiv__less) ).
thf(5248,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)],[744]) ).
thf(812,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_1170_of__nat__le__iff) ).
thf(5575,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)],[812]) ).
thf(1604,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_1952_minf_I1_J) ).
thf(9197,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)],[1604]) ).
thf(895,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_6826_dvd__mult__right) ).
thf(5976,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)],[895]) ).
thf(1373,axiom,
! [A: set_nat,B: nat,C: set_nat] :
( ( C @ ( B @ replicate_set_nat ) @ set_set_nat2 @ ( A @ member_set_nat ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8561_in__set__replicate) ).
thf(8175,plain,
! [A: set_nat,B: nat,C: set_nat] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_set_nat ) @ set_set_nat2 @ ( A @ member_set_nat ) ) )
& ( ( C @ ( B @ replicate_set_nat ) @ set_set_nat2 @ ( A @ member_set_nat ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).
thf(1186,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_228_less__add__same__cancel1) ).
thf(7324,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)],[1186]) ).
thf(1800,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_7350_gcd__nat_Ostrict__implies__order) ).
thf(10407,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)],[1800]) ).
thf(173,axiom,
! [A: extended_enat,B: extended_enat,C: nat] :
( ( C @ extended_enat2 @ ( B @ ( A @ plus_p3455044024723400733d_enat ) @ ord_le2932123472753598470d_enat ) )
<=> ? [D: nat,E: nat] :
( ( C @ ( D @ ( E @ ( 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 @ extended_enat2 ) )
& ( A
= ( E @ extended_enat2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9871_iadd__le__enat__iff) ).
thf(2592,plain,
! [A: extended_enat,B: extended_enat,C: nat] :
( ( ? [D: nat,E: nat] :
( ( C @ ( D @ ( E @ ( 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 @ extended_enat2 ) )
& ( A
= ( E @ extended_enat2 ) ) )
=> ( C @ extended_enat2 @ ( B @ ( A @ plus_p3455044024723400733d_enat ) @ ord_le2932123472753598470d_enat ) ) )
& ( ( C @ extended_enat2 @ ( B @ ( A @ plus_p3455044024723400733d_enat ) @ ord_le2932123472753598470d_enat ) )
=> ? [D: nat,E: nat] :
( ( C @ ( D @ ( E @ ( 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 @ extended_enat2 ) )
& ( A
= ( E @ extended_enat2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(81,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_int @ power_power_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5947_one__power2) ).
thf(2244,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_int @ power_power_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1681,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3942_zero__power) ).
thf(9698,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681]) ).
thf(1804,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_2143_order__less__imp__triv) ).
thf(10424,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)],[1804]) ).
thf(540,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) )
= ( C @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
<=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3604_of__nat__eq__of__nat__power__cancel__iff) ).
thf(4304,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) )
= ( C @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ) )
& ( ( ( B @ ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) @ power_power_rat @ aa_nat_rat ) )
= ( C @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(681,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_340_add__implies__diff) ).
thf(4954,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)],[681]) ).
thf(1232,axiom,
! [A: nat,B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ ( B @ nth_VEBT_VEBT ) @ member_VEBT_VEBT ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6419_nth__mem) ).
thf(7558,plain,
! [A: nat,B: list_VEBT_VEBT] :
( ( B @ size_s6755466524823107622T_VEBT @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ ( B @ nth_VEBT_VEBT ) @ member_VEBT_VEBT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).
thf(260,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_348_diff__commute) ).
thf(2967,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)],[260]) ).
thf(833,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_1313_of__nat__mono) ).
thf(5667,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)],[833]) ).
thf(752,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_6626_dvd__times__left__cancel__iff) ).
thf(5299,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)],[752]) ).
thf(1188,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_7062_dvd__div__div__eq__mult) ).
thf(7339,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)],[1188]) ).
thf(99,axiom,
! [A: real] :
( ( A @ ( exp_real @ aa_real_real ) )
!= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4305_exp__not__eq__zero) ).
thf(2303,plain,
! [A: real] :
( ( A @ ( exp_real @ aa_real_real ) )
!= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(757,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_3969_power__Suc__less__one) ).
thf(5326,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)],[757]) ).
thf(669,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_7178_dvd__minus__add) ).
thf(4890,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)],[669]) ).
thf(1502,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_2526_nonzero__mult__div__cancel__right) ).
thf(8763,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)],[1502]) ).
thf(908,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_212_nat__add__left__cancel__less) ).
thf(6029,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)],[908]) ).
thf(451,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_3863_power__add) ).
thf(3908,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)],[451]) ).
thf(1162,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_9300_map__Suc__upt) ).
thf(7232,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)],[1162]) ).
thf(1540,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_3639_gbinomial__0_I1_J) ).
thf(8922,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)],[1540]) ).
thf(1051,axiom,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4331_fact__ge__1) ).
thf(6698,plain,
! [A: nat] : ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( one_one_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(1337,axiom,
! [A: num,B: nat] :
( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
!= one_one_nat )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5266_Suc__times__numeral__mod__eq) ).
thf(8035,plain,
! [A: num,B: nat] :
( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
!= one_one_nat )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[1337]) ).
thf(521,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_3554_nat__diff__add__eq2) ).
thf(4209,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)],[521]) ).
thf(1694,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_7353_gcd__nat_Ostrict__iff__not) ).
thf(9762,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)],[1694]) ).
thf(575,axiom,
( ( one_one_real @ ( sgn_sgn_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4895_sgn__one) ).
thf(4481,plain,
( ( one_one_real @ ( sgn_sgn_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(241,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_346_Nat_Odiff__cancel) ).
thf(2867,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)],[241]) ).
thf(1760,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_1804_le__trans) ).
thf(10226,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)],[1760]) ).
thf(572,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( 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_6092_Suc__n__div__2__gt__zero) ).
thf(4473,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( 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)],[572]) ).
thf(345,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3858_gbinomial__of__nat__symmetric) ).
thf(3380,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(495,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7664_semiring__bit__operations__class_Oeven__mask__iff) ).
thf(4084,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(23,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1755_abs__minus) ).
thf(2005,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(257,axiom,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_even__odd__cases) ).
thf(2952,plain,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(409,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7444_flip__bit__0) ).
thf(3672,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(243,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_1636_less__diff__conv2) ).
thf(2878,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)],[243]) ).
thf(1547,axiom,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_of__nat__1) ).
thf(8949,plain,
( ( one_one_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547]) ).
thf(1355,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_4914_Suc__mod__mult__self3) ).
thf(8106,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)],[1355]) ).
thf(376,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_126_add__right__cancel) ).
thf(3522,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)],[376]) ).
thf(1567,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ upt ) )
= nil_nat )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9293_upt__eq__Nil__conv) ).
thf(9054,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ upt ) )
= nil_nat ) )
& ( ( ( B @ ( A @ upt ) )
= nil_nat )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567]) ).
thf(268,axiom,
( ( zero_zero_real @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1738_abs__zero) ).
thf(3009,plain,
( ( zero_zero_real @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1088,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_1196_le__add__same__cancel2) ).
thf(6858,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)],[1088]) ).
thf(31,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8047_push__bit__Suc__numeral) ).
thf(2054,plain,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(806,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_3622_power__0__Suc) ).
thf(5548,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)],[806]) ).
thf(1820,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_2199_pinf_I8_J) ).
thf(10517,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)],[1820]) ).
thf(1549,axiom,
! [A: nat,B: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
<=> ( ( A != B )
& ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9690_gcd__nat_Ostrict__order__iff) ).
thf(8954,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_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 ) ) )
=> ( ( A != B )
& ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549]) ).
thf(275,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_1225_le__add__diff__inverse) ).
thf(3031,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)],[275]) ).
thf(1784,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_34_less__Suc__induct) ).
thf(10311,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)],[1784]) ).
thf(1786,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2113_order__less__irrefl) ).
thf(10322,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786]) ).
thf(1884,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_2364_order__neq__le__trans) ).
thf(10824,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)],[1884]) ).
thf(1284,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_3617_power__inject__exp) ).
thf(7788,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)],[1284]) ).
thf(40,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5941_zero__power2) ).
thf(2096,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1637,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_2068_linorder__neqE) ).
thf(9403,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)],[1637]) ).
thf(477,axiom,
! [A: nat] :
( ( A @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7836_bit__1__iff) ).
thf(4013,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) ) )
& ( ( A @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(1227,axiom,
! [A: real] :
( ( zero_zero_real = A )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__reorient) ).
thf(7526,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( zero_zero_real = A ) )
& ( ( zero_zero_real = A )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).
thf(457,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_195_add__diff__cancel__left) ).
thf(3936,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)],[457]) ).
thf(1143,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7798_bit__numeral__Bit1__Suc__iff) ).
thf(7117,plain,
! [A: num,B: nat] :
( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1306,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3623_power__0__Suc) ).
thf(7896,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).
thf(873,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9960_lcm__proj1__iff__nat) ).
thf(5886,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( A @ ( B @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(800,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_3196_div__positive) ).
thf(5528,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)],[800]) ).
thf(1677,axiom,
! [A: int,B: nat] :
( ( ( B @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3671_power__eq__0__iff) ).
thf(9673,plain,
! [A: int,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_int ) )
=> ( ( B @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int ) )
& ( ( ( B @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677]) ).
thf(948,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_1440_diff__le__self) ).
thf(6225,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)],[948]) ).
thf(1235,axiom,
! [A: nat,B: real,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ power_power_real @ aa_nat_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( C @ ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4354_real__root__power) ).
thf(7571,plain,
! [A: nat,B: real,C: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ power_power_real @ aa_nat_real ) @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( C @ ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).
thf(668,axiom,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( ( one_one_nat @ ( C @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( one_one_nat @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8364_prod__le__1) ).
thf(4886,plain,
! [A: set_complex,B: fun_complex_nat] :
( ! [C: complex] :
( ( A @ ( C @ member_complex ) )
=> ( ( one_one_nat @ ( C @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( one_one_nat @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(1201,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_1430_add__le__mono1) ).
thf(7403,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)],[1201]) ).
thf(1754,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_6520_binomial__eq__0) ).
thf(10191,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)],[1754]) ).
thf(601,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ upt ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9327_upt__add__eq__append) ).
thf(4580,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ upt ) @ ( B @ ( A @ upt ) @ append_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(184,axiom,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1764_abs__of__nat) ).
thf(2652,plain,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1669,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_valid__tree__deg__neq__0) ).
thf(9651,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669]) ).
thf(588,axiom,
! [A: real] :
( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1815_abs__eq__0__iff) ).
thf(4529,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1703,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_af @ 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_10275_ATP_Olambda__124) ).
thf(9826,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( aTP_Lamm_af @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( aTP_Lamm_af @ 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)],[1703]) ).
thf(79,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5032_norm__minus__cancel) ).
thf(2234,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( real_V7735802525324610683m_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(942,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_6679_pow__divides__pow__iff) ).
thf(6191,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)],[942]) ).
thf(543,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se547839408752420682it_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_8104_push__bit__add) ).
thf(4319,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se547839408752420682it_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)],[543]) ).
thf(1442,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_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_7566_split__of__bool) ).
thf(8505,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 @ aa_o_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_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)],[1442]) ).
thf(538,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_434_diffs0__imp__equal) ).
thf(4292,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)],[538]) ).
thf(1737,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_2148_linorder__less__linear) ).
thf(10132,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)],[1737]) ).
thf(1883,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_2221_nless__le) ).
thf(10814,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)],[1883]) ).
thf(1671,axiom,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6801_dvd__refl) ).
thf(9656,plain,
! [A: nat] : ( A @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5962_double__not__eq__Suc__double) ).
thf(2684,plain,
! [A: nat,B: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1471,axiom,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4246_fact__0) ).
thf(8637,plain,
( ( zero_zero_nat @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471]) ).
thf(85,axiom,
( ( $false @ zero_n3304061248610475627l_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7455_of__bool__eq_I1_J) ).
thf(2256,plain,
( ( $false @ zero_n3304061248610475627l_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(501,axiom,
! [A: num,B: num] :
( ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6464_cong__exp__iff__simps_I11_J) ).
thf(4113,plain,
! [A: num,B: num] :
( ( ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(829,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_2531_nonzero__mult__div__cancel__left) ).
thf(5652,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)],[829]) ).
thf(1530,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5015_of__nat__numeral) ).
thf(8885,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530]) ).
thf(901,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_6528_zero__less__binomial) ).
thf(6008,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)],[901]) ).
thf(1437,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_6628_dvd__times__right__cancel__iff) ).
thf(8477,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)],[1437]) ).
thf(1332,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 @ ( divide_divide_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3516_div__mult2__eq_H) ).
thf(8020,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 @ ( divide_divide_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(1118,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_6498_binomial__1) ).
thf(6998,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)],[1118]) ).
thf(722,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4429_fact__reduce) ).
thf(5133,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(1421,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_3464_le__square) ).
thf(8409,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)],[1421]) ).
thf(1720,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_3_not__gr__zero) ).
thf(10016,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)],[1720]) ).
thf(1322,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_7181_mod__nat__eqI) ).
thf(7982,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)],[1322]) ).
thf(547,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_of__nat__eq__iff) ).
thf(4336,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(688,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_1568_Nat_Ole__imp__diff__is__add) ).
thf(4986,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)],[688]) ).
thf(1040,axiom,
! [A: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_of__nat__eq__0__iff) ).
thf(6641,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)],[1040]) ).
thf(438,axiom,
! [A: nat] :
( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= zero_zero_rat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_of__nat__eq__0__iff) ).
thf(3849,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= zero_zero_rat ) )
& ( ( ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) )
= zero_zero_rat )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(775,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_1557_inc__induct) ).
thf(5414,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)],[775]) ).
thf(1852,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_6905_gcd__nat_Oextremum__unique) ).
thf(10653,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)],[1852]) ).
thf(1028,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_1345_add__le__imp__le__left) ).
thf(6577,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)],[1028]) ).
thf(1137,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_6862_dvdE) ).
thf(7087,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)],[1137]) ).
thf(371,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7882_and__one__eq) ).
thf(3507,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(55,axiom,
! [A: real] :
( ( A
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_equal__neg__zero) ).
thf(2143,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( A
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( A
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1663,axiom,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7492_zero__less__of__bool__iff) ).
thf(9535,plain,
! [A: $o] :
( ( A
=> ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663]) ).
thf(640,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_439_nat__arith_Osuc1) ).
thf(4754,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)],[640]) ).
thf(552,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_7393_take__bit__nat__less__self__iff) ).
thf(4377,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[552]) ).
thf(1879,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_1801_nat__le__linear) ).
thf(10797,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)],[1879]) ).
thf(349,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_372_nat__diff__split) ).
thf(3391,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)],[349]) ).
thf(1125,axiom,
! [A: list_int,B: fun_int_o] :
( ! [C: int] :
( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C @ ( B @ aa_int_o ) ) )
<=> ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6444_all__set__conv__all__nth) ).
thf(7026,plain,
! [A: list_int,B: fun_int_o] :
( ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) )
=> ! [C: int] :
( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C @ ( B @ aa_int_o ) ) ) )
& ( ! [C: int] :
( ( A @ set_int2 @ ( C @ member_int ) )
=> ( C @ ( B @ aa_int_o ) ) )
=> ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(823,axiom,
! [A: int] :
~ ! [B: nat] :
( ! [C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
<=> ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) ) )
=> ~ ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
<=> ~ ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7887_int__bit__bound) ).
thf(5624,plain,
! [A: int] :
~ ! [B: nat] :
( ! [C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ( C @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) )
& ( ( C @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) ) ) )
=> ~ ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ~ ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) )
=> ~ ( B @ ( A @ bit_se1146084159140164899it_int @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(201,axiom,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_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_6045_power2__sum) ).
thf(2715,plain,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_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)],[201]) ).
thf(953,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_3961_power__Suc__less) ).
thf(6249,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)],[953]) ).
thf(923,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_6538_choose__reduce__nat) ).
thf(6120,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)],[923]) ).
thf(1266,axiom,
! [A: num,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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_5068_distrib__left__numeral) ).
thf(7705,plain,
! [A: num,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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)],[1266]) ).
thf(818,axiom,
! [A: list_set_nat,B: fun_set_nat_o,C: nat] :
( ! [D: set_nat] :
( ( A @ set_set_nat2 @ ( D @ member_set_nat ) )
=> ( D @ ( B @ aa_set_nat_o ) ) )
=> ( ( A @ size_s3254054031482475050et_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_set_nat @ aa_nat_set_nat ) @ ( B @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6337_inthall) ).
thf(5607,plain,
! [A: list_set_nat,B: fun_set_nat_o,C: nat] :
( ! [D: set_nat] :
( ( A @ set_set_nat2 @ ( D @ member_set_nat ) )
=> ( D @ ( B @ aa_set_nat_o ) ) )
=> ( ( A @ size_s3254054031482475050et_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_set_nat @ aa_nat_set_nat ) @ ( B @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(1856,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_1424_nat__less__le) ).
