%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP233_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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:04 AM UTC 2026
% Result : Theorem 26.53s 8.25s
% Output : Refutation 28.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 374
% Syntax : Number of formulae : 750 ( 502 unt; 0 typ; 0 def)
% Number of atoms : 1400 (1133 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 9370 ( 238 ~; 52 |; 172 &;8479 @)
% ( 64 <=>; 365 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 494 ( 493 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 44 con; 0-4 aty)
% Number of variables : 1661 ( 0 ^;1590 !; 44 ?;1661 :)
% ( 0 !>; 0 ?*; 0 @-; 27 @+)
% Comments :
%------------------------------------------------------------------------------
thf(fun_Pr1212089810744049917at_nat_type,type,
fun_Pr1212089810744049917at_nat: $tType ).
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_o: $tType ).
thf(fun_fu2295278630349710275d_enat_type,type,
fun_fu2295278630349710275d_enat: $tType ).
thf(fun_Pr5303981572562559465at_nat_type,type,
fun_Pr5303981572562559465at_nat: $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_fu5040975675184911655d_enat_type,type,
fun_fu5040975675184911655d_enat: $tType ).
thf(set_Pr1542805901266377927at_nat_type,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(produc9217583074051984497at_nat_type,type,
produc9217583074051984497at_nat: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_op1221328669798608686_nat_o_type,type,
fun_op1221328669798608686_nat_o: $tType ).
thf(fun_fu3686806697881729723t_real_type,type,
fun_fu3686806697881729723t_real: $tType ).
thf(produc6392793444374437607at_nat_type,type,
produc6392793444374437607at_nat: $tType ).
thf(fun_fu5303113179588540421d_enat_type,type,
fun_fu5303113179588540421d_enat: $tType ).
thf(fun_fu8366861321737653343at_nat_type,type,
fun_fu8366861321737653343at_nat: $tType ).
thf(fun_fu2469135700067826619at_int_type,type,
fun_fu2469135700067826619at_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_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_fu9045186299510176150at_o_o_type,type,
fun_fu9045186299510176150at_o_o: $tType ).
thf(fun_fu3612569900928539882l_real_type,type,
fun_fu3612569900928539882l_real: $tType ).
thf(fun_fu1584491925252458057omplex_type,type,
fun_fu1584491925252458057omplex: $tType ).
thf(fun_VE5572235297906325245d_enat_type,type,
fun_VE5572235297906325245d_enat: $tType ).
thf(fun_fu7039103635370308747enat_o_type,type,
fun_fu7039103635370308747enat_o: $tType ).
thf(fun_fu709861064203714431x_real_type,type,
fun_fu709861064203714431x_real: $tType ).
thf(list_P8469869581646625389at_nat_type,type,
list_P8469869581646625389at_nat: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(fun_fu3593947265352647275omplex_type,type,
fun_fu3593947265352647275omplex: $tType ).
thf(fun_fu2513798379308225899ex_nat_type,type,
fun_fu2513798379308225899ex_nat: $tType ).
thf(fun_fu4692242605864086655ex_int_type,type,
fun_fu4692242605864086655ex_int: $tType ).
thf(fun_Pr363642936170290612_nat_o_type,type,
fun_Pr363642936170290612_nat_o: $tType ).
thf(fun_fu7523448966510524487plex_o_type,type,
fun_fu7523448966510524487plex_o: $tType ).
thf(fun_fu7998770217265696895plex_o_type,type,
fun_fu7998770217265696895plex_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_Ex1869439690531410417d_enat_type,type,
fun_Ex1869439690531410417d_enat: $tType ).
thf(set_Pr1916528119006554503T_VEBT_type,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $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_fu3768230810189712741al_nat_type,type,
fun_fu3768230810189712741al_nat: $tType ).
thf(fun_fu5645595436833112697al_int_type,type,
fun_fu5645595436833112697al_int: $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_VE7750965991535404103BT_nat_type,type,
fun_VE7750965991535404103BT_nat: $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_fu7872074469501006851d_enat_type,type,
fun_fu7872074469501006851d_enat: $tType ).
thf(fun_co6469028316994822131omplex_type,type,
fun_co6469028316994822131omplex: $tType ).
thf(fun_fu5533088652784741581real_o_type,type,
fun_fu5533088652784741581real_o: $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_fu973771059875708133nt_nat_type,type,
fun_fu973771059875708133nt_nat: $tType ).
thf(fun_co3194742168270691230omplex_type,type,
fun_co3194742168270691230omplex: $tType ).
thf(fun_fu5575653946431489541real_o_type,type,
fun_fu5575653946431489541real_o: $tType ).
thf(fun_se2100927751953696370t_real_type,type,
fun_se2100927751953696370t_real: $tType ).
thf(fun_Ex6561714628001473733d_enat_type,type,
fun_Ex6561714628001473733d_enat: $tType ).
thf(fun_Ex4306801469811899753d_enat_type,type,
fun_Ex4306801469811899753d_enat: $tType ).
thf(fun_fu6813129056075673441_nat_o_type,type,
fun_fu6813129056075673441_nat_o: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_fu875838123782038019d_enat_type,type,
fun_fu875838123782038019d_enat: $tType ).
thf(fun_fu2357351296865450298t_real_type,type,
fun_fu2357351296865450298t_real: $tType ).
thf(produc9211091688327510695T_VEBT_type,type,
produc9211091688327510695T_VEBT: $tType ).
thf(fun_fu9090758901314268781nt_o_o_type,type,
fun_fu9090758901314268781nt_o_o: $tType ).
thf(fun_fu4528473944208963392omplex_type,type,
fun_fu4528473944208963392omplex: $tType ).
thf(fun_fu6075382464776002713_nat_o_type,type,
fun_fu6075382464776002713_nat_o: $tType ).
thf(fun_fu2760153274138146437_int_o_type,type,
fun_fu2760153274138146437_int_o: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_Ex2554415589101556406d_enat_type,type,
fun_Ex2554415589101556406d_enat: $tType ).
thf(fun_li8515462164684499182VEBT_o_type,type,
fun_li8515462164684499182VEBT_o: $tType ).
thf(fun_fu5354524256550068955t_real_type,type,
fun_fu5354524256550068955t_real: $tType ).
thf(fun_fu3477889739401271834t_real_type,type,
fun_fu3477889739401271834t_real: $tType ).
thf(fun_na1689058941480031347at_nat_type,type,
fun_na1689058941480031347at_nat: $tType ).
thf(fun_in3204970175496335219at_int_type,type,
fun_in3204970175496335219at_int: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(fun_co7890082732823579651omplex_type,type,
fun_co7890082732823579651omplex: $tType ).
thf(fun_co5214255584322676319omplex_type,type,
fun_co5214255584322676319omplex: $tType ).
thf(fun_fu1590586450949517859at_nat_type,type,
fun_fu1590586450949517859at_nat: $tType ).
thf(fun_fu3492966305048685787at_int_type,type,
fun_fu3492966305048685787at_int: $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_fu7336479014630192387t_real_type,type,
fun_fu7336479014630192387t_real: $tType ).
thf(fun_re7819166435457029784t_real_type,type,
fun_re7819166435457029784t_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_fu2955637221277575299d_enat_type,type,
fun_fu2955637221277575299d_enat: $tType ).
thf(fun_fu5112335056569181187at_nat_type,type,
fun_fu5112335056569181187at_nat: $tType ).
thf(fun_fu6685514224203069699at_int_type,type,
fun_fu6685514224203069699at_int: $tType ).
thf(fun_Ex8979681104671372885d_enat_type,type,
fun_Ex8979681104671372885d_enat: $tType ).
thf(fun_fu7075445697382584196_int_o_type,type,
fun_fu7075445697382584196_int_o: $tType ).
thf(fun_fu521531014127253423enat_o_type,type,
fun_fu521531014127253423enat_o: $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_na6032788992908162308at_nat_type,type,
fun_na6032788992908162308at_nat: $tType ).
thf(fun_li5427887795262106488d_enat_type,type,
fun_li5427887795262106488d_enat: $tType ).
thf(fun_in281396392327853336at_int_type,type,
fun_in281396392327853336at_int: $tType ).
thf(fun_co6147893885205795665omplex_type,type,
fun_co6147893885205795665omplex: $tType ).
thf(set_Pr3451248702717554689st_nat_type,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(set_Pr765067013931698361st_int_type,type,
set_Pr765067013931698361st_int: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(fun_fu3581538110357139729_o_nat_type,type,
fun_fu3581538110357139729_o_nat: $tType ).
thf(fun_fu9026017786105829997_o_int_type,type,
fun_fu9026017786105829997_o_int: $tType ).
thf(set_Pr6192946355708809607T_VEBT_type,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(list_P6254988961118846195et_nat_type,type,
list_P6254988961118846195et_nat: $tType ).
thf(fun_fu7714627026455246123x_real_type,type,
fun_fu7714627026455246123x_real: $tType ).
thf(fun_fu746971108421118025t_real_type,type,
fun_fu746971108421118025t_real: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_li3032794628081365576omplex_type,type,
fun_li3032794628081365576omplex: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(set_Pr5488025237498180813et_nat_type,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(list_P6356568628958627295d_enat_type,type,
list_P6356568628958627295d_enat: $tType ).
thf(fun_fu1994797156054922755_nat_o_type,type,
fun_fu1994797156054922755_nat_o: $tType ).
thf(fun_in2640216123419753727at_int_type,type,
fun_in2640216123419753727at_int: $tType ).
thf(fun_in5653523039088217947at_int_type,type,
fun_in5653523039088217947at_int: $tType ).
thf(fun_fu7383104390662542801enat_o_type,type,
fun_fu7383104390662542801enat_o: $tType ).
thf(fun_fu8278438252182731309enat_o_type,type,
fun_fu8278438252182731309enat_o: $tType ).
thf(fun_fu4016676428956456173at_nat_type,type,
fun_fu4016676428956456173at_nat: $tType ).
thf(set_Pr2457182780427864761d_enat_type,type,
set_Pr2457182780427864761d_enat: $tType ).
thf(fun_fu40286998686754419omplex_type,type,
fun_fu40286998686754419omplex: $tType ).
thf(fun_fu705315015666092147ex_nat_type,type,
fun_fu705315015666092147ex_nat: $tType ).
thf(fun_fu4213752561377164075ex_int_type,type,
fun_fu4213752561377164075ex_int: $tType ).
thf(fun_fu8756204934394872281un_o_o_type,type,
fun_fu8756204934394872281un_o_o: $tType ).
thf(fun_Pr5843119925985263810enat_o_type,type,
fun_Pr5843119925985263810enat_o: $tType ).
thf(fun_na6632006986671646835omplex_type,type,
fun_na6632006986671646835omplex: $tType ).
thf(fun_co6883864892131739507omplex_type,type,
fun_co6883864892131739507omplex: $tType ).
thf(fun_fu2445682883699234307plex_o_type,type,
fun_fu2445682883699234307plex_o: $tType ).
thf(fun_na927404270896789692_nat_o_type,type,
fun_na927404270896789692_nat_o: $tType ).
thf(fun_fu2408719596384163971_nat_o_type,type,
fun_fu2408719596384163971_nat_o: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(fun_fu5915781709770235737un_o_o_type,type,
fun_fu5915781709770235737un_o_o: $tType ).
thf(fun_na4013023315904204544BT_nat_type,type,
fun_na4013023315904204544BT_nat: $tType ).
thf(fun_VE3839197795564616566t_real_type,type,
fun_VE3839197795564616566t_real: $tType ).
thf(fun_op493924057549976310_num_o_type,type,
fun_op493924057549976310_num_o: $tType ).
thf(fun_li9037389432102202218at_nat_type,type,
fun_li9037389432102202218at_nat: $tType ).
thf(fun_li6547306287170475462at_int_type,type,
fun_li6547306287170475462at_int: $tType ).
thf(fun_Pr4738963024209204295_int_o_type,type,
fun_Pr4738963024209204295_int_o: $tType ).
thf(fun_na3970208099681795815_nat_o_type,type,
fun_na3970208099681795815_nat_o: $tType ).
thf(fun_fu806425790188207109plex_o_type,type,
fun_fu806425790188207109plex_o: $tType ).
thf(fun_fu3043978019632300333x_real_type,type,
fun_fu3043978019632300333x_real: $tType ).
thf(fun_VE6544184183685019418et_nat_type,type,
fun_VE6544184183685019418et_nat: $tType ).
thf(fun_VE1730635764897100662et_int_type,type,
fun_VE1730635764897100662et_int: $tType ).
thf(fun_se6072594010446775118enat_o_type,type,
fun_se6072594010446775118enat_o: $tType ).
thf(fun_fu3077872570260440615l_real_type,type,
fun_fu3077872570260440615l_real: $tType ).
thf(fun_fu9148622857633396327enat_o_type,type,
fun_fu9148622857633396327enat_o: $tType ).
thf(fun_op8028897214545316308_nat_o_type,type,
fun_op8028897214545316308_nat_o: $tType ).
thf(list_P2623026923184700063T_real_type,type,
list_P2623026923184700063T_real: $tType ).
thf(list_P877281246627933069T_VEBT_type,type,
list_P877281246627933069T_VEBT: $tType ).
thf(fun_fu6122667721776870753plex_o_type,type,
fun_fu6122667721776870753plex_o: $tType ).
thf(fun_fu6229866931165912581plex_o_type,type,
fun_fu6229866931165912581plex_o: $tType ).
thf(fun_fu1553612835185860561ex_nat_type,type,
fun_fu1553612835185860561ex_nat: $tType ).
thf(fun_li8451336403896997736d_enat_type,type,
fun_li8451336403896997736d_enat: $tType ).
thf(fun_li3291226679607837196d_enat_type,type,
fun_li3291226679607837196d_enat: $tType ).
