%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP227_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 : n004.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 07:36:59 AM UTC 2026
% Result : Theorem 15.45s 10.07s
% Output : Refutation 15.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 17 ~; 5 |; 4 &; 0 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 309 ( 309 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(fun_li6914387844523535256_nat_o_type,type,
fun_li6914387844523535256_nat_o: $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_fu7180905015247952065t_real_type,type,
fun_fu7180905015247952065t_real: $tType ).
thf(fun_fu4217534345154246979t_real_type,type,
fun_fu4217534345154246979t_real: $tType ).
thf(fun_Pr8877776288780692068_nat_o_type,type,
fun_Pr8877776288780692068_nat_o: $tType ).
thf(fun_fu7732904369943091395at_nat_type,type,
fun_fu7732904369943091395at_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_fu1584491925252458057omplex_type,type,
fun_fu1584491925252458057omplex: $tType ).
thf(fun_fu8084223252616112272omplex_type,type,
fun_fu8084223252616112272omplex: $tType ).
thf(fun_fu3593947265352647275omplex_type,type,
fun_fu3593947265352647275omplex: $tType ).
thf(fun_fu3275390434952296369_nat_o_type,type,
fun_fu3275390434952296369_nat_o: $tType ).
thf(fun_fu8998703528969179354omplex_type,type,
fun_fu8998703528969179354omplex: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(fun_fu6810213084838398785t_real_type,type,
fun_fu6810213084838398785t_real: $tType ).
thf(fun_VE2573032740582156747_nat_o_type,type,
fun_VE2573032740582156747_nat_o: $tType ).
thf(fun_co3732688428756473980omplex_type,type,
fun_co3732688428756473980omplex: $tType ).
thf(fun_fu1620311477532340197t_real_type,type,
fun_fu1620311477532340197t_real: $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_fu5304001865264412401at_rat_type,type,
fun_fu5304001865264412401at_rat: $tType ).
thf(fun_fu5935951186182374353at_nat_type,type,
fun_fu5935951186182374353at_nat: $tType ).
thf(fun_fu960360787657196261at_int_type,type,
fun_fu960360787657196261at_int: $tType ).
thf(fun_fu4902120768161409089at_int_type,type,
fun_fu4902120768161409089at_int: $tType ).
thf(fun_fu6652553491520710942omplex_type,type,
fun_fu6652553491520710942omplex: $tType ).
thf(fun_fu1400560744564786701nteger_type,type,
fun_fu1400560744564786701nteger: $tType ).
thf(fun_co3194742168270691230omplex_type,type,
fun_co3194742168270691230omplex: $tType ).
thf(fun_Co8502721031311864414nteger_type,type,
fun_Co8502721031311864414nteger: $tType ).
thf(fun_fu3306995184869731826t_real_type,type,
fun_fu3306995184869731826t_real: $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_fu2454420574033104442at_nat_type,type,
fun_fu2454420574033104442at_nat: $tType ).
thf(fun_fu4528473944208963392omplex_type,type,
fun_fu4528473944208963392omplex: $tType ).
thf(fun_fu3739269683040691718nt_int_type,type,
fun_fu3739269683040691718nt_int: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_fu8643405727515436425nteger_type,type,
fun_fu8643405727515436425nteger: $tType ).
thf(fun_fu3477889739401271834t_real_type,type,
fun_fu3477889739401271834t_real: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_fu2499394402704830801nteger_type,type,
fun_fu2499394402704830801nteger: $tType ).
thf(fun_fu3628599891403802633nteger_type,type,
fun_fu3628599891403802633nteger: $tType ).
thf(fun_fu5956788528830221615omplex_type,type,
fun_fu5956788528830221615omplex: $tType ).
thf(fun_re6135230694098607860t_real_type,type,
fun_re6135230694098607860t_real: $tType ).
thf(fun_fu5589980185390252312t_real_type,type,
fun_fu5589980185390252312t_real: $tType ).
thf(fun_fu8064956510386623256t_real_type,type,
fun_fu8064956510386623256t_real: $tType ).
thf(fun_re7819166435457029784t_real_type,type,
fun_re7819166435457029784t_real: $tType ).
