%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP226_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 : n006.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 07:36:58 AM UTC 2026
% Result : Theorem 16.96s 5.58s
% Output : Refutation 17.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 70 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 22 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 618 ( 34 ~; 0 |; 18 &; 499 @)
% ( 13 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 330 ( 329 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 8 con; 0-2 aty)
% Number of variables : 130 ( 0 ^; 128 !; 2 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_Co1105491363547889651atural_type,type,
fun_Co1105491363547889651atural: $tType ).
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_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_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_fu6699046866436802030_int_o_type,type,
fun_fu6699046866436802030_int_o: $tType ).
thf(fun_op1221328669798608686_nat_o_type,type,
fun_op1221328669798608686_nat_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_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_se374060482380105870_nat_o_type,type,
fun_se374060482380105870_nat_o: $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_op7653269905477231939_num_o_type,type,
fun_op7653269905477231939_num_o: $tType ).
thf(fun_op5373868528577402299_nat_o_type,type,
fun_op5373868528577402299_nat_o: $tType ).
thf(fun_fu8391177546919232046_nat_o_type,type,
fun_fu8391177546919232046_nat_o: $tType ).
thf(fun_Pr4799464687642144302_num_o_type,type,
fun_Pr4799464687642144302_num_o: $tType ).
thf(fun_Pr2028404973800837934_nat_o_type,type,
fun_Pr2028404973800837934_nat_o: $tType ).
thf(fun_Pr9018117161326028078_int_o_type,type,
fun_Pr9018117161326028078_int_o: $tType ).
thf(fun_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_fu1574286537503582443on_num_type,type,
fun_fu1574286537503582443on_num: $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(fun_fu1502755112258691281at_nat_type,type,
fun_fu1502755112258691281at_nat: $tType ).
thf(fun_fu5130958774822480081on_num_type,type,
fun_fu5130958774822480081on_num: $tType ).
thf(fun_fu7714627026455246123x_real_type,type,
fun_fu7714627026455246123x_real: $tType ).
thf(fun_se1865396762483378772_nat_o_type,type,
fun_se1865396762483378772_nat_o: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $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_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_se2389560805064864136_nat_o_type,type,
fun_se2389560805064864136_nat_o: $tType ).
thf(fun_na927404270896789692_nat_o_type,type,
fun_na927404270896789692_nat_o: $tType ).
thf(fun_fu2897328509465618819_nat_o_type,type,
fun_fu2897328509465618819_nat_o: $tType ).
thf(fun_fu1622112948621879430al_o_o_type,type,
fun_fu1622112948621879430al_o_o: $tType ).
thf(fun_fu2797749360310127211on_num_type,type,
fun_fu2797749360310127211on_num: $tType ).
thf(fun_fu4168831735773172575er_o_o_type,type,
fun_fu4168831735773172575er_o_o: $tType ).
thf(fun_op493924057549976310_num_o_type,type,
fun_op493924057549976310_num_o: $tType ).
thf(fun_fu7631928937237476593t_real_type,type,
fun_fu7631928937237476593t_real: $tType ).
thf(fun_Pr4738963024209204295_int_o_type,type,
fun_Pr4738963024209204295_int_o: $tType ).
thf(fun_Pr7537129237977221859_rat_o_type,type,
fun_Pr7537129237977221859_rat_o: $tType ).
thf(fun_na3970208099681795815_nat_o_type,type,
fun_na3970208099681795815_nat_o: $tType ).
thf(fun_fu3077872570260440615l_real_type,type,
fun_fu3077872570260440615l_real: $tType ).
thf(fun_op8028897214545316308_nat_o_type,type,
fun_op8028897214545316308_nat_o: $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(list_P5647936690300460905T_VEBT_type,type,
list_P5647936690300460905T_VEBT: $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_co7673397065115134084omplex_type,type,
fun_co7673397065115134084omplex: $tType ).
thf(fun_fu2916398056546941156ural_o_type,type,
fun_fu2916398056546941156ural_o: $tType ).