thf(produc1828647624359046049st_nat_type,type,
produc1828647624359046049st_nat: $tType ).
thf(produc1186641810826059865st_int_type,type,
produc1186641810826059865st_int: $tType ).
thf(fun_re8542384036533109323t_real_type,type,
fun_re8542384036533109323t_real: $tType ).
thf(fun_re4112884445705685835l_real_type,type,
fun_re4112884445705685835l_real: $tType ).
thf(set_Pr7765410600122031685T_real_type,type,
set_Pr7765410600122031685T_real: $tType ).
thf(set_Pr6019664923565264691T_VEBT_type,type,
set_Pr6019664923565264691T_VEBT: $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(list_P7524865323317820941T_VEBT_type,type,
list_P7524865323317820941T_VEBT: $tType ).
thf(produc8243902056947475879T_VEBT_type,type,
produc8243902056947475879T_VEBT: $tType ).
thf(fun_fu3214020956574444655al_nat_type,type,
fun_fu3214020956574444655al_nat: $tType ).
thf(fun_fu3737244727311182119al_int_type,type,
fun_fu3737244727311182119al_int: $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(set_Pr7556676689462069481BT_nat_type,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(set_Pr5066593544530342725BT_int_type,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(set_Pr6167073792073659919T_VEBT_type,type,
set_Pr6167073792073659919T_VEBT: $tType ).
thf(set_Pr8044002425091019955T_VEBT_type,type,
set_Pr8044002425091019955T_VEBT: $tType ).
thf(fun_fu7444430165986413063real_o_type,type,
fun_fu7444430165986413063real_o: $tType ).
thf(fun_Pr7546709192626087934_nat_o_type,type,
fun_Pr7546709192626087934_nat_o: $tType ).
thf(fun_na4138138649119996554_nat_o_type,type,
fun_na4138138649119996554_nat_o: $tType ).
thf(fun_li1025265955262268170_nat_o_type,type,
fun_li1025265955262268170_nat_o: $tType ).
thf(fun_li1334793589135804498_int_o_type,type,
fun_li1334793589135804498_int_o: $tType ).
thf(produc7819656566062154093et_nat_type,type,
produc7819656566062154093et_nat: $tType ).
thf(fun_na7718645245721260691t_real_type,type,
fun_na7718645245721260691t_real: $tType ).
thf(fun_na5873943405026509934VEBT_o_type,type,
fun_na5873943405026509934VEBT_o: $tType ).
thf(fun_na1154345429118027792d_enat_type,type,
fun_na1154345429118027792d_enat: $tType ).
thf(fun_li6438084239591463512omplex_type,type,
fun_li6438084239591463512omplex: $tType ).
thf(fun_li3213232893379486388omplex_type,type,
fun_li3213232893379486388omplex: $tType ).
thf(fun_Ex2441982661509597004d_enat_type,type,
fun_Ex2441982661509597004d_enat: $tType ).
thf(fun_fu6891447142836604759at_o_o_type,type,
fun_fu6891447142836604759at_o_o: $tType ).
thf(fun_na1108963418173300452_nat_o_type,type,
fun_na1108963418173300452_nat_o: $tType ).
thf(fun_na6948449159361463396_nat_o_type,type,
fun_na6948449159361463396_nat_o: $tType ).
thf(produc7272778201969148633d_enat_type,type,
produc7272778201969148633d_enat: $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_VE7913661350430487824_set_o_type,type,
fun_VE7913661350430487824_set_o: $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_fu7994259084669964039_int_o_type,type,
fun_fu7994259084669964039_int_o: $tType ).
thf(fun_se2170385732985038782_nat_o_type,type,
fun_se2170385732985038782_nat_o: $tType ).
thf(fun_se9162176452187397432plex_o_type,type,
fun_se9162176452187397432plex_o: $tType ).
thf(fun_na3711450577076729278_nat_o_type,type,
fun_na3711450577076729278_nat_o: $tType ).
thf(fun_fu1358370060594899587plex_o_type,type,
fun_fu1358370060594899587plex_o: $tType ).
thf(fun_na4030263931958639548enat_o_type,type,
fun_na4030263931958639548enat_o: $tType ).
thf(fun_fu3022329567491847689real_o_type,type,
fun_fu3022329567491847689real_o: $tType ).
thf(fun_fu4478067837645853357l_real_type,type,
fun_fu4478067837645853357l_real: $tType ).
thf(fun_VE3387248342596292540enat_o_type,type,
fun_VE3387248342596292540enat_o: $tType ).
thf(fun_Pr672294278902479040t_real_type,type,
fun_Pr672294278902479040t_real: $tType ).
thf(fun_Ex5372025725550730656VEBT_o_type,type,
fun_Ex5372025725550730656VEBT_o: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(fun_na9114950421169325794enat_o_type,type,
fun_na9114950421169325794enat_o: $tType ).
thf(fun_fu1852998413150313061real_o_type,type,
fun_fu1852998413150313061real_o: $tType ).
thf(fun_fu3729927046167673097real_o_type,type,
fun_fu3729927046167673097real_o: $tType ).
thf(fun_fu2707946803925496145al_nat_type,type,
fun_fu2707946803925496145al_nat: $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_in4514472496968388910at_nat_type,type,
fun_in4514472496968388910at_nat: $tType ).
thf(fun_in4211310926729683942nt_int_type,type,
fun_in4211310926729683942nt_int: $tType ).
thf(set_Pr3175402225741728619VEBT_o_type,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(set_Pr7543698050874017315T_VEBT_type,type,
set_Pr7543698050874017315T_VEBT: $tType ).
thf(fun_na312559527389416956t_real_type,type,
fun_na312559527389416956t_real: $tType ).
thf(fun_na819858167508000762st_nat_type,type,
fun_na819858167508000762st_nat: $tType ).
thf(fun_li281227058796928470at_int_type,type,
fun_li281227058796928470at_int: $tType ).
thf(fun_li4232671687212637746at_int_type,type,
fun_li4232671687212637746at_int: $tType ).
thf(fun_in6553099857819052212t_real_type,type,
fun_in6553099857819052212t_real: $tType ).
thf(fun_fu6621322437453427393_nat_o_type,type,
fun_fu6621322437453427393_nat_o: $tType ).
thf(fun_fu7030473000426307245t_real_type,type,
fun_fu7030473000426307245t_real: $tType ).
thf(fun_na2418085665696872764plex_o_type,type,
fun_na2418085665696872764plex_o: $tType ).
thf(fun_Ex239764483819389678enat_o_type,type,
fun_Ex239764483819389678enat_o: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(list_P8689742595348180415l_real_type,type,
list_P8689742595348180415l_real: $tType ).
thf(filter1242075044329608583at_nat_type,type,
filter1242075044329608583at_nat: $tType ).
thf(fun_na6128946301132549280et_nat_type,type,
fun_na6128946301132549280et_nat: $tType ).
thf(fun_na1315397882344630524et_int_type,type,
fun_na1315397882344630524et_int: $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_fu1805223966450871909_int_o_type,type,
fun_fu1805223966450871909_int_o: $tType ).
thf(fun_fu4534828536049688329_int_o_type,type,
fun_fu4534828536049688329_int_o: $tType ).
thf(fun_fu1078644964449000785nt_nat_type,type,
fun_fu1078644964449000785nt_nat: $tType ).
thf(fun_na6069412773753413270plex_o_type,type,
fun_na6069412773753413270plex_o: $tType ).
thf(fun_na7928631014926962227_nat_o_type,type,
fun_na7928631014926962227_nat_o: $tType ).
thf(fun_na2978037997607195054t_real_type,type,
fun_na2978037997607195054t_real: $tType ).
thf(set_Pr6218003697084177305l_real_type,type,
set_Pr6218003697084177305l_real: $tType ).
thf(list_P6834414599653733731al_nat_type,type,
list_P6834414599653733731al_nat: $tType ).
thf(list_P4344331454722006975al_int_type,type,
list_P4344331454722006975al_int: $tType ).
thf(list_P6863124054624500543t_real_type,type,
list_P6863124054624500543t_real: $tType ).
thf(produc5170161368751668367T_real_type,type,
produc5170161368751668367T_real: $tType ).
thf(produc3757001726724277373T_VEBT_type,type,
produc3757001726724277373T_VEBT: $tType ).
thf(fun_na7542918316964655096d_enat_type,type,
fun_na7542918316964655096d_enat: $tType ).
thf(set_Pr3510011417693777981al_nat_type,type,
set_Pr3510011417693777981al_nat: $tType ).
thf(set_Pr1019928272762051225al_int_type,type,
set_Pr1019928272762051225al_int: $tType ).
thf(set_Pr3538720872664544793t_real_type,type,
set_Pr3538720872664544793t_real: $tType ).
thf(list_P6011104703257516679at_nat_type,type,
list_P6011104703257516679at_nat: $tType ).
thf(list_P3521021558325789923at_int_type,type,
list_P3521021558325789923at_int: $tType ).
thf(list_P8198026277950538467nt_nat_type,type,
list_P8198026277950538467nt_nat: $tType ).
thf(list_P5707943133018811711nt_int_type,type,
list_P5707943133018811711nt_int: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(produc8025551001238799321T_VEBT_type,type,
produc8025551001238799321T_VEBT: $tType ).
thf(produc1531783533982839933T_VEBT_type,type,
produc1531783533982839933T_VEBT: $tType ).
thf(fun_se2161501677553633980real_o_type,type,
fun_se2161501677553633980real_o: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr7995236796853374141at_int_type,type,
set_Pr7995236796853374141at_int: $tType ).
thf(set_Pr3448869479623346877nt_nat_type,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(fun_fu9050450510664235267real_o_type,type,
fun_fu9050450510664235267real_o: $tType ).
thf(fun_fu8103376058317145219o_real_type,type,
fun_fu8103376058317145219o_real: $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_na5723442673449079972x_real_type,type,
fun_na5723442673449079972x_real: $tType ).
thf(fun_na7234455742697417626_nat_o_type,type,
fun_na7234455742697417626_nat_o: $tType ).
thf(fun_na7306406234920378942_int_o_type,type,
fun_na7306406234920378942_int_o: $tType ).
thf(fun_VE6480751511521678896_nat_o_type,type,
fun_VE6480751511521678896_nat_o: $tType ).
thf(fun_na6887940067898170868VEBT_o_type,type,
fun_na6887940067898170868VEBT_o: $tType ).
thf(fun_na1142814060743658952omplex_type,type,
fun_na1142814060743658952omplex: $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_na8635581178960477080_int_o_type,type,
fun_na8635581178960477080_int_o: $tType ).
thf(fun_na3100059926620910090_set_o_type,type,
fun_na3100059926620910090_set_o: $tType ).
thf(fun_in4068701459849370962_set_o_type,type,
fun_in4068701459849370962_set_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_fu6701067901881939075_o_nat_type,type,
fun_fu6701067901881939075_o_nat: $tType ).
thf(fun_fu6940589326549028739_o_int_type,type,
fun_fu6940589326549028739_o_int: $tType ).
thf(fun_VE3569950477627547253d_enat_type,type,
fun_VE3569950477627547253d_enat: $tType ).
thf(list_P3595434254542482545real_o_type,type,
list_P3595434254542482545real_o: $tType ).
thf(list_P5232166724548748803o_real_type,type,
list_P5232166724548748803o_real: $tType ).
thf(fun_fu3569133559346579503un_o_o_type,type,
fun_fu3569133559346579503un_o_o: $tType ).
thf(list_list_VEBT_VEBT_type,type,
list_list_VEBT_VEBT: $tType ).
thf(fun_re4238438383274954274t_real_type,type,
fun_re4238438383274954274t_real: $tType ).
thf(fun_na6724076748692969250l_real_type,type,
fun_na6724076748692969250l_real: $tType ).
thf(set_Pr4936984352647145239real_o_type,type,
set_Pr4936984352647145239real_o: $tType ).
thf(set_Pr6573716822653411497o_real_type,type,
set_Pr6573716822653411497o_real: $tType ).
thf(set_list_list_nat_type,type,
set_list_list_nat: $tType ).
thf(list_P5087981734274514673_int_o_type,type,
list_P5087981734274514673_int_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(fun_list_list_nat_o_type,type,
fun_list_list_nat_o: $tType ).
thf(set_list_VEBT_VEBT_type,type,
set_list_VEBT_VEBT: $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_Ex5852502975177633731d_enat_type,type,
fun_Ex5852502975177633731d_enat: $tType ).
thf(set_set_list_nat_type,type,
set_set_list_nat: $tType ).
thf(set_Pr903927857289325719_int_o_type,type,
set_Pr903927857289325719_int_o: $tType ).
thf(set_Pr2101469702781467981_o_nat_type,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(set_Pr8834758594704517033_o_int_type,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(set_list_set_nat_type,type,
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thf(fun_VE5569070535936029429omplex_type,type,
fun_VE5569070535936029429omplex: $tType ).
thf(fun_set_list_nat_o_type,type,
fun_set_list_nat_o: $tType ).
thf(fun_list_set_nat_o_type,type,
fun_list_set_nat_o: $tType ).
thf(fun_co4998825143550818160real_o_type,type,
fun_co4998825143550818160real_o: $tType ).
thf(fun_real_filter_nat_type,type,
fun_real_filter_nat: $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,
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thf(fun_filter_nat_real_type,type,
fun_filter_nat_real: $tType ).
thf(set_set_set_nat_type,type,
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thf(fun_fu2389858412225411757un_o_o_type,type,
fun_fu2389858412225411757un_o_o: $tType ).
thf(fun_fu3042504704906485677o_real_type,type,
fun_fu3042504704906485677o_real: $tType ).