thf(10685,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)],[1856]) ).
thf(664,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_4768_minus__mult__div__eq__mod) ).
thf(4864,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)],[664]) ).
thf(986,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_4532_mod__mult__self4) ).
thf(6399,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)],[986]) ).
thf(1588,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Suc__neq__Zero) ).
thf(9138,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588]) ).
thf(578,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_zero__neq__one) ).
thf(4490,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3744_of__nat__gbinomial) ).
thf(2661,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( gbinomial_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ gbinomial_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(721,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_2777_mult__not__zero) ).
thf(5125,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)],[721]) ).
thf(1733,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_2204_pinf_I6_J) ).
thf(10112,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)],[1733]) ).
thf(1448,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4918_mod__Suc__eq) ).
thf(8537,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448]) ).
thf(718,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_3523_nat__mult__le__cancel__disj) ).
thf(5111,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)],[718]) ).
thf(33,axiom,
! [A: real,B: real] :
( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( abs_abs_real @ aa_real_real ) ) )
<=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1827_abs__eq__iff) ).
thf(2060,plain,
! [A: real,B: real] :
( ( ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) )
=> ( ( A @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( abs_abs_real @ aa_real_real ) ) ) )
& ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= ( B @ ( abs_abs_real @ aa_real_real ) ) )
=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(678,axiom,
! [A: nat,B: set_set_nat,C: set_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 ) @ ( B @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_set_nat ) @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8011_card__insert__le__m1) ).
thf(4939,plain,
! [A: nat,B: set_set_nat,C: set_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 ) @ ( B @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_set_nat ) @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(551,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_2813_crossproduct__eq) ).
thf(4366,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)],[551]) ).
thf(1434,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9029_max__numeral__Suc) ).
thf(8466,plain,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434]) ).
thf(1892,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_1412_bot__nat__0_Oextremum__unique) ).
thf(10856,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)],[1892]) ).
thf(1684,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_98_infinite__descent0) ).
thf(9710,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)],[1684]) ).
thf(680,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_1527_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(4950,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)],[680]) ).
thf(1128,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_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 ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4086_pochhammer__of__nat) ).
thf(7045,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri1316708129612266289at_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 ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(798,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_1437_add__leE) ).
thf(5523,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)],[798]) ).
thf(585,axiom,
! [A: real] :
( ( one_one_real @ ( A @ divide_divide_real @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2488_div__by__1) ).
thf(4517,plain,
! [A: real] :
( ( one_one_real @ ( A @ divide_divide_real @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1535,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_3057_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono) ).
thf(8904,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)],[1535]) ).
thf(64,axiom,
! [A: real,B: nat] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( @+[C: real] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ power_power_real @ aa_nat_real ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7210_uminus__power__if) ).
thf(2175,plain,
! [A: real,B: nat] :
( ( B @ ( A @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( @+[C: real] :
( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( A @ power_power_real @ aa_nat_real ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(128,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( B @ ( A @ minus_minus_real @ aa_real_real ) )
= ( D @ ( C @ minus_minus_real @ aa_real_real ) ) )
=> ( ( A = B )
<=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_diff__eq__diff__eq) ).
thf(2407,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( B @ ( A @ minus_minus_real @ aa_real_real ) )
= ( D @ ( C @ minus_minus_real @ aa_real_real ) ) )
=> ( ( ( C = D )
=> ( A = B ) )
& ( ( A = B )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(421,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_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_8115_numeral__code_I3_J) ).
thf(3786,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( one_one_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_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)],[421]) ).
thf(1006,axiom,
! [A: $o,B: list_o] :
( ( B @ set_o2 @ ( A @ member_o ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_o @ aa_nat_o ) )
<=> A )
& ( B @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6431_in__set__conv__nth) ).
thf(6481,plain,
! [A: $o,B: list_o] :
( ( ? [C: nat] :
( ( A
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> A )
& ( B @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_o2 @ ( A @ member_o ) ) )
& ( ( B @ set_o2 @ ( A @ member_o ) )
=> ? [C: nat] :
( ( A
=> ( C @ ( B @ nth_o @ aa_nat_o ) ) )
& ( ( C @ ( B @ nth_o @ aa_nat_o ) )
=> A )
& ( B @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(710,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3619_power__0__Suc) ).
thf(5079,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(1743,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_14_Suc__mono) ).
thf(10159,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)],[1743]) ).
thf(1513,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_435_diff__less__mono2) ).
thf(8813,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)],[1513]) ).
thf(59,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10012_nat__of__num__code_I2_J) ).
thf(2160,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(695,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_437_add__Suc__shift) ).
thf(5018,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)],[695]) ).
thf(983,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_1695_discrete) ).
thf(6384,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)],[983]) ).
thf(1496,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= ( @+[C: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( 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 ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9045_prod__decode__aux_Osimps) ).
thf(8744,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= ( @+[C: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( 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 ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496]) ).
thf(1338,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_3445_mult__less__cancel2) ).
thf(8039,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)],[1338]) ).
thf(892,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_3626_power__Suc0__right) ).
thf(5955,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)],[892]) ).
thf(694,axiom,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5165_norm__of__nat) ).
thf(5015,plain,
! [A: nat] :
( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( real_V7735802525324610683m_real @ aa_real_real ) )
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(1860,axiom,
! [A: real,B: list_real] :
( ( B @ set_real2 @ ( A @ member_real ) )
=> ( B @ size_size_list_real @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6297_length__pos__if__in__set) ).
thf(10717,plain,
! [A: real,B: list_real] :
( ( B @ set_real2 @ ( A @ member_real ) )
=> ( B @ size_size_list_real @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860]) ).
thf(1010,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_493_less__add__Suc2) ).
thf(6513,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)],[1010]) ).
thf(898,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( ( 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3838_left__right__inverse__power) ).
thf(5995,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( ( 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 ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(105,axiom,
( zero_zero_real
!= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_zero__neq__neg__one) ).
thf(2322,plain,
( zero_zero_real
!= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1818,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_au @ aa_nat_o ) )
<=> ~ ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10387_ATP_Olambda__236) ).
thf(10509,plain,
! [A: fun_nat_o,B: nat] :
( ( ~ ( B @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_au @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_au @ aa_nat_o ) )
=> ~ ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818]) ).
thf(734,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( C @ ( B @ ( bit_se1148574629649215175it_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_7841_bit__take__bit__iff) ).
thf(5186,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( B @ ( bit_se1148574629649215175it_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)],[734]) ).
thf(557,axiom,
! [A: nat] :
( ( A @ ( one_one_rat @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3588_power__one) ).
thf(4409,plain,
! [A: nat] :
( ( A @ ( one_one_rat @ power_power_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(1759,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_1153_le__zero__eq) ).
thf(10218,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)],[1759]) ).
thf(1464,axiom,
! [A: nat] :
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6114_mult__numeral__1__right) ).
thf(8612,plain,
! [A: nat] :
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464]) ).
thf(1093,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_3064_mult__strict__right__mono) ).
thf(6880,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)],[1093]) ).
thf(1846,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_4923_mod__less__divisor) ).
thf(10636,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)],[1846]) ).
thf(747,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_7099_is__unit__power__iff) ).
thf(5262,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)],[747]) ).
thf(556,axiom,
! [A: real,B: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real )
<=> ( ( A = B )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2554_divide__eq__1__iff) ).
thf(4398,plain,
! [A: real,B: real] :
( ( ( ( A = B )
& ( B != zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= one_one_real )
=> ( ( A = B )
& ( B != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(1715,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_16_zero__less__Suc) ).
thf(9991,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)],[1715]) ).
thf(529,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_4835_mod__mult2__eq_H) ).
thf(4240,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)],[529]) ).
thf(1789,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_2017_antisym__conv3) ).
thf(10328,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)],[1789]) ).
thf(496,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6767_take__bit__Suc__0) ).
thf(4092,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(1616,axiom,
zero_zero_nat @ ( ord_max_nat @ semila9081495762789891438tr_nat @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9916_max__nat_Osemilattice__neutr__axioms) ).
thf(9281,plain,
zero_zero_nat @ ( ord_max_nat @ semila9081495762789891438tr_nat @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616]) ).
thf(1207,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_6644_unit__div) ).
thf(7429,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)],[1207]) ).
thf(429,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_203_add__diff__cancel__right) ).
thf(3818,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)],[429]) ).
thf(447,axiom,
! [A: real] :
( ( ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2569_one__divide__eq__0__iff) ).
thf(3885,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(411,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6004_less__2__cases__iff) ).
thf(3691,plain,
! [A: nat] :
( ( ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( A = zero_zero_nat ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(1524,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_4544_mod__mult__self1) ).
thf(8858,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)],[1524]) ).
thf(194,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_4002_power__diff) ).
thf(2688,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)],[194]) ).
thf(320,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_325_add_Oleft__commute) ).
thf(3273,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)],[320]) ).
thf(423,axiom,
! [A: real] :
( ( field_5140801741446780682s_real @ ( A @ member_real ) )
=> ~ ! [B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) )
=> ~ ( C @ ( B @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9772_Rats__abs__nat__div__natE) ).
thf(3791,plain,
! [A: real] :
( ( field_5140801741446780682s_real @ ( A @ member_real ) )
=> ~ ! [B: nat,C: nat] :
( ( C != zero_zero_nat )
=> ( ( ( A @ ( abs_abs_real @ aa_real_real ) )
= ( C @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ divide_divide_real @ aa_real_real ) ) )
=> ~ ( C @ ( B @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(283,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_3466_add__mult__distrib) ).
thf(3063,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)],[283]) ).
thf(1018,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_18_Suc__inject) ).
thf(6545,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)],[1018]) ).
thf(1568,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_3973_power__strict__decreasing) ).
thf(9065,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)],[1568]) ).
thf(1234,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_4027_power__strict__mono) ).
thf(7568,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)],[1234]) ).
thf(990,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_3856_power__0) ).
thf(6421,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)],[990]) ).
thf(383,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_441_add__eq__self__zero) ).
thf(3554,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)],[383]) ).
thf(1713,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_1298_verit__comp__simplify1_I2_J) ).
thf(9986,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)],[1713]) ).
thf(880,axiom,
! [A: nat,B: nat,C: nat] :
( ( fun_pair_less @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) )
<=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9786_pair__less__iff1) ).
thf(5912,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( fun_pair_less @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) )
& ( ( fun_pair_less @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) )
=> ( C @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(1468,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ aTP_Lamm_bh @ collect_complex @ ( aTP_Lamm_az @ groups7754918857620584856omplex ) )
= zero_zero_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8858_sum__roots__unity) ).
thf(8625,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ aTP_Lamm_bh @ collect_complex @ ( aTP_Lamm_az @ groups7754918857620584856omplex ) )
= zero_zero_complex ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468]) ).
thf(808,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6338_inthall) ).
thf(5555,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o,C: nat] :
( ! [D: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(307,axiom,
! [A: nat] :
( ( zero_zero_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_of__nat__0__eq__iff) ).
thf(3202,plain,
! [A: nat] :
( ( ( zero_zero_nat = A )
=> ( zero_zero_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ) )
& ( ( zero_zero_real
= ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1661,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_1972_pinf_I3_J) ).
thf(9518,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)],[1661]) ).
thf(1285,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_6971_unit__mult__left__cancel) ).
thf(7796,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)],[1285]) ).
thf(132,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( size_size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6482_num_Osize_I5_J) ).
thf(2429,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( size_size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1628,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_33_strict__inc__induct) ).
thf(9358,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)],[1628]) ).
thf(809,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_7089_is__unit__div__mult2__eq) ).
thf(5560,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)],[809]) ).
thf(110,axiom,
! [A: num,B: num] :
( ( ( A @ ( size_size_num @ aa_num_nat ) )
!= ( B @ ( size_size_num @ aa_num_nat ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6290_size__neq__size__imp__neq) ).
thf(2337,plain,
! [A: num,B: num] :
( ( ( A @ ( size_size_num @ aa_num_nat ) )
!= ( B @ ( size_size_num @ aa_num_nat ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(1303,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9665_gcd__nat_Oneutr__eq__iff) ).
thf(7879,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).
thf(425,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ~ ( A @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7872_exp__eq__0__imp__not__bit) ).
thf(3801,plain,
! [A: nat,B: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ~ ( A @ ( B @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(50,axiom,
! [A: num,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5000_numeral__plus__numeral) ).
thf(2128,plain,
! [A: num,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1280,axiom,
( ( $false @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7458_of__bool__eq_I1_J) ).
thf(7769,plain,
( ( $false @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).
thf(1678,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_1967_pinf_I4_J) ).
thf(9683,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)],[1678]) ).
thf(1674,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_36_Suc__less__SucD) ).
thf(9666,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)],[1674]) ).
thf(1239,axiom,
! [A: real,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4101_pochhammer__eq__0__mono) ).
thf(7583,plain,
! [A: real,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
=> ( ( C @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).
thf(1640,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_1456_not__one__le__zero) ).
thf(9413,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)],[1640]) ).
thf(650,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6697_odd__add) ).
thf(4800,plain,
! [A: nat,B: nat] :
( ( ~ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ~ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( ( ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(1381,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_3429_div__by__Suc__0) ).
thf(8206,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)],[1381]) ).
thf(1473,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_6529_Suc__times__binomial__add) ).
thf(8644,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)],[1473]) ).
thf(1793,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_1803_eq__imp__le) ).
thf(10343,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)],[1793]) ).
thf(647,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_3550_nat__eq__add__iff2) ).
thf(4781,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)],[647]) ).
thf(331,axiom,
! [A: nat] :
( ( zero_zero_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
<=> ( zero_zero_nat = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_of__nat__0__eq__iff) ).
thf(3329,plain,
! [A: nat] :
( ( ( zero_zero_nat = A )
=> ( zero_zero_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) ) )
& ( ( zero_zero_rat
= ( A @ ( semiri681578069525770553at_rat @ aa_nat_rat ) ) )
=> ( zero_zero_nat = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1890,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_7349_gcd__nat_Ostrict__implies__not__eq) ).
thf(10846,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)],[1890]) ).
thf(290,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_4764_cancel__div__mod__rules_I2_J) ).
thf(3095,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)],[290]) ).
thf(1680,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_1410_le__0__eq) ).
thf(9690,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)],[1680]) ).
thf(836,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_7036_bezout__add__nat) ).
thf(5675,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)],[836]) ).
thf(368,axiom,
! [A: nat,B: nat,C: product_prod_nat_nat] :
( ( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= C )
=> ( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( nat_pr5047031295181774490ux_rel @ accp_P4275260045618599050at_nat ) )
=> ~ ( ( C
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) )
=> ~ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( nat_pr5047031295181774490ux_rel @ accp_P4275260045618599050at_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9630_prod__decode__aux_Opelims) ).
thf(3493,plain,
! [A: nat,B: nat,C: product_prod_nat_nat] :
( ( ( B @ ( A @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) )
= C )
=> ( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( nat_pr5047031295181774490ux_rel @ accp_P4275260045618599050at_nat ) )
=> ~ ( ( C
= ( @+[D: product_prod_nat_nat] :
( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ nat_prod_decode_aux @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ) ) ) ) )
=> ~ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( nat_pr5047031295181774490ux_rel @ accp_P4275260045618599050at_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(1723,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7654_less__mask) ).
thf(10028,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723]) ).
thf(1610,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_2336_order__less__le) ).
thf(9242,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)],[1610]) ).
thf(348,axiom,
! [A: nat,B: nat] :
( ( B @ ( 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 ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4048_neg__one__power__add__eq__neg__one__power__diff) ).
thf(3388,plain,
! [A: nat,B: nat] :
( ( B @ ( 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 ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(533,axiom,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( A @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = zero_zero_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7144_stable__imp__take__bit__eq) ).
thf(4267,plain,
! [A: nat,B: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( A @ ( B @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( one_one_nat @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = zero_zero_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(1426,axiom,
! [A: set_nat,B: list_set_nat] :
( ( B @ set_set_nat2 @ ( A @ member_set_nat ) )
<=> ? [C: nat] :
( ( ( C @ ( B @ nth_set_nat @ aa_nat_set_nat ) )
= A )
& ( B @ size_s3254054031482475050et_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6429_in__set__conv__nth) ).
thf(8433,plain,
! [A: set_nat,B: list_set_nat] :
( ( ? [C: nat] :
( ( ( C @ ( B @ nth_set_nat @ aa_nat_set_nat ) )
= A )
& ( B @ size_s3254054031482475050et_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ set_set_nat2 @ ( A @ member_set_nat ) ) )
& ( ( B @ set_set_nat2 @ ( A @ member_set_nat ) )
=> ? [C: nat] :
( ( ( C @ ( B @ nth_set_nat @ aa_nat_set_nat ) )
= A )
& ( B @ size_s3254054031482475050et_nat @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426]) ).