thf(fun_fu4806068833880117316t_real_type,type,
fun_fu4806068833880117316t_real: $tType ).
thf(fun_fu2115079063411676732t_real_type,type,
fun_fu2115079063411676732t_real: $tType ).
thf(fun_fu4540635375566031512t_real_type,type,
fun_fu4540635375566031512t_real: $tType ).
thf(fun_fu163975356400620604t_real_type,type,
fun_fu163975356400620604t_real: $tType ).
thf(fun_fu8968174646369908141x_real_type,type,
fun_fu8968174646369908141x_real: $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_fu923337204662071120nt_int_type,type,
fun_fu923337204662071120nt_int: $tType ).
thf(fun_ra8505079968215247908at_rat_type,type,
fun_ra8505079968215247908at_rat: $tType ).
thf(fun_ra2740371568465858076at_rat_type,type,
fun_ra2740371568465858076at_rat: $tType ).
thf(fun_in281396392327853336at_int_type,type,
fun_in281396392327853336at_int: $tType ).
thf(fun_co6147893885205795665omplex_type,type,
fun_co6147893885205795665omplex: $tType ).
thf(fun_Co1981900195452921617nteger_type,type,
fun_Co1981900195452921617nteger: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(fun_fu7714627026455246123x_real_type,type,
fun_fu7714627026455246123x_real: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(fun_fu1994797156054922755_nat_o_type,type,
fun_fu1994797156054922755_nat_o: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(fun_fu40286998686754419omplex_type,type,
fun_fu40286998686754419omplex: $tType ).
thf(fun_fu705315015666092147ex_nat_type,type,
fun_fu705315015666092147ex_nat: $tType ).
thf(fun_se7512233253626865466omplex_type,type,
fun_se7512233253626865466omplex: $tType ).
thf(fun_na6632006986671646835omplex_type,type,
fun_na6632006986671646835omplex: $tType ).
thf(fun_co6883864892131739507omplex_type,type,
fun_co6883864892131739507omplex: $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_fu6344110373156359337l_real_type,type,
fun_fu6344110373156359337l_real: $tType ).
thf(produc2963631642982155120at_num_type,type,
produc2963631642982155120at_num: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(fun_fu7631928937237476593t_real_type,type,
fun_fu7631928937237476593t_real: $tType ).
thf(fun_fu3594690983434520489t_real_type,type,
fun_fu3594690983434520489t_real: $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_fu4781654129426620053omplex_type,type,
fun_fu4781654129426620053omplex: $tType ).
thf(fun_Co6226381647958292740nteger_type,type,
fun_Co6226381647958292740nteger: $tType ).
thf(fun_Co8521658056209057742er_num_type,type,
fun_Co8521658056209057742er_num: $tType ).
thf(fun_Co3583066429914935172er_nat_type,type,
fun_Co3583066429914935172er_nat: $tType ).
thf(fun_Co1092983284983208416er_int_type,type,
fun_Co1092983284983208416er_int: $tType ).
thf(fun_re8542384036533109323t_real_type,type,
fun_re8542384036533109323t_real: $tType ).
thf(fun_re4112884445705685835l_real_type,type,
fun_re4112884445705685835l_real: $tType ).
thf(list_P7037539587688870467BT_nat_type,type,
list_P7037539587688870467BT_nat: $tType ).
thf(list_P4547456442757143711BT_int_type,type,
list_P4547456442757143711BT_int: $tType ).
thf(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_re4756235295228751087t_real_type,type,
fun_re4756235295228751087t_real: $tType ).
thf(fun_na5225841814499866095t_real_type,type,
fun_na5225841814499866095t_real: $tType ).
thf(fun_Pr4050773816208733250omplex_type,type,
fun_Pr4050773816208733250omplex: $tType ).
thf(fun_li1025265955262268170_nat_o_type,type,
fun_li1025265955262268170_nat_o: $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_na7718645245721260691t_real_type,type,
fun_na7718645245721260691t_real: $tType ).
thf(fun_VE2962686792283380846VEBT_o_type,type,
fun_VE2962686792283380846VEBT_o: $tType ).