thf(fun_set_set_nat_o_type,type,
fun_set_set_nat_o: $tType ).
thf(fun_na1554462459066888140plex_o_type,type,
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thf(set_li5464603477888414924d_enat_type,type,
set_li5464603477888414924d_enat: $tType ).
thf(produc2422161461964618553l_real_type,type,
produc2422161461964618553l_real: $tType ).
thf(fun_num_option_num_type,type,
fun_num_option_num: $tType ).
thf(fun_nat_filter_nat_type,type,
fun_nat_filter_nat: $tType ).
thf(fun_li827083013690791791enat_o_type,type,
fun_li827083013690791791enat_o: $tType ).
thf(fun_fu6781074197733401937un_o_o_type,type,
fun_fu6781074197733401937un_o_o: $tType ).
thf(fun_fu7756609662939579309un_o_o_type,type,
fun_fu7756609662939579309un_o_o: $tType ).
thf(fun_fu7210065372943547985_o_nat_type,type,
fun_fu7210065372943547985_o_nat: $tType ).
thf(fun_Ex3741802288643809319omplex_type,type,
fun_Ex3741802288643809319omplex: $tType ).
thf(fun_co6496365337113880337d_enat_type,type,
fun_co6496365337113880337d_enat: $tType ).
thf(set_se7270636423289371942d_enat_type,type,
set_se7270636423289371942d_enat: $tType ).
thf(produc3741383161447143261al_nat_type,type,
produc3741383161447143261al_nat: $tType ).
thf(produc8786904178792722361al_int_type,type,
produc8786904178792722361al_int: $tType ).
thf(produc679980390762269497t_real_type,type,
produc679980390762269497t_real: $tType ).
thf(fun_se8123728892507317397enat_o_type,type,
fun_se8123728892507317397enat_o: $tType ).
thf(fun_real_fun_real_o_type,type,
fun_real_fun_real_o: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_nat_int_type,type,
product_prod_nat_int: $tType ).
thf(product_prod_int_nat_type,type,
product_prod_int_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_nat_set_real_type,type,
fun_nat_set_real: $tType ).
thf(fun_nat_list_nat_type,type,
fun_nat_list_nat: $tType ).
thf(fun_int_set_real_type,type,
fun_int_set_real: $tType ).
thf(set_list_complex_type,type,
set_list_complex: $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_fun_real_o_type,type,
fun_nat_fun_real_o: $tType ).
thf(fun_list_complex_o_type,type,
fun_list_complex_o: $tType ).
thf(fun_int_fun_real_o_type,type,
fun_int_fun_real_o: $tType ).
thf(set_Product_prod_o_o_type,type,
set_Product_prod_o_o: $tType ).
thf(fun_set_nat_nat_type,type,
fun_set_nat_nat: $tType ).
thf(fun_set_nat_int_type,type,
fun_set_nat_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_complex_complex_type,type,
fun_complex_complex: $tType ).
thf(set_set_complex_type,type,
set_set_complex: $tType ).
thf(fun_fun_int_int_o_type,type,
fun_fun_int_int_o: $tType ).
thf(fun_set_complex_o_type,type,
fun_set_complex_o: $tType ).
thf(fun_re6065469302365115155d_enat_type,type,
fun_re6065469302365115155d_enat: $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_Ex1451620480498224165t_real_type,type,
fun_Ex1451620480498224165t_real: $tType ).
thf(option_VEBT_VEBT_type,type,
option_VEBT_VEBT: $tType ).
thf(fun_complex_fun_o_o_type,type,
fun_complex_fun_o_o: $tType ).
thf(set_filter_nat_type,type,
set_filter_nat: $tType ).
thf(option_set_nat_type,type,
option_set_nat: $tType ).
thf(fun_set_o_fun_o_o_type,type,
fun_set_o_fun_o_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_in5914218760682845459d_enat_type,type,
fun_in5914218760682845459d_enat: $tType ).
thf(fun_filter_nat_o_type,type,
fun_filter_nat_o: $tType ).
thf(fun_Ex7660298398204468809at_nat_type,type,
fun_Ex7660298398204468809at_nat: $tType ).
thf(fun_Ex3482447378695272101at_int_type,type,
fun_Ex3482447378695272101at_int: $tType ).
thf(fun_fun_o_o_fun_o_o_type,type,
fun_fun_o_o_fun_o_o: $tType ).
thf(product_prod_real_o_type,type,
product_prod_real_o: $tType ).
thf(product_prod_o_real_type,type,
product_prod_o_real: $tType ).
thf(list_list_nat_type,type,
list_list_nat: $tType ).
thf(list_list_int_type,type,
list_list_int: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(fun_real_complex_type,type,
fun_real_complex: $tType ).
thf(fun_complex_real_type,type,
fun_complex_real: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(set_list_int_type,type,
set_list_int: $tType ).
thf(product_prod_int_o_type,type,
product_prod_int_o: $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_set_real_o_type,type,
fun_set_real_o: $tType ).
thf(fun_list_nat_o_type,type,
fun_list_nat_o: $tType ).
thf(fun_list_int_o_type,type,
fun_list_int_o: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(fun_VEBT_VEBT_o_type,type,
fun_VEBT_VEBT_o: $tType ).
thf(fun_real_fun_o_o_type,type,
fun_real_fun_o_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_fun_real_o_type,type,
fun_o_fun_real_o: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $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_nat_set_o_type,type,
fun_nat_set_o: $tType ).
thf(fun_int_set_o_type,type,
fun_int_set_o: $tType ).
thf(list_Extended_enat_type,type,
list_Extended_enat: $tType ).
thf(fun_nat_fun_o_o_type,type,
fun_nat_fun_o_o: $tType ).
thf(fun_int_fun_o_o_type,type,
fun_int_fun_o_o: $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_Product_unit_o_type,type,
fun_Product_unit_o: $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_o_Product_unit_type,type,
fun_o_Product_unit: $tType ).
thf(fun_o_Extended_enat_type,type,
fun_o_Extended_enat: $tType ).
thf(fun_real_nat_type,type,
fun_real_nat: $tType ).
thf(fun_real_int_type,type,
fun_real_int: $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_num_num_type,type,
fun_num_num: $tType ).
thf(fun_num_nat_type,type,
fun_num_nat: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_int_type,type,
fun_nat_int: $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(option_real_type,type,
option_real: $tType ).
thf(filter_real_type,type,
filter_real: $tType ).
thf(fun_complex_o_type,type,
fun_complex_o: $tType ).
thf(fun_o_complex_type,type,
fun_o_complex: $tType ).
thf(fun_set_o_o_type,type,
fun_set_o_o: $tType ).
thf(option_num_type,type,
option_num: $tType ).
thf(option_nat_type,type,
option_nat: $tType ).
thf(option_int_type,type,
option_int: $tType ).
thf(filter_nat_type,type,
filter_nat: $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(fun_o_real_type,type,
fun_o_real: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $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(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(option_o_type,type,
option_o: $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(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(aTP_Lamm_bc_decl,type,
aTP_Lamm_bc: fun_nat_nat ).
thf(aTP_Lamm_dq_decl,type,
aTP_Lamm_dq: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_iv_decl,type,
aTP_Lamm_iv: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_lc_decl,type,
aTP_Lamm_lc: fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_mr_decl,type,
aTP_Lamm_mr: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ne_decl,type,
aTP_Lamm_ne: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_pr_decl,type,
aTP_Lamm_pr: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_ps_decl,type,
aTP_Lamm_ps: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_pt_decl,type,
aTP_Lamm_pt: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_pu_decl,type,
aTP_Lamm_pu: nat > fun_nat_fun_nat_nat ).
thf(aTP_Lamm_vm_decl,type,
aTP_Lamm_vm: fun_o_nat > fun_fu318872218122388049at_nat ).
thf(aTP_Lamm_vn_decl,type,
aTP_Lamm_vn: fun_nat_o > fun_fu5477517762487726877_nat_o ).
thf(aTP_Lamm_vq_decl,type,
aTP_Lamm_vq: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_vr_decl,type,
aTP_Lamm_vr: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xg_decl,type,
aTP_Lamm_xg: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xh_decl,type,
aTP_Lamm_xh: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_xx_decl,type,
aTP_Lamm_xx: fun_nat_fun_nat_nat ).
thf(aTP_Lamm_yf_decl,type,
aTP_Lamm_yf: fun_nat_o > fun_nat_o ).
thf(aTP_Lamm_ys_decl,type,
aTP_Lamm_ys: fun_nat_fun_nat_nat ).
thf(binomial_decl,type,
binomial: fun_nat_fun_nat_nat ).
thf(divmod_nat_decl,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: fun_nat_fun_nat_nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(times_times_nat_decl,type,
times_times_nat: fun_nat_fun_nat_nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(drop_nat_decl,type,
drop_nat: nat > list_nat > list_nat ).
thf(find_VEBT_VEBT_decl,type,
find_VEBT_VEBT: fun_VEBT_VEBT_o > list_VEBT_VEBT > option_VEBT_VEBT ).
thf(linord738340561235409698at_nat_decl,type,
linord738340561235409698at_nat: fun_nat_nat > list_nat > list_nat ).
thf(map_nat_nat_decl,type,
map_nat_nat: fun_nat_nat > list_nat > list_nat ).
thf(set_VEBT_VEBT2_decl,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(tl_nat_decl,type,
tl_nat: list_nat > list_nat ).
thf(list_u6961636818849549845T_VEBT_decl,type,
list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT ).
thf(list_u1324408373059187874T_VEBT_decl,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(member_VEBT_VEBT_decl,type,
member_VEBT_VEBT: list_VEBT_VEBT > fun_VEBT_VEBT_o ).
thf(nth_VEBT_VEBT_decl,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(upt_decl,type,
upt: nat > nat > list_nat ).
thf(zip_VE537291747668921783T_VEBT_decl,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(case_nat_o_decl,type,
case_nat_o: $o > fun_nat_o > fun_nat_o ).
thf(case_nat_nat_decl,type,
case_nat_nat: nat > fun_nat_nat > fun_nat_nat ).
thf(size_size_list_nat_decl,type,
size_size_list_nat: list_nat > nat ).
thf(nat_triangle_decl,type,
nat_triangle: fun_nat_nat ).
thf(none_P5556105721700978146at_nat_decl,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(some_P7363390416028606310at_nat_decl,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(ord_le4337996190870823476T_VEBT_decl,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(ord_max_nat_decl,type,
ord_max_nat: fun_nat_fun_nat_nat ).
thf(power_power_nat_decl,type,
power_power_nat: fun_nat_fun_nat_nat ).
thf(product_Pair_nat_nat_decl,type,
product_Pair_nat_nat: fun_na4138050610385705875at_nat ).
thf(produc537772716801021591T_VEBT_decl,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(produc6118266651365575811T_VEBT_decl,type,
produc6118266651365575811T_VEBT: produc8243902056947475879T_VEBT > vEBT_VEBT ).
thf(produc351232539757196229T_VEBT_decl,type,
produc351232539757196229T_VEBT: produc8243902056947475879T_VEBT > vEBT_VEBT ).
thf(divide_divide_nat_decl,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
thf(modulo_modulo_nat_decl,type,
modulo_modulo_nat: fun_nat_fun_nat_nat ).
thf(zero_n2687167440665602831ol_nat_decl,type,
zero_n2687167440665602831ol_nat: fun_o_nat ).
thf(collect_nat_decl,type,
collect_nat: fun_nat_o > set_nat ).
thf(vEBT_Node_decl,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: fun_VE6480751511521678896_nat_o ).
thf(vEBT_VEBT_high_decl,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
thf(vEBT_V5917875025757280293ildren_decl,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > fun_nat_o ).
thf(vEBT_VEBT_low_decl,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
thf(vEBT_VEBT_membermima_decl,type,
vEBT_VEBT_membermima: fun_VE6480751511521678896_nat_o ).
thf(vEBT_V5719532721284313246member_decl,type,
vEBT_V5719532721284313246member: fun_VE6480751511521678896_nat_o ).
thf(vEBT_VEBT_valid_decl,type,
vEBT_VEBT_valid: fun_VE6480751511521678896_nat_o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: fun_VE6480751511521678896_nat_o ).
thf(vEBT_set_vebt_decl,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_vebt_buildup_decl,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(vEBT_vebt_insert_decl,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(vEBT_VEBT_bit_concat_decl,type,
vEBT_VEBT_bit_concat: nat > fun_nat_fun_nat_nat ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: fun_VEBT_VEBT_o ).
thf(vEBT_VEBT_set_vebt_decl,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: fun_VE6480751511521678896_nat_o ).
thf(aa_o_nat_decl,type,
aa_o_nat: fun_o_nat > $o > nat ).
thf(aa_nat_o_decl,type,
aa_nat_o: fun_nat_o > nat > $o ).
thf(aa_nat_nat_decl,type,
aa_nat_nat: fun_nat_nat > nat > nat ).
thf(aa_nat7603221163087113075at_nat_decl,type,
aa_nat7603221163087113075at_nat: fun_na1476630412504255114at_nat > nat > product_prod_nat_nat ).
thf(aa_nat_fun_nat_nat_decl,type,
aa_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).
thf(aa_nat8803788312118491388at_nat_decl,type,
aa_nat8803788312118491388at_nat: fun_na4138050610385705875at_nat > nat > fun_na1476630412504255114at_nat ).
thf(aa_VEBT_VEBT_o_decl,type,
aa_VEBT_VEBT_o: fun_VEBT_VEBT_o > vEBT_VEBT > $o ).
thf(aa_VEB2314620471664397097_nat_o_decl,type,
aa_VEB2314620471664397097_nat_o: fun_VE6480751511521678896_nat_o > vEBT_VEBT > fun_nat_o ).
