%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP222_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 07:36:54 AM UTC 2026
% Result : Theorem 16.14s 14.97s
% Output : Refutation 16.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 107 ( 14 ~; 6 |; 6 &; 68 @)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 385 ( 385 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_Pr7588637180273442094_num_o_type,type,
fun_Pr7588637180273442094_num_o: $tType ).
thf(fun_Pr8463018485500633518_nat_o_type,type,
fun_Pr8463018485500633518_nat_o: $tType ).
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(fun_fu6384561554008368101_nat_o_type,type,
fun_fu6384561554008368101_nat_o: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(fun_fu3898734532474705027nt_int_type,type,
fun_fu3898734532474705027nt_int: $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_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(produc8114805097830739791at_num_type,type,
produc8114805097830739791at_num: $tType ).
thf(produc9217583074051984497at_nat_type,type,
produc9217583074051984497at_nat: $tType ).
thf(fun_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_op1221328669798608686_nat_o_type,type,
fun_op1221328669798608686_nat_o: $tType ).
thf(fun_fu717549361983437348nt_int_type,type,
fun_fu717549361983437348nt_int: $tType ).
thf(fun_fu918106826131887214nt_int_type,type,
fun_fu918106826131887214nt_int: $tType ).
thf(fun_Pr8877776288780692068_nat_o_type,type,
fun_Pr8877776288780692068_nat_o: $tType ).
thf(fun_fu3064074204415222357nt_int_type,type,
fun_fu3064074204415222357nt_int: $tType ).
thf(fun_Pr557098546508347797at_nat_type,type,
fun_Pr557098546508347797at_nat: $tType ).
thf(fun_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(fun_fu4592178885959468770_int_o_type,type,
fun_fu4592178885959468770_int_o: $tType ).
thf(fun_fu8427683764667544036nt_int_type,type,
fun_fu8427683764667544036nt_int: $tType ).
thf(fun_o_5488095450495718970o_char_type,type,
fun_o_5488095450495718970o_char: $tType ).
thf(fun_fu7109581867628470992d_enat_type,type,
fun_fu7109581867628470992d_enat: $tType ).
thf(fun_fu3593947265352647275omplex_type,type,
fun_fu3593947265352647275omplex: $tType ).
thf(fun_fu3275390434952296369_nat_o_type,type,
fun_fu3275390434952296369_nat_o: $tType ).
thf(fun_fu8148986511470497476_num_o_type,type,
fun_fu8148986511470497476_num_o: $tType ).
thf(fun_fu2571895429041709858_nat_o_type,type,
fun_fu2571895429041709858_nat_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_o_6360995121869435791o_char_type,type,
fun_o_6360995121869435791o_char: $tType ).
thf(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(fun_VE2573032740582156747_nat_o_type,type,
fun_VE2573032740582156747_nat_o: $tType ).
thf(fun_co3732688428756473980omplex_type,type,
fun_co3732688428756473980omplex: $tType ).
thf(fun_fu1620311477532340197t_real_type,type,
fun_fu1620311477532340197t_real: $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_fu6579618355643354601at_rat_type,type,
fun_fu6579618355643354601at_rat: $tType ).
thf(fun_fu5935951186182374353at_nat_type,type,
fun_fu5935951186182374353at_nat: $tType ).
thf(fun_fu960360787657196261at_int_type,type,
fun_fu960360787657196261at_int: $tType ).
thf(fun_fu6652553491520710942omplex_type,type,
fun_fu6652553491520710942omplex: $tType ).
thf(fun_fu6092417073193843705nt_int_type,type,
fun_fu6092417073193843705nt_int: $tType ).
thf(fun_fu689363623238371998omplex_type,type,
fun_fu689363623238371998omplex: $tType ).
thf(fun_Co8502721031311864414nteger_type,type,
fun_Co8502721031311864414nteger: $tType ).
thf(fun_o_2683029531876921444o_char_type,type,
fun_o_2683029531876921444o_char: $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_fu847012557204443036omplex_type,type,
fun_fu847012557204443036omplex: $tType ).