thf(317,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7605_num_Osize__gen_I3_J) ).
thf(3256,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( size_num @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( size_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(235,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_433_minus__nat_Odiff__0) ).
thf(2848,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)],[235]) ).
thf(1309,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_nr @ aa_nat_o ) )
<=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10301_ATP_Olambda__150) ).
thf(7908,plain,
! [A: fun_nat_o,B: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_nr @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_nr @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).
thf(1075,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_1439_le__diff__iff_H) ).
thf(6793,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)],[1075]) ).
thf(1736,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_verit__comp__simplify1_I1_J) ).
thf(10129,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736]) ).
thf(7,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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_8020_xor__one__eq) ).
thf(1934,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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)],[7]) ).
thf(150,axiom,
! [A: real] :
( ( zero_zero_real
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) )
<=> ( zero_zero_real = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_neg__0__equal__iff__equal) ).
thf(2500,plain,
! [A: real] :
( ( ( zero_zero_real = A )
=> ( zero_zero_real
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( zero_zero_real
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( zero_zero_real = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1302,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_1008_Suc__eq__plus1__left) ).
thf(7876,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)],[1302]) ).
thf(877,axiom,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6494_binomial__Suc__n) ).
thf(5902,plain,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1405,axiom,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ vEBT_vebt_buildup )
= ( $false @ ( $false @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_vebt__buildup_Osimps_I2_J) ).
thf(8316,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ vEBT_vebt_buildup )
= ( $false @ ( $false @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).
thf(294,axiom,
! [A: nat] :
( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= one_one_real )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_of__nat__eq__1__iff) ).
thf(3107,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= one_one_real ) )
& ( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= one_one_real )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(971,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_3487_mult__Suc) ).
thf(6337,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)],[971]) ).
thf(1656,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_4366_fact__less__mono) ).
thf(9505,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)],[1656]) ).
thf(1,conjecture,
m @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( m @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(1898,plain,
~ ( m @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1046,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_426_add__less__imp__less__left) ).
thf(6679,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)],[1046]) ).
thf(405,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6733_even__plus__one__iff) ).
thf(3652,plain,
! [A: nat] :
( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(1223,axiom,
! [A: nat,B: set_complex,C: complex] :
( ( 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 ) @ ( B @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_complex ) @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8009_card__insert__le__m1) ).
thf(7515,plain,
! [A: nat,B: set_complex,C: complex] :
( ( 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 ) @ ( B @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_complex ) @ finite_card_complex @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).
thf(1238,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_3915_power__0__left) ).
thf(7580,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)],[1238]) ).
thf(1708,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7607_mask__nat__positive__iff) ).
thf(9863,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708]) ).
thf(1654,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_1149_le0) ).
thf(9500,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)],[1654]) ).
thf(611,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_9033_nat__add__max__left) ).
thf(4624,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)],[611]) ).
thf(1033,axiom,
at_top_nat @ ( at_top_nat @ ( suc @ filterlim_nat_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9456_filterlim__Suc) ).
thf(6601,plain,
at_top_nat @ ( at_top_nat @ ( suc @ filterlim_nat_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(1592,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_6584_dvd__add__triv__right__iff) ).
thf(9151,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)],[1592]) ).
thf(978,axiom,
! [A: nat] :
( ( A @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3914_power__0__left) ).
thf(6369,plain,
! [A: nat] :
( ( A @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1626,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ order_mono_nat_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9364_mono__times__nat) ).
thf(9353,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ order_mono_nat_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626]) ).
thf(1168,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_3216_mult__less__le__imp__less) ).
thf(7251,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)],[1168]) ).
thf(1070,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_2494_of__nat__mult) ).
thf(6775,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)],[1070]) ).
thf(639,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7792_bit__numeral__Bit0__Suc__iff) ).
thf(4748,plain,
! [A: num,B: nat] :
( ( ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(793,axiom,
! [A: num] :
( zero_zero_nat
!= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5427_zero__neq__numeral) ).
thf(5504,plain,
! [A: num] :
( zero_zero_nat
!= ( A @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(116,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5943_zero__power2) ).
thf(2357,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1521,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_3026_mult__right__mono) ).
thf(8850,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)],[1521]) ).
thf(152,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6450_eval__nat__numeral_I3_J) ).
thf(2511,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(615,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7311_even__mask__div__iff) ).
thf(4634,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(918,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_real @ gbinomial_real @ aa_nat_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3632_gbinomial__0_I2_J) ).
thf(6086,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_real @ gbinomial_real @ aa_nat_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(838,axiom,
! [A: list_complex,B: fun_complex_o,C: nat] :
( ! [D: complex] :
( ( A @ set_complex2 @ ( D @ member_complex ) )
=> ( D @ ( B @ aa_complex_o ) ) )
=> ( ( A @ size_s3451745648224563538omplex @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_complex @ aa_nat_complex ) @ ( B @ aa_complex_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6335_inthall) ).
thf(5685,plain,
! [A: list_complex,B: fun_complex_o,C: nat] :
( ! [D: complex] :
( ( A @ set_complex2 @ ( D @ member_complex ) )
=> ( D @ ( B @ aa_complex_o ) ) )
=> ( ( A @ size_s3451745648224563538omplex @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_complex @ aa_nat_complex ) @ ( B @ aa_complex_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(1638,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_7362_gcd__nat_Oasym) ).
thf(9406,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)],[1638]) ).
thf(1742,axiom,
! [A: nat] :
( ( A = zero_zero_nat )
<=> ( A @ ( aTP_Lamm_ke @ ( $true @ case_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8971_nat_Odisc__eq__case_I1_J) ).
thf(10150,plain,
! [A: nat] :
( ( ( A @ ( aTP_Lamm_ke @ ( $true @ case_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( A @ ( aTP_Lamm_ke @ ( $true @ case_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742]) ).
thf(256,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7955_Suc__0__and__eq) ).
thf(2949,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1099,axiom,
! [A: nat] :
( ( A @ extended_enat2 @ extended_eSuc )
= ( A @ ( suc @ aa_nat_nat ) @ extended_enat2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9894_eSuc__enat) ).
thf(6917,plain,
! [A: nat] :
( ( A @ extended_enat2 @ extended_eSuc )
= ( A @ ( suc @ aa_nat_nat ) @ extended_enat2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(844,axiom,
! [A: num,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5323_numeral__power__less__of__nat__cancel__iff) ).
thf(5717,plain,
! [A: num,B: nat,C: nat] :
( ( ( C @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[844]) ).
thf(935,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9957_lcm__proj2__if__dvd__nat) ).
thf(6161,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1670,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_2324_dual__order_Ostrict__implies__order) ).
thf(9654,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)],[1670]) ).
thf(649,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_282_group__cancel_Oadd1) ).
thf(4795,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)],[649]) ).
thf(303,axiom,
! [A: $o,B: nat,C: nat] :
( ( @+[D: nat] :
( ( ~ A
=> ( D = C ) )
& ( A
=> ( D = B ) ) )
@ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( @+[D: int] :
( ( ~ A
=> ( D
= ( C @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( A
=> ( D
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_int__if) ).
thf(3156,plain,
! [A: $o,B: nat,C: nat] :
( ( @+[D: nat] :
( ( ~ A
=> ( D = C ) )
& ( A
=> ( D = B ) ) )
@ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( @+[D: int] :
( ( ~ A
=> ( D
= ( C @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) )
& ( A
=> ( D
= ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(453,axiom,
! [A: real] :
( ( zero_zero_real
= ( A @ ( abs_abs_real @ aa_real_real ) ) )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1730_abs__0__eq) ).
thf(3914,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( zero_zero_real
= ( A @ ( abs_abs_real @ aa_real_real ) ) ) )
& ( ( zero_zero_real
= ( A @ ( abs_abs_real @ aa_real_real ) ) )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(1750,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4319_fact__not__neg) ).
thf(10178,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750]) ).
thf(1525,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_6681_take__bit__of__1__eq__0__iff) ).
thf(8861,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)],[1525]) ).
thf(88,axiom,
! [A: nat,B: real] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6702_power__minus__odd) ).
thf(2266,plain,
! [A: nat,B: real] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6751_even__take__bit__eq) ).
thf(2760,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = zero_zero_nat ) )
=> ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(355,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
| ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7895_odd__bit__iff__bit__pred) ).
thf(3433,plain,
! [A: nat,B: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( ( B = zero_zero_nat )
| ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
| ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1882,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_79_gr0__conv__Suc) ).
thf(10806,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)],[1882]) ).
thf(113,axiom,
! [A: num] :
( ( A @ ( one @ plus_plus_num @ aa_num_num ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5938_add__One__commute) ).
thf(2347,plain,
! [A: num] :
( ( A @ ( one @ plus_plus_num @ aa_num_num ) )
= ( one @ ( A @ plus_plus_num @ aa_num_num ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(106,axiom,
! [A: real] :
( ( A @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_diff__self) ).
thf(2325,plain,
! [A: real] :
( ( A @ ( A @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(1079,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_4933_div__less__mono) ).
thf(6814,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)],[1079]) ).
thf(1757,axiom,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8438_suminf__pos) ).
thf(10214,plain,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757]) ).
thf(305,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_2809_combine__common__factor) ).
thf(3168,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)],[305]) ).
thf(9,axiom,
! [A: $o] :
( ( ~ A @ zero_n3304061248610475627l_real )
= ( A @ zero_n3304061248610475627l_real @ ( one_one_real @ minus_minus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7498_of__bool__not__iff) ).
thf(1940,plain,
! [A: $o] :
( ( ~ A @ zero_n3304061248610475627l_real )
= ( A @ zero_n3304061248610475627l_real @ ( one_one_real @ minus_minus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1230,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_mf @ 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_10274_ATP_Olambda__123) ).
thf(7552,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_mf @ 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)],[1230]) ).
thf(1772,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ aTP_Lamm_bh @ collect_complex @ ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) @ ( A @ aTP_Lamm_je @ bij_betw_nat_complex ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8877_bij__betw__roots__unity) ).
thf(10261,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ aTP_Lamm_bh @ collect_complex @ ( A @ ( set_ord_lessThan_nat @ aa_nat_set_nat ) @ ( A @ aTP_Lamm_je @ bij_betw_nat_complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772]) ).
thf(962,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_4520_bits__mod__by__1) ).
thf(6286,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)],[962]) ).
thf(251,axiom,
( ( zero_zero_int @ bit_se1146084159140164899it_int )
= bot_bot_fun_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7774_bit__0__eq) ).
thf(2924,plain,
( ( zero_zero_int @ bit_se1146084159140164899it_int )
= bot_bot_fun_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(389,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 ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4939_modulo__nat__def) ).
thf(3584,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 ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(618,axiom,
! [A: real,B: real] :
( ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) )
<=> ( ( A = B )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2557_one__eq__divide__iff) ).
thf(4651,plain,
! [A: real,B: real] :
( ( ( ( A = B )
& ( B != zero_zero_real ) )
=> ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) ) )
& ( ( one_one_real
= ( B @ ( A @ divide_divide_real @ aa_real_real ) ) )
=> ( ( A = B )
& ( B != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(1870,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_7360_gcd__nat_Otrans) ).
thf(10754,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)],[1870]) ).
thf(1148,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_4945_split__mod) ).
thf(7146,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)],[1148]) ).
thf(897,axiom,
! [A: $o,B: nat] :
( ( B @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B = zero_zero_nat )
& A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7843_bit__of__bool__iff) ).
thf(5981,plain,
! [A: $o,B: nat] :
( ( ( ( B = zero_zero_nat )
& A )
=> ( B @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B = zero_zero_nat )
& A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1634,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_1464_zero__less__one__class_Ozero__le__one) ).
thf(9395,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)],[1634]) ).
thf(1868,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( top_top_set_real @ ( A @ ( aTP_Lamm_mh @ aa_nat_fun_real_real ) @ inj_on_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9482_inj__sgn__power) ).
thf(10744,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( top_top_set_real @ ( A @ ( aTP_Lamm_mh @ aa_nat_fun_real_real ) @ inj_on_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868]) ).
thf(1863,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_7351_gcd__nat_Ostrict__iff__order) ).
thf(10727,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863]) ).
thf(138,axiom,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_diff__numeral__special_I12_J) ).
thf(2458,plain,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ minus_minus_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(505,axiom,
! [A: nat] :
( ( A @ ( zero_zero_real @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4117_pochhammer__0__left) ).
thf(4138,plain,
! [A: nat] :
( ( A @ ( zero_zero_real @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_real ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(1546,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_3495_one__less__mult) ).
thf(8946,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)],[1546]) ).
thf(361,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_1240_diff__Suc__diff__eq1) ).
thf(3457,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)],[361]) ).
thf(14,axiom,
! [A: num] :
( ( one @ ( A @ unique5055182867167087721od_nat ) )
= ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7736_divmod__algorithm__code_I2_J) ).
thf(1966,plain,
! [A: num] :
( ( one @ ( A @ unique5055182867167087721od_nat ) )
= ( zero_zero_nat @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1149,axiom,
( ( zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7614_mask__0) ).
thf(7177,plain,
( ( zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(1278,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_3015_mult__nonneg__nonneg) ).
thf(7764,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)],[1278]) ).
thf(988,axiom,
! [A: rat,B: nat] :
( ( A != zero_zero_rat )
=> ( ( B @ ( A @ power_power_rat @ aa_nat_rat ) )
!= zero_zero_rat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3748_power__not__zero) ).
thf(6408,plain,
! [A: rat,B: nat] :
( ( A != zero_zero_rat )
=> ( ( B @ ( A @ power_power_rat @ aa_nat_rat ) )
!= zero_zero_rat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1621,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3944_zero__power) ).
thf(9306,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( zero_zero_real @ power_power_real @ aa_nat_real ) )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621]) ).
thf(1576,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( gcd_gcd_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_9693_gcd__nat_OcoboundedI1) ).
thf(9092,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( C @ ( A @ ( gcd_gcd_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)],[1576]) ).
thf(1734,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_jz @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10443_ATP_Olambda__292) ).
thf(10114,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_jz @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_jz @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( C @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734]) ).
thf(1200,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_7027_dvd__minus__self) ).
thf(7395,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)],[1200]) ).
thf(11,axiom,
! [A: $o] :
( ( A @ zero_n3304061248610475627l_real @ ( abs_abs_real @ aa_real_real ) )
= ( A @ zero_n3304061248610475627l_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7480_abs__bool__eq) ).
thf(1949,plain,
! [A: $o] :
( ( A @ zero_n3304061248610475627l_real @ ( abs_abs_real @ aa_real_real ) )
= ( A @ zero_n3304061248610475627l_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(242,axiom,
! [A: num] :
( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat )
<=> ( A = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5737_numeral__eq__one__iff) ).
thf(2870,plain,
! [A: num] :
( ( ( A = one )
=> ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat ) )
& ( ( ( A @ ( numeral_numeral_nat @ aa_num_nat ) )
= one_one_nat )
=> ( A = one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(1112,axiom,
! [A: list_int,B: nat,C: int] :
( ( ( A @ size_size_list_int )
= B )
=> ( ! [D: int] :
( ( A @ set_int2 @ ( D @ member_int ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8655_replicate__eqI) ).
thf(6970,plain,
! [A: list_int,B: nat,C: int] :
( ( ( A @ size_size_list_int )
= B )
=> ( ! [D: int] :
( ( A @ set_int2 @ ( D @ member_int ) )
=> ( D = C ) )
=> ( A
= ( C @ ( B @ replicate_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(903,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_2650_mult_Oassoc) ).
thf(6013,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)],[903]) ).
thf(306,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_3456_split__div) ).
thf(3171,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)],[306]) ).
thf(915,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9030_max__Suc__numeral) ).
thf(6068,plain,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(5,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7945_xor__numerals_I8_J) ).
thf(1913,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,axiom,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1787_abs__neg__one) ).
thf(2078,plain,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(560,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_1175_Nat_Oadd__diff__assoc2) ).
thf(4419,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)],[560]) ).
thf(1204,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_1438_diff__le__mono2) ).
thf(7412,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)],[1204]) ).
thf(1394,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_3449_mult__le__cancel2) ).
thf(8260,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)],[1394]) ).
thf(378,axiom,
! [A: real,B: nat] :
( ( B @ ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( one_one_real @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3841_power__one__over) ).
thf(3533,plain,
! [A: real,B: nat] :
( ( B @ ( A @ ( one_one_real @ divide_divide_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( B @ ( A @ power_power_real @ aa_nat_real ) @ ( one_one_real @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(101,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7950_xor__nat__numerals_I2_J) ).
thf(2310,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(984,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_3007_mult__nonpos__nonneg) ).