thf(aa_fun4204860950123276802at_nat_decl,type,
aa_fun4204860950123276802at_nat: fun_fu318872218122388049at_nat > fun_nat_o > fun_nat_nat ).
thf(aa_fun8673969331427483654_nat_o_decl,type,
aa_fun8673969331427483654_nat_o: fun_fu5477517762487726877_nat_o > fun_nat_nat > fun_nat_o ).
thf(member_VEBT_VEBT2_decl,type,
member_VEBT_VEBT2: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(deg_decl,type,
deg: nat ).
thf(i_decl,type,
i: nat ).
thf(m_decl,type,
m: nat ).
thf(ma_decl,type,
ma: nat ).
thf(mi_decl,type,
mi: nat ).
thf(na_decl,type,
na: nat ).
thf(summary_decl,type,
summary: vEBT_VEBT ).
thf(treeList_decl,type,
treeList: list_VEBT_VEBT ).
thf(xa_decl,type,
xa: nat ).
thf(105,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
<=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_VEBT_Oinject_I1_J) ).
thf(892,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: option4927543243414619207at_nat,F: nat,G: list_VEBT_VEBT,H: vEBT_VEBT] :
( ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) )
= ( H @ ( G @ ( F @ ( E @ vEBT_Node ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(198,axiom,
( ( xa != ma )
& ( xa != mi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_mimaxrel) ).
thf(1322,plain,
( ( xa != ma )
& ( xa != mi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2401_mult__cancel__left) ).
thf(629,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_add__Suc) ).
thf(1559,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(189,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3149_mod__add__left__eq) ).
thf(1295,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(363,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_group__cancel_Oadd2) ).
thf(1950,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( D @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__is__0) ).
thf(1083,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(373,axiom,
! [A: list_VEBT_VEBT,B: nat] :
( ( B @ ( A @ nth_VEBT_VEBT ) @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list__update__id) ).
thf(1982,plain,
! [A: list_VEBT_VEBT,B: nat] :
( ( B @ ( A @ nth_VEBT_VEBT ) @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(81,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1432_size__neq__size__imp__neq) ).
thf(777,plain,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_max__nat_Oneutr__eq__iff) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(119,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2553_mult_Ocomm__neutral) ).
thf(977,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(35,axiom,
( aTP_Lamm_bc
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3747_lambda__one) ).
thf(523,plain,
( aTP_Lamm_bc
= ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(222,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3082_Suc__mod__mult__self2) ).
thf(1406,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_ys @ aa_nat_fun_nat_nat ) @ map_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8908_map__add__upt) ).
thf(1073,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ upt ) @ ( A @ ( aTP_Lamm_ys @ aa_nat_fun_nat_nat ) @ map_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3396_mod__mult__div__eq) ).
thf(1544,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(299,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3009_mod__add__self2) ).
thf(1728,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(31,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2409_mult__1) ).
thf(511,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2020_nat__power__eq__Suc__0__iff) ).
thf(677,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_max__nat_Oeq__neutr__iff) ).
thf(861,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(333,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xg @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9243_ATP_Olambda__158) ).
thf(1855,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xg @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2432_nat__1__eq__mult__iff) ).
thf(1200,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_dq @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9566_ATP_Olambda__481) ).
thf(1497,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_dq @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(314,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9363_ATP_Olambda__278) ).
thf(1788,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_mr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(266,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2746_power__add) ).
thf(1608,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_max__add__distrib__right) ).
thf(1310,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(337,axiom,
na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_tc) ).
thf(1872,plain,
na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(89,axiom,
! [A: fun_nat_o,B: nat,C: fun_nat_nat,D: nat] :
( ( D @ ( C @ ( B @ case_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
<=> ( D @ ( C @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ ( B @ ( A @ aa_nat_o ) @ case_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8186_nat_Ocase__distrib) ).
thf(814,plain,
! [A: fun_nat_o,B: nat,C: fun_nat_nat,D: nat] :
( ( ( D @ ( C @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ ( B @ ( A @ aa_nat_o ) @ case_nat_o ) @ aa_nat_o ) )
=> ( D @ ( C @ ( B @ case_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( D @ ( C @ ( B @ case_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( D @ ( C @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ ( B @ ( A @ aa_nat_o ) @ case_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(233,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_member__valid__both__member__options) ).
thf(1458,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( C @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(165,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_old_Onat_Odistinct_I2_J) ).
thf(1196,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(127,axiom,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_vebt__member_Osimps_I3_J) ).
thf(1001,plain,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(352,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aTP_Lamm_yf @ aa_nat_o ) )
<=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9270_ATP_Olambda__185) ).
thf(1914,plain,
! [A: fun_nat_o,B: nat] :
( ( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( B @ ( A @ aTP_Lamm_yf @ aa_nat_o ) ) )
& ( ( B @ ( A @ aTP_Lamm_yf @ aa_nat_o ) )
=> ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(175,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ( ( B @ ( C @ member_VEBT_VEBT2 ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_set__update__subsetI) ).
thf(1243,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ( ( B @ ( C @ member_VEBT_VEBT2 ) )
=> ( B @ ( C @ ( D @ ( A @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(217,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_pu @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9427_ATP_Olambda__342) ).
thf(1391,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_pu @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(280,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_min__Null__member) ).
thf(1650,plain,
! [A: vEBT_VEBT,B: nat] :
( ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ~ ( B @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(208,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_nat_Oinject) ).
thf(1359,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(43,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3602_diff__self__eq__0) ).
thf(565,plain,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(271,axiom,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_iv @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9574_ATP_Olambda__489) ).
thf(1623,plain,
! [A: fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_iv @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(15,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_plus__nat_Oadd__0) ).
thf(436,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(319,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_max_Oright__idem) ).
thf(1803,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(223,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2592_combine__common__factor) ).
thf(1409,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(45,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_nat_Odistinct_I1_J) ).
thf(570,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_max__add__distrib__left) ).
thf(1430,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(374,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( E @ ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( A @ ( E @ ( B @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list__update__swap) ).
thf(1985,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( E @ ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( A @ ( E @ ( B @ ( C @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2577_comm__semiring__class_Odistrib) ).
thf(1264,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(232,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3408_div__mult1__eq) ).
thf(1455,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(305,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2615_nat__mult__max__right) ).
thf(1760,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(284,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_set__vebt__set__vebt_H__valid) ).
thf(1660,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A @ vEBT_set_vebt )
= ( A @ vEBT_VEBT_set_vebt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(190,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3067_mod__mult__self4) ).
thf(1298,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(246,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_add__is__1) ).
thf(1511,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(107,axiom,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1427_Ex__list__of__length) ).
thf(917,plain,
! [A: nat] :
? [B: list_nat] :
( ( B @ size_size_list_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(195,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2587_distrib__right) ).
thf(1313,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(187,axiom,
! [A: $o,B: $o] :
( ( ( B
& A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3779_of__bool__conj) ).
thf(1279,plain,
! [A: $o,B: $o] :
( ( ( B
& A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(354,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ upt ) @ ( A @ drop_nat ) )
= ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8900_drop__upt) ).
thf(1922,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ upt ) @ ( A @ drop_nat ) )
= ( C @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(318,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1800,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(345,axiom,
! [A: vEBT_VEBT] :
( ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__C11_C) ).
thf(1892,plain,
! [A: vEBT_VEBT] :
( ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3145_mod__add__eq) ).
thf(1319,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(277,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6885_choose__mult__lemma) ).
thf(1641,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(51,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2558_comm__monoid__mult__class_Omult__1) ).
thf(606,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(204,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_vq @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9293_ATP_Olambda__208) ).
thf(1347,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_vq @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(357,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( D @ ( B @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__update__overwrite) ).
thf(1931,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( D @ ( B @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ list_u1324408373059187874T_VEBT ) ) )
= ( D @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3859_diff__add__inverse) ).
thf(1568,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(19,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3570_diff__zero) ).
thf(448,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(242,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3671_diff__Suc__1) ).
thf(1494,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_add__cancel__left__right) ).
thf(475,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(361,axiom,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62__C3_C) ).
thf(1946,plain,
( deg
= ( m @ ( na @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(285,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3862_diff__mult__distrib) ).
thf(1664,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(351,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_buildup__nothing__in__leaf) ).
thf(1911,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3400_div__mult__mod__eq) ).
thf(1632,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(1,conjecture,
? [A: nat] : ( A @ ( i @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] : ( A @ ( i @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(376,plain,
~ ? [A: nat] : ( A @ ( i @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(54,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2386_mult__zero__left) ).
thf(623,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(201,axiom,
~ ( ( xa = ma )
| ( xa = mi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_False) ).
thf(1334,plain,
~ ( ( xa = ma )
| ( xa = mi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(291,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3163_mod__Suc__eq) ).
thf(1682,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(371,axiom,
na @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__C165_C) ).
thf(1978,plain,
na @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(32,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3603_diff__0__eq__0) ).
thf(514,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(46,axiom,
! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
( ( ( A @ some_P7363390416028606310at_nat )
= ( B @ some_P7363390416028606310at_nat ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_option_Oinject) ).
thf(574,plain,
! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
( ( ( A = B )
=> ( ( A @ some_P7363390416028606310at_nat )
= ( B @ some_P7363390416028606310at_nat ) ) )
& ( ( ( A @ some_P7363390416028606310at_nat )
= ( B @ some_P7363390416028606310at_nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(87,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_old_Onat_Odistinct_I1_J) ).
thf(806,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(138,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1990_div__0) ).
thf(1051,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(334,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_max_Oassoc) ).
thf(1858,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(336,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_add__right__cancel) ).
thf(1864,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(329,axiom,
( ( i @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C164_C) ).
thf(1843,plain,
( ( i @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(160,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1642_verit__sum__simplify) ).
thf(1169,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(356,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2520_mult_Oassoc) ).
thf(1928,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_nat__add__max__left) ).
thf(1377,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(100,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2006_power__0__Suc) ).
thf(877,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(343,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3725_diff__commute) ).
thf(1886,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(316,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_add_Ocommute) ).
thf(1796,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(80,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( D @ ( D @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3505_vebt__insert_Osimps_I4_J) ).
thf(774,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( D @ ( D @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(218,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3586_add__diff__cancel__left_H) ).
thf(1394,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(61,axiom,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2306_plus__1__eq__Suc) ).
thf(660,plain,
( ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(126,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_not0__implies__Suc) ).
thf(998,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( aTP_Lamm_bc @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8200_diff__Suc) ).
thf(988,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( aTP_Lamm_bc @ ( zero_zero_nat @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(228,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3580_add__diff__cancel__right_H) ).
thf(1433,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(360,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_add_Oassoc) ).
thf(1943,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(147,axiom,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1502_old_Oprod_Oexhaust) ).
thf(1104,plain,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(370,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3728_diff__right__commute) ).
thf(1975,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(108,axiom,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_vebt__insert_Osimps_I3_J) ).
thf(920,plain,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(16,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2997_mod__0) ).
thf(439,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(88,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_old_Onat_Oexhaust) ).
thf(810,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3398_mod__div__mult__eq) ).
thf(1470,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(37,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_add__0) ).
thf(534,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(140,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) )
<=> ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3887_split__of__bool) ).
thf(1057,plain,
! [A: fun_nat_o,B: $o] :
( ( ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) )
=> ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) )
=> ( ( ~ B
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) )
& ( B
=> ( one_one_nat @ ( A @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2467_div__mult__mult2) ).
thf(1153,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(79,axiom,
! [A: fun_nat_o,B: $o] :
( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) )
<=> ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3892_split__of__bool__asm) ).
thf(761,plain,
! [A: fun_nat_o,B: $o] :
( ( ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) )
=> ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) ) )
& ( ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ aa_nat_o ) )
=> ~ ( ( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
& ~ B )
| ( ~ ( one_one_nat @ ( A @ aa_nat_o ) )
& B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(347,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_max_Oleft__idem) ).
thf(1900,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3151_mod__add__right__eq) ).
thf(1223,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2540_no__zero__divisors) ).
thf(1021,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(179,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3063_mod__mult__self2) ).
thf(1255,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6941_binomial__absorption) ).
thf(1676,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(169,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2304_One__nat__def) ).
thf(1217,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(90,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2015_power__Suc0__right) ).
thf(820,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2610_add__mult__distrib) ).
thf(1487,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(9,axiom,
! [A: list_VEBT_VEBT,B: vEBT_VEBT,C: nat] :
~ ( C @ ( B @ ( A @ ( zero_zero_nat @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3458_VEBT__internal_Omembermima_Osimps_I2_J) ).
thf(407,plain,
! [A: list_VEBT_VEBT,B: vEBT_VEBT,C: nat] :
~ ( C @ ( B @ ( A @ ( zero_zero_nat @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3057_bits__mod__div__trivial) ).
thf(429,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,axiom,
! [A: $o,B: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) )
<=> ( A
<=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3723_of__bool__eq__iff) ).
thf(729,plain,
! [A: $o,B: $o] :
( ( ( ( B
=> A )
& ( A
=> B ) )
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) )
=> ( ( B
=> A )
& ( A
=> B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(342,axiom,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ne @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9360_ATP_Olambda__275) ).
thf(1883,plain,
! [A: fun_nat_fun_nat_nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_ne @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(323,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_max_Ocommute) ).
thf(1824,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(84,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_Suc__neq__Zero) ).
thf(788,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(225,axiom,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_nat__arith_Osuc1) ).
thf(1423,plain,
! [A: nat,B: nat,C: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(23,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_add__cancel__left__left) ).
thf(467,plain,
! [A: nat,B: nat] :
( ( ( A = zero_zero_nat )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(353,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_valid__eq1) ).
thf(1920,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1517_Pair__inject) ).
thf(665,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(104,axiom,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_vebt__insert_Osimps_I2_J) ).