thf(fun_fu7808106308057563584omplex_type,type,
fun_fu7808106308057563584omplex: $tType ).
thf(fun_fu4528473944208963392omplex_type,type,
fun_fu4528473944208963392omplex: $tType ).
thf(fun_fu6465309499045537820omplex_type,type,
fun_fu6465309499045537820omplex: $tType ).
thf(fun_fu1481857817119020493_int_o_type,type,
fun_fu1481857817119020493_int_o: $tType ).
thf(fun_fu6453395667394816515nt_int_type,type,
fun_fu6453395667394816515nt_int: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_Pr2478283820680522243nt_int_type,type,
fun_Pr2478283820680522243nt_int: $tType ).
thf(fun_fu7426956082801719578t_real_type,type,
fun_fu7426956082801719578t_real: $tType ).
thf(fun_re3844104906058862192omplex_type,type,
fun_re3844104906058862192omplex: $tType ).
thf(fun_Pr3455331679158536364_nat_o_type,type,
fun_Pr3455331679158536364_nat_o: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_Co4602396739301704407eger_o_type,type,
fun_Co4602396739301704407eger_o: $tType ).
thf(fun_fu5956788528830221615omplex_type,type,
fun_fu5956788528830221615omplex: $tType ).
thf(fun_re6135230694098607860t_real_type,type,
fun_re6135230694098607860t_real: $tType ).
thf(fun_o_3037882179896959673o_char_type,type,
fun_o_3037882179896959673o_char: $tType ).
thf(fun_fu5104398059618711576t_real_type,type,
fun_fu5104398059618711576t_real: $tType ).
thf(fun_fu5589980185390252312t_real_type,type,
fun_fu5589980185390252312t_real: $tType ).
thf(fun_fu8064956510386623256t_real_type,type,
fun_fu8064956510386623256t_real: $tType ).
thf(fun_fu138107234227827011_int_o_type,type,
fun_fu138107234227827011_int_o: $tType ).
thf(fun_fu2115079063411676732t_real_type,type,
fun_fu2115079063411676732t_real: $tType ).
thf(fun_fu163975356400620604t_real_type,type,
fun_fu163975356400620604t_real: $tType ).
thf(fun_fu7141299348810748056t_real_type,type,
fun_fu7141299348810748056t_real: $tType ).
thf(fun_Ex8979681104671372885d_enat_type,type,
fun_Ex8979681104671372885d_enat: $tType ).
thf(set_fi4554929511873752355omplex_type,type,
set_fi4554929511873752355omplex: $tType ).
thf(fun_fu7979797992566127108at_nat_type,type,
fun_fu7979797992566127108at_nat: $tType ).
thf(fun_fu4710970720072501148at_rat_type,type,
fun_fu4710970720072501148at_rat: $tType ).
thf(fun_fu6228432884689642900at_rat_type,type,
fun_fu6228432884689642900at_rat: $tType ).
thf(fun_fu4413992040155564420at_nat_type,type,
fun_fu4413992040155564420at_nat: $tType ).
thf(fun_fu1567874110255095356at_int_type,type,
fun_fu1567874110255095356at_int: $tType ).
thf(fun_fu5519318738670804632at_int_type,type,
fun_fu5519318738670804632at_int: $tType ).
thf(fun_fu688336635129761048at_int_type,type,
fun_fu688336635129761048at_int: $tType ).
thf(fun_ra8505079968215247908at_rat_type,type,
fun_ra8505079968215247908at_rat: $tType ).
thf(fun_co6147893885205795665omplex_type,type,
fun_co6147893885205795665omplex: $tType ).
thf(fun_Co1981900195452921617nteger_type,type,
fun_Co1981900195452921617nteger: $tType ).
thf(fun_re5512370375968561900l_real_type,type,
fun_re5512370375968561900l_real: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(fun_se1865396762483378772_nat_o_type,type,
fun_se1865396762483378772_nat_o: $tType ).
thf(fun_nu4037332675543032467um_num_type,type,
fun_nu4037332675543032467um_num: $tType ).