thf(6390,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)],[984]) ).
thf(928,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_3634_gbinomial__0_I2_J) ).
thf(6137,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)],[928]) ).
thf(1241,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_6872_one__dvd) ).
thf(7589,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)],[1241]) ).
thf(1719,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_6572_dvd__0__left__iff) ).
thf(10008,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)],[1719]) ).
thf(70,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_complex @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5950_one__power2) ).
thf(2194,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_complex @ power_power_complex @ aa_nat_complex ) )
= one_one_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(595,axiom,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1726_abs__idempotent) ).
thf(4559,plain,
! [A: real] :
( ( A @ ( abs_abs_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(776,axiom,
! [A: nat,B: list_o,C: fun_o_o] :
( ( B @ size_size_list_o @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: $o] :
( ( B @ set_o2 @ ( D @ member_o ) )
=> ( D @ ( C @ aa_o_o ) ) )
=> ( A @ ( B @ nth_o @ aa_nat_o ) @ ( C @ aa_o_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6424_list__ball__nth) ).
thf(5421,plain,
! [A: nat,B: list_o,C: fun_o_o] :
( ( B @ size_size_list_o @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ! [D: $o] :
( ( B @ set_o2 @ ( D @ member_o ) )
=> ( D @ ( C @ aa_o_o ) ) )
=> ( A @ ( B @ nth_o @ aa_nat_o ) @ ( C @ aa_o_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1304,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_6497_binomial__0__Suc) ).
thf(7889,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)],[1304]) ).
thf(1829,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_17_less__Suc0) ).
thf(10541,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)],[1829]) ).
thf(1045,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_1566_less__diff__iff) ).
thf(6674,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)],[1045]) ).
thf(499,axiom,
! [A: nat] :
( ( A @ ( zero_zero_rat @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= ( @+[B: rat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_rat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_rat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4118_pochhammer__0__left) ).
thf(4102,plain,
! [A: nat] :
( ( A @ ( zero_zero_rat @ comm_s4028243227959126397er_rat @ aa_nat_rat ) )
= ( @+[B: rat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_rat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_rat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(68,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( B @ divide_divide_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2988_nonzero__minus__divide__right) ).
thf(2187,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( B @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( B @ divide_divide_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(335,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7796_and__numerals_I8_J) ).
thf(3346,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(330,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7819_bit__mod__2__iff) ).
thf(3320,plain,
! [A: nat,B: nat] :
( ( ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B = zero_zero_nat ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(569,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_573_add__eq__if) ).
thf(4463,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)],[569]) ).
thf(78,axiom,
! [A: rat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat )
<=> ( A = zero_zero_rat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5793_zero__eq__power2) ).
thf(2226,plain,
! [A: rat] :
( ( ( A = zero_zero_rat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_rat @ aa_nat_rat ) )
= zero_zero_rat )
=> ( A = zero_zero_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(788,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_3688_of__nat__le__of__nat__power__cancel__iff) ).
thf(5485,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)],[788]) ).
thf(34,axiom,
! [A: set_complex,B: fun_complex_nat,C: fun_complex_nat] :
( ! [D: complex] :
( ( A @ ( D @ member_complex ) )
=> ( ( D @ ( C @ aa_complex_nat ) @ ( D @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( A @ ( C @ groups861055069439313189ex_nat ) @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8338_prod__mono) ).
thf(2071,plain,
! [A: set_complex,B: fun_complex_nat,C: fun_complex_nat] :
( ! [D: complex] :
( ( A @ ( D @ member_complex ) )
=> ( ( D @ ( C @ aa_complex_nat ) @ ( D @ ( B @ aa_complex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( D @ ( B @ aa_complex_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) )
=> ( A @ ( C @ groups861055069439313189ex_nat ) @ ( A @ ( B @ groups861055069439313189ex_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(186,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7530_bits__1__div__exp) ).
thf(2658,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1456,axiom,
! [A: num,B: num] :
( ( A = B )
<=> ( ( A @ ( nat_of_num @ aa_num_nat ) )
= ( B @ ( nat_of_num @ aa_num_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10007_num__eq__iff) ).
thf(8579,plain,
! [A: num,B: num] :
( ( ( ( A @ ( nat_of_num @ aa_num_nat ) )
= ( B @ ( nat_of_num @ aa_num_nat ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( nat_of_num @ aa_num_nat ) )
= ( B @ ( nat_of_num @ aa_num_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456]) ).
thf(1794,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_93_nat__neq__iff) ).
thf(10347,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)],[1794]) ).
thf(706,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_243_diff__add__zero) ).
thf(5068,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)],[706]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( times_times_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7589_exp__div__exp__eq) ).
thf(2792,plain,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat )
@ ( ( ( A @ ( B @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( times_times_nat @ aa_nat_fun_nat_nat )
@ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(1435,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_1009_diff__Suc__eq__diff__pred) ).
thf(8469,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)],[1435]) ).
thf(488,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_215_diff__0__eq__0) ).
thf(4061,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)],[488]) ).
thf(1056,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 @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7501_Suc__0__mod__eq) ).
thf(6711,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 @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(393,axiom,
! [A: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5965_less__exp) ).
thf(3593,plain,
! [A: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[393]) ).
thf(599,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4085_pochhammer__of__nat) ).
thf(4574,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= ( B @ ( A @ ( comm_s4663373288045622133er_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(1346,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_1443_le__diff__iff) ).
thf(8075,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)],[1346]) ).
thf(41,axiom,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4679_sgn__minus__1) ).
thf(2098,plain,
( ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(692,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_4618_mod__add__cong) ).
thf(5008,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)],[692]) ).
thf(906,axiom,
! [A: real,B: nat] :
( ( B @ ( A @ aTP_Lamm_nf @ aa_nat_real ) )
= ( A @ ( B @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10287_ATP_Olambda__136) ).
thf(6023,plain,
! [A: real,B: nat] :
( ( B @ ( A @ aTP_Lamm_nf @ aa_nat_real ) )
= ( A @ ( B @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(1098,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_1371_add__mono__thms__linordered__semiring_I3_J) ).
thf(6913,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)],[1098]) ).
thf(1470,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 @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7522_take__bit__of__1) ).
thf(8634,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 @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470]) ).
thf(1845,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_38_Suc__less__eq2) ).
thf(10627,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)],[1845]) ).
thf(502,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_157_add__eq__0__iff__both__eq__0) ).
thf(4121,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)],[502]) ).
thf(452,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7662_Suc__mask__eq__exp) ).
thf(3911,plain,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(1738,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_9_less__zeroE) ).
thf(10135,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)],[1738]) ).
thf(198,axiom,
( ( one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5964_nat__1__add__1) ).
thf(2707,plain,
( ( one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(628,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_6470_Suc__mod__eq__add3__mod) ).
thf(4710,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[628]) ).
thf(950,axiom,
! [A: real] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4248_real__root__Suc__0) ).
thf(6230,plain,
! [A: real] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1082,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_6524_choose__mult__lemma) ).
thf(6829,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)],[1082]) ).
thf(90,axiom,
! [A: real] :
( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_neg__equal__0__iff__equal) ).
thf(2273,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= zero_zero_real ) )
& ( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1066,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_4072_nat__zero__less__power__iff) ).
thf(6753,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)],[1066]) ).
thf(1080,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_nr @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9615_Least__Suc) ).
thf(6818,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_nr @ ord_Least_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(1746,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_1328_le__numeral__extra_I3_J) ).
thf(10169,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)],[1746]) ).
thf(422,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5949_one__power2) ).
thf(3789,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(237,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_3457_dividend__less__div__times) ).
thf(2855,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)],[237]) ).
thf(1507,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_6646_unit__div__1__unit) ).
thf(8780,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)],[1507]) ).
thf(748,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( gcd_lcm_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_9961_lcm__1__iff__nat) ).
thf(5272,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( gcd_lcm_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)],[748]) ).
thf(94,axiom,
( ( $true @ zero_n3304061248610475627l_real )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7469_of__bool__eq_I2_J) ).
thf(2290,plain,
( ( $true @ zero_n3304061248610475627l_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1095,axiom,
! [A: real,B: nat,C: real] :
( ( C @ ( B @ replicate_real ) @ set_real2 @ ( A @ member_real ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8560_in__set__replicate) ).
thf(6893,plain,
! [A: real,B: nat,C: real] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_real ) @ set_real2 @ ( A @ member_real ) ) )
& ( ( C @ ( B @ replicate_real ) @ set_real2 @ ( A @ member_real ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(165,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 ) )
=> ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5859_power2__eq__iff__nonneg) ).
thf(2554,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 ) )
=> ( ( ( A = B )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1878,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_1_neq0__conv) ).
thf(10789,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)],[1878]) ).
thf(346,axiom,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99__C3_Ohyps_C_I4_J) ).
thf(3383,plain,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(763,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ob @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( B @ ( 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_10432_ATP_Olambda__281) ).
thf(5351,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( C @ ( 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 @ ( A @ aTP_Lamm_ob @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_ob @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( 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)],[763]) ).
thf(1326,axiom,
! [A: nat,B: num,C: nat] :
( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( A
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5229_real__of__nat__eq__numeral__power__cancel__iff) ).
thf(7996,plain,
! [A: nat,B: num,C: nat] :
( ( ( A
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A
= ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).
thf(1809,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_91_less__not__refl2) ).
thf(10468,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)],[1809]) ).
thf(876,axiom,
! [A: $o] : ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7551_zero__less__eq__of__bool) ).
thf(5899,plain,
! [A: $o] : ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(777,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_6848_dvd__mult) ).
thf(5426,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)],[777]) ).
thf(1074,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4268_fact__Suc) ).
thf(6790,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) )
= ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(483,axiom,
( ( zero_zero_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_of__nat__0) ).
thf(4042,plain,
( ( zero_zero_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(1538,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_1172_diff__is__0__eq) ).
thf(8912,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)],[1538]) ).
thf(1787,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_15_lessI) ).
thf(10325,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)],[1787]) ).
thf(1625,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_2294_dual__order_Ostrict__iff__order) ).
thf(9343,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)],[1625]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4139_pochhammer__of__nat__eq__0__lemma) ).
thf(3104,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1840,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_7354_gcd__nat_Ostrict__trans2) ).
thf(10610,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)],[1840]) ).
thf(403,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) ) )
| ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
| ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7316_even__mult__exp__div__exp__iff) ).
thf(3630,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) ) )
| ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
| ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) ) )
| ( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
| ( B @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(369,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7794_and__numerals_I2_J) ).
thf(3501,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(266,axiom,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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_7669_mask__eq__exp__minus__1) ).
thf(3003,plain,
! [A: nat] :
( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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)],[266]) ).
thf(1196,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_1480_add__increasing2) ).
thf(7384,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)],[1196]) ).
thf(476,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6140_bits__stable__imp__add__self) ).
thf(4010,plain,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(374,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_504_linordered__semidom__class_Oadd__diff__inverse) ).
thf(3516,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)],[374]) ).
thf(300,axiom,
( ( zero_zero_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_int__ops_I1_J) ).
thf(3136,plain,
( ( zero_zero_nat @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(341,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_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 = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7321_take__bit__rec) ).
thf(3368,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_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 = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(1389,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_7095_unit__imp__mod__eq__0) ).
thf(8240,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)],[1389]) ).
thf(87,axiom,
! [A: num] :
( ( A != one )
=> ( ! [B: num] :
( A
!= ( B @ ( bit0 @ aa_num_num ) ) )
=> ~ ! [B: num] :
( A
!= ( B @ ( bit1 @ aa_num_num ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6410_num_Oexhaust) ).
thf(2262,plain,
! [A: num] :
( ( A != one )
=> ( ! [B: num] :
( A
!= ( B @ ( bit0 @ aa_num_num ) ) )
=> ~ ! [B: num] :
( A
!= ( B @ ( bit1 @ aa_num_num ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(883,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_7037_bezout1__nat) ).
thf(5922,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)],[883]) ).
thf(1799,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_2278_order_Ostrict__iff__not) ).
thf(10400,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)],[1799]) ).
thf(1875,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_8567_nth__replicate) ).
thf(10777,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)],[1875]) ).
thf(258,axiom,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int @ aa_nat_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3589_power__one) ).
thf(2956,plain,
! [A: nat] :
( ( A @ ( one_one_int @ power_power_int @ aa_nat_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1685,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_982_not__one__less__zero) ).
thf(9718,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)],[1685]) ).
thf(1648,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_990_less__numeral__extra_I1_J) ).
thf(9470,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)],[1648]) ).
thf(1021,axiom,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_of__nat__0) ).
thf(6554,plain,
( ( zero_zero_nat @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(574,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7581_exp__mod__exp) ).
thf(4478,plain,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(118,axiom,
! [A: real] :
( ( A @ ( zero_zero_real @ minus_minus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_diff__0) ).
thf(2362,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ minus_minus_real @ aa_real_real ) )
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(638,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_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 ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8016_and__nat__unfold) ).
thf(4745,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ~ ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( C
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_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 ) ) ) )
& ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(137,axiom,
! [A: real,B: real] :
( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) )
<=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3208_divide__eq__minus__1__iff) ).
thf(2447,plain,
! [A: real,B: real] :
( ( ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B != zero_zero_real ) )
=> ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( ( B @ ( A @ divide_divide_real @ aa_real_real ) )
= ( one_one_real @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
& ( B != zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(143,axiom,
( ( zero_zero_real @ ( uminus_uminus_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_add_Oinverse__neutral) ).
thf(2475,plain,
( ( zero_zero_real @ ( uminus_uminus_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(606,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_440_plus__nat_Oadd__0) ).
thf(4602,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)],[606]) ).
thf(993,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_7008_mod__0__imp__dvd) ).
thf(6430,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)],[993]) ).
thf(728,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_6286_size__neq__size__imp__neq) ).
thf(5162,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)],[728]) ).
thf(773,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_2551_div__self) ).
thf(5408,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)],[773]) ).
thf(1153,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_7130_mod__eq__dvd__iff__nat) ).
thf(7187,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)],[1153]) ).
thf(1886,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_2043_order_Ostrict__trans) ).
thf(10828,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)],[1886]) ).
thf(1682,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ov @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10430_ATP_Olambda__279) ).
thf(9701,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_ov @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_ov @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( B @ ( C @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682]) ).
thf(515,axiom,
! [A: real] :
( ( zero_zero_nat @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4074_pochhammer__0) ).
thf(4175,plain,
! [A: real] :
( ( zero_zero_nat @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1518,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_6884_dvd__add__right__iff) ).
thf(8837,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)],[1518]) ).
thf(1541,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_4720_unique__euclidean__semiring__numeral__class_Omod__less) ).
thf(8925,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)],[1541]) ).
thf(1658,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_96_not__less__zero) ).
thf(9510,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)],[1658]) ).
thf(183,axiom,
! [A: complex,B: set_complex,C: set_complex] :
( ( B @ ( A @ member_complex ) )
=> ( ~ ( C @ ( A @ member_complex ) )
=> ( ( C @ ( A @ insert_complex ) @ ( B @ minus_811609699411566653omplex ) @ finite_card_complex )
= ( one_one_nat @ ( C @ ( B @ minus_811609699411566653omplex ) @ finite_card_complex @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7934_card__Diff__insert) ).
thf(2648,plain,
! [A: complex,B: set_complex,C: set_complex] :
( ( B @ ( A @ member_complex ) )
=> ( ~ ( C @ ( A @ member_complex ) )
=> ( ( C @ ( A @ insert_complex ) @ ( B @ minus_811609699411566653omplex ) @ finite_card_complex )
= ( one_one_nat @ ( C @ ( B @ minus_811609699411566653omplex ) @ finite_card_complex @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(354,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3513_unique__euclidean__semiring__with__nat__class_Oof__nat__div) ).
thf(3430,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_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 ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(395,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_3492_div__if) ).
thf(3598,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)],[395]) ).
thf(1184,axiom,
! [A: nat] : ( A @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4371_fact__le__power) ).
thf(7312,plain,
! [A: nat] : ( A @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( A @ ( semiri1408675320244567234ct_nat @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).
thf(140,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5942_zero__power2) ).
thf(2462,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_int @ power_power_int @ aa_nat_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1127,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_3701_power__increasing__iff) ).
thf(7039,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)],[1127]) ).
thf(1276,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 ) @ ( $false @ case_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8979_less__eq__nat_Osimps_I2_J) ).
thf(7747,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ ( $false @ case_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_eq_nat @ aa_nat_fun_nat_o ) @ ( $false @ case_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).
thf(1857,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_7_not__gr0) ).
thf(10695,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)],[1857]) ).
thf(1605,axiom,
! [A: nat,B: nat] :
( ( B @ extended_enat2 @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9861_enat__ord__simps_I2_J) ).