thf(889,plain,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(327,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2525_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1836,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2427_mult__is__0) ).
thf(710,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4037_power__eq__if) ).
thf(1032,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( B != zero_zero_nat )
=> ( C
= ( one_one_nat @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( C = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_add__Suc__right) ).
thf(1602,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(28,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2428_mult__0__right) ).
thf(493,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(167,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1357_vebt__buildup_Ocases) ).
thf(1210,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(205,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2951_left__add__mult__distrib) ).
thf(1350,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(248,axiom,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_even__odd__cases) ).
thf(1534,plain,
! [A: nat] :
( ! [B: nat] :
( A
!= ( B @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(199,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1747_triangle__Suc) ).
thf(1328,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( nat_triangle @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) @ ( A @ ( nat_triangle @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(149,axiom,
! [A: $o,B: fun_nat_o,C: nat] :
( ( C @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
<=> @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( one_one_nat @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8201_Nitpick_Ocase__nat__unfold) ).
thf(1111,plain,
! [A: $o,B: fun_nat_o,C: nat] :
( ( @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( one_one_nat @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D = A ) ) )
=> ( C @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
=> @+[D: $o] :
( ( ( C != zero_zero_nat )
=> ( D
= ( one_one_nat @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_o ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(120,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_comm__monoid__add__class_Oadd__0) ).
thf(980,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(340,axiom,
~ ( i @ ( summary @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__C163_C) ).
thf(1878,plain,
~ ( i @ ( summary @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(296,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3814_diff__diff__eq) ).
thf(1719,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(219,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3061_mod__mult__self1) ).
thf(1397,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1383_prod_Oinject) ).
thf(697,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(250,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3583_add__diff__cancel__right) ).
thf(1541,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(99,axiom,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_VEBT__internal_Onaive__member_Osimps_I2_J) ).
thf(874,plain,
! [A: option4927543243414619207at_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( A @ vEBT_Node ) ) ) @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2535_divisors__zero) ).
thf(1143,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(184,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_add__Suc__shift) ).
thf(1270,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(310,axiom,
! [A: nat] :
( ( A @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_max_Oidem) ).
thf(1772,plain,
! [A: nat] :
( ( A @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2504_div__mult__self1) ).
thf(1028,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(367,axiom,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nsprop) ).
thf(1964,plain,
( ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) ) )
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2582_distrib__left) ).
thf(1292,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(162,axiom,
! [A: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat )
<=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3629_of__bool__eq__1__iff) ).
thf(1182,plain,
! [A: $o] :
( ( A
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= one_one_nat )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2053_power__not__zero) ).
thf(489,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(315,axiom,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3839_zero__induct__lemma) ).
thf(1791,plain,
! [A: fun_nat_o,B: nat,C: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [D: nat] :
( ( D @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( D @ ( A @ aa_nat_o ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(168,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2133_bits__div__by__0) ).
thf(1214,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_nat__add__max__right) ).
thf(1461,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2530_mult__not__zero) ).
thf(537,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= zero_zero_nat )
=> ( ( B != zero_zero_nat )
& ( A != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(344,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_pr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9250_ATP_Olambda__165) ).
thf(1889,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_pr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(278,axiom,
! [A: vEBT_VEBT] :
( ( A @ vEBT_VEBT_set_vebt )
= ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3552_set__vebt_H__def) ).
thf(1644,plain,
! [A: vEBT_VEBT] :
( ( A @ vEBT_VEBT_set_vebt )
= ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(6,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] : ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3368_VEBT__internal_OminNull_Osimps_I4_J) ).
thf(393,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT] : ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(214,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3653_diff__add__zero) ).
thf(1382,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2465_div__mult__mult1) ).
thf(1192,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(73,axiom,
! [A: $o,B: fun_nat_o] :
( ( zero_zero_nat @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
<=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8190_old_Onat_Osimps_I4_J) ).
thf(721,plain,
! [A: $o,B: fun_nat_o] :
( ( A
=> ( zero_zero_nat @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) ) )
& ( ( zero_zero_nat @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(317,axiom,
( m
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o )
@ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__C12_C) ).
thf(1799,plain,
( m
@ ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o )
@ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(332,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ vEBT_VEBT_bit_concat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bit__split__inv) ).
thf(1852,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ vEBT_VEBT_bit_concat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(372,axiom,
! [A: nat] :
( ( A @ ( aTP_Lamm_bc @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9737_ATP_Olambda__652) ).
thf(1979,plain,
! [A: nat] :
( ( A @ ( aTP_Lamm_bc @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1646_add__0__iff) ).
thf(503,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ divmod_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4842_divmod__nat__def) ).
thf(1150,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ divmod_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3858_diff__add__inverse2) ).
thf(1249,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(263,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3810_right__diff__distrib_H) ).
thf(1599,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(176,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3164_mod__Suc__Suc__eq) ).
thf(1246,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(85,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2613_nat__mult__1) ).
thf(792,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_add__left__cancel) ).
thf(1814,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(60,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2152_div__self) ).
thf(657,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(139,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2127_div__by__Suc__0) ).
thf(1054,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(136,axiom,
! [A: $o,B: fun_nat_o,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8188_old_Onat_Osimps_I5_J) ).
thf(1035,plain,
! [A: $o,B: fun_nat_o,C: nat] :
( ( ( C @ ( B @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ case_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(65,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2414_mult_Oright__neutral) ).
thf(674,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(62,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_valid__0__not) ).
thf(662,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(110,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_zero__reorient) ).
thf(926,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat = A ) )
& ( ( zero_zero_nat = A )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(76,axiom,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_nat__induct) ).
thf(750,plain,
! [A: fun_nat_o,B: nat] :
( ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( A @ aa_nat_o ) )
=> ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) )
=> ( B @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(170,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_n__not__Suc__n) ).
thf(1219,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3037_mod__mult__self2__is__0) ).
thf(1273,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(191,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6882_Suc__times__binomial) ).
thf(1301,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(211,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3601_Suc__diff__diff) ).
thf(1374,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2247_div__add__self2) ).
thf(1146,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(303,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_vr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9294_ATP_Olambda__209) ).
thf(1754,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_vr @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_add__cancel__right__right) ).
thf(584,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(326,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_max_Oleft__commute) ).
thf(1833,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2549_mult__right__cancel) ).
thf(843,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(270,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3860_diff__cancel2) ).
thf(1620,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2740_power__Suc) ).
thf(1388,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(295,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o,D: fun_VEBT_VEBT_o] :
( ( A = B )
=> ( ! [E: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( E @ member_VEBT_VEBT2 ) )
=> ( ( E @ ( C @ aa_VEBT_VEBT_o ) )
<=> ( E @ ( D @ aa_VEBT_VEBT_o ) ) ) )
=> ( ( A @ ( C @ find_VEBT_VEBT ) )
= ( B @ ( D @ find_VEBT_VEBT ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1875_find__cong) ).
thf(1701,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: fun_VEBT_VEBT_o,D: fun_VEBT_VEBT_o] :
( ( A = B )
=> ( ! [E: vEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( E @ member_VEBT_VEBT2 ) )
=> ( ( ( E @ ( D @ aa_VEBT_VEBT_o ) )
=> ( E @ ( C @ aa_VEBT_VEBT_o ) ) )
& ( ( E @ ( C @ aa_VEBT_VEBT_o ) )
=> ( E @ ( D @ aa_VEBT_VEBT_o ) ) ) ) )
=> ( ( A @ ( C @ find_VEBT_VEBT ) )
= ( B @ ( D @ find_VEBT_VEBT ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
=> ( ~ ? [F: nat] : ( F @ ( E @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
& ! [F: vEBT_VEBT] :
( ( D @ set_VEBT_VEBT2 @ ( F @ member_VEBT_VEBT2 ) )
=> ~ ? [G: nat] : ( G @ ( F @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_mi__eq__ma__no__ch) ).
thf(1007,plain,
! [A: nat,B: nat,C: nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( A = B )
=> ( ~ ? [F: nat] : ( F @ ( E @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
& ! [F: vEBT_VEBT] :
( ( D @ set_VEBT_VEBT2 @ ( F @ member_VEBT_VEBT2 ) )
=> ~ ? [G: nat] : ( G @ ( F @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(69,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2612_nat__mult__1__right) ).
thf(694,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(115,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3566_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(958,plain,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6839_binomial__Suc__Suc) ).
thf(1403,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_bc @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8956_sort__upt) ).
thf(1226,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( aTP_Lamm_bc @ linord738340561235409698at_nat ) )
= ( B @ ( A @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(39,axiom,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_vebt__member_Osimps_I4_J) ).
thf(545,plain,
! [A: product_prod_nat_nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2603_Suc__mult__cancel1) ).
thf(1503,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(313,axiom,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__C0_C) ).
thf(1786,plain,
! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ( na @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( aTP_Lamm_vr @ aa_nat_fun_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8196_max__Suc2) ).
thf(445,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( aTP_Lamm_vr @ aa_nat_fun_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3039_mod__mult__self1__is__0) ).
thf(1371,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3945_diff__add__0) ).
thf(1635,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(180,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2614_nat__mult__max__left) ).
thf(1258,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(276,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2611_add__mult__distrib2) ).
thf(1638,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(207,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3806_left__diff__distrib_H) ).
thf(1356,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3589_add__diff__cancel__left) ).
thf(1464,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2545_mult__left__cancel) ).
thf(947,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(346,axiom,
! [A: fun_nat_o,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( B @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9590_ATP_Olambda__505) ).
thf(1894,plain,
! [A: fun_nat_o,B: fun_nat_nat,C: nat] :
( ( ( C @ ( B @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ aTP_Lamm_vn @ aa_fun8673969331427483654_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ aa_nat_nat ) @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2245_div__add__self1) ).
thf(784,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(320,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_both__member__options__def) ).
thf(1806,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
=> ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( B @ ( A @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
| ( B @ ( A @ ( vEBT_V5719532721284313246member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(137,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2391_mult__zero__right) ).
thf(1048,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2481_one__eq__mult__iff) ).
thf(1589,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(20,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_max__nat_Oleft__neutral) ).
thf(451,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(297,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6836_binomial__1) ).
thf(1722,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_Suc__inject) ).
thf(1690,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_old_Onat_Oinject) ).
thf(1571,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3996_minus__mod__eq__div__mult) ).
thf(1307,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(101,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2604_mult__0) ).
thf(880,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_add__cancel__right__left) ).
thf(649,plain,
! [A: nat,B: nat] :
( ( ( B = zero_zero_nat )
=> ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(286,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3404_cancel__div__mod__rules_I1_J) ).
thf(1667,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(144,axiom,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_valid__tree__deg__neq__0) ).
thf(1080,plain,
! [A: vEBT_VEBT] :
~ ( zero_zero_nat @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(78,axiom,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_deg__deg__n) ).
thf(758,plain,
! [A: option4927543243414619207at_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( B @ ( A @ vEBT_Node ) ) ) @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4027_add__eq__if) ).
thf(552,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2430_mult__cancel2) ).
thf(609,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(300,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3084_Suc__mod__mult__self4) ).
thf(1731,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(25,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3043_bits__mod__by__1) ).
thf(483,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2938_nat__mult__div__cancel__disj) ).
thf(520,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__eq__self__zero) ).
thf(964,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(55,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2135_bits__div__0) ).
thf(626,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( suc @ map_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8911_map__Suc__upt) ).
thf(1344,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ ( suc @ map_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(255,axiom,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6829_binomial__Suc__n) ).
thf(1556,plain,
! [A: nat] :
( ( A @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(121,axiom,
! [A: nat] :
( ( A @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3001_mod__self) ).
thf(983,plain,
! [A: nat] :
( ( A @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8,axiom,
! [A: option4927543243414619207at_nat] :
( ( A != none_P5556105721700978146at_nat )
<=> ? [B: product_prod_nat_nat] :
( A
= ( B @ some_P7363390416028606310at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3013_not__None__eq) ).
thf(399,plain,
! [A: option4927543243414619207at_nat] :
( ( ? [B: product_prod_nat_nat] :
( A
= ( B @ some_P7363390416028606310at_nat ) )
=> ( A != none_P5556105721700978146at_nat ) )
& ( ( A != none_P5556105721700978146at_nat )
=> ? [B: product_prod_nat_nat] :
( A
= ( B @ some_P7363390416028606310at_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(247,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
<=> ( A @ ( B @ member_VEBT_VEBT @ aa_VEBT_VEBT_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_in__set__member) ).
thf(1528,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( ( A @ ( B @ member_VEBT_VEBT @ aa_VEBT_VEBT_o ) )
=> ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) ) )
& ( ( B @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ( A @ ( B @ member_VEBT_VEBT @ aa_VEBT_VEBT_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(102,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3573_zero__diff) ).
thf(883,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(130,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_max__nat_Oright__neutral) ).
thf(1015,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(122,axiom,
( ( one_one_nat @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2161_max__0__1_I1_J) ).
thf(986,plain,
( ( one_one_nat @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(311,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_both__member__options__equiv__member) ).
thf(1775,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_add__eq__0__iff__both__eq__0) ).
thf(851,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(257,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3394_mult__div__mod__eq) ).
thf(1562,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(143,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2460_nonzero__mult__div__cancel__right) ).
thf(1076,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(272,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3081_Suc__mod__mult__self1) ).
thf(1626,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(362,axiom,
( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_insprop) ).
thf(1948,plain,
( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(12,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3672_Suc__0__mod__eq) ).
thf(426,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( ( A
!= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(236,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3275_div__add1__eq) ).
thf(1467,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( C @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A = C )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2405_mult__cancel__right) ).
thf(795,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A = C )
| ( B = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = C )
| ( B = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(40,axiom,
! [A: fun_nat_o] :
( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
=> ? [B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ~ ( B @ ( A @ aa_nat_o ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1404_exists__least__lemma) ).