thf(fun_fu1769128043447206010eger_o_type,type,
fun_fu1769128043447206010eger_o: $tType ).
thf(fun_se9162176452187397432plex_o_type,type,
fun_se9162176452187397432plex_o: $tType ).
thf(fun_Co7302518231560758906ural_o_type,type,
fun_Co7302518231560758906ural_o: $tType ).
thf(fun_Co2081214437782444048eger_o_type,type,
fun_Co2081214437782444048eger_o: $tType ).
thf(fun_na7595719129879163854on_num_type,type,
fun_na7595719129879163854on_num: $tType ).
thf(fun_fu3022329567491847689real_o_type,type,
fun_fu3022329567491847689real_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(fun_op8989173174992673105on_num_type,type,
fun_op8989173174992673105on_num: $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_na1591161823130732966omplex_type,type,
fun_na1591161823130732966omplex: $tType ).
thf(fun_co3258106519541737638omplex_type,type,
fun_co3258106519541737638omplex: $tType ).
thf(fun_fu5477517762487726877_nat_o_type,type,
fun_fu5477517762487726877_nat_o: $tType ).
thf(fun_fu318872218122388049at_nat_type,type,
fun_fu318872218122388049at_nat: $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(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_num: $tType ).
thf(list_P1726324292696863441at_num_type,type,
list_P1726324292696863441at_num: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(fun_se2161501677553633980real_o_type,type,
fun_se2161501677553633980real_o: $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_co8378349014452122532t_real_type,type,
fun_co8378349014452122532t_real: $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_Co8499238673658658103nteger_type,type,
fun_Co8499238673658658103nteger: $tType ).
thf(fun_se382663106265794036_nat_o_type,type,
fun_se382663106265794036_nat_o: $tType ).
thf(fun_se867122708194164540_int_o_type,type,
fun_se867122708194164540_int_o: $tType ).
thf(fun_na8563630686737515764_nat_o_type,type,
fun_na8563630686737515764_nat_o: $tType ).
thf(fun_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_fu4001317426178549763_nat_o_type,type,
fun_fu4001317426178549763_nat_o: $tType ).
thf(fun_re7681423839302404990l_real_type,type,
fun_re7681423839302404990l_real: $tType ).
thf(fun_re4238438383274954274t_real_type,type,
fun_re4238438383274954274t_real: $tType ).
thf(fun_na6724076748692969250l_real_type,type,
fun_na6724076748692969250l_real: $tType ).
thf(list_P7333126701944960589_nat_o_type,type,
list_P7333126701944960589_nat_o: $tType ).
thf(list_P6285523579766656935_o_nat_type,type,
list_P6285523579766656935_o_nat: $tType ).
thf(list_P3795440434834930179_o_int_type,type,
list_P3795440434834930179_o_int: $tType ).
thf(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_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_option_num_nat_type,type,
fun_option_num_nat: $tType ).
thf(fun_num_option_num_type,type,
fun_num_option_num: $tType ).
thf(fun_nat_option_num_type,type,
fun_nat_option_num: $tType ).
thf(fun_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_num_num_type,type,
product_prod_num_num: $tType ).
thf(product_prod_nat_num_type,type,
product_prod_nat_num: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(list_P4002435161011370285od_o_o_type,type,
list_P4002435161011370285od_o_o: $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_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(fun_option_num_o_type,type,
fun_option_num_o: $tType ).
thf(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(fun_o_option_num_type,type,
fun_o_option_num: $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(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_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_num_type,type,
list_num: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(fun_real_o_type,type,
fun_real_o: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(set_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_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_ad_decl,type,
aTP_Lamm_ad: set_nat > fun_nat_o ).
thf(aTP_Lamm_aj_decl,type,
aTP_Lamm_aj: set_nat > fun_nat_o ).
thf(aTP_Lamm_an_decl,type,
aTP_Lamm_an: fun_set_nat_o > fun_set_nat_o ).