thf(9223,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ extended_enat2 @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) ) )
& ( ( B @ extended_enat2 @ ( A @ extended_enat2 @ ord_le72135733267957522d_enat ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605]) ).
thf(989,axiom,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o] :
( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) )
<=> ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6441_all__set__conv__all__nth) ).
thf(6412,plain,
! [A: list_VEBT_VEBT,B: fun_VEBT_VEBT_o] :
( ( ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT ) )
=> ( C @ ( B @ aa_VEBT_VEBT_o ) ) )
=> ! [C: nat] :
( ( A @ size_s6755466524823107622T_VEBT @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_VEBT_VEBT ) @ ( B @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(1013,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( gcd_gcd_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_9973_prod__gcd__lcm__nat) ).
thf(6521,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_lcm_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( gcd_gcd_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)],[1013]) ).
thf(954,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_4512_mod__mult__self2__is__0) ).
thf(6252,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)],[954]) ).
thf(1811,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( aTP_Lamm_nb @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9425_mult__nat__right__at__top) ).
thf(10483,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( at_top_nat @ ( at_top_nat @ ( A @ ( aTP_Lamm_nb @ aa_nat_fun_nat_nat ) @ filterlim_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811]) ).
thf(337,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( A @ ( pred_numeral @ aa_num_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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_7603_mask__numeral) ).
thf(3351,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= ( A @ ( pred_numeral @ aa_num_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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)],[337]) ).
thf(869,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_6568_nat__dvd__1__iff__1) ).
thf(5869,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)],[869]) ).
thf(472,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_217_diff__diff__left) ).
thf(3993,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)],[472]) ).
thf(247,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_151_add__cancel__right__left) ).
thf(2902,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)],[247]) ).
thf(1673,axiom,
! [A: extended_enat,B: nat] :
( ( B @ ( A @ aTP_Lamm_pf @ aa_nat_o ) )
<=> ( A @ ( $true @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ extended_case_enat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10184_ATP_Olambda__33) ).
thf(9660,plain,
! [A: extended_enat,B: nat] :
( ( ( A @ ( $true @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ extended_case_enat_o ) ) )
=> ( B @ ( A @ aTP_Lamm_pf @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_pf @ aa_nat_o ) )
=> ( A @ ( $true @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ extended_case_enat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673]) ).
thf(719,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_3977_power__decreasing) ).
thf(5119,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)],[719]) ).
thf(492,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_1526_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(4074,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)],[492]) ).
thf(814,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_6900_dvd__div__eq__iff) ).
thf(5590,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)],[814]) ).
thf(566,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8135_take__bit__push__bit) ).
thf(4446,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(797,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_6917_dvd__mod__iff) ).
thf(5517,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)],[797]) ).
thf(96,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_7197_fold__atLeastAtMost__nat_Osimps) ).
thf(2294,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)],[96]) ).
thf(835,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_3106_mult__pos__neg) ).
thf(5672,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)],[835]) ).
thf(207,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( 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_6017_diff__le__diff__pow) ).
thf(2739,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( 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)],[207]) ).
thf(1202,axiom,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7625_mask__Suc__0) ).
thf(7406,plain,
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).
thf(1091,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_185_add__less__cancel__right) ).
thf(6871,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)],[1091]) ).
thf(1135,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_4114_power__gt__expt) ).
thf(7080,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)],[1135]) ).
thf(1286,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9668_gcd__0__left__nat) ).
thf(7804,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).
thf(1696,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_2346_linorder__not__less) ).
thf(9787,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)],[1696]) ).
thf(1595,axiom,
! [A: nat,B: nat] :
? [C: nat,D: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9713_bezout__gcd__nat_H) ).
thf(9162,plain,
! [A: nat,B: nat] :
? [C: nat,D: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
| ( ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
& ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595]) ).
thf(19,axiom,
( ( one @ ( size_num @ aa_num_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7661_num_Osize__gen_I1_J) ).
thf(1994,plain,
( ( one @ ( size_num @ aa_num_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1146,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_4665_mod__eq__self__iff__div__eq__0) ).
thf(7135,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)],[1146]) ).
thf(479,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_122_add__left__cancel) ).
thf(4025,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)],[479]) ).
thf(609,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6091_div__2__gt__zero) ).
thf(4619,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(751,axiom,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
<=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8555_Ball__set__replicate) ).
thf(5287,plain,
! [A: nat,B: vEBT_VEBT,C: fun_VEBT_VEBT_o] :
( ( ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) ) )
& ( ! [D: vEBT_VEBT] :
( ( B @ ( A @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( D @ member_VEBT_VEBT ) )
=> ( D @ ( C @ aa_VEBT_VEBT_o ) ) )
=> ( ( A = zero_zero_nat )
| ( B @ ( C @ aa_VEBT_VEBT_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(131,axiom,
! [A: int] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5794_zero__eq__power2) ).
thf(2421,plain,
! [A: int] :
( ( ( A = zero_zero_int )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_int @ aa_nat_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(1407,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_6287_size__neq__size__imp__neq) ).
thf(8324,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)],[1407]) ).
thf(413,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_3458_dividend__less__times__div) ).
thf(3705,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)],[413]) ).
thf(158,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_real @ power_power_real @ aa_nat_real ) )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5948_one__power2) ).
thf(2534,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_real @ power_power_real @ aa_nat_real ) )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1866,axiom,
! [A: nat,B: real,C: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( C @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4255_real__root__eq__iff) ).
thf(10733,plain,
! [A: nat,B: real,C: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( C @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) ) ) )
& ( ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= ( C @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866]) ).
thf(1600,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_6523_binomial__symmetric) ).
thf(9183,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)],[1600]) ).
thf(363,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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_7918_xor__Suc__0__eq) ).
thf(3464,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat )
@ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( 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)],[363]) ).
thf(587,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6676_even__Suc__Suc__iff) ).
thf(4523,plain,
! [A: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(659,axiom,
! [A: nat,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se2925701944663578781it_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_7283_take__bit__Suc__bit1) ).
thf(4843,plain,
! [A: nat,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit_se2925701944663578781it_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)],[659]) ).
thf(1156,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_410_add__mono__thms__linordered__field_I1_J) ).
thf(7210,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)],[1156]) ).
thf(406,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
<=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_7385_take__bit__nat__eq__self__iff) ).
thf(3658,plain,
! [A: nat,B: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) )
& ( ( ( B @ ( A @ ( bit_se2925701944663578781it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[406]) ).
thf(86,axiom,
! [A: nat,B: real] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6707_Parity_Oring__1__class_Opower__minus__even) ).
thf(2258,plain,
! [A: nat,B: real] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( uminus_uminus_real @ aa_real_real ) @ power_power_real @ aa_nat_real ) )
= ( A @ ( B @ power_power_real @ aa_nat_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(702,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_4622_mod__add__left__eq) ).
thf(5051,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)],[702]) ).
thf(122,axiom,
! [A: real] :
( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= A )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_neg__equal__zero) ).
thf(2374,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= A ) )
& ( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= A )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(1129,axiom,
! [A: list_int,B: list_int] :
( ( ( A @ size_size_list_int )
= ( B @ size_size_list_int ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_int @ aa_nat_int ) )
= ( C @ ( B @ nth_int @ aa_nat_int ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6401_nth__equalityI) ).
thf(7048,plain,
! [A: list_int,B: list_int] :
( ( ( A @ size_size_list_int )
= ( B @ size_size_list_int ) )
=> ( ! [C: nat] :
( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ nth_int @ aa_nat_int ) )
= ( C @ ( B @ nth_int @ aa_nat_int ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(93,axiom,
! [A: num,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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_7957_xor__numerals_I6_J) ).
thf(2287,plain,
! [A: num,B: num] :
( ( B @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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)],[93]) ).
thf(1608,axiom,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5470_zero__less__numeral) ).
thf(9239,plain,
! [A: num] : ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608]) ).
thf(1256,axiom,
! [A: nat,B: list_set_nat] :
( ( B @ size_s3254054031482475050et_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_set_nat2 @ ( A @ ( B @ nth_set_nat @ aa_nat_set_nat ) @ member_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6418_nth__mem) ).
thf(7649,plain,
! [A: nat,B: list_set_nat] :
( ( B @ size_s3254054031482475050et_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_set_nat2 @ ( A @ ( B @ nth_set_nat @ aa_nat_set_nat ) @ member_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).
thf(764,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_3985_power__eq__iff__eq__base) ).
thf(5357,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)],[764]) ).
thf(154,axiom,
! [A: num,B: num,C: nat] :
( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4995_add__numeral__left) ).
thf(2517,plain,
! [A: num,B: num,C: nat] :
( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_num @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1382,axiom,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8435_suminf__nonneg) ).
thf(8209,plain,
! [A: fun_nat_nat] :
( ( A @ summable_nat )
=> ( ! [B: nat] : ( B @ ( A @ aa_nat_nat ) @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ suminf_nat @ ( zero_zero_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).
thf(13,axiom,
! [A: real,B: real] :
( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
<=> ( B
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_equation__minus__iff) ).
thf(1957,plain,
! [A: real,B: real] :
( ( ( B
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) ) )
& ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
=> ( B
= ( A @ ( uminus_uminus_real @ aa_real_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(625,axiom,
( ( zero_zero_real @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4898_sgn__zero) ).
thf(4687,plain,
( ( zero_zero_real @ ( sgn_sgn_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(124,axiom,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1760_abs__minus__cancel) ).
thf(2385,plain,
! [A: real] :
( ( A @ ( uminus_uminus_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( A @ ( abs_abs_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(440,axiom,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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_7821_and__numerals_I7_J) ).
thf(3860,plain,
! [A: num,B: num] :
( ( B @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_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)],[440]) ).
thf(622,axiom,
! [A: $o] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7528_of__bool__half__eq__0) ).
thf(4670,plain,
! [A: $o] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(1049,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_1558_Suc__le__lessD) ).
thf(6693,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)],[1049]) ).
thf(1606,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_462_less__imp__of__nat__less) ).
thf(9229,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)],[1606]) ).
thf(996,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_6989_div__unit__dvd__iff) ).
thf(6439,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)],[996]) ).
thf(1081,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_1559_le__less__Suc__eq) ).
thf(6822,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)],[1081]) ).
thf(855,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_3220_mult__le__less__imp__less) ).
thf(5796,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)],[855]) ).
thf(651,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_2805_distrib__right) ).
thf(4811,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)],[651]) ).
thf(171,axiom,
( ( one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5791_one__add__one) ).
thf(2587,plain,
( ( one_one_nat @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(396,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10018_nat__of__num_Osimps_I3_J) ).
thf(3601,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( nat_of_num @ aa_num_nat ) )
= ( A @ ( nat_of_num @ aa_num_nat ) @ ( A @ ( nat_of_num @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1401,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_6969_mult__unit__dvd__iff_H) ).
thf(8296,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)],[1401]) ).
thf(1261,axiom,
! [A: list_o,B: nat,C: $o] :
( ( ( A @ size_size_list_o )
= B )
=> ( ! [D: $o] :
( ( A @ set_o2 @ ( D @ member_o ) )
=> ( D
<=> C ) )
=> ( A
= ( C @ ( B @ replicate_o ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8653_replicate__eqI) ).
thf(7666,plain,
! [A: list_o,B: nat,C: $o] :
( ( ( A @ size_size_list_o )
= B )
=> ( ! [D: $o] :
( ( A @ set_o2 @ ( D @ member_o ) )
=> ( ( C
=> D )
& ( D
=> C ) ) )
=> ( A
= ( C @ ( B @ replicate_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).
thf(604,axiom,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6758_even__succ__div__two) ).
thf(4596,plain,
! [A: nat] :
( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(1837,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_107_less__numeral__extra_I3_J) ).
thf(10601,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)],[1837]) ).
thf(446,axiom,
! [A: fun_list_nat_nat,B: set_list_nat] :
( ( B @ ( A @ aTP_Lamm_in @ groups4396056296759096172at_nat ) )
= ( B @ finite_card_list_nat @ ( B @ ( A @ groups4396056296759096172at_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8845_sum__Suc) ).
thf(3882,plain,
! [A: fun_list_nat_nat,B: set_list_nat] :
( ( B @ ( A @ aTP_Lamm_in @ groups4396056296759096172at_nat ) )
= ( B @ finite_card_list_nat @ ( B @ ( A @ groups4396056296759096172at_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(976,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_6983_div__mult__swap) ).
thf(6361,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)],[976]) ).
thf(1294,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_1588_add__strict__increasing2) ).
thf(7836,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)],[1294]) ).
thf(227,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_2817_crossproduct__noteq) ).
thf(2815,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)],[227]) ).
thf(206,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_4772_minus__mod__eq__mult__div) ).
thf(2736,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)],[206]) ).
thf(24,axiom,
! [A: complex] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex )
<=> ( A = zero_zero_complex ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5797_zero__eq__power2) ).
thf(2008,plain,
! [A: complex] :
( ( ( A = zero_zero_complex )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex )
=> ( A = zero_zero_complex ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1490,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_2769_no__zero__divisors) ).
thf(8720,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)],[1490]) ).
thf(332,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6076_div__exp__eq) ).
thf(3337,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(799,axiom,
suc @ order_mono_nat_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9363_mono__Suc) ).
thf(5527,plain,
suc @ order_mono_nat_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(1819,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7710_bot__nat__def) ).
thf(10515,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819]) ).
thf(1566,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_1355_add__left__mono) ).
thf(9051,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)],[1566]) ).
thf(816,axiom,
! [A: nat] :
( ( A @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6109_mult__numeral__1) ).
thf(5601,plain,
! [A: nat] :
( ( A @ ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(1167,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_9024_max__nat_Oleft__neutral) ).
thf(7248,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)],[1167]) ).
thf(1570,axiom,
! [A: list_int,B: fun_int_o,C: nat] :
( ! [D: int] :
( ( A @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( B @ aa_int_o ) ) )
=> ( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6341_inthall) ).
thf(9070,plain,
! [A: list_int,B: fun_int_o,C: nat] :
( ! [D: int] :
( ( A @ set_int2 @ ( D @ member_int ) )
=> ( D @ ( B @ aa_int_o ) ) )
=> ( ( A @ size_size_list_int @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_int @ aa_nat_int ) @ ( B @ aa_int_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570]) ).
thf(1646,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_2210_leD) ).
thf(9463,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)],[1646]) ).
thf(568,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
<=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4144_pochhammer__of__nat__eq__0__iff) ).
thf(4455,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
= zero_zero_real )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(1543,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_4167_pochhammer__product) ).
thf(8933,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)],[1543]) ).
thf(328,axiom,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7834_not__bit__1__Suc) ).
thf(3309,plain,
! [A: nat] :
~ ( A @ ( suc @ aa_nat_nat ) @ ( one_one_int @ bit_se1146084159140164899it_int @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(1725,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_6398_nth__equalityI) ).
thf(10036,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)],[1725]) ).
thf(614,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6553_choose__two) ).
thf(4631,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( A @ ( minus_minus_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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(956,axiom,
! [A: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat )
<=> ~ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7454_of__bool__eq__0__iff) ).
thf(6258,plain,
! [A: $o] :
( ( ~ A
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(1764,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_2073_order__less__asym) ).
thf(10237,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)],[1764]) ).
thf(1698,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_13_Suc__less__eq) ).
thf(9795,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)],[1698]) ).
thf(1104,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_1367_add__mono__thms__linordered__semiring_I2_J) ).
thf(6929,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)],[1104]) ).
thf(1108,axiom,
! [A: nat,B: list_int] :
( ( B @ size_size_list_int @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_int2 @ ( A @ ( B @ nth_int @ aa_nat_int ) @ member_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6422_nth__mem) ).
thf(6952,plain,
! [A: nat,B: list_int] :
( ( B @ size_size_list_int @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ set_int2 @ ( A @ ( B @ nth_int @ aa_nat_int ) @ member_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(1851,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_2063_dual__order_Ostrict__implies__not__eq) ).
thf(10649,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)],[1851]) ).
thf(1282,axiom,
! [A: int] :
( ( zero_zero_int = A )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__reorient) ).
thf(7772,plain,
! [A: int] :
( ( ( A = zero_zero_int )
=> ( zero_zero_int = A ) )
& ( ( zero_zero_int = A )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).
thf(211,axiom,
! [A: nat,B: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se2925701944663578781it_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_7386_take__bit__nat__less__exp) ).
thf(2751,plain,
! [A: nat,B: nat] : ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( bit_se2925701944663578781it_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(463,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5812_add__2__eq__Suc_H) ).
thf(3956,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1517,axiom,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( B @ ( sgn_sgn_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4791_sgn__root) ).
thf(8833,plain,
! [A: nat,B: real] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) @ ( sgn_sgn_real @ aa_real_real ) )
= ( B @ ( sgn_sgn_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517]) ).
thf(516,axiom,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7805_and__numerals_I5_J) ).