thf(fun_na157340750583166227at_num_type,type,
fun_na157340750583166227at_num: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(fun_fu1994797156054922755_nat_o_type,type,
fun_fu1994797156054922755_nat_o: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(fun_o_335877185394996366o_char_type,type,
fun_o_335877185394996366o_char: $tType ).
thf(fun_fu40286998686754419omplex_type,type,
fun_fu40286998686754419omplex: $tType ).
thf(fun_na6632006986671646835omplex_type,type,
fun_na6632006986671646835omplex: $tType ).
thf(fun_co6883864892131739507omplex_type,type,
fun_co6883864892131739507omplex: $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_Ex8341929632020906428d_enat_type,type,
fun_Ex8341929632020906428d_enat: $tType ).
thf(fun_co51012501629074457plex_o_type,type,
fun_co51012501629074457plex_o: $tType ).
thf(fun_fu2408719596384163971_nat_o_type,type,
fun_fu2408719596384163971_nat_o: $tType ).
thf(produc2963631642982155120at_num_type,type,
produc2963631642982155120at_num: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(set_fi7789364187291644575l_real_type,type,
set_fi7789364187291644575l_real: $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_fu4556575633211565186enat_o_type,type,
fun_fu4556575633211565186enat_o: $tType ).
thf(fun_na3970208099681795815_nat_o_type,type,
fun_na3970208099681795815_nat_o: $tType ).
thf(filter6041513312241820739omplex_type,type,
filter6041513312241820739omplex: $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_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_Co5015990272074005067omplex_type,type,
fun_Co5015990272074005067omplex: $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_fu6899955116716589935t_real_type,type,
fun_fu6899955116716589935t_real: $tType ).
thf(fun_re4756235295228751087t_real_type,type,
fun_re4756235295228751087t_real: $tType ).
thf(fun_na5225841814499866095t_real_type,type,
fun_na5225841814499866095t_real: $tType ).
thf(fun_Pr7546709192626087934_nat_o_type,type,
fun_Pr7546709192626087934_nat_o: $tType ).
thf(set_Pr5085853215250843933omplex_type,type,
set_Pr5085853215250843933omplex: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(fun_fu3106432010075488275t_real_type,type,
fun_fu3106432010075488275t_real: $tType ).
thf(fun_fu6119738925743952495t_real_type,type,
fun_fu6119738925743952495t_real: $tType ).
thf(fun_Pr7716844367077540446plex_o_type,type,
fun_Pr7716844367077540446plex_o: $tType ).
thf(fun_na1154345429118027792d_enat_type,type,
fun_na1154345429118027792d_enat: $tType ).
thf(fun_o_2016307092959984611o_char_type,type,
fun_o_2016307092959984611o_char: $tType ).
thf(fun_fu6891447142836604759at_o_o_type,type,
fun_fu6891447142836604759at_o_o: $tType ).
thf(fun_Co5368275265270938953t_real_type,type,
fun_Co5368275265270938953t_real: $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_ra3995598502166916815at_rat_type,type,
fun_ra3995598502166916815at_rat: $tType ).
thf(fun_ra5513060666784058567at_rat_type,type,
fun_ra5513060666784058567at_rat: $tType ).
thf(fun_nu9041852840018610706omplex_type,type,
fun_nu9041852840018610706omplex: $tType ).
thf(fun_na3925014923085203400omplex_type,type,
fun_na3925014923085203400omplex: $tType ).
thf(fun_na3244735409550470327at_nat_type,type,
fun_na3244735409550470327at_nat: $tType ).
thf(fun_in6793278964266839919at_int_type,type,
fun_in6793278964266839919at_int: $tType ).
thf(fun_in1521351555827773387at_int_type,type,
fun_in1521351555827773387at_int: $tType ).
thf(fun_co7673397065115134084omplex_type,type,
fun_co7673397065115134084omplex: $tType ).
thf(fun_se9162176452187397432plex_o_type,type,
fun_se9162176452187397432plex_o: $tType ).
thf(fun_Co2081214437782444048eger_o_type,type,
fun_Co2081214437782444048eger_o: $tType ).
thf(fun_Co7401227239307276909et_nat_type,type,
fun_Co7401227239307276909et_nat: $tType ).