thf(aTP_Lamm_ao_decl,type,
aTP_Lamm_ao: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_bu_decl,type,
aTP_Lamm_bu: set_nat > fun_se382663106265794036_nat_o ).
thf(inj_on_nat_int_decl,type,
inj_on_nat_int: fun_nat_int > fun_set_nat_o ).
thf(inj_on_nat_list_nat_decl,type,
inj_on_nat_list_nat: fun_nat_list_nat > fun_set_nat_o ).
thf(inj_on5538052773655684606at_nat_decl,type,
inj_on5538052773655684606at_nat: fun_na1476630412504255114at_nat > fun_set_nat_o ).
thf(minus_minus_set_nat_decl,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(minus_8972599623528345224_nat_o_decl,type,
minus_8972599623528345224_nat_o: fun_nat_o > fun_nat_o > fun_nat_o ).
thf(uminus5710092332889474511et_nat_decl,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(uminus613421341184616069et_nat_decl,type,
uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
thf(uminus6183504819137795864_nat_o_decl,type,
uminus6183504819137795864_nat_o: fun_nat_o > fun_nat_o ).
thf(nat_int_decode_decl,type,
nat_int_decode: fun_nat_int ).
thf(nat_list_decode_decl,type,
nat_list_decode: fun_nat_list_nat ).
thf(nat_prod_decode_decl,type,
nat_prod_decode: fun_na1476630412504255114at_nat ).
thf(collect_nat_decl,type,
collect_nat: fun_nat_o > set_nat ).
thf(collect_set_nat_decl,type,
collect_set_nat: fun_set_nat_o > set_set_nat ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > fun_nat_o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > fun_nat_o ).
thf(vEBT_set_vebt_decl,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: fun_VEBT_VEBT_o ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > fun_nat_o ).
thf(aa_nat_o_decl,type,
aa_nat_o: fun_nat_o > nat > $o ).
thf(aa_set_nat_o_decl,type,
aa_set_nat_o: fun_set_nat_o > set_nat > $o ).
thf(aa_set_nat_fun_nat_o_decl,type,
aa_set_nat_fun_nat_o: fun_se382663106265794036_nat_o > set_nat > fun_nat_o ).
thf(aa_VEBT_VEBT_o_decl,type,
aa_VEBT_VEBT_o: fun_VEBT_VEBT_o > vEBT_VEBT > $o ).
thf(member_nat_decl,type,
member_nat: nat > fun_set_nat_o ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: vEBT_VEBT ).
thf(x_decl,type,
x: nat ).
thf(8,axiom,
! [A: set_nat] :
( ( A @ aTP_Lamm_ad @ collect_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Collect__mem__eq) ).
thf(56,plain,
! [A: set_nat] :
( ( A @ aTP_Lamm_ad @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: set_nat,B: set_nat] :
( ( B @ ( B @ ( A @ minus_minus_set_nat ) @ minus_minus_set_nat ) )
= ( B @ ( A @ minus_minus_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7749_Diff__idemp) ).
thf(42,plain,
! [A: set_nat,B: set_nat] :
( ( B @ ( B @ ( A @ minus_minus_set_nat ) @ minus_minus_set_nat ) )
= ( B @ ( A @ minus_minus_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
! [A: set_nat] : ( A @ ( nat_list_decode @ inj_on_nat_list_nat @ aa_set_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9883_inj__list__decode) ).
thf(157,plain,
! [A: set_nat] : ( A @ ( nat_list_decode @ inj_on_nat_list_nat @ aa_set_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [A: set_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_ad @ aa_nat_o ) )
<=> ( A @ ( B @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10301_ATP_Olambda__148) ).
thf(92,plain,
! [A: set_nat,B: nat] :
( ( ( A @ ( B @ member_nat @ aa_set_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_ad @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_ad @ aa_nat_o ) )
=> ( A @ ( B @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: set_nat,B: set_nat] :
( ( B @ ( A @ minus_minus_set_nat ) )
= ( B @ aTP_Lamm_ad @ ( A @ aTP_Lamm_ad @ minus_8972599623528345224_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8218_minus__set__def) ).