thf(4178,plain,
! [A: num] :
( ( one_one_nat @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(449,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5816_mod2__Suc__Suc) ).
thf(3897,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(597,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_6609_take__bit__of__0) ).
thf(4565,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)],[597]) ).
thf(938,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9712_bezout__nat) ).
thf(6169,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ? [C: nat,D: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(549,axiom,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4570_abs__sgn__eq__1) ).
thf(4350,plain,
! [A: real] :
( ( A != zero_zero_real )
=> ( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(1444,axiom,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int @ aa_nat_int ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3611_power__one__right) ).
thf(8521,plain,
! [A: int] :
( ( one_one_nat @ ( A @ power_power_int @ aa_nat_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444]) ).
thf(1792,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_2053_dual__order_Ostrict__trans) ).
thf(10340,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)],[1792]) ).
thf(1152,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_1429_trans__le__add1) ).
thf(7184,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)],[1152]) ).
thf(109,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7926_xor_Oright__neutral) ).
thf(2334,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(843,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= B )
& ( B @ ( C @ ( A @ ( gcd_gcd_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_9689_gcd__nat_Ostrict__coboundedI1) ).
thf(5709,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A != B )
& ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( ( C @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= B )
& ( B @ ( C @ ( A @ ( gcd_gcd_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)],[843]) ).
thf(670,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_1523_add__le__add__imp__diff__le) ).
thf(4895,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)],[670]) ).
thf(562,axiom,
! [A: nat,B: nat] :
( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_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_7300_even__mask__div__iff_H) ).
thf(4427,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one_one_nat @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(1665,axiom,
! [A: $o,B: $o,C: $o,D: $o,E: $o,F: $o,G: $o,H: $o] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ char2 ) ) ) ) ) ) ) @ size_char )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9910_char_Osize__gen) ).
thf(9541,plain,
! [A: $o,B: $o,C: $o,D: $o,E: $o,F: $o,G: $o,H: $o] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ char2 ) ) ) ) ) ) ) @ size_char )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665]) ).
thf(683,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_1532_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(4968,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)],[683]) ).
thf(475,axiom,
! [A: real] :
( ( A @ ( zero_zero_real @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2446_div__0) ).
thf(4007,plain,
! [A: real] :
( ( A @ ( zero_zero_real @ divide_divide_real @ aa_real_real ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(1526,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_7180_power__dvd__imp__le) ).
thf(8869,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)],[1526]) ).
thf(1424,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_1630_ex__least__nat__less) ).
thf(8424,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)],[1424]) ).
thf(1057,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6513_le__Suc__numeral) ).
thf(6714,plain,
! [A: nat,B: num] :
( ( ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(197,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6514_diff__Suc__numeral) ).
thf(2704,plain,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( pred_numeral @ aa_num_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1341,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7966_bit__Suc__0__iff) ).
thf(8051,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).
thf(1617,axiom,
! [A: fun_list_VEBT_VEBT_o,B: list_VEBT_VEBT] :
( ! [C: list_VEBT_VEBT] :
( ! [D: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( D @ size_s6755466524823107622T_VEBT @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( C @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ aa_list_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6291_length__induct) ).
thf(9282,plain,
! [A: fun_list_VEBT_VEBT_o,B: list_VEBT_VEBT] :
( ! [C: list_VEBT_VEBT] :
( ! [D: list_VEBT_VEBT] :
( ( C @ size_s6755466524823107622T_VEBT @ ( D @ size_s6755466524823107622T_VEBT @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( D @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( C @ ( A @ aa_list_VEBT_VEBT_o ) ) )
=> ( B @ ( A @ aa_list_VEBT_VEBT_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617]) ).
thf(810,axiom,
! [A: $o] : ( one_one_nat @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7556_of__bool__less__eq__one) ).
thf(5564,plain,
! [A: $o] : ( one_one_nat @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(849,axiom,
! [A: int,B: nat,C: int] :
( ( C @ ( B @ replicate_int ) @ set_int2 @ ( A @ member_int ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8563_in__set__replicate) ).
thf(5741,plain,
! [A: int,B: nat,C: int] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_int ) @ set_int2 @ ( A @ member_int ) ) )
& ( ( C @ ( B @ replicate_int ) @ set_int2 @ ( A @ member_int ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1810,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_78_All__less__Suc2) ).
thf(10472,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)],[1810]) ).
thf(1061,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_2426_mult__cancel__left) ).
thf(6729,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)],[1061]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
<=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3602_of__nat__eq__of__nat__power__cancel__iff) ).
thf(2913,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_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 ) )
= ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(127,axiom,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6096_numeral__Bit0) ).
thf(2404,plain,
! [A: num] :
( ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(1176,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_6946_pinf_I10_J) ).
thf(7280,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).
thf(1395,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9698_gcd__nat_Oorder__iff) ).
thf(8268,plain,
! [A: nat,B: nat] :
( ( ( A
= ( B @ ( A @ ( gcd_gcd_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 ) )
=> ( A
= ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).
thf(77,axiom,
! [A: real] :
( ( zero_zero_real @ ( A @ minus_minus_real @ aa_real_real ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_diff__0__right) ).
thf(2223,plain,
! [A: real] :
( ( zero_zero_real @ ( A @ minus_minus_real @ aa_real_real ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(221,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_207_add__diff__cancel__right_H) ).
thf(2795,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)],[221]) ).
thf(826,axiom,
! [A: list_set_nat] : ( A @ size_s3254054031482475050et_nat @ ( A @ set_set_nat2 @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6305_card__length) ).
thf(5642,plain,
! [A: list_set_nat] : ( A @ size_s3254054031482475050et_nat @ ( A @ set_set_nat2 @ finite_card_set_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(519,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_3549_nat__eq__add__iff1) ).
thf(4193,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)],[519]) ).
thf(985,axiom,
! [A: nat,B: num,C: nat] :
( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5318_of__nat__less__numeral__power__cancel__iff) ).
thf(6393,plain,
! [A: nat,B: num,C: nat] :
( ( ( C @ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[985]) ).
thf(1573,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_6674_unit__div__mult__self) ).
thf(9083,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)],[1573]) ).
thf(436,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_2448_div__0) ).
thf(3843,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)],[436]) ).
thf(1812,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_2318_order_Ostrict__implies__order) ).
thf(10485,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)],[1812]) ).
thf(426,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7878_one__and__eq) ).
thf(3805,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(780,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_4927_mod__if) ).
thf(5440,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)],[780]) ).
thf(1262,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_7022_dvd__minus__mod) ).
thf(7684,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)],[1262]) ).
thf(1876,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_valid__0__not) ).
thf(10781,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ vEBT_invar_vebt @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876]) ).
thf(1008,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_3524_nat__mult__less__cancel__disj) ).
thf(6503,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)],[1008]) ).
thf(1730,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_2408_nat__descend__induct) ).
thf(10092,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)],[1730]) ).
thf(1157,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_4076_pochhammer__0) ).
thf(7214,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)],[1157]) ).
thf(273,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8053_push__bit__of__1) ).
thf(3025,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(351,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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_5994_left__add__twice) ).
thf(3411,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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)],[351]) ).
thf(813,axiom,
! [A: rat] :
( ( zero_zero_rat = A )
<=> ( A = zero_zero_rat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_zero__reorient) ).
thf(5581,plain,
! [A: rat] :
( ( ( A = zero_zero_rat )
=> ( zero_zero_rat = A ) )
& ( ( zero_zero_rat = A )
=> ( A = zero_zero_rat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(318,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_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_6155_div__exp__mod__exp__eq) ).
thf(3259,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_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 @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_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)],[318]) ).
thf(1292,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_6890_div__div__div__same) ).
thf(7829,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)],[1292]) ).
thf(859,axiom,
! [A: nat] :
( ( A @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= ( @+[B: rat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_rat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_rat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3912_power__0__left) ).
thf(5821,plain,
! [A: nat] :
( ( A @ ( zero_zero_rat @ power_power_rat @ aa_nat_rat ) )
= ( @+[B: rat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_rat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_rat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1629,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_39_All__less__Suc) ).
thf(9370,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)],[1629]) ).
thf(991,axiom,
! [A: nat,B: set_list_nat,C: list_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 ) @ ( B @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_list_nat ) @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8010_card__insert__le__m1) ).
thf(6424,plain,
! [A: nat,B: set_list_nat,C: list_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 ) @ ( B @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( B @ ( C @ insert_list_nat ) @ finite_card_list_nat @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1642,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_2248_not__le__imp__less) ).
thf(9441,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)],[1642]) ).
thf(975,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_3733_of__nat__zero__less__power__iff) ).
thf(6351,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)],[975]) ).
thf(115,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_verit__negate__coefficient_I3_J) ).
thf(2353,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(969,axiom,
! [A: nat,B: nat,C: nat] :
( ( ! [D: nat] :
( ( ( C @ ( D @ ( 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 @ ( D @ ( 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 ) ) )
<=> ( A
= ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9687_gcd__unique__nat) ).
thf(6316,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
= ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ! [D: nat] :
( ( ( C @ ( D @ ( 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 @ ( D @ ( 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 ) ) ) )
& ( ( ! [D: nat] :
( ( ( C @ ( D @ ( 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 @ ( D @ ( 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 ) ) )
=> ( A
= ( C @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(1065,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_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 ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4601_of__nat__mod) ).
thf(6750,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_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 ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(1408,axiom,
! [A: real,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4099_pochhammer__neq__0__mono) ).
thf(8328,plain,
! [A: real,B: nat,C: nat] :
( ( ( B @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real )
=> ( ( B @ ( C @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).
thf(281,axiom,
zero_zero_complex != one_one_complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_zero__neq__one) ).
thf(3057,plain,
zero_zero_complex != one_one_complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(934,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_6880_dvd__add__left__iff) ).
thf(6155,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)],[934]) ).
thf(223,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_211_Nat_Oadd__0__right) ).
thf(2803,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)],[223]) ).
thf(234,axiom,
one_one_int = one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8976_one__integer_Orsp) ).
thf(2847,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(995,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9708_gcd__nat_Oelims) ).
thf(6435,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(340,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ~ ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7850_and__exp__eq__0__iff__not__bit) ).
thf(3360,plain,
! [A: nat,B: nat] :
( ( ~ ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( bit_se727722235901077358nd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ~ ( B @ ( A @ ( bit_se1148574629649215175it_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(1116,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ki @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10333_ATP_Olambda__182) ).
thf(6993,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ki @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(1769,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_2370_order__le__less__trans) ).
thf(10255,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)],[1769]) ).
thf(1003,axiom,
! [A: set_complex,B: fun_complex_nat,C: nat] :
( ! [D: complex] :
( ( A @ ( D @ member_complex ) )
=> ( C @ ( D @ ( B @ aa_complex_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ finite_card_complex @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ finite_card_complex @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8747_sum__bounded__above__strict) ).
thf(6471,plain,
! [A: set_complex,B: fun_complex_nat,C: nat] :
( ! [D: complex] :
( ( A @ ( D @ member_complex ) )
=> ( C @ ( D @ ( B @ aa_complex_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( ( A @ finite_card_complex @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ finite_card_complex @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ groups5693394587270226106ex_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(1126,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_old_Onat_Odistinct_I1_J) ).
thf(7035,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1492,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_1633_of__nat__diff) ).
thf(8730,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)],[1492]) ).
thf(951,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_7066_div__dvd__iff__mult) ).
thf(6233,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)],[951]) ).
thf(1197,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_484_pos__add__strict) ).
thf(7387,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)],[1197]) ).
thf(657,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_of__nat__eq__iff) ).
thf(4831,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) ) )
& ( ( ( A @ ( semiri5074537144036343181t_real @ aa_nat_real ) )
= ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1267,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_9028_max__0R) ).
thf(7708,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)],[1267]) ).
thf(1582,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_1173_diff__is__0__eq_H) ).
thf(9110,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)],[1582]) ).
thf(893,axiom,
! [A: nat,B: extended_enat] :
( ( ( A @ extended_enat2 )
= ( B @ extended_eSuc ) )
<=> ? [C: nat] :
( ( ( C @ extended_enat2 )
= B )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9892_enat__eSuc__iff) ).
thf(5958,plain,
! [A: nat,B: extended_enat] :
( ( ? [C: nat] :
( ( ( C @ extended_enat2 )
= B )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( A @ extended_enat2 )
= ( B @ extended_eSuc ) ) )
& ( ( ( A @ extended_enat2 )
= ( B @ extended_eSuc ) )
=> ? [C: nat] :
( ( ( C @ extended_enat2 )
= B )
& ( A
= ( C @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(1783,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_2358_order__le__neq__trans) ).
thf(10308,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)],[1783]) ).
thf(700,axiom,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_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 ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6022_power2__less__imp__less) ).
thf(5046,plain,
! [A: nat,B: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( power_power_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 ) )
=> ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(629,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( C @ ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) ) )
<=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3594_of__nat__power__eq__of__nat__cancel__iff) ).
thf(4713,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( C @ ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) ) ) )
& ( ( ( A @ ( semiri1314217659103216013at_int @ aa_nat_int ) )
= ( C @ ( B @ ( semiri1314217659103216013at_int @ aa_nat_int ) @ power_power_int @ aa_nat_int ) ) )
=> ( A
= ( C @ ( B @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(999,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_3548_nat__mult__le__cancel1) ).
thf(6452,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)],[999]) ).
thf(1248,axiom,
! [A: list_o,B: fun_o_o] :
( ! [C: $o] :
( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C @ ( B @ aa_o_o ) ) )
<=> ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6442_all__set__conv__all__nth) ).
thf(7617,plain,
! [A: list_o,B: fun_o_o] :
( ( ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) )
=> ! [C: $o] :
( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C @ ( B @ aa_o_o ) ) ) )
& ( ! [C: $o] :
( ( A @ set_o2 @ ( C @ member_o ) )
=> ( C @ ( B @ aa_o_o ) ) )
=> ! [C: nat] :
( ( A @ size_size_list_o @ ( C @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ nth_o @ aa_nat_o ) @ ( B @ aa_o_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).
thf(741,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( gcd_nat_rel @ accp_P4275260045618599050at_nat ) )
=> ~ ( ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) )
=> ~ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( gcd_nat_rel @ accp_P4275260045618599050at_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9724_gcd__nat_Opelims) ).
thf(5236,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( gcd_nat_rel @ accp_P4275260045618599050at_nat ) )
=> ~ ( ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) )
=> ~ ( B @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( gcd_nat_rel @ accp_P4275260045618599050at_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(1430,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ ( gcd_gcd_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_9692_gcd__nat_OcoboundedI2) ).
thf(8453,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( dvd_dvd_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( C @ ( gcd_gcd_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)],[1430]) ).
thf(545,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5853_bits__1__div__2) ).
thf(4330,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(458,axiom,
! [A: rat] :
( ( zero_zero_nat @ ( A @ gbinomial_rat @ aa_nat_rat ) )
= one_one_rat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3638_gbinomial__0_I1_J) ).
thf(3939,plain,
! [A: rat] :
( ( zero_zero_nat @ ( A @ gbinomial_rat @ aa_nat_rat ) )
= one_one_rat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4152_pochhammer__of__nat__eq__0__lemma_H) ).
thf(2539,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( B @ ( semiri5074537144036343181t_real @ aa_nat_real ) @ ( uminus_uminus_real @ aa_real_real ) @ comm_s7457072308508201937r_real @ aa_nat_real ) )
!= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1848,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_2001_order_Oasym) ).
thf(10642,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)],[1848]) ).
thf(1375,axiom,
aTP_Lamm_ou @ ( dvd_dvd_nat @ ( gcd_gcd_nat @ semila1248733672344298208er_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10035_gcd__nat_Osemilattice__order__axioms) ).
thf(8189,plain,
aTP_Lamm_ou @ ( dvd_dvd_nat @ ( gcd_gcd_nat @ semila1248733672344298208er_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).
thf(1782,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_90_less__not__refl3) ).
thf(10304,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)],[1782]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( 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 @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( binomial @ 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_6542_binomial__strict__antimono) ).
thf(2864,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( 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 @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( C @ ( binomial @ 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(491,axiom,
zero_zero_rat != one_one_rat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_zero__neq__one) ).
thf(4071,plain,
zero_zero_rat != one_one_rat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(4,axiom,
! [A: real,B: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ power_power_real @ aa_nat_real ) ) )
<=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5956_power2__eq__iff) ).
thf(1902,plain,
! [A: real,B: real] :
( ( ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ power_power_real @ aa_nat_real ) ) ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ power_power_real @ aa_nat_real ) ) )
=> ( ( A
= ( B @ ( uminus_uminus_real @ aa_real_real ) ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(768,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_3431_mult__is__0) ).
thf(5376,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)],[768]) ).
thf(1707,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_8512_replicate__eq__replicate) ).