thf(fun_Co2587678820519358153et_int_type,type,
fun_Co2587678820519358153et_int: $tType ).
thf(fun_fu1358370060594899587plex_o_type,type,
fun_fu1358370060594899587plex_o: $tType ).
thf(fun_na7595719129879163854on_num_type,type,
fun_na7595719129879163854on_num: $tType ).
thf(fun_fu3022329567491847689real_o_type,type,
fun_fu3022329567491847689real_o: $tType ).
thf(fun_re6988797352886916895real_o_type,type,
fun_re6988797352886916895real_o: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(filter2146258269922977983l_real_type,type,
filter2146258269922977983l_real: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(fun_Pr2602117396471556196at_nat_type,type,
fun_Pr2602117396471556196at_nat: $tType ).
thf(fun_Pr7647638413817135296at_int_type,type,
fun_Pr7647638413817135296at_int: $tType ).
thf(fun_Pr982841511892225912nt_int_type,type,
fun_Pr982841511892225912nt_int: $tType ).
thf(fun_nu5148503272595741012um_num_type,type,
fun_nu5148503272595741012um_num: $tType ).
thf(fun_nu3130108178629567498at_num_type,type,
fun_nu3130108178629567498at_num: $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_nu4698968662094489488t_real_type,type,
fun_nu4698968662094489488t_real: $tType ).
thf(fun_na3666575854997362246t_real_type,type,
fun_na3666575854997362246t_real: $tType ).
thf(set_Pr448751882837621926eger_o_type,type,
set_Pr448751882837621926eger_o: $tType ).
thf(fun_Pr3290071492984375169er_o_o_type,type,
fun_Pr3290071492984375169er_o_o: $tType ).
thf(fun_o_7731073897867246747eger_o_type,type,
fun_o_7731073897867246747eger_o: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(filter1242075044329608583at_nat_type,type,
filter1242075044329608583at_nat: $tType ).
thf(fun_nu530747996811530292et_nat_type,type,
fun_nu530747996811530292et_nat: $tType ).
thf(fun_nu4940571614878387344et_int_type,type,
fun_nu4940571614878387344et_int: $tType ).
thf(fun_na1591161823130732966omplex_type,type,
fun_na1591161823130732966omplex: $tType ).
thf(fun_co3258106519541737638omplex_type,type,
fun_co3258106519541737638omplex: $tType ).
thf(fun_nu7188104440484974293_num_o_type,type,
fun_nu7188104440484974293_num_o: $tType ).
thf(fun_nu2628545618185965215_num_o_type,type,
fun_nu2628545618185965215_num_o: $tType ).
thf(fun_na8255220838387308393_num_o_type,type,
fun_na8255220838387308393_num_o: $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(set_Pr6218003697084177305l_real_type,type,
set_Pr6218003697084177305l_real: $tType ).
thf(fun_Pr4814023175418636514real_o_type,type,
fun_Pr4814023175418636514real_o: $tType ).
thf(fun_na7542918316964655096d_enat_type,type,
fun_na7542918316964655096d_enat: $tType ).
thf(fun_o_7148296245751160776un_o_o_type,type,
fun_o_7148296245751160776un_o_o: $tType ).
thf(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_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(fun_Co681828205884031672o_char_type,type,
fun_Co681828205884031672o_char: $tType ).
thf(set_Pr8218934625190621173um_num_type,type,
set_Pr8218934625190621173um_num: $tType ).
thf(set_Pr6200539531224447659at_num_type,type,
set_Pr6200539531224447659at_num: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(fun_fu9050450510664235267real_o_type,type,
fun_fu9050450510664235267real_o: $tType ).
thf(fun_VE3165209603783583043T_VEBT_type,type,
fun_VE3165209603783583043T_VEBT: $tType ).
thf(fun_re2084383175013312036omplex_type,type,
fun_re2084383175013312036omplex: $tType ).
thf(fun_Pr6331313853612757382_num_o_type,type,
fun_Pr6331313853612757382_num_o: $tType ).