thf(548,plain,
! [A: fun_nat_o] :
( ~ ( zero_zero_nat @ ( A @ aa_nat_o ) )
=> ( ? [B: nat] : ( B @ ( A @ aa_nat_o ) )
=> ? [B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
& ~ ( B @ ( A @ aa_nat_o ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(349,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2515_mult_Ocommute) ).
thf(1905,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(112,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
<=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT2 ) )
=> ( B @ ( C @ member_VEBT_VEBT2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_subset__code_I1_J) ).
thf(939,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT2 ) )
=> ( B @ ( C @ member_VEBT_VEBT2 ) ) )
=> ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) ) )
& ( ( B @ ( A @ set_VEBT_VEBT2 @ ord_le4337996190870823476T_VEBT ) )
=> ! [C: vEBT_VEBT] :
( ( A @ set_VEBT_VEBT2 @ ( C @ member_VEBT_VEBT2 ) )
=> ( B @ ( C @ member_VEBT_VEBT2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(131,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3003_bits__mod__0) ).
thf(1018,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(365,axiom,
! [A: fun_o_nat,B: fun_nat_o,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_vm @ aa_fun4204860950123276802at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ aa_nat_o ) @ ( A @ aa_o_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9589_ATP_Olambda__504) ).
thf(1958,plain,
! [A: fun_o_nat,B: fun_nat_o,C: nat] :
( ( C @ ( B @ ( A @ aTP_Lamm_vm @ aa_fun4204860950123276802at_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ aa_nat_o ) @ ( A @ aa_o_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_nat_OdiscI) ).
thf(823,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( suc @ aa_nat_nat ) ) )
=> ( A != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6910_Suc__times__binomial__add) ).
thf(1304,plain,
! [A: nat,B: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(338,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xx @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9242_ATP_Olambda__157) ).
thf(1873,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xx @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(330,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( A = B ) )
=> ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_add__mono__thms__linordered__semiring_I4_J) ).
thf(1845,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C = D )
& ( A = B ) )
=> ( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(252,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3452_mod__mult2__eq) ).
thf(1547,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(36,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2229_one__reorient) ).
thf(525,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_nat = A ) )
& ( ( one_one_nat = A )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(309,axiom,
( i
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
thf(1770,plain,
( i
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(133,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2236_zero__neq__one) ).
thf(1025,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(141,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2300_power__0) ).
thf(1070,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(267,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3953_diff__Suc__eq__diff__pred) ).
thf(1611,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(265,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6881_Suc__times__binomial__eq) ).
thf(1605,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(279,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_deg__SUcn__Node) ).
thf(1647,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ? [C: option4927543243414619207at_nat,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( A
= ( E @ ( D @ ( B @ ( suc @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( C @ vEBT_Node ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3340_mod__eq__0D) ).
thf(1252,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(183,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( E @ ( B @ ( D @ list_u1324408373059187874T_VEBT ) ) @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ zip_VE537291747668921783T_VEBT ) )
= ( E @ ( C @ produc537772716801021591T_VEBT ) @ ( B @ ( D @ ( A @ zip_VE537291747668921783T_VEBT ) @ list_u6961636818849549845T_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1905_zip__update) ).
thf(1267,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( E @ ( B @ ( D @ list_u1324408373059187874T_VEBT ) ) @ ( C @ ( B @ ( A @ list_u1324408373059187874T_VEBT ) ) @ zip_VE537291747668921783T_VEBT ) )
= ( E @ ( C @ produc537772716801021591T_VEBT ) @ ( B @ ( D @ ( A @ zip_VE537291747668921783T_VEBT ) @ list_u6961636818849549845T_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2498_div__mult__self4) ).
thf(640,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(366,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_add__left__imp__eq) ).
thf(1961,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(220,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2735_power__Suc2) ).
thf(1400,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(71,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_add_Ocomm__neutral) ).
thf(707,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(231,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3083_Suc__mod__mult__self3) ).
thf(1452,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(249,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3451_div__mod__decomp) ).
thf(1538,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(290,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3071_mod__by__Suc__0) ).
thf(1679,plain,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(261,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
<=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2482_mult__eq__1__iff) ).
thf(1579,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
=> ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(325,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xh @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9236_ATP_Olambda__151) ).
thf(1830,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_xh @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(306,axiom,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_lc @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9310_ATP_Olambda__225) ).
thf(1763,plain,
! [A: fun_nat_nat,B: nat] :
( ( B @ ( A @ aTP_Lamm_lc @ aa_nat_fun_nat_nat ) )
= ( B @ ( A @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(358,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_valid__eq) ).
thf(1934,plain,
! [A: vEBT_VEBT,B: nat] :
( ( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(307,axiom,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3870_set__vebt__def) ).
thf(1766,plain,
! [A: vEBT_VEBT] :
( ( A @ vEBT_set_vebt )
= ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(331,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_valid__member__both__member__options) ).
thf(1849,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( C @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( A @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(369,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: nat,D: produc8243902056947475879T_VEBT] :
( ( D @ ( C @ ( B @ ( A @ zip_VE537291747668921783T_VEBT ) @ list_u6961636818849549845T_VEBT ) ) )
= ( D @ produc351232539757196229T_VEBT @ ( C @ ( B @ list_u1324408373059187874T_VEBT ) ) @ ( D @ produc6118266651365575811T_VEBT @ ( C @ ( A @ list_u1324408373059187874T_VEBT ) ) @ zip_VE537291747668921783T_VEBT ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8382_update__zip) ).
thf(1972,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: nat,D: produc8243902056947475879T_VEBT] :
( ( D @ ( C @ ( B @ ( A @ zip_VE537291747668921783T_VEBT ) @ list_u6961636818849549845T_VEBT ) ) )
= ( D @ produc351232539757196229T_VEBT @ ( C @ ( B @ list_u1324408373059187874T_VEBT ) ) @ ( D @ produc6118266651365575811T_VEBT @ ( C @ ( A @ list_u1324408373059187874T_VEBT ) ) @ zip_VE537291747668921783T_VEBT ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(226,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2754_mult__Suc) ).
thf(1427,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(287,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2485_mult__Suc__right) ).
thf(1670,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
<=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3272_mod__eq__self__iff__div__eq__0) ).
thf(595,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A )
=> ( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(206,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_max__Suc__Suc) ).
thf(1353,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(364,axiom,
~ ? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__C162_C) ).
thf(1955,plain,
~ ? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3059_mod__div__trivial) ).
thf(1140,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(4,axiom,
! [A: option4927543243414619207at_nat] :
( ( A != none_P5556105721700978146at_nat )
=> ~ ! [B: product_prod_nat_nat] :
( A
!= ( B @ some_P7363390416028606310at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3251_option_Oexhaust) ).
thf(386,plain,
! [A: option4927543243414619207at_nat] :
( ( A != none_P5556105721700978146at_nat )
=> ~ ! [B: product_prod_nat_nat] :
( A
!= ( B @ some_P7363390416028606310at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3600_diff__Suc__Suc) ).
thf(1240,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(124,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_Zero__not__Suc) ).
thf(991,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(269,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3007_mod__add__self1) ).
thf(1617,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(359,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_buildup__nothing__in__min__max) ).
thf(1940,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ vEBT_vebt_buildup @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(22,axiom,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1816_triangle__0) ).
thf(465,plain,
( ( zero_zero_nat @ ( nat_triangle @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(328,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( B @ ( C @ nth_VEBT_VEBT ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nth__list__update__neq) ).
thf(1839,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( B @ ( D @ ( A @ ( C @ list_u1324408373059187874T_VEBT ) ) @ nth_VEBT_VEBT ) )
= ( B @ ( C @ nth_VEBT_VEBT ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(196,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3605_diff__diff__left) ).
thf(1316,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(368,axiom,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) )
<=> ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__children__def) ).
thf(1966,plain,
! [A: nat,B: list_VEBT_VEBT,C: nat] :
( ( ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) ) )
& ( ( C @ ( B @ ( A @ vEBT_V5917875025757280293ildren ) @ aa_nat_o ) )
=> ( A @ ( C @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( C @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ nth_VEBT_VEBT ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(292,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( A != zero_zero_nat )
=> ( ( ( D != E )
& ( B = C ) )
=> ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2714_add__scale__eq__noteq) ).
thf(1685,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( A != zero_zero_nat )
=> ( ( ( D != E )
& ( B = C ) )
=> ( ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( E @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(254,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ size_size_list_nat )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8901_length__upt) ).
thf(1553,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ size_size_list_nat )
= ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(64,axiom,
! [A: product_prod_nat_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
~ ( D @ ( C @ ( B @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_VEBT__internal_OminNull_Osimps_I5_J) ).
thf(671,plain,
! [A: product_prod_nat_nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
~ ( D @ ( C @ ( B @ ( A @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2500_div__mult__self3) ).
thf(1157,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( C @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3843_diffs0__imp__equal) ).
thf(688,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(312,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_group__cancel_Oadd1) ).
thf(1781,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( D @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(150,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3844_minus__nat_Odiff__0) ).
thf(1126,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(163,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_max__0R) ).
thf(1189,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(301,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2305_Suc__eq__plus1__left) ).
thf(1734,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4031_mult__eq__if) ).
thf(1108,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( A != zero_zero_nat )
=> ( C
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(282,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3863_diff__mult__distrib2) ).
thf(1654,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',fact_79_Collect__cong) ).
thf(1412,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)],[224]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3998_minus__mod__eq__mult__div) ).
thf(1276,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(33,axiom,
! [A: product_prod_nat_nat] :
? [B: nat,C: nat] :
( A
= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1507_surj__pair) ).
thf(517,plain,
! [A: product_prod_nat_nat] :
? [B: nat,C: nat] :
( A
= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( C != D )
& ( A != B ) )
<=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2567_crossproduct__noteq) ).
thf(1476,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( C != D )
& ( A != B ) ) )
& ( ( ( C != D )
& ( A != B ) )
=> ( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
!= ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(202,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ tl_nat )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8929_tl__upt) ).
thf(1341,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ upt ) @ tl_nat )
= ( B @ ( A @ ( suc @ aa_nat_nat ) @ upt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(348,axiom,
( ( na @ ( suc @ aa_nat_nat ) )
= m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584__C8_C) ).
thf(1903,plain,
( ( na @ ( suc @ aa_nat_nat ) )
= m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(5,axiom,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3364_vebt__member_Osimps_I2_J) ).
thf(390,plain,
! [A: nat,B: list_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
~ ( D @ ( C @ ( B @ ( A @ ( none_P5556105721700978146at_nat @ vEBT_Node ) ) ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(273,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_pt @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9146_ATP_Olambda__61) ).
thf(1629,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_pt @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(322,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_valid__eq2) ).
thf(1822,plain,
! [A: vEBT_VEBT,B: nat] :
( ( B @ ( A @ ( vEBT_VEBT_valid @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( B @ ( A @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2469_div__mult__mult1__if) ).
thf(781,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( A != zero_zero_nat )
=> ( D
= ( C @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( A = zero_zero_nat )
=> ( D = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(125,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1996_div__by__0) ).
thf(995,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(116,axiom,
! [A: nat,B: fun_nat_nat] :
( ( zero_zero_nat @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8191_old_Onat_Osimps_I4_J) ).
thf(961,plain,
! [A: nat,B: fun_nat_nat] :
( ( zero_zero_nat @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(215,axiom,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3402_mod__div__decomp) ).
thf(1385,plain,
! [A: nat,B: nat] :
( A
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(335,axiom,
~ ? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C161_C) ).
thf(1861,plain,
~ ? [A: nat] : ( A @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_vebt_member @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(44,axiom,
( ( zero_zero_nat @ ( one_one_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2165_max__0__1_I2_J) ).
thf(568,plain,
( ( zero_zero_nat @ ( one_one_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2755_mult__eq__self__implies__10) ).
thf(914,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(3,axiom,
! [A: option4927543243414619207at_nat] :
( ! [B: product_prod_nat_nat] :
( A
!= ( B @ some_P7363390416028606310at_nat ) )
<=> ( A = none_P5556105721700978146at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3015_not__Some__eq) ).
thf(378,plain,
! [A: option4927543243414619207at_nat] :
( ( ( A = none_P5556105721700978146at_nat )
=> ! [B: product_prod_nat_nat] :
( A
!= ( B @ some_P7363390416028606310at_nat ) ) )
& ( ! [B: product_prod_nat_nat] :
( A
!= ( B @ some_P7363390416028606310at_nat ) )
=> ( A = none_P5556105721700978146at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(158,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1641_list__decode_Ocases) ).
thf(1161,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(268,axiom,
! [A: fun_o_nat,B: $o,C: fun_nat_o,D: nat] :
( ( D @ ( C @ ( B @ case_nat_o ) @ aa_nat_o ) @ ( A @ aa_o_nat ) )
= ( D @ ( C @ ( A @ aTP_Lamm_vm @ aa_fun4204860950123276802at_nat ) @ ( B @ ( A @ aa_o_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8185_nat_Ocase__distrib) ).
thf(1614,plain,
! [A: fun_o_nat,B: $o,C: fun_nat_o,D: nat] :
( ( D @ ( C @ ( B @ case_nat_o ) @ aa_nat_o ) @ ( A @ aa_o_nat ) )
= ( D @ ( C @ ( A @ aTP_Lamm_vm @ aa_fun4204860950123276802at_nat ) @ ( B @ ( A @ aa_o_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(350,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_add__right__imp__eq) ).
thf(1908,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(53,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_add_Oright__neutral) ).
thf(620,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(298,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6837_binomial__0__Suc) ).
thf(1725,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) @ ( zero_zero_nat @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(14,axiom,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1730_prod__decode__aux_Ocases) ).