thf(53,plain,
! [A: set_nat,B: set_nat] :
( ( B @ ( A @ minus_minus_set_nat ) )
= ( B @ aTP_Lamm_ad @ ( A @ aTP_Lamm_ad @ minus_8972599623528345224_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: fun_set_nat_o] :
( ( A @ aTP_Lamm_an @ collect_set_nat )
= ( A @ collect_set_nat @ uminus613421341184616069et_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8154_Collect__neg__eq) ).
thf(59,plain,
! [A: fun_set_nat_o] :
( ( A @ aTP_Lamm_an @ collect_set_nat )
= ( A @ collect_set_nat @ uminus613421341184616069et_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
<=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_both__member__options__equiv__member) ).
thf(159,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) )
& ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
! [A: set_nat,B: set_nat] :
( ( B @ ( A @ minus_minus_set_nat ) )
= ( B @ ( A @ aTP_Lamm_bu @ aa_set_nat_fun_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8211_set__diff__eq) ).
thf(50,plain,
! [A: set_nat,B: set_nat] :
( ( B @ ( A @ minus_minus_set_nat ) )
= ( B @ ( A @ aTP_Lamm_bu @ aa_set_nat_fun_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: nat,B: set_nat] :
( ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7888_ComplI) ).
thf(143,plain,
! [A: nat,B: set_nat] :
( ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(18,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7817_DiffD2) ).
thf(104,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
( ( x @ ( t @ vEBT_vebt_member @ aa_nat_o ) )
<=> ( t @ vEBT_set_vebt @ ( x @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( ( x @ ( t @ vEBT_vebt_member @ aa_nat_o ) )
<=> ( t @ vEBT_set_vebt @ ( x @ member_nat @ aa_set_nat_o ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ( ( ( t @ vEBT_set_vebt @ ( x @ member_nat @ aa_set_nat_o ) )
=> ( x @ ( t @ vEBT_vebt_member @ aa_nat_o ) ) )
& ( ( x @ ( t @ vEBT_vebt_member @ aa_nat_o ) )
=> ( t @ vEBT_set_vebt @ ( x @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_ao @ aa_nat_o ) )
<=> ~ ( B @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10388_ATP_Olambda__235) ).
thf(79,plain,
! [A: fun_nat_o,B: nat] :
( ( ~ ( B @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_ao @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_ao @ aa_nat_o ) )
=> ~ ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: fun_nat_o,B: fun_nat_o] :
( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
<=> ( C @ ( B @ aa_nat_o ) ) )
=> ( ( A @ collect_nat )
= ( B @ collect_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Collect__cong) ).
thf(62,plain,
! [A: fun_nat_o,B: fun_nat_o] :
( ! [C: nat] :
( ( ( C @ ( B @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
& ( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) ) )
=> ( ( A @ collect_nat )
= ( B @ collect_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: set_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_aj @ aa_nat_o ) )
<=> ~ ( A @ ( B @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10347_ATP_Olambda__194) ).
thf(106,plain,
! [A: set_nat,B: nat] :
( ( ~ ( A @ ( B @ member_nat @ aa_set_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_aj @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_aj @ aa_nat_o ) )
=> ~ ( A @ ( B @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: set_nat] : ( A @ ( nat_int_decode @ inj_on_nat_int @ aa_set_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9669_inj__int__decode) ).
thf(121,plain,
! [A: set_nat] : ( A @ ( nat_int_decode @ inj_on_nat_int @ aa_set_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( C @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7829_DiffE) ).
thf(117,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( C @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: nat,B: fun_nat_o] :
( ( B @ collect_nat @ ( A @ member_nat @ aa_set_nat_o ) )
<=> ( A @ ( B @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_mem__Collect__eq) ).
thf(85,plain,
! [A: nat,B: fun_nat_o] :
( ( ( A @ ( B @ aa_nat_o ) )
=> ( B @ collect_nat @ ( A @ member_nat @ aa_set_nat_o ) ) )
& ( ( B @ collect_nat @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( A @ ( B @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(26,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7761_DiffI) ).