thf(fun_Pr5555124106300582480_num_o_type,type,
fun_Pr5555124106300582480_num_o: $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_na1957955181367619364omplex_type,type,
fun_na1957955181367619364omplex: $tType ).
thf(fun_na5723442673449079972x_real_type,type,
fun_na5723442673449079972x_real: $tType ).
thf(fun_co8378349014452122532t_real_type,type,
fun_co8378349014452122532t_real: $tType ).
thf(fun_o_8988054265482332260nt_int_type,type,
fun_o_8988054265482332260nt_int: $tType ).
thf(fun_na7234455742697417626_nat_o_type,type,
fun_na7234455742697417626_nat_o: $tType ).
thf(fun_set_nat_set_nat_type,type,
fun_set_nat_set_nat: $tType ).
thf(fun_na6887940067898170868VEBT_o_type,type,
fun_na6887940067898170868VEBT_o: $tType ).
thf(fun_na1142814060743658952omplex_type,type,
fun_na1142814060743658952omplex: $tType ).
thf(fun_na5558608354090810916omplex_type,type,
fun_na5558608354090810916omplex: $tType ).
thf(fun_in8056368165505483812omplex_type,type,
fun_in8056368165505483812omplex: $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_co1148497455491383662plex_o_type,type,
fun_co1148497455491383662plex_o: $tType ).
thf(fun_fu4001317426178549763_nat_o_type,type,
fun_fu4001317426178549763_nat_o: $tType ).
thf(fun_fu3883539188510166275_int_o_type,type,
fun_fu3883539188510166275_int_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_nat_fun_nat_real_type,type,
fun_nat_fun_nat_real: $tType ).
thf(fun_nat_fun_int_real_type,type,
fun_nat_fun_int_real: $tType ).
thf(fun_list_VEBT_VEBT_o_type,type,
fun_list_VEBT_VEBT_o: $tType ).
thf(fun_int_fun_nat_real_type,type,
fun_int_fun_nat_real: $tType ).
thf(fun_Ex5852502975177633731d_enat_type,type,
fun_Ex5852502975177633731d_enat: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(fun_set_nat_complex_type,type,
fun_set_nat_complex: $tType ).
thf(fun_rat_fun_nat_rat_type,type,
fun_rat_fun_nat_rat: $tType ).
thf(fun_num_set_complex_type,type,
fun_num_set_complex: $tType ).
thf(fun_nat_fun_rat_rat_type,type,
fun_nat_fun_rat_rat: $tType ).
thf(fun_nat_fun_num_num_type,type,
fun_nat_fun_num_num: $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_int_type,type,
fun_int_fun_int_int: $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_nat_option_num_type,type,
fun_nat_option_num: $tType ).
thf(fun_Co480733329897759773un_o_o_type,type,
fun_Co480733329897759773un_o_o: $tType ).
thf(fun_real_fun_real_o_type,type,
fun_real_fun_real_o: $tType ).
thf(fun_o_1321283479831784608enat_o_type,type,
fun_o_1321283479831784608enat_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_set_nat_real_type,type,
fun_set_nat_real: $tType ).
thf(fun_num_set_real_type,type,
fun_num_set_real: $tType ).
thf(fun_VEBT_VEBT_nat_type,type,
fun_VEBT_VEBT_nat: $tType ).
thf(fun_VEBT_VEBT_int_type,type,
fun_VEBT_VEBT_int: $tType ).
thf(fun_nat_VEBT_VEBT_type,type,
fun_nat_VEBT_VEBT: $tType ).
thf(fun_int_VEBT_VEBT_type,type,
fun_int_VEBT_VEBT: $tType ).
thf(fun_set_nat_nat_type,type,
fun_set_nat_nat: $tType ).
thf(fun_num_set_nat_type,type,
fun_num_set_nat: $tType ).
thf(fun_num_set_int_type,type,
fun_num_set_int: $tType ).
thf(fun_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_set_int_type,type,
fun_nat_set_int: $tType ).
thf(fun_nat_Code_integer_type,type,
fun_nat_Code_integer: $tType ).
thf(fun_int_set_int_type,type,
fun_int_set_int: $tType ).