thf(9848,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)],[1707]) ).
thf(1071,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_1151_nat__add__left__cancel__le) ).
thf(6778,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)],[1071]) ).
thf(146,axiom,
! [A: num,B: num] :
( ( ( A @ ( bit0 @ aa_num_num ) )
= ( B @ ( bit0 @ aa_num_num ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5730_verit__eq__simplify_I8_J) ).
thf(2484,plain,
! [A: num,B: num] :
( ( ( A = B )
=> ( ( A @ ( bit0 @ aa_num_num ) )
= ( B @ ( bit0 @ aa_num_num ) ) ) )
& ( ( ( A @ ( bit0 @ aa_num_num ) )
= ( B @ ( bit0 @ aa_num_num ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(947,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ ( last_nat @ aa_list_nat_nat ) )
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9778_last__upt) ).
thf(6222,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ upt ) @ ( last_nat @ aa_list_nat_nat ) )
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(1019,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_996_add__mono1) ).
thf(6548,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)],[1019]) ).
thf(1403,axiom,
! [A: num,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ cons_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9315_upt__rec__numeral) ).
thf(8305,plain,
! [A: num,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ upt ) )
= ( @+[C: list_nat] :
( ( ~ ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C = nil_nat ) )
& ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( C
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( suc @ aa_nat_nat ) @ upt ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ cons_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).
thf(1872,axiom,
! [A: real,B: nat] :
( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3672_power__eq__0__iff) ).
thf(10758,plain,
! [A: real,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_real ) )
=> ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real ) )
& ( ( ( B @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
& ( A = zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872]) ).
thf(1181,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_ke @ aa_nat_o ) )
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10567_ATP_Olambda__416) ).
thf(7299,plain,
! [A: nat] :
~ ( A @ ( aTP_Lamm_ke @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).
thf(534,axiom,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7214_odd__pos) ).
thf(4271,plain,
! [A: nat] :
( ~ ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(89,axiom,
! [A: real,B: real] :
( ( B @ ( A @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ divide_divide_real @ aa_real_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2750_minus__divide__right) ).
thf(2270,plain,
! [A: real,B: real] :
( ( B @ ( A @ divide_divide_real @ aa_real_real ) @ ( uminus_uminus_real @ aa_real_real ) )
= ( B @ ( uminus_uminus_real @ aa_real_real ) @ ( A @ divide_divide_real @ aa_real_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1775,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_4922_gcd__nat__induct) ).
thf(10276,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)],[1775]) ).
thf(1199,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_3447_mult__Suc__right) ).
thf(7392,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)],[1199]) ).
thf(731,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_1600_add__nonpos__neg) ).
thf(5172,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)],[731]) ).
thf(191,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_1570_Nat_Odiff__add__assoc) ).
thf(2672,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)],[191]) ).
thf(1614,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_2330_order__le__less) ).
thf(9267,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)],[1614]) ).
thf(733,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_9035_nat__mult__max__right) ).
thf(5183,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)],[733]) ).
thf(1841,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( fun_pair_leq @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9788_pair__leqI1) ).
thf(10618,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( fun_pair_leq @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841]) ).
thf(1362,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_3425_div__mult__mult1__if) ).
thf(8130,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)],[1362]) ).
thf(662,axiom,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4795_abs__sgn__eq) ).
thf(4858,plain,
! [A: real] :
( ( A @ ( sgn_sgn_real @ aa_real_real ) @ ( abs_abs_real @ aa_real_real ) )
= ( @+[B: real] :
( ( ( A != zero_zero_real )
=> ( B = one_one_real ) )
& ( ( A = zero_zero_real )
=> ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(1873,axiom,
! [A: nat] :
~ ( bot_bot_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7643_bot_Oextremum__strict) ).
thf(10768,plain,
! [A: nat] :
~ ( bot_bot_nat @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873]) ).
thf(1154,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_6587_dvd__1__iff__1) ).
thf(7195,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)],[1154]) ).
thf(1141,axiom,
! [A: num,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6510_less__numeral__Suc) ).
thf(7103,plain,
! [A: num,B: nat] :
( ( ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( pred_numeral @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(1089,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_101_vebt__buildup_Ocases) ).
thf(6864,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)],[1089]) ).
thf(889,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_3501_le__div__geq) ).
thf(5943,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)],[889]) ).
thf(462,axiom,
! [A: nat,B: complex] :
( ( ( B = one_one_complex )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ power_power_complex @ aa_nat_complex ) @ ( B @ dvd_dvd_complex @ aa_complex_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7169_dvd__power) ).
thf(3950,plain,
! [A: nat,B: complex] :
( ( ( B = one_one_complex )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) )
=> ( A @ ( B @ power_power_complex @ aa_nat_complex ) @ ( B @ dvd_dvd_complex @ aa_complex_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(362,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_mb @ 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_9304_map__add__upt) ).
thf(3461,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_mb @ 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)],[362]) ).
thf(870,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_4098_nat__power__less__imp__less) ).
thf(5877,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)],[870]) ).
thf(1484,axiom,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5006_power__zero__numeral) ).
thf(8702,plain,
! [A: num] :
( ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_complex @ power_power_complex @ aa_nat_complex ) )
= zero_zero_complex ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484]) ).
thf(939,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se8570568707652914677it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9076_drop__bit__of__Suc__0) ).
thf(6173,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit_se8570568707652914677it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A = zero_zero_nat ) @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(708,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_2490_div__by__1) ).
thf(5073,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)],[708]) ).
thf(586,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( one @ unique5055182867167087721od_nat ) )
= ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7742_divmod__algorithm__code_I4_J) ).
thf(4520,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( one @ unique5055182867167087721od_nat ) )
= ( one @ ( numeral_numeral_nat @ aa_num_nat ) @ ( zero_zero_nat @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(612,axiom,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5799_one__mod__two__eq__one) ).
thf(4627,plain,
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(602,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6066_exp__not__zero__imp__exp__diff__not__zero) ).
thf(4584,plain,
! [A: nat,B: nat] :
( ( ( A @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_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 ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1752,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_7357_gcd__nat_Oantisym) ).
thf(10187,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)],[1752]) ).
thf(753,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_4112_pochhammer__nonneg) ).
thf(5307,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)],[753]) ).
thf(1822,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ vEBT_vebt_buildup @ vEBT_invar_vebt @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_buildup__gives__valid) ).
thf(10522,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( A @ ( A @ vEBT_vebt_buildup @ vEBT_invar_vebt @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822]) ).
thf(790,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_real @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4274_real__root__one) ).
thf(5494,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ( one_one_real @ ( A @ ( root @ aa_nat_fun_real_real ) @ aa_real_real ) )
= one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(1333,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_1160_add__le__cancel__left) ).
thf(8023,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)],[1333]) ).
thf(1636,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_1937_minf_I4_J) ).
thf(9399,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)],[1636]) ).
thf(1297,axiom,
! [A: num,B: nat,C: nat] :
( ( C @ ( semiri1316708129612266289at_nat @ aa_nat_nat ) @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_5329_numeral__power__le__of__nat__cancel__iff) ).
thf(7848,plain,
! [A: num,B: nat,C: nat] :
( ( ( C @ ( B @ ( A @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_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 @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[1297]) ).
thf(1767,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_2233_antisym__conv2) ).
thf(10245,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)],[1767]) ).
thf(784,axiom,
! [A: nat] :
( ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7616_mask__eq__0__iff) ).
thf(5458,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( bit_se2002935070580805687sk_nat @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(73,axiom,
! [A: real] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real )
<=> ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5795_zero__eq__power2) ).
thf(2206,plain,
! [A: real] :
( ( ( A = zero_zero_real )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ power_power_real @ aa_nat_real ) )
= zero_zero_real )
=> ( A = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(821,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9710_gcd__non__0__nat) ).
thf(5618,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( gcd_gcd_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(1288,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_487_Suc__diff__Suc) ).
thf(7812,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)],[1288]) ).
thf(26,axiom,
! [A: $o] :
( ( A @ zero_n3304061248610475627l_real )
= ( @+[B: real] :
( ( ~ A
=> ( B = zero_zero_real ) )
& ( A
=> ( B = one_one_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7568_of__bool__def) ).
thf(2018,plain,
! [A: $o] :
( ( A @ zero_n3304061248610475627l_real )
= ( @+[B: real] :
( ( ~ A
=> ( B = zero_zero_real ) )
& ( A
=> ( B = one_one_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1623,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_1977_pinf_I2_J) ).
thf(9310,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)],[1623]) ).
thf(230,axiom,
! [A: nat] :
( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= one_one_nat )
<=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5892_not__mod__2__eq__1__eq__0) ).
thf(2832,plain,
! [A: nat] :
( ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= one_one_nat ) )
& ( ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= one_one_nat )
=> ( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(134,axiom,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7941_xor__numerals_I2_J) ).
thf(2436,plain,
! [A: num] :
( ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one_one_nat @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1300,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_9319_upt__eq__Cons__conv) ).
thf(7861,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)],[1300]) ).
thf(1178,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_1472_add__increasing) ).
thf(7284,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)],[1178]) ).
thf(1328,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_4115_nat__one__le__power) ).
thf(8006,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)],[1328]) ).
thf(637,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_173_diff__zero) ).
thf(4742,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)],[637]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8018_xor__nat__unfold) ).
thf(2297,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( @+[D: nat] :
( ( ( B != zero_zero_nat )
=> ( D
= ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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 ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( D = A ) ) ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(356,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_209_add__Suc__right) ).
thf(3443,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)],[356]) ).
thf(1174,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( fun_pair_less @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9787_pair__lessI1) ).
thf(7274,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( fun_pair_less @ ( D @ ( B @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ ( C @ ( A @ product_Pair_nat_nat @ aa_nat7603221163087113075at_nat ) @ produc6161850002892822231at_nat ) @ member8206827879206165904at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).
thf(1578,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_3919_power__gt1) ).
thf(9098,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)],[1578]) ).
thf(685,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3613_power__one__right) ).
thf(4977,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(561,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_6650_div__add) ).
thf(4423,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)],[561]) ).
thf(832,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_3821_power__mono) ).
thf(5664,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)],[832]) ).
thf(1085,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_3693_of__nat__power__le__of__nat__cancel__iff) ).
thf(6839,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)],[1085]) ).
thf(518,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: $o,F: $o] :
( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
!= ( F @ ( E @ vEBT_Leaf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_VEBT_Odistinct_I1_J) ).
thf(4189,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: $o,F: $o] :
( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
!= ( F @ ( E @ vEBT_Leaf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(909,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_3474_split__div_H) ).
thf(6035,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)],[909]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8136_flip__bit__nat__def) ).
thf(2191,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( bit_se2161824704523386999it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( bit_se547839408752420682it_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( bit_se6528837805403552850or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1574,axiom,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6124_numeral__1__eq__Suc__0) ).
thf(9087,plain,
( ( one @ ( numeral_numeral_nat @ aa_num_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574]) ).
thf(1717,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_2306_dual__order_Ostrict__trans2) ).
thf(10002,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)],[1717]) ).
thf(957,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( gcd_gcd_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_9697_gcd__nat_Ocobounded1) ).
thf(6265,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( gcd_gcd_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)],[957]) ).
thf(1744,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_1957_pinf_I7_J) ).
thf(10161,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)],[1744]) ).
thf(44,axiom,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8996_or__nat__numerals_I3_J) ).
thf(2106,plain,
! [A: num] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( bit_se1412395901928357646or_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(39,axiom,
! [A: real,B: real] :
( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= B )
<=> ( ( B @ ( uminus_uminus_real @ aa_real_real ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_minus__equation__iff) ).
thf(2087,plain,
! [A: real,B: real] :
( ( ( ( B @ ( uminus_uminus_real @ aa_real_real ) )
= A )
=> ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= B ) )
& ( ( ( A @ ( uminus_uminus_real @ aa_real_real ) )
= B )
=> ( ( B @ ( uminus_uminus_real @ aa_real_real ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(456,axiom,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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_6380_Suc__mod__eq__add3__mod__numeral) ).
thf(3933,plain,
! [A: nat,B: num] :
( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( one @ ( bit1 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( 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)],[456]) ).
thf(1478,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_4125_pochhammer__rec) ).
thf(8670,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)],[1478]) ).
thf(1469,axiom,
! [A: num,B: num] :
( ( B @ numera1916890842035813515d_enat @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) )
<=> ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5718_enat__ord__number_I2_J) ).
thf(8628,plain,
! [A: num,B: num] :
( ( ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( B @ numera1916890842035813515d_enat @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) ) )
& ( ( B @ numera1916890842035813515d_enat @ ( A @ numera1916890842035813515d_enat @ ord_le72135733267957522d_enat ) )
=> ( B @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( numeral_numeral_nat @ aa_num_nat ) @ ( ord_less_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469]) ).
thf(1828,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__Nat__Onat_T) ).
thf(10537,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828]) ).
thf(1105,axiom,
! [A: vEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
<=> ( ( B != zero_zero_nat )
& ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8564_in__set__replicate) ).
thf(6933,plain,
! [A: vEBT_VEBT,B: nat,C: vEBT_VEBT] :
( ( ( ( B != zero_zero_nat )
& ( A = C ) )
=> ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) ) )
& ( ( C @ ( B @ replicate_VEBT_VEBT ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT ) )
=> ( ( B != zero_zero_nat )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(185,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_347_diff__cancel2) ).
thf(2655,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)],[185]) ).
thf(408,axiom,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( A @ ( plus_plus_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_5915_add__self__mod__2) ).
thf(3669,plain,
! [A: nat] :
( ( one @ ( bit0 @ aa_num_num ) @ ( numeral_numeral_nat @ aa_num_nat ) @ ( A @ ( A @ ( plus_plus_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)],[408]) ).
thf(1225,axiom,
! [A: nat] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9768_coprime__Suc__0__right) ).
thf(7521,plain,
! [A: nat] : ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( algebr934650988132801477me_nat @ aa_nat_fun_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).