thf(137,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(34,axiom,
! [A: nat,B: set_nat] :
( ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) )
<=> ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7893_Compl__iff) ).
thf(165,plain,
! [A: nat,B: set_nat] :
( ( ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) ) )
& ( ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(25,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_valid__member__both__member__options) ).
thf(134,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ vEBT_invar_vebt @ aa_nat_o ) )
=> ( ( C @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) )
=> ( C @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: set_nat] :
( ( A @ uminus5710092332889474511et_nat )
= ( A @ aTP_Lamm_aj @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8150_Compl__eq) ).
thf(73,plain,
! [A: set_nat] :
( ( A @ uminus5710092332889474511et_nat )
= ( A @ aTP_Lamm_aj @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [A: set_nat] : ( A @ ( nat_prod_decode @ inj_on5538052773655684606at_nat @ aa_set_nat_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9874_inj__prod__decode) ).
thf(148,plain,
! [A: set_nat] : ( A @ ( nat_prod_decode @ inj_on5538052773655684606at_nat @ aa_set_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
! [A: fun_nat_o] :
( ( A @ aTP_Lamm_ao @ collect_nat )
= ( A @ collect_nat @ uminus5710092332889474511et_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8155_Collect__neg__eq) ).
thf(45,plain,
! [A: fun_nat_o] :
( ( A @ aTP_Lamm_ao @ collect_nat )
= ( A @ collect_nat @ uminus5710092332889474511et_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: set_nat] :
( ( A @ uminus5710092332889474511et_nat )
= ( A @ aTP_Lamm_ad @ uminus6183504819137795864_nat_o @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8161_uminus__set__def) ).
thf(76,plain,
! [A: set_nat] :
( ( A @ uminus5710092332889474511et_nat )
= ( A @ aTP_Lamm_ad @ uminus6183504819137795864_nat_o @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: fun_set_nat_o,B: set_nat] :
( ( B @ ( A @ aTP_Lamm_an @ aa_set_nat_o ) )
<=> ~ ( B @ ( A @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10387_ATP_Olambda__234) ).
thf(98,plain,
! [A: fun_set_nat_o,B: set_nat] :
( ( ~ ( B @ ( A @ aa_set_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_an @ aa_set_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_an @ aa_set_nat_o ) )
=> ~ ( B @ ( A @ aa_set_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7823_DiffD1) ).
thf(140,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
n @ ( t @ vEBT_invar_vebt @ aa_nat_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(91,plain,
n @ ( t @ vEBT_invar_vebt @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: nat,B: set_nat] :
( ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7939_ComplD) ).
thf(112,plain,
! [A: nat,B: set_nat] :
( ( B @ uminus5710092332889474511et_nat @ ( A @ member_nat @ aa_set_nat_o ) )
=> ~ ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [A: fun_set_nat_o,B: fun_set_nat_o] :
( ! [C: set_nat] :
( ( C @ ( A @ aa_set_nat_o ) )
<=> ( C @ ( B @ aa_set_nat_o ) ) )
=> ( ( A @ collect_set_nat )
= ( B @ collect_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Collect__cong) ).
thf(123,plain,
! [A: fun_set_nat_o,B: fun_set_nat_o] :
( ! [C: set_nat] :
( ( ( C @ ( B @ aa_set_nat_o ) )
=> ( C @ ( A @ aa_set_nat_o ) ) )
& ( ( C @ ( A @ aa_set_nat_o ) )
=> ( C @ ( B @ aa_set_nat_o ) ) ) )
=> ( ( A @ collect_set_nat )
= ( B @ collect_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ vEBT_V8194947554948674370ptions @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8231_set__vebt__def) ).
thf(145,plain,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ vEBT_V8194947554948674370ptions @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_not__min__Null__member) ).
thf(48,plain,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ vEBT_V8194947554948674370ptions @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,axiom,
! [A: nat,B: set_nat,C: set_nat] :
( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
<=> ( ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) )
& ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7755_Diff__iff) ).