thf(fun_complex_complex_type,type,
fun_complex_complex: $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_rat_fun_rat_o_type,type,
fun_rat_fun_rat_o: $tType ).
thf(fun_num_fun_num_o_type,type,
fun_num_fun_num_o: $tType ).
thf(fun_nat_fun_num_o_type,type,
fun_nat_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_o_set_complex_type,type,
fun_o_set_complex: $tType ).
thf(fun_option_num_o_type,type,
fun_option_num_o: $tType ).
thf(fun_na8797796813480665199d_enat_type,type,
fun_na8797796813480665199d_enat: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(fun_real_complex_type,type,
fun_real_complex: $tType ).
thf(fun_complex_real_type,type,
fun_complex_real: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(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(fun_o_set_real_type,type,
fun_o_set_real: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(fun_VEBT_VEBT_o_type,type,
fun_VEBT_VEBT_o: $tType ).
thf(fun_nat_complex_type,type,
fun_nat_complex: $tType ).
thf(fun_int_complex_type,type,
fun_int_complex: $tType ).
thf(fun_complex_nat_type,type,
fun_complex_nat: $tType ).
thf(fun_complex_int_type,type,
fun_complex_int: $tType ).
thf(fun_o_VEBT_VEBT_type,type,
fun_o_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(fun_set_nat_o_type,type,
fun_set_nat_o: $tType ).
thf(fun_set_int_o_type,type,
fun_set_int_o: $tType ).
thf(fun_Code_integer_o_type,type,
fun_Code_integer_o: $tType ).
thf(fun_o_set_nat_type,type,
fun_o_set_nat: $tType ).
thf(fun_o_set_int_type,type,
fun_o_set_int: $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(set_Extended_enat_type,type,
set_Extended_enat: $tType ).
thf(fun_char_nat_type,type,
fun_char_nat: $tType ).
thf(fun_real_real_type,type,
fun_real_real: $tType ).
thf(fun_nat_char_type,type,
fun_nat_char: $tType ).
thf(fun_Extended_enat_o_type,type,
fun_Extended_enat_o: $tType ).
thf(fun_real_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(set_set_o_type,type,
set_set_o: $tType ).
thf(fun_set_o_o_type,type,
fun_set_o_o: $tType ).
thf(fun_o_set_o_type,type,
fun_o_set_o: $tType ).
thf(option_num_type,type,
option_num: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(fun_o_char_type,type,
fun_o_char: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(list_num_type,type,
list_num: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(fun_real_o_type,type,
fun_real_o: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(set_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(fun_rat_o_type,type,
fun_rat_o: $tType ).
thf(fun_num_o_type,type,
fun_num_o: $tType ).
thf(fun_nat_o_type,type,
fun_nat_o: $tType ).
thf(fun_int_o_type,type,
fun_int_o: $tType ).
thf(fun_o_nat_type,type,
fun_o_nat: $tType ).
thf(fun_o_int_type,type,
fun_o_int: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(fun_o_o_type,type,
fun_o_o: $tType ).
thf(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(extend5688581933313929465d_enat_decl,type,
extend5688581933313929465d_enat: extended_enat ).
thf(minus_3235023915231533773d_enat_decl,type,
minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
thf(one_on7984719198319812577d_enat_decl,type,
one_on7984719198319812577d_enat: extended_enat ).
thf(plus_p3455044024723400733d_enat_decl,type,
plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
thf(zero_z5237406670263579293d_enat_decl,type,
zero_z5237406670263579293d_enat: extended_enat ).
thf(numera1916890842035813515d_enat_decl,type,
numera1916890842035813515d_enat: num > extended_enat ).
thf(top_to3028658606643905974d_enat_decl,type,
top_to3028658606643905974d_enat: extended_enat ).
thf(vEBT_VEBT_elim_dead_decl,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(summarya_decl,type,
summarya: vEBT_VEBT ).
thf(18,axiom,
! [A: num] :
( ( A @ numera1916890842035813515d_enat )
!= extend5688581933313929465d_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_numeral__ne__infinity) ).