thf(11307,plain,
$false,
inference(e,[status(thm)],[5136,4169,5320,3863,6845,6566,6954,2163,8607,7375,2199,8536,5437,8618,4201,6836,10647,5365,8186,10410,6979,6167,5918,5088,10259,3053,2341,2109,2131,7854,4909,5260,5329,8097,4899,3798,9516,3666,4729,5950,9754,2921,10730,7660,8283,1899,3581,7143,8030,8843,1982,3449,10081,6448,5999,5778,10319,2331,5733,8639,4166,6808,2250,8855,9020,7358,6868,6695,5644,7132,2676,10837,2114,7182,6602,9241,4931,4037,2976,10299,3072,2117,2940,7935,7083,6944,2495,8082,6744,6883,7641,6199,3377,6458,9045,8463,3959,8118,6798,3098,10705,8169,5224,5669,8943,7781,5691,9135,4487,6214,9003,6295,5501,4105,3530,4739,9127,2184,2712,6515,9000,4058,1988,4980,6877,3017,4543,6278,4234,10282,8733,3120,7203,10433,10181,7695,2035,4839,3942,10869,10881,10358,7873,7824,6127,8747,9261,1999,2316,3446,8667,10864,6089,9813,6727,10138,7484,10827,6241,3414,5005,6996,10170,9801,6117,8650,1954,8012,10414,9540,7220,9481,9774,3276,5227,2432,2548,8816,9396,8546,10530,2531,4775,7858,9443,7839,4047,7018,10427,7944,5252,4496,5935,7499,6381,7734,8133,4679,7235,5476,9159,6904,9195,5723,8472,9708,7364,8705,9465,6306,9148,3880,4665,4322,7993,5342,7390,4386,9116,7496,10042,3644,9410,6987,8647,8785,6968,5160,5108,7241,4546,10121,10286,5429,2603,2328,9172,7277,7914,5883,6538,3131,4415,9988,4224,3574,7349,10722,3821,2444,2217,7771,8951,3148,10719,4778,8214,3542,4275,6113,2562,10337,9668,6662,9805,5706,4568,4766,6208,5836,2745,8753,4243,6130,6010,8121,6049,2169,10850,6579,3084,10570,4383,4390,8161,6071,8907,3374,3385,7711,10534,5214,4353,6681,8819,6149,10891,6379,8571,8717,5193,5604,8600,5397,5622,5323,4928,3216,6365,4675,3470,6923,3312,8615,5851,7728,8543,7560,3014,2730,8384,9869,2520,4141,3835,3708,5076,8126,3557,7965,7633,10292,3231,2388,7464,3866,7226,10527,2829,9304,8190,10746,9832,7986,2777,2178,5682,8109,10519,2237,8394,2616,7268,7492,3966,8029,9336,6227,4173,4903,4443,3075,9490,6670,7423,5861,10623,7245,3724,2893,6657,4733,8158,3702,3983,8929,9811,7845,4050,6176,10757,8065,4724,3621,6964,5541,5032,7015,5650,3357,9415,5805,6559,9388,5761,4162,7899,6562,8411,9309,5929,7807,6498,5169,2103,8443,3870,3588,2718,7408,2508,9875,5738,10799,10442,10145,4033,7931,2281,2861,8774,5096,6740,5370,7004,9743,8406,6947,8141,5772,3808,2523,2371,2979,5246,10273,10784,2137,5897,6772,6702,4825,8691,4040,2002,6700,8459,2809,10106,2639,2154,5824,4588,9024,6787,8362,4475,2884,4483,7305,3510,5695,8742,4700,7657,5012,7179,7022,7725,5443,7217,5968,9009,10639,9175,5122,10216,9048,8123,10243,9720,7254,3011,7535,3857,5157,4216,2910,8201,4629,2473,8046,8302,2574,3720,5411,10506,9836,6064,6058,5142,4557,8397,7019,7518,6571,10258,10831,9252,2307,8250,2083,4312,9041,5334,2382,8343,9753,6343,6605,7229,9031,10843,6990,3610,4344,4499,3816,7378,2589,3735,4466,6124,8211,9296,6079,3827,9522,7989,2733,3972,6550,8091,9075,5002,10229,8756,8888,4878,3022,5815,8724,8910,3069,8550,3371,10102,4449,3134,4493,5085,2032,5102,4821,8714,3514,4021,9734,4044,9993,3286,6620,6582,7957,8623,9455,7902,5779,2609,4942,7591,3408,9095,3282,3948,7097,4295,10263,6303,9113,5826,6926,2464,2758,3980,5937,3618,8920,8540,8788,8048,2628,8371,7555,4608,10490,8085,2477,9658,7063,8503,6427,4155,6445,9671,2826,7314,7432,3349,5690,9277,6556,3578,7361,5021,6708,10583,3877,5551,5038,3028,3050,6402,10235,6267,2344,2313,5858,2492,3727,9080,2112,4080,7767,8518,10580,5515,3595,7686,4316,5285,8155,8238,9730,4668,8604,2709,4789,10335,8451,2726,3237,5497,3968,8354,5854,7346,8694,3467,2300,2498,7281,8068,2157,2840,3254,2100,6101,9145,2946,10295,7962,4974,9355,8009,8562,5345,10413,6375,2359,2973,8414,9889,2692,10644,10661,4227,5978,2858,10430,4095,5373,10771,8149,8429,3087,3060,8117,6299,5830,5166,6518,3922,8017,6720,8687,2196,8346,6724,2460,2798,7091,9186,7631,4983,9508,3846,7054,7453,7717,7629,4772,3210,4721,10391,2080,8594,5547,6164,2613,6630,1937,5932,6763,4861,2172,4648,8968,9288,5662,2551,7577,8390,10163,4867,10239,2666,5905,6541,7976,6275,4814,9392,4621,6271,7523,10487,3294,4736,9513,5387,8230,9645,10575,9012,10560,4508,2845,5639,10026,8294,2581,4237,4540,4231,7123,10252,9068,6349,5947,4846,8673,6134,7948,2932,2125,8219,8442,7651,8072,2536,8891,3354,4068,6433,10603,7587,2851,6475,9461,1947,8896,7614,6005,3115,5217,4135,6784,4152,4259,7826,6152,4689,5026,2140,2756,3454,10058,3624,8989,8080,10524,2748,2368,10503,8708,3824,8846,8796,1991,2788,5544,5310,8527,2926,4644,3225,8739,2546,3563,8247,2043,3279,3587,8871,8559,2057,3306,8279,9104,8004,4906,8609,7476,9793,7941,2645,3422,7289,5909,3841,10190,4004,1996,3675,7074,4995,6524,6922,4131,5508,5048,4577,9650,4599,5400,5598,9107,9484,10592,10683,8164,10703,4470,10607,2292,10175,6026,4872,2391,8760,9231,8095,2253,5138,6615,3042,9502,8195,5451,3607,10030,3491,7742,4412,2570,4256,9122,3985,7753,9181,4562,3262,8591,10327,8771,6469,3738,7636,7257,10625,8874,6052,3343,8495,7833,3504,9471,5612,3900,3590,3604,5799,2695,3536,6140,7611,3741,4662,5456,7287,7714,7968,7938,10194,2970,10232,1916,8259,3234,3925,9142,6617,4283,4077,6510,5395,6312,3519,5065,5844,4159,9733,2981,7487,9157,8711,5940,3945,8809,2016,2514,8894,8684,4605,8777,9189,2806,8332,8167,6019,7472,5752,4758,4769,7815,6705,2134,4505,2959,3213,8767,10883,5567,7270,7109,3340,8059,8497,6334,6372,10741,4537,8318,9638,2220,10393,8227,7689,6532,4099,7719,9687,4149,8877,5282,9178,6649,7094,3123,10728,2753,10493,2166,5539,5735,10024,4273,8524,9089,9258,2319,4433,6016,8244,7482,9835,9390,6478,5071,8276,5631,2284,2246,6340,7502,5616,6061,6585,7546,6144,3101,7415,10532,10297,8088,7594,3996,2151,2642,7643,6920,2214,5244,7077,2415,3038,10204,8135,3551,10066,6461,10677,6147,2774,4828,6197,7607,10385,5491,5880,6832,5054,7330,2669,7001,4958,7265,4213,9015,8986,5531,6289,8485,8937,7626,3138,6184,3066,2896,1969,7238,2180,3219,2742,2625,8983,7302,7892,8750,3483,6769,5511,8826,8192,2025,10621,2812,5920,4445,5894,5082,8103,8661,5175,4064,4818,10005,3165,4181,4332,8974,3034,3977,6747,7654,4850,3006,3451,5656,3298,7575,5466,8782,8032,2542,10172,6847,4726,2664,7450,9101,7066,8340,2842,3893,4554,8198,2578,2350,9478,4502,7469,4918,10803,8291,3539,2418,6589,2770,9873,2075,10147,6255,8853,5340,5057,2439,7603,6574,6811,2365,8456,6687,8588,3838,7479,6907,5197,5094,2481,8308,10549,9741,5482,9381,5248,5575,9197,5976,8175,7324,10407,2592,2244,9698,10424,4304,4954,7558,2967,5667,5299,7339,2303,5326,4890,8763,6029,3908,7232,8922,6698,8035,4209,9762,4481,2867,10226,4473,3380,4084,2005,2952,3672,2878,8949,8106,3522,9054,3009,6858,2054,5548,10517,8954,3031,10311,10322,10824,7788,2096,9403,4013,7526,3936,7117,7896,5886,5528,9673,6225,7571,4886,7403,10191,4580,2652,9651,4529,9826,2234,6191,4319,8505,4292,10132,10814,9656,2684,8637,2256,4113,5652,8885,6008,8477,8020,6998,5133,8409,10016,7982,4336,4986,6641,3849,5414,10653,6577,7087,3507,2143,9535,4754,4377,10797,3391,7026,5624,2715,6249,6120,7705,5607,10685,4864,6399,9138,4490,2661,5125,10112,8537,5111,2060,4939,4366,8466,10856,9710,4950,7045,5523,4517,8904,2175,2407,3786,6481,5079,10159,8813,2160,5018,6384,8744,8039,5955,5015,10717,6513,5995,2322,10509,5186,4409,10218,8612,6880,10636,5262,4398,9991,4240,10328,4092,9281,7429,3818,3885,3691,8858,2688,3273,3791,3063,6545,9065,7568,6421,3554,9986,5912,8625,5555,3202,9518,7796,2429,9358,5560,2337,7879,3801,2128,7769,9683,9666,7583,9413,4800,8206,8644,10343,4781,3329,10846,3095,9690,5675,3493,10028,9242,3388,4267,8433,3256,2848,7908,6793,10129,1934,2500,7876,5902,8316,3107,6337,9505,1898,6679,3652,7515,7580,9863,9500,4624,6601,9151,6369,9353,7251,6775,4748,5504,2357,8850,2511,4634,6086,5685,9406,10150,2949,6917,5717,6161,9654,4795,3156,3914,10178,8861,2266,2760,3433,10806,2347,2325,6814,10214,3168,1940,7552,10261,6286,2924,3584,4651,10754,7146,5981,9395,10744,10727,2458,4138,8946,3457,1966,7177,7764,6408,9306,9092,10114,7395,1949,2870,6970,6013,3171,6068,1913,2078,4419,7412,8260,3533,2310,6390,6137,7589,10008,2194,4559,5421,7889,10541,6674,4102,2187,3346,3320,4463,2226,5485,2071,2658,8579,10347,5068,2792,8469,4061,6711,3593,4574,8075,2098,5008,6023,6913,8634,10627,4121,3911,10135,2707,4710,6230,6829,2273,6753,6818,10169,3789,2855,8780,5272,2290,6893,2554,10789,3383,5351,7996,10468,5899,5426,6790,4042,8912,10325,9343,3104,10610,3630,3501,3003,7384,4010,3516,3136,3368,8240,2262,5922,10400,10777,2956,9718,9470,6554,4478,2362,4745,2447,2475,4602,6430,5162,5408,7187,10828,9701,4175,8837,8925,9510,2648,3430,3598,7312,2462,7039,7747,10695,9223,6412,6521,6252,10483,3351,5869,3993,2902,9660,5119,4074,5590,4446,5517,2294,5672,2739,7406,6871,7080,7804,9787,9162,1994,7135,4025,4619,5287,2421,8324,3705,2534,10733,9183,3464,4523,4843,7210,3658,2258,5051,2374,7048,2287,9239,7649,5357,2517,8209,1957,4687,2385,3860,4670,6693,9229,6439,6822,5796,4811,2587,3601,8296,7666,4596,10601,3882,6361,7836,2815,2736,2008,8720,3337,5527,10515,9051,5601,7248,9070,9463,4455,8933,3309,10036,4631,6258,10237,9795,6929,6952,10649,7772,2751,3956,8833,4178,3897,4565,6169,4350,8521,10340,7184,2334,5709,4895,4427,9541,4968,4007,8869,8424,6714,2704,8051,9282,5564,5741,10472,6729,2913,2404,7280,8268,2223,2795,5642,4193,6393,9083,3843,10485,3805,5440,7684,10781,6503,10092,7214,3025,3411,5581,3259,7829,5821,9370,6424,9441,6351,2353,6316,6750,8328,3057,6155,2803,2847,6435,3360,6993,10255,6471,7035,8730,6233,7387,4831,7708,9110,5958,10308,5046,4713,6452,7617,5236,8453,4330,3939,2539,10642,8189,10304,2864,4071,1902,5376,9848,6778,2484,6222,6548,8305,10758,7299,4271,2270,10276,7392,5172,2672,9267,5183,10618,8130,4858,10768,7195,7103,6864,5943,3950,3461,5877,8702,6173,5073,4520,4627,4584,10187,5307,10522,5494,8023,9399,7848,10245,5458,2206,5618,7812,2018,9310,2832,2436,7861,7284,8006,4742,2297,3443,7274,9098,4977,4423,5664,6839,4189,6035,2191,9087,10002,6265,10161,2106,2087,3933,8670,8628,10537,6933,2655,3669,7521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP225_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
% 0.14/0.47 % Computer : n020.cluster.edu
% 0.14/0.47 % Model : x86_64 x86_64
% 0.14/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.47 % Memory : 8046.5625MB
% 0.14/0.47 % OS : Linux 6.8.0-71-generic
% 0.14/0.47 % CPULimit : 300
% 0.14/0.47 % WCLimit : 300
% 0.14/0.47 % DateTime : Fri Sep 25 18:17:49 UTC 2026
% 0.14/0.47 % CPUTime :
% 0.14/0.47 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
% 1.00/1.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 7.83/2.78 % [INFO] Parsing done (1746ms).
% 8.28/2.81 % [INFO] Running in sequential loop mode.
% 9.31/3.11 % [INFO] eprover registered as external prover.
% 9.31/3.12 % [INFO] Scanning for conjecture ...
% 13.47/4.03 % [INFO] Found a conjecture (or negated_conjecture) and 10580 axioms. Running axiom selection ...
% 18.23/7.07 % [INFO] Axiom selection finished. Selected 1895 axioms (removed 8685 axioms).
% 18.54/7.15 % [INFO] Let expressions in the input problem have been expanded exhaustively.
% 21.22/8.00 % [INFO] Problem is typed first-order (TPTP TFF).
% 21.76/8.07 % [INFO] Type checking passed.
% 21.76/8.07 % [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 ...
% 58.50/19.21 % External prover 'e' found a proof!
% 58.50/19.21 % [INFO] Killing All external provers ...
% 58.50/19.21 % Time passed: 18602ms (effective reasoning time: 16401ms)
% 58.50/19.21 % 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)>
% 58.50/19.23 % Axioms used in derivation (1895): fact_7356_gcd__nat_Ostrict__trans, fact_9663_gcd__nat_Oeq__neutr__iff, fact_4457_mod__by__0, fact_6287_size__neq__size__imp__neq, fact_2248_not__le__imp__less, fact_744_of__nat__1, fact_6733_even__plus__one__iff, fact_1722_abs__abs, fact_3595_of__nat__power__eq__of__nat__cancel__iff, fact_3550_nat__eq__add__iff2, fact_7451_of__bool__eq__0__iff, fact_9062_prod__decode__aux_Oelims, fact_9670_gcd__proj2__if__dvd__nat, fact_6630_unit__prod, fact_7689_product__nth, fact_8559_in__set__replicate, fact_1225_le__add__diff__inverse, fact_3733_of__nat__zero__less__power__iff, fact_1014_vebt__buildup_Osimps_I2_J, fact_4070_power__Suc__0, fact_6946_pinf_I10_J, fact_4744_mod__mult__div__eq, fact_4125_pochhammer__rec, fact_4072_nat__zero__less__power__iff, fact_6498_binomial__1, fact_6778_semiring__parity__class_Oeven__mask__iff, fact_6973_unit__mult__right__cancel, fact_7026_nat__dvd__not__less, fact_5730_verit__eq__simplify_I8_J, fact_2221_nless__le, fact_6436_all__nth__imp__all__set, fact_10332_ATP_Olambda__181, fact_6711_odd__Suc__div__two, fact_831_one__reorient, fact_9707_gcd__mult__distrib__nat, fact_6158_ex__power__ivl1, fact_7238_mod2__eq__if, fact_7654_less__mask, fact_8979_less__eq__nat_Osimps_I2_J, fact_7387_take__bit__nat__eq__self, fact_3671_power__eq__0__iff, fact_1363_add__mono__thms__linordered__semiring_I1_J, fact_4263_fact__Suc__0, fact_3539_nat__mult__less__cancel1, fact_6674_unit__div__mult__self, fact_5005_power__zero__numeral, fact_3915_power__0__left, fact_1600_add__nonpos__neg, fact_9017_or__nat__rec, fact_9376_root__def, fact_9028_max__0R, fact_743_of__nat__1, fact_3682_of__nat__power__less__of__nat__cancel__iff, fact_3516_div__mult2__eq_H, fact_4308_fact__nonzero, fact_8051_push__bit__Suc, fact_7180_power__dvd__imp__le, fact_195_add__diff__cancel__left, fact_3513_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_7556_of__bool__less__eq__one, fact_7522_take__bit__of__1, fact_9673_gcd__nat_Oabsorb2, fact_8017_and__nat__rec, fact_3465_le__cube, fact_6059_exp__add__not__zero__imp__right, fact_7934_card__Diff__insert, fact_8651_replicate__eqI, fact_1432_le__Suc__ex, fact_348_diff__commute, fact_6428_in__set__conv__nth, fact_7079_unit__eq__div1, fact_9697_gcd__nat_Ocobounded1, fact_7289_take__bit__Suc, fact_4273_real__root__eq__1__iff, fact_3026_mult__right__mono, fact_157_add__eq__0__iff__both__eq__0, fact_5165_norm__of__nat, fact_6938_not__is__unit__0, fact_10162_ATP_Olambda__11, fact_8133_push__bit__take__bit, fact_1152_diff__diff__cancel, fact_6502_binomial__n__0, fact_5229_real__of__nat__eq__numeral__power__cancel__iff, fact_1823_abs__minus__commute, fact_9764_coprime__crossproduct__nat, fact_5814_div2__Suc__Suc, fact_6494_binomial__Suc__n, fact_8148_flip__bit__eq__xor, fact_8054_push__bit__of__Suc__0, fact_6398_nth__equalityI, fact_2148_linorder__less__linear, fact_2336_order__less__le, fact_3252_mult__strict__mono, fact_6540_binomial__altdef__nat, 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% 58.50/19.23 % No. of inferences in proof: 3794
% 58.50/19.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18602 ms resp. 16401 ms w/o parsing
% 62.87/20.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.11/20.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------