thf(432,plain,
! [A: product_prod_nat_nat] :
~ ! [B: nat,C: nat] :
( A
!= ( C @ ( B @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(93,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_Zero__neq__Suc) ).
thf(835,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = D )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2563_crossproduct__eq) ).
thf(1229,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
| ( A = C ) )
=> ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( D @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( D @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = D )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(213,axiom,
( ( xa @ ( summary @ ( treeList @ ( deg @ ( ma @ ( mi @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ ( deg @ ( ma @ ( xa @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( mi @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__C10_C) ).
thf(1380,plain,
( ( xa @ ( summary @ ( treeList @ ( deg @ ( ma @ ( mi @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ vEBT_vebt_insert ) )
= ( @+[A: vEBT_VEBT] :
( ( ~ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A = summary ) )
& ( ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ( A
= ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( summary @ vEBT_vebt_insert ) ) ) ) )
@ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ list_u1324408373059187874T_VEBT ) ) @ ( deg @ ( ma @ ( xa @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( mi @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(339,axiom,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_not__min__Null__member) ).
thf(1876,plain,
! [A: vEBT_VEBT] :
( ~ ( A @ ( vEBT_VEBT_minNull @ aa_VEBT_VEBT_o ) )
=> ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(288,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4000_minus__mult__div__eq__mod) ).
thf(1673,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(304,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6913_binomial__Suc__Suc__eq__times) ).
thf(1757,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(50,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2999_mod__by__0) ).
thf(603,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [A: option4927543243414619207at_nat,B: product_prod_nat_nat] :
( ( A
= ( B @ some_P7363390416028606310at_nat ) )
=> ( A != none_P5556105721700978146at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3249_option_OdiscI) ).
thf(410,plain,
! [A: option4927543243414619207at_nat,B: product_prod_nat_nat] :
( ( A
= ( B @ some_P7363390416028606310at_nat ) )
=> ( A != none_P5556105721700978146at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_zero__eq__add__iff__both__eq__0) ).
thf(967,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( zero_zero_nat
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(229,axiom,
! [A: $o,B: $o] :
( ( ( B
| A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3632_of__bool__or__iff) ).
thf(1436,plain,
! [A: $o,B: $o] :
( ( ( B
| A )
@ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( B @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(375,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ys @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9245_ATP_Olambda__160) ).
thf(1989,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ys @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(283,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3065_mod__mult__self3) ).
thf(1657,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(294,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3353_nat__mod__eq__iff) ).
thf(1693,plain,
! [A: nat,B: nat,C: nat] :
( ( ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ? [D: nat,E: nat] :
( ( D @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( E @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2431_nat__mult__eq__1__iff) ).
thf(1172,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(92,axiom,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3882_of__bool__def) ).
thf(828,plain,
! [A: $o] :
( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= ( @+[B: nat] :
( ( ~ A
=> ( B = zero_zero_nat ) )
& ( A
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3958_nat__minus__add__max) ).
thf(1473,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2502_div__mult__self2) ).
thf(1165,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(114,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2320_power__0__left) ).
thf(955,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[B: nat] :
( ( ( A != zero_zero_nat )
=> ( B = zero_zero_nat ) )
& ( ( A = zero_zero_nat )
=> ( B = one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(103,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Nat_Oadd__0__right) ).
thf(886,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(11,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( E @ ( D @ ( C @ ( zero_zero_nat @ ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
<=> ( ( E = B )
| ( E = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_VEBT__internal_Omembermima_Osimps_I3_J) ).
thf(415,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: nat] :
( ( ( ( E = B )
| ( E = A ) )
=> ( E @ ( D @ ( C @ ( zero_zero_nat @ ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) )
& ( ( E @ ( D @ ( C @ ( zero_zero_nat @ ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) @ some_P7363390416028606310at_nat @ vEBT_Node ) ) ) @ ( vEBT_VEBT_membermima @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) )
=> ( ( E = B )
| ( E = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
<=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1378_old_Oprod_Oinject) ).
thf(740,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( B = D )
& ( A = C ) )
=> ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) ) )
& ( ( ( B @ ( A @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) )
= ( D @ ( C @ ( product_Pair_nat_nat @ aa_nat8803788312118491388at_nat ) @ aa_nat7603221163087113075at_nat ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2950_nat__mult__eq__cancel__disj) ).
thf(1129,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= B )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= B )
=> ( C = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3313_mod__Suc) ).
thf(1500,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( @+[C: nat] :
( ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
!= B )
=> ( C
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( suc @ aa_nat_nat ) )
= B )
=> ( C = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(355,axiom,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ~ ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C5_C) ).
thf(1925,plain,
( ( mi = ma )
=> ! [A: vEBT_VEBT] :
( ( treeList @ set_VEBT_VEBT2 @ ( A @ member_VEBT_VEBT2 ) )
=> ~ ? [B: nat] : ( B @ ( A @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(68,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_max__0L) ).
thf(691,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(17,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3041_mod__by__1) ).
thf(442,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(98,axiom,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8189_old_Onat_Osimps_I5_J) ).
thf(871,plain,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2396_mult__eq__0__iff) ).
thf(1093,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(7,axiom,
! [A: product_prod_nat_nat] :
( none_P5556105721700978146at_nat
!= ( A @ some_P7363390416028606310at_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3247_option_Odistinct_I1_J) ).
thf(395,plain,
! [A: product_prod_nat_nat] :
( none_P5556105721700978146at_nat
!= ( A @ some_P7363390416028606310at_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1424_neq__if__length__neq) ).
thf(839,plain,
! [A: list_nat,B: list_nat] :
( ( ( A @ size_size_list_nat )
!= ( B @ size_size_list_nat ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(324,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_add_Oleft__commute) ).
thf(1827,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(181,axiom,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2307_Suc__eq__plus1) ).
thf(1261,plain,
! [A: nat] :
( ( A @ ( suc @ aa_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(58,axiom,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_zero__induct) ).
thf(644,plain,
! [A: fun_nat_o,B: nat] :
( ( B @ ( A @ aa_nat_o ) )
=> ( ! [C: nat] :
( ( C @ ( suc @ aa_nat_nat ) @ ( A @ aa_nat_o ) )
=> ( C @ ( A @ aa_nat_o ) ) )
=> ( zero_zero_nat @ ( A @ aa_nat_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(253,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3994_minus__div__mult__eq__mod) ).
thf(1550,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(341,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2510_mult_Oleft__commute) ).
thf(1880,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(128,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( aTP_Lamm_vq @ aa_nat_fun_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8195_max__Suc1) ).
thf(1004,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ aa_nat_nat ) @ ( ord_max_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( A @ ( aTP_Lamm_vq @ aa_nat_fun_nat_nat ) @ ( A @ ( suc @ aa_nat_nat ) @ case_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(200,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3406_cancel__div__mod__rules_I2_J) ).
thf(1331,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( B @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( B @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(26,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2019_power__Suc__0) ).
thf(486,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( suc @ aa_nat_nat ) @ ( power_power_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2452_nonzero__mult__div__cancel__left) ).
thf(935,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( A @ ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(258,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ps @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9147_ATP_Olambda__62) ).
thf(1565,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( aTP_Lamm_ps @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(241,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3147_mod__add__cong) ).
thf(1490,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ( B @ ( A @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( C @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B @ ( D @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( B @ ( D @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( B @ ( E @ ( C @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( modulo_modulo_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(230,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3861_Nat_Odiff__cancel) ).
thf(1449,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(48,axiom,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( C != zero_zero_nat )
=> ( D
= ( one_one_nat @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_nat ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8202_Nitpick_Ocase__nat__unfold) ).
thf(592,plain,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ case_nat_nat ) @ aa_nat_nat ) )
= ( @+[D: nat] :
( ( ( C != zero_zero_nat )
=> ( D
= ( one_one_nat @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( B @ aa_nat_nat ) ) ) )
& ( ( C = zero_zero_nat )
=> ( D = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(281,axiom,
m @ ( summary @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__C1_C) ).
thf(1653,plain,
m @ ( summary @ ( vEBT_invar_vebt @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(209,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( A
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3817_add__implies__diff) ).
thf(1367,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= C )
=> ( A
= ( B @ ( C @ ( minus_minus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(109,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2138_div__by__1) ).
thf(923,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( divide_divide_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(302,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_one__is__add) ).
thf(1737,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ aa_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ aa_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(308,axiom,
na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C166_C) ).
thf(1769,plain,
na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_low @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( na @ ( xa @ ( vEBT_VEBT_high @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) @ ( treeList @ nth_VEBT_VEBT ) @ vEBT_vebt_insert ) @ ( vEBT_V8194947554948674370ptions @ aa_VEB2314620471664397097_nat_o ) @ aa_nat_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(77,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6840_binomial__n__0) ).
thf(755,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( binomial @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [A: $o] :
( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat )
<=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3612_of__bool__eq__0__iff) ).
thf(496,plain,
! [A: $o] :
( ( ~ A
=> ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat ) )
& ( ( ( A @ ( zero_n2687167440665602831ol_nat @ aa_o_nat ) )
= zero_zero_nat )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
<=> ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2429_mult__cancel1) ).
thf(454,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ aa_nat_fun_nat_nat ) @ aa_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(2065,plain,
$false,
inference(e,[status(thm)],[892,1322,629,1559,1295,1950,1083,1982,777,555,977,523,1406,1073,1544,1728,511,677,861,1855,1200,1497,1788,1608,1310,1872,814,1458,1196,1001,1914,1243,1391,1650,1359,565,1623,436,1803,1409,570,1430,1985,1264,1455,1760,1660,1298,1511,917,1313,1279,1922,1800,1892,1319,1641,606,1347,1931,1568,448,1494,475,1946,1664,1911,1632,376,623,1334,1682,1978,514,574,806,1051,1858,1864,1843,1169,1928,1377,877,1886,1796,774,1394,660,998,988,1433,1943,1104,1975,920,439,810,1470,534,1057,1153,761,1900,1223,1021,1255,1676,1217,820,1487,407,429,729,1883,1824,788,1423,467,1920,665,889,1836,710,1032,1602,493,1210,1350,1534,1328,1111,980,1878,1719,1397,697,1541,874,1143,1270,1772,1028,1964,1292,1182,489,1791,1214,1461,537,1889,1644,393,1382,1192,721,1799,1852,1979,503,1150,1249,1599,1246,792,1814,657,1054,1035,674,662,926,750,1219,1273,1301,1374,1146,1754,584,1833,843,1620,1388,1701,1007,694,958,1403,1226,545,1503,1786,445,1371,1635,1258,1638,1356,1464,947,1894,784,1806,1048,1589,451,1722,1690,1571,1307,880,649,1667,1080,758,552,609,1731,483,520,964,626,1344,1556,983,399,1528,883,1015,986,1775,851,1562,1076,1626,1948,426,1467,795,548,1905,939,1018,1958,823,1304,1873,1845,1547,525,1770,1025,1070,1611,1605,1647,1252,1267,640,1961,1400,707,1452,1538,1679,1579,1830,1763,1934,1766,1849,1972,1427,1670,595,1353,1955,1140,386,1240,991,1617,1940,465,1839,1316,1966,1685,1553,671,1157,688,1781,1126,1189,1734,1108,1654,1412,1276,517,1476,1341,1903,390,1629,1822,781,995,961,1385,1861,568,914,378,1161,1614,1908,620,1725,432,835,1229,1380,1876,1673,1757,603,410,967,1436,1989,1657,1693,1172,828,1473,1165,955,886,415,740,1129,1500,1925,691,442,871,1093,395,839,1827,1261,644,1550,1880,1004,1331,486,935,1565,1490,1449,592,1653,1367,923,1737,1769,755,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP233_3 : TPTP v9.3.1. Bugfixed v9.3.0.
% 0.00/0.08 % 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
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 18:22:02 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 0.86/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.60/2.42 % [INFO] Parsing done (1394ms).
% 6.60/2.43 % [INFO] Running in sequential loop mode.
% 7.34/2.64 % [INFO] eprover registered as external prover.
% 7.34/2.65 % [INFO] Scanning for conjecture ...
% 10.20/3.32 % [INFO] Found a conjecture (or negated_conjecture) and 9766 axioms. Running axiom selection ...
% 12.86/4.24 % [INFO] Axiom selection finished. Selected 373 axioms (removed 9393 axioms).
% 13.89/4.54 % [INFO] Problem is typed first-order (TPTP TFF).
% 13.89/4.58 % [INFO] Type checking passed.
% 13.89/4.58 % [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 ...
% 26.53/8.24 % External prover 'e' found a proof!
% 26.53/8.24 % [INFO] Killing All external provers ...