thf(fun_fu8328862064278946247at_rat_type,type,
fun_fu8328862064278946247at_rat: $tType ).
thf(fun_fu7002938529518989751at_nat_type,type,
fun_fu7002938529518989751at_nat: $tType ).
thf(fun_fu4512855384587262995at_int_type,type,
fun_fu4512855384587262995at_int: $tType ).
thf(fun_fu8464300013002972271at_int_type,type,
fun_fu8464300013002972271at_int: $tType ).
thf(fun_fu1008360527747082367nt_rat_type,type,
fun_fu1008360527747082367nt_rat: $tType ).
thf(fun_fu8905809029841901679nt_nat_type,type,
fun_fu8905809029841901679nt_nat: $tType ).
thf(fun_fu6415725884910174923nt_int_type,type,
fun_fu6415725884910174923nt_int: $tType ).
thf(fun_fu1143798476471108391nt_int_type,type,
fun_fu1143798476471108391nt_int: $tType ).
thf(fun_ra3995598502166916815at_rat_type,type,
fun_ra3995598502166916815at_rat: $tType ).
thf(fun_ra5513060666784058567at_rat_type,type,
fun_ra5513060666784058567at_rat: $tType ).
thf(fun_na1148497095348402375at_rat_type,type,
fun_na1148497095348402375at_rat: $tType ).
thf(fun_na3244735409550470327at_nat_type,type,
fun_na3244735409550470327at_nat: $tType ).
thf(fun_na7654559027617327379at_int_type,type,
fun_na7654559027617327379at_int: $tType ).
thf(fun_na2382631619178260847at_int_type,type,
fun_na2382631619178260847at_int: $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_Co2081214437782444048eger_o_type,type,
fun_Co2081214437782444048eger_o: $tType ).
thf(fun_fu1358370060594899587plex_o_type,type,
fun_fu1358370060594899587plex_o: $tType ).
thf(fun_nu1049378303802735384on_num_type,type,
fun_nu1049378303802735384on_num: $tType ).
thf(fun_na7595719129879163854on_num_type,type,
fun_na7595719129879163854on_num: $tType ).
thf(fun_Pr672294278902479040t_real_type,type,
fun_Pr672294278902479040t_real: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(fun_ra4503298312962071866nt_int_type,type,
fun_ra4503298312962071866nt_int: $tType ).
thf(fun_Pr2602117396471556196at_nat_type,type,
fun_Pr2602117396471556196at_nat: $tType ).
thf(fun_Pr7647638413817135296at_int_type,type,
fun_Pr7647638413817135296at_int: $tType ).
thf(fun_na1476630412504255114at_nat_type,type,
fun_na1476630412504255114at_nat: $tType ).
thf(fun_in4211310926729683942nt_int_type,type,
fun_in4211310926729683942nt_int: $tType ).
thf(fun_se1654316830156123260t_real_type,type,
fun_se1654316830156123260t_real: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(fun_se1179353343636554400at_nat_type,type,
fun_se1179353343636554400at_nat: $tType ).
thf(fun_se4827636401813558708nt_int_type,type,
fun_se4827636401813558708nt_int: $tType ).
thf(fun_na1591161823130732966omplex_type,type,
fun_na1591161823130732966omplex: $tType ).
thf(fun_co3258106519541737638omplex_type,type,
fun_co3258106519541737638omplex: $tType ).
thf(fun_na7928631014926962227_nat_o_type,type,
fun_na7928631014926962227_nat_o: $tType ).
thf(fun_in5570076352459579423_int_o_type,type,
fun_in5570076352459579423_int_o: $tType ).
thf(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_num: $tType ).
thf(list_P6011104703257516679at_nat_type,type,
list_P6011104703257516679at_nat: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(fun_fu9050450510664235267real_o_type,type,
fun_fu9050450510664235267real_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_na5723442673449079972x_real_type,type,
fun_na5723442673449079972x_real: $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_Co8499238673658658103nteger_type,type,
fun_Co8499238673658658103nteger: $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_rat_real_type,type,
fun_nat_fun_rat_real: $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_Ex5852502975177633731d_enat_type,type,
fun_Ex5852502975177633731d_enat: $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_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_co8153928105989009288nteger_type,type,
fun_co8153928105989009288nteger: $tType ).