thf(88,plain,
! [A: num] :
( ( A @ numera1916890842035813515d_enat )
!= extend5688581933313929465d_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: extended_enat,B: extended_enat] :
( ( A != extend5688581933313929465d_enat )
=> ( ( A @ ( B @ ( A @ plus_p3455044024723400733d_enat ) @ minus_3235023915231533773d_enat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4419_add__diff__cancel__enat) ).
thf(37,plain,
! [A: extended_enat,B: extended_enat] :
( ( A != extend5688581933313929465d_enat )
=> ( ( A @ ( B @ ( A @ plus_p3455044024723400733d_enat ) @ minus_3235023915231533773d_enat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
extend5688581933313929465d_enat != zero_z5237406670263579293d_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1724_infinity__ne__i0) ).
thf(61,plain,
extend5688581933313929465d_enat != zero_z5237406670263579293d_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: extended_enat] :
( ( A @ ( extend5688581933313929465d_enat @ minus_3235023915231533773d_enat ) )
= extend5688581933313929465d_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4406_idiff__infinity) ).
thf(85,plain,
! [A: extended_enat] :
( ( A @ ( extend5688581933313929465d_enat @ minus_3235023915231533773d_enat ) )
= extend5688581933313929465d_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= zero_z5237406670263579293d_enat )
<=> ( ( B = zero_z5237406670263579293d_enat )
& ( A = zero_z5237406670263579293d_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1736_iadd__is__0) ).
thf(21,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( ( B = zero_z5237406670263579293d_enat )
& ( A = zero_z5237406670263579293d_enat ) )
=> ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= zero_z5237406670263579293d_enat ) )
& ( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= zero_z5237406670263579293d_enat )
=> ( ( B = zero_z5237406670263579293d_enat )
& ( A = zero_z5237406670263579293d_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: extended_enat] :
( ( extend5688581933313929465d_enat @ ( A @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_plus__enat__simps_I3_J) ).
thf(77,plain,
! [A: extended_enat] :
( ( extend5688581933313929465d_enat @ ( A @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: extended_enat] :
( ( zero_z5237406670263579293d_enat @ ( A @ minus_3235023915231533773d_enat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4408_idiff__0__right) ).
thf(41,plain,
! [A: extended_enat] :
( ( zero_z5237406670263579293d_enat @ ( A @ minus_3235023915231533773d_enat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: extended_enat] :
( ( A @ ( zero_z5237406670263579293d_enat @ minus_3235023915231533773d_enat ) )
= zero_z5237406670263579293d_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4407_idiff__0) ).
thf(44,plain,
! [A: extended_enat] :
( ( A @ ( zero_z5237406670263579293d_enat @ minus_3235023915231533773d_enat ) )
= zero_z5237406670263579293d_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
top_to3028658606643905974d_enat = extend5688581933313929465d_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9922_top__enat__def) ).
thf(80,plain,
top_to3028658606643905974d_enat = extend5688581933313929465d_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( ( extend5688581933313929465d_enat @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( extend5688581933313929465d_enat @ ( summarya @ vEBT_VEBT_elim_dead ) )
!= summarya ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
( ( extend5688581933313929465d_enat @ ( summarya @ vEBT_VEBT_elim_dead ) )
!= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
extend5688581933313929465d_enat != one_on7984719198319812577d_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_infinity__ne__i1) ).
thf(47,plain,
extend5688581933313929465d_enat != one_on7984719198319812577d_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1536_zero__one__enat__neq_I1_J) ).
thf(34,plain,
zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat )
<=> ( ( B = extend5688581933313929465d_enat )
| ( A = extend5688581933313929465d_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_plus__eq__infty__iff__enat) ).
thf(64,plain,
! [A: extended_enat,B: extended_enat] :
( ( ( ( B = extend5688581933313929465d_enat )
| ( A = extend5688581933313929465d_enat ) )
=> ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat ) )
& ( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat )
=> ( ( B = extend5688581933313929465d_enat )
| ( A = extend5688581933313929465d_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= ( C @ ( A @ plus_p3455044024723400733d_enat ) ) )
<=> ( ( B = C )
| ( A = extend5688581933313929465d_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_enat__add__left__cancel) ).