thf(150,plain,
! [A: nat,B: set_nat,C: set_nat] :
( ( ( ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) )
& ( B @ ( A @ member_nat @ aa_set_nat_o ) ) )
=> ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) ) )
& ( ( C @ ( B @ minus_minus_set_nat ) @ ( A @ member_nat @ aa_set_nat_o ) )
=> ( ~ ( C @ ( A @ member_nat @ aa_set_nat_o ) )
& ( B @ ( A @ member_nat @ aa_set_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_min__Null__member) ).
thf(114,plain,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ vEBT_vebt_member @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(35,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_bu @ aa_set_nat_fun_nat_o ) @ aa_nat_o ) )
<=> ( ~ ( B @ ( C @ member_nat @ aa_set_nat_o ) )
& ( A @ ( C @ member_nat @ aa_set_nat_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10440_ATP_Olambda__287) ).
thf(171,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ( ~ ( B @ ( C @ member_nat @ aa_set_nat_o ) )
& ( A @ ( C @ member_nat @ aa_set_nat_o ) ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_bu @ aa_set_nat_fun_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_bu @ aa_set_nat_fun_nat_o ) @ aa_nat_o ) )
=> ( ~ ( B @ ( C @ member_nat @ aa_set_nat_o ) )
& ( A @ ( C @ member_nat @ aa_set_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(178,plain,
$false,
inference(e,[status(thm)],[56,42,157,92,53,59,159,50,143,104,36,79,62,106,121,117,85,137,165,134,73,148,45,76,98,140,91,112,123,145,48,150,114,171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP226_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.08 % 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
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 18:17:10 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 7.47/2.68 % [INFO] Parsing done (1677ms).
% 7.47/2.70 % [INFO] Running in sequential loop mode.
% 8.92/3.07 % [INFO] eprover registered as external prover.
% 8.92/3.08 % [INFO] Scanning for conjecture ...
% 12.68/4.14 % [INFO] Found a conjecture (or negated_conjecture) and 10572 axioms. Running axiom selection ...
% 13.79/4.51 % [INFO] Axiom selection finished. Selected 33 axioms (removed 10539 axioms).
% 13.79/4.58 % [INFO] Problem is typed first-order (TPTP TFF).
% 13.79/4.59 % [INFO] Type checking passed.
% 14.11/4.60 % [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 ...
% 16.96/5.58 % External prover 'e' found a proof!
% 16.96/5.58 % [INFO] Killing All external provers ...
% 16.96/5.58 % Time passed: 5022ms (effective reasoning time: 2877ms)
% 16.96/5.58 % 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)>
% 16.96/5.58 % Axioms used in derivation (33): fact_7755_Diff__iff, fact_7817_DiffD2, fact_58_Collect__cong, fact_7939_ComplD, fact_7761_DiffI, fact_7823_DiffD1, fact_7893_Compl__iff, fact_8154_Collect__neg__eq, fact_8231_set__vebt__def, fact_7749_Diff__idemp, fact_7888_ComplI, fact_54_Collect__mem__eq, fact_0_min__Null__member, fact_9883_inj__list__decode, fact_59_Collect__cong, fact_4_both__member__options__equiv__member, fact_10388_ATP_Olambda__235, fact_10387_ATP_Olambda__234, fact_8150_Compl__eq, fact_12_not__min__Null__member, fact_9669_inj__int__decode, fact_5_valid__member__both__member__options, fact_8161_uminus__set__def, fact_9874_inj__prod__decode, fact_10347_ATP_Olambda__194, fact_10301_ATP_Olambda__148, fact_48_mem__Collect__eq, fact_7829_DiffE, fact_8211_set__diff__eq, fact_10440_ATP_Olambda__287, fact_8218_minus__set__def, conj_0, fact_8155_Collect__neg__eq
% 16.96/5.58 % No. of inferences in proof: 70
% 16.96/5.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5022 ms resp. 2877 ms w/o parsing
% 17.68/5.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.68/5.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------