thf(fun_na1554462459066888140plex_o_type,type,
fun_na1554462459066888140plex_o: $tType ).
thf(fun_num_option_num_type,type,
fun_num_option_num: $tType ).
thf(fun_nat_option_num_type,type,
fun_nat_option_num: $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_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_set_int_type,type,
fun_nat_set_int: $tType ).
thf(fun_nat_Code_integer_type,type,
fun_nat_Code_integer: $tType ).
thf(fun_int_Code_integer_type,type,
fun_int_Code_integer: $tType ).
thf(fun_complex_complex_type,type,
fun_complex_complex: $tType ).
thf(fun_Code_integer_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_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(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_Code_integer_type,type,
list_Code_integer: $tType ).
thf(fun_list_nat_o_type,type,
fun_list_nat_o: $tType ).
thf(fun_list_int_o_type,type,
fun_list_int_o: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(fun_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_set_int_type,type,
set_set_int: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(fun_set_int_o_type,type,
fun_set_int_o: $tType ).
thf(fun_Code_integer_o_type,type,
fun_Code_integer_o: $tType ).
thf(fun_nat_fun_o_o_type,type,
fun_nat_fun_o_o: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(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(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(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_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(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(xa_decl,type,
xa: nat ).
thf(1,conjecture,
( ( xa != ma )
& ( xa != mi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( xa != ma )
& ( xa != mi ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( ( xa != ma )
& ( xa != mi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( xa = ma )
| ( xa = mi ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( xa = ma )
| ( xa = mi ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(3,axiom,
~ ( ( xa = ma )
| ( xa = mi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(7,plain,
~ ( ( xa = ma )
| ( xa = mi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
~ ( ( xa = ma )
| ( xa = mi ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( xa != ma )
& ( xa != mi ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
xa != mi,
inference(cnfConj,[status(thm)],[9]) ).
thf(12,plain,
xa != mi,
inference(lifteq,[status(thm)],[10]) ).
thf(11,plain,
xa != ma,
inference(cnfConj,[status(thm)],[9]) ).
thf(13,plain,
xa != ma,
inference(lifteq,[status(thm)],[11]) ).
thf(14,plain,
$false,
inference(simplifyReflect,[status(thm)],[6,12,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP227_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/5.42 % Computer : n004.cluster.edu
% 0.13/5.42 % Model : x86_64 x86_64
% 0.13/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.42 % Memory : 8046.5625MB
% 0.13/5.42 % OS : Linux 6.8.0-71-generic
% 0.13/5.42 % CPULimit : 300
% 0.13/5.42 % WCLimit : 300
% 0.13/5.42 % DateTime : Fri Sep 25 18:18:27 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.43 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
% 0.19/5.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 8.21/7.85 % [INFO] Parsing done (1849ms).
% 8.21/7.87 % [INFO] Running in sequential loop mode.
% 9.27/8.26 % [INFO] eprover registered as external prover.
% 9.27/8.27 % [INFO] Scanning for conjecture ...
% 13.48/9.44 % [INFO] Found a conjecture (or negated_conjecture) and 10799 axioms. Running axiom selection ...
% 13.68/9.59 % [INFO] Axiom selection finished. Selected 1 axioms (removed 10798 axioms).
% 13.68/9.59 % [INFO] Problem is typed first-order (TPTP TFF).
% 14.11/9.60 % [INFO] Type checking passed.
% 14.11/9.60 % [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 ...
% 15.45/10.06 % [INFO] Killing All external provers ...
% 15.45/10.06 % Time passed: 4499ms (effective reasoning time: 2168ms)
% 15.45/10.06 % 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)>
% 15.45/10.06 % Axioms used in derivation (1): fact_0_False
% 15.45/10.06 % No. of inferences in proof: 14
% 15.45/10.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4499 ms resp. 2168 ms w/o parsing
% 15.45/10.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.45/10.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------