thf(50,plain,
! [A: extended_enat,B: extended_enat,C: extended_enat] :
( ( ( ( B = C )
| ( A = extend5688581933313929465d_enat ) )
=> ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= ( C @ ( A @ plus_p3455044024723400733d_enat ) ) ) )
& ( ( ( B @ ( A @ plus_p3455044024723400733d_enat ) )
= ( C @ ( A @ plus_p3455044024723400733d_enat ) ) )
=> ( ( B = C )
| ( A = extend5688581933313929465d_enat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: extended_enat] :
( ( A != extend5688581933313929465d_enat )
=> ( ( A @ ( A @ minus_3235023915231533773d_enat ) )
= zero_z5237406670263579293d_enat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4418_idiff__self) ).
thf(31,plain,
! [A: extended_enat] :
( ( A != extend5688581933313929465d_enat )
=> ( ( A @ ( A @ minus_3235023915231533773d_enat ) )
= zero_z5237406670263579293d_enat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
( ( extend5688581933313929465d_enat @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C2_OIH_C_I2_J) ).
thf(75,plain,
( ( extend5688581933313929465d_enat @ ( summarya @ vEBT_VEBT_elim_dead ) )
= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: extended_enat] :
( ( A @ ( extend5688581933313929465d_enat @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_plus__enat__simps_I2_J) ).
thf(82,plain,
! [A: extended_enat] :
( ( A @ ( extend5688581933313929465d_enat @ plus_p3455044024723400733d_enat ) )
= extend5688581933313929465d_enat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(92,plain,
$false,
inference(e,[status(thm)],[88,37,61,85,21,77,41,44,80,19,47,34,64,50,31,75,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP222_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/10.40 % Computer : n019.cluster.edu
% 0.14/10.40 % Model : x86_64 x86_64
% 0.14/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.40 % Memory : 8046.5625MB
% 0.14/10.40 % OS : Linux 6.8.0-71-generic
% 0.14/10.40 % CPULimit : 300
% 0.14/10.40 % WCLimit : 300
% 0.14/10.40 % DateTime : Fri Sep 25 18:15:46 UTC 2026
% 0.14/10.41 % CPUTime :
% 0.14/10.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/11.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.58/12.62 % [INFO] Parsing done (1619ms).
% 7.58/12.64 % [INFO] Running in sequential loop mode.
% 8.39/12.87 % [INFO] eprover registered as external prover.
% 8.39/12.88 % [INFO] Scanning for conjecture ...
% 12.57/14.00 % [INFO] Found a conjecture (or negated_conjecture) and 10792 axioms. Running axiom selection ...
% 13.53/14.15 % [INFO] Axiom selection finished. Selected 16 axioms (removed 10776 axioms).
% 13.53/14.18 % [INFO] Problem is typed first-order (TPTP TFF).
% 13.53/14.19 % [INFO] Type checking passed.
% 13.53/14.19 % [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 ...
% 16.14/14.96 % External prover 'e' found a proof!
% 16.14/14.97 % [INFO] Killing All external provers ...
% 16.14/14.97 % Time passed: 4416ms (effective reasoning time: 2319ms)
% 16.14/14.97 % 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)>
% 16.14/14.97 % Axioms used in derivation (16): fact_4408_idiff__0__right, fact_1001_infinity__ne__i1, fact_4407_idiff__0, fact_1__C2_OIH_C_I2_J, fact_1536_zero__one__enat__neq_I1_J, fact_121_enat__add__left__cancel, fact_4418_idiff__self, fact_1736_iadd__is__0, fact_4419_add__diff__cancel__enat, fact_107_plus__enat__simps_I3_J, fact_122_numeral__ne__infinity, fact_1724_infinity__ne__i0, fact_9922_top__enat__def, fact_4406_idiff__infinity, fact_120_plus__eq__infty__iff__enat, fact_106_plus__enat__simps_I2_J
% 16.14/14.97 % No. of inferences in proof: 36
% 16.14/14.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4416 ms resp. 2319 ms w/o parsing
% 16.69/15.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.69/15.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------