% 26.53/8.24 % Time passed: 7674ms (effective reasoning time: 5809ms)
% 26.53/8.24 % 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)>
% 26.53/8.25 % Axioms used in derivation (373): fact_2135_bits__div__0, fact_20__C11_C, fact_3__C164_C, fact_6910_Suc__times__binomial__add, fact_2540_no__zero__divisors, fact_2391_mult__zero__right, fact_3573_zero__diff, fact_2999_mod__by__0, fact_62__C3_C, fact_8186_nat_Ocase__distrib, fact_615_nat__induct, fact_397_group__cancel_Oadd1, fact_3860_diff__cancel2, fact_35_valid__eq, fact_3858_diff__add__inverse2, fact_584__C8_C, fact_3067_mod__mult__self4, fact_9270_ATP_Olambda__185, fact_3163_mod__Suc__eq, fact_2396_mult__eq__0__iff, fact_9293_ATP_Olambda__208, fact_6839_binomial__Suc__Suc, fact_3601_Suc__diff__diff, fact_9147_ATP_Olambda__62, fact_28__C0_C, fact_2428_mult__0__right, fact_131_add__eq__self__zero, fact_2520_mult_Oassoc, fact_691_vebt__insert_Osimps_I3_J, fact_151_nat__add__max__left, fact_3364_vebt__member_Osimps_I2_J, fact_337_add__cancel__right__right, fact_8191_old_Onat_Osimps_I4_J, fact_2247_div__add__self2, fact_3863_diff__mult__distrib2, fact_685_add__is__1, fact_2530_mult__not__zero, fact_3452_mod__mult2__eq, fact_1357_vebt__buildup_Ocases, fact_2414_mult_Oright__neutral, fact_2610_add__mult__distrib, fact_187_max_Oleft__commute, fact_1502_old_Oprod_Oexhaust, fact_8901_length__upt, fact_3629_of__bool__eq__1__iff, fact_3817_add__implies__diff, fact_3839_zero__induct__lemma, fact_37_valid__eq2, fact_2553_mult_Ocomm__neutral, fact_651_add__Suc__shift, fact_130_plus__nat_Oadd__0, fact_2740_power__Suc, fact_23_min__Null__member, fact_3996_minus__mod__eq__div__mult, fact_9737_ATP_Olambda__652, fact_3998_minus__mod__eq__mult__div, fact_113_max_Oright__idem, fact_3149_mod__add__left__eq, fact_1646_add__0__iff, fact_2558_comm__monoid__mult__class_Omult__1, fact_2755_mult__eq__self__implies__10, fact_612_old_Onat_Odistinct_I1_J, fact_3151_mod__add__right__eq, fact_2_bit__split__inv, fact_4__C162_C, fact_583_vebt__insert_Osimps_I2_J, fact_698_member__valid__both__member__options, fact_81_max__0R, fact_3396_mod__mult__div__eq, fact_618_Suc__neq__Zero, fact_2604_mult__0, fact_620_Zero__not__Suc, fact_1383_prod_Oinject, fact_36_valid__eq1, fact_3394_mult__div__mod__eq, fact_1996_div__by__0, fact_3566_cancel__comm__monoid__add__class_Odiff__cancel, fact_345_add__cancel__left__right, fact_2577_comm__semiring__class_Odistrib, fact_18_not__min__Null__member, fact_152_nat__add__max__right, fact_2405_mult__cancel__right, fact_2427_mult__is__0, fact_83_max__nat_Oright__neutral, fact_461_comm__monoid__add__class_Oadd__0, fact_9294_ATP_Olambda__209, fact_3671_diff__Suc__1, fact_3009_mod__add__self2, fact_2515_mult_Ocommute, fact_6836_binomial__1, fact_610_nat_Odistinct_I1_J, fact_730_buildup__nothing__in__min__max, fact_684_one__is__add, fact_8195_max__Suc1, fact_34_set__vebt__set__vebt_H__valid, fact_1507_surj__pair, fact_3007_mod__add__self1, fact_3340_mod__eq__0D, fact_1875_find__cong, fact_2053_power__not__zero, fact_3859_diff__add__inverse, fact_617_zero__induct, fact_377_add_Oleft__commute, fact_3059_mod__div__trivial, fact_2452_nonzero__mult__div__cancel__left, fact_110_max_Oleft__idem, fact_315_add__left__cancel, fact_6837_binomial__0__Suc, fact_3994_minus__div__mult__eq__mod, fact_107_max_Oidem, fact_3505_vebt__insert_Osimps_I4_J, fact_3862_diff__mult__distrib, fact_2498_div__mult__self4, fact_2229_one__reorient, fact_3844_minus__nat_Odiff__0, fact_16__C163_C, fact_2245_div__add__self1, fact_2460_nonzero__mult__div__cancel__right, fact_2138_div__by__1, fact_122_Nat_Oadd__0__right, fact_2510_mult_Oleft__commute, fact_3147_mod__add__cong, fact_1730_prod__decode__aux_Ocases, fact_328_add__0, fact_3249_option_OdiscI, fact_1404_exists__least__lemma, fact_19_nsprop, fact_3882_of__bool__def, fact_3892_split__of__bool__asm, fact_3723_of__bool__eq__iff, fact_17_list__update__overwrite, fact_4000_minus__mult__div__eq__mod, fact_9363_ATP_Olambda__278, fact_389_add_Oassoc, fact_3653_diff__add__zero, fact_1__C166_C, fact_8189_old_Onat_Osimps_I5_J, fact_8185_nat_Ocase__distrib, fact_2746_power__add, fact_8200_diff__Suc, fact_3406_cancel__div__mod__rules_I2_J, fact_599_add__Suc__right, fact_6_tc, fact_30__C1_C, fact_3958_nat__minus__add__max, fact_4027_add__eq__if, fact_3570_diff__zero, fact_335_add__eq__0__iff__both__eq__0, fact_9427_ATP_Olambda__342, fact_600_max__Suc__Suc, fact_1112_VEBT__internal_Omembermima_Osimps_I3_J, fact_85_max__nat_Oleft__neutral, fact_2592_combine__common__factor, fact_9245_ATP_Olambda__160, fact_8382_update__zip, fact_3586_add__diff__cancel__left_H, fact_2401_mult__cancel__left, fact_8929_tl__upt, fact_3057_bits__mod__div__trivial, fact_2300_power__0, fact_594_nat_Oinject, fact_393_group__cancel_Oadd2, fact_3672_Suc__0__mod__eq, fact_649_nat__arith_Osuc1, fact_371_add__right__imp__eq, fact_40__C10_C, fact_3402_mod__div__decomp, fact_3071_mod__by__Suc__0, fact_3728_diff__right__commute, fact_2611_add__mult__distrib2, fact_719_both__member__options__def, fact_3039_mod__mult__self1__is__0, fact_6941_binomial__absorption, fact_86_max__nat_Oeq__neutr__iff, fact_1378_old_Oprod_Oinject, fact_3065_mod__mult__self3, fact_355_add_Oright__neutral, fact_3779_of__bool__conj, fact_4842_divmod__nat__def, fact_3247_option_Odistinct_I1_J, fact_621_not0__implies__Suc, fact_2409_mult__1, fact_9360_ATP_Olambda__275, fact_3003_bits__mod__0, fact_1517_Pair__inject, fact_8190_old_Onat_Osimps_I4_J, fact_9310_ATP_Olambda__225, fact_2950_nat__mult__eq__cancel__disj, fact_721_VEBT_Oinject_I1_J, fact_2714_add__scale__eq__noteq, fact_2615_nat__mult__max__right, fact_3313_mod__Suc, fact_21_list__update__swap, fact_9146_ATP_Olambda__61, fact_697_vebt__member_Osimps_I4_J, fact_619_Zero__neq__Suc, fact_603_n__not__Suc__n, fact_2465_div__mult__mult1, fact_2500_div__mult__self3, fact_2481_one__eq__mult__iff, fact_1427_Ex__list__of__length, fact_2430_mult__cancel2, fact_38_valid__0__not, fact_61_mi__eq__ma__no__ch, fact_3806_left__diff__distrib_H, fact_3400_div__mult__mod__eq, fact_2306_plus__1__eq__Suc, fact_2525_ab__semigroup__mult__class_Omult__ac_I1_J, fact_2614_nat__mult__max__left, fact_401_add__mono__thms__linordered__semiring_I4_J, fact_2320_power__0__left, fact_44_in__set__member, fact_7_in__children__def, fact_333_zero__eq__add__iff__both__eq__0, fact_22_False, fact_2236_zero__neq__one, fact_3747_lambda__one, fact_3589_add__diff__cancel__left, fact_9566_ATP_Olambda__481, fact_3368_VEBT__internal_OminNull_Osimps_I4_J, fact_8956_sort__upt, fact_8900_drop__upt, fact_580_buildup__nothing__in__leaf, fact_15_nth__list__update__neq, fact_341_add__cancel__right__left, fact_2133_bits__div__by__0, fact_3145_mod__add__eq, fact_8196_max__Suc2, fact_614_old_Onat_Oexhaust, fact_3945_diff__add__0, fact_3861_Nat_Odiff__cancel, fact_650_add__Suc, fact_3084_Suc__mod__mult__self4, fact_2951_left__add__mult__distrib, fact_6882_Suc__times__binomial, fact_2305_Suc__eq__plus1__left, fact_579_vebt__member_Osimps_I3_J, fact_3600_diff__Suc__Suc, fact_5_insprop, fact_1905_zip__update, fact_9243_ATP_Olambda__158, fact_165_set__update__subsetI, fact_2613_nat__mult__1, fact_8202_Nitpick_Ocase__nat__unfold, fact_82_max__0L, fact_9242_ATP_Olambda__157, fact_3953_diff__Suc__eq__diff__pred, fact_2938_nat__mult__div__cancel__disj, fact_2020_nat__power__eq__Suc__0__iff, fact_1432_size__neq__size__imp__neq, fact_2504_div__mult__self1, fact_405_ab__semigroup__add__class_Oadd__ac_I1_J, fact_3870_set__vebt__def, fact_2015_power__Suc0__right, fact_492_max__add__distrib__right, fact_592_deg__SUcn__Node, fact_2429_mult__cancel1, fact_3164_mod__Suc__Suc__eq, fact_2545_mult__left__cancel, fact_47_deg__deg__n, fact_722_option_Oinject, fact_4031_mult__eq__if, fact_2161_max__0__1_I1_J, fact_720_VEBT__internal_Onaive__member_Osimps_I2_J, fact_3082_Suc__mod__mult__self2, fact_6885_choose__mult__lemma, fact_2563_crossproduct__eq, fact_8911_map__Suc__upt, fact_3451_div__mod__decomp, fact_33__C12_C, fact_374_add__left__imp__eq, fact_9574_ATP_Olambda__489, fact_3603_diff__0__eq__0, fact_4037_power__eq__if, fact_2549_mult__right__cancel, fact_2469_div__mult__mult1__if, fact_2432_nat__1__eq__mult__iff, fact_2006_power__0__Suc, fact_1641_list__decode_Ocases, fact_3013_not__None__eq, fact_9__C165_C, fact_3353_nat__mod__eq__iff, fact_3015_not__Some__eq, fact_3041_mod__by__1, fact_2997_mod__0, fact_9590_ATP_Olambda__505, fact_3251_option_Oexhaust, fact_2485_mult__Suc__right, fact_1990_div__0, fact_181_max_Oassoc, fact_2587_distrib__right, fact_9589_ATP_Olambda__504, fact_3612_of__bool__eq__0__iff, fact_3063_mod__mult__self2, fact_366_zero__reorient, fact_591_even__odd__cases, fact_3037_mod__mult__self2__is__0, fact_381_add_Ocommute, fact_79_Collect__cong, fact_3408_div__mult1__eq, fact_3001_mod__self, fact_582_VEBT__internal_OminNull_Osimps_I5_J, fact_9236_ATP_Olambda__151, fact_456_add_Ocomm__neutral, fact_3552_set__vebt_H__def, fact_3843_diffs0__imp__equal, fact_6840_binomial__n__0, fact_2612_nat__mult__1__right, fact_3602_diff__self__eq__0, fact_2567_crossproduct__noteq, fact_2127_div__by__Suc__0, fact_2482_mult__eq__1__iff, fact_2386_mult__zero__left, fact_2019_power__Suc__0, fact_2735_power__Suc2, fact_3275_div__add1__eq, fact_6881_Suc__times__binomial__eq, fact_2535_divisors__zero, fact_29_mimaxrel, fact_8908_map__add__upt, fact_3583_add__diff__cancel__right, fact_3272_mod__eq__self__iff__div__eq__0, fact_495_max__add__distrib__left, fact_24_valid__member__both__member__options, fact_0_True, fact_2431_nat__mult__eq__1__iff, fact_8__C161_C, fact_3605_diff__diff__left, fact_2603_Suc__mult__cancel1, fact_156_subset__code_I1_J, fact_1424_neq__if__length__neq, fact_3398_mod__div__mult__eq, fact_3632_of__bool__or__iff, fact_121_add__is__0, fact_3083_Suc__mod__mult__self3, fact_8188_old_Onat_Osimps_I5_J, fact_604_Suc__inject, fact_84_max__nat_Oneutr__eq__iff, fact_3061_mod__mult__self1, fact_3043_bits__mod__by__1, fact_3081_Suc__mod__mult__self1, fact_349_add__cancel__left__left, fact_2307_Suc__eq__plus1, fact_3810_right__diff__distrib_H, fact_6913_binomial__Suc__Suc__eq__times, fact_12_list__update__id, fact_1642_verit__sum__simplify, fact_2304_One__nat__def, fact_25_both__member__options__equiv__member, fact_2754_mult__Suc, fact_9250_ATP_Olambda__165, fact_3887_split__of__bool, fact_611_old_Onat_Odistinct_I2_J, fact_2467_div__mult__mult2, fact_3725_diff__commute, fact_2502_div__mult__self2, fact_3814_diff__diff__eq, fact_184_max_Ocommute, fact_8201_Nitpick_Ocase__nat__unfold, fact_613_nat_OdiscI, fact_2165_max__0__1_I2_J, fact_6829_binomial__Suc__n, fact_312_add__right__cancel, fact_2152_div__self, fact_593_old_Onat_Oinject, fact_39_valid__tree__deg__neq__0, fact_1816_triangle__0, fact_3458_VEBT__internal_Omembermima_Osimps_I2_J, fact_1747_triangle__Suc, fact_3404_cancel__div__mod__rules_I1_J, fact_2582_distrib__left, fact_3580_add__diff__cancel__right_H, fact_26__C5_C
% 26.53/8.25 % No. of inferences in proof: 750
% 26.53/8.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7674 ms resp. 5809 ms w/o parsing
% 27.61/8.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.00/8.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------