%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP233^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n003.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 : Wed Sep 30 08:07:20 AM UTC 2026
% Result : Theorem 19.69s 6.34s
% Output : Refutation 20.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 37
% Syntax : Number of formulae : 76 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 62 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 701 ( 26 ~; 0 |; 4 &; 639 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 144 ( 143 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 161 ( 6 ^; 142 !; 13 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1542805901266377927at_nat_type,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(produc4471711990508489141at_nat_type,type,
produc4471711990508489141at_nat: $tType ).
thf(produc6392793444374437607at_nat_type,type,
produc6392793444374437607at_nat: $tType ).
thf(list_P8469869581646625389at_nat_type,type,
list_P8469869581646625389at_nat: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(set_Pr1916528119006554503T_VEBT_type,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(produc9211091688327510695T_VEBT_type,type,
produc9211091688327510695T_VEBT: $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(set_Pr6192946355708809607T_VEBT_type,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(list_P6254988961118846195et_nat_type,type,
list_P6254988961118846195et_nat: $tType ).
thf(set_Pr5488025237498180813et_nat_type,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(list_P6356568628958627295d_enat_type,type,
list_P6356568628958627295d_enat: $tType ).
thf(set_Pr2457182780427864761d_enat_type,type,
set_Pr2457182780427864761d_enat: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(list_P2623026923184700063T_real_type,type,
list_P2623026923184700063T_real: $tType ).
thf(list_P877281246627933069T_VEBT_type,type,
list_P877281246627933069T_VEBT: $tType ).
thf(produc1828647624359046049st_nat_type,type,
produc1828647624359046049st_nat: $tType ).
thf(produc1186641810826059865st_int_type,type,
produc1186641810826059865st_int: $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(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(produc7819656566062154093et_nat_type,type,
produc7819656566062154093et_nat: $tType ).
thf(produc7272778201969148633d_enat_type,type,
produc7272778201969148633d_enat: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(set_Pr3175402225741728619VEBT_o_type,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(set_Pr7543698050874017315T_VEBT_type,type,
set_Pr7543698050874017315T_VEBT: $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(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(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(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(list_P3595434254542482545real_o_type,type,
list_P3595434254542482545real_o: $tType ).
thf(list_P5232166724548748803o_real_type,type,
list_P5232166724548748803o_real: $tType ).
thf(list_list_VEBT_VEBT_type,type,
list_list_VEBT_VEBT: $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(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(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,
set_list_set_nat: $tType ).
thf(set_set_set_nat_type,type,
set_set_set_nat: $tType ).
thf(set_li5464603477888414924d_enat_type,type,
set_li5464603477888414924d_enat: $tType ).
thf(produc2422161461964618553l_real_type,type,
produc2422161461964618553l_real: $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(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(set_list_complex_type,type,
set_list_complex: $tType ).
thf(set_Product_prod_o_o_type,type,
set_Product_prod_o_o: $tType ).
thf(set_set_complex_type,type,
set_set_complex: $tType ).
thf(option_VEBT_VEBT_type,type,
option_VEBT_VEBT: $tType ).
thf(set_filter_nat_type,type,
set_filter_nat: $tType ).
thf(option_set_nat_type,type,
option_set_nat: $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(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(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(list_Extended_enat_type,type,
list_Extended_enat: $tType ).
thf(set_Extended_enat_type,type,
set_Extended_enat: $tType ).
thf(list_complex_type,type,
list_complex: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $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(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(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(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(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(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(if_VEBT_VEBT_decl,type,
if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(set_VEBT_VEBT2_decl,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(list_u3071683517702156500d_enat_decl,type,
list_u3071683517702156500d_enat: list_Extended_enat > nat > extended_enat > list_Extended_enat ).
thf(list_u2241885204319820103d_enat_decl,type,
list_u2241885204319820103d_enat: list_P6356568628958627295d_enat > nat > produc7272778201969148633d_enat > list_P6356568628958627295d_enat ).
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 > vEBT_VEBT > $o ).
thf(nth_VEBT_VEBT_decl,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(zip_VE7205001627739651817d_enat_decl,type,
zip_VE7205001627739651817d_enat: list_VEBT_VEBT > list_Extended_enat > list_P6356568628958627295d_enat ).
thf(zip_VE537291747668921783T_VEBT_decl,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(ord_le4337996190870823476T_VEBT_decl,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(produc581526299967858633d_enat_decl,type,
produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
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(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(vEBT_VEBT_high_decl,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(vEBT_V5917875025757280293ildren_decl,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
thf(vEBT_VEBT_low_decl,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
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 > nat > nat > nat ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(member_VEBT_VEBT2_decl,type,
member_VEBT_VEBT2: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(i_decl,type,
i: nat ).
thf(m_decl,type,
m: 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(9,axiom,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28__C0_C) ).
thf(69,plain,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ treeList ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( vEBT_VEBT_high @ xa @ na ) )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_insprop) ).
thf(120,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( vEBT_VEBT_high @ xa @ na ) )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ B ) )
= ( member_VEBT_VEBT @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_in__set__member) ).
thf(57,plain,
! [A: vEBT_VEBT,B: list_VEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ B ) )
= ( member_VEBT_VEBT @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_not__min__Null__member) ).
thf(106,plain,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(37,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ B @ D )
= ( list_u1324408373059187874T_VEBT @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__update__overwrite) ).
thf(137,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ B @ D )
= ( list_u1324408373059187874T_VEBT @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_both__member__options__equiv__member) ).
thf(65,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
= ( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ C @ ( set_VEBT_VEBT2 @ A ) )
=> ( member_VEBT_VEBT2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_subset__code_I1_J) ).
thf(41,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
= ( ! [C: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ C @ ( set_VEBT_VEBT2 @ A ) )
=> ( member_VEBT_VEBT2 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(39,plain,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C164_C) ).
thf(114,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
( vEBT_V5917875025757280293ildren
= ( ^ [A: nat,B: list_VEBT_VEBT,C: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ B @ ( vEBT_VEBT_high @ C @ A ) ) @ ( vEBT_VEBT_low @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__children__def) ).
thf(94,plain,
( vEBT_V5917875025757280293ildren
= ( ^ [A: nat,B: list_VEBT_VEBT,C: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ B @ ( vEBT_VEBT_high @ C @ A ) ) @ ( vEBT_VEBT_low @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,axiom,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C166_C) ).
thf(131,plain,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(35,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_Extended_enat,E: extended_enat] :
( ( zip_VE7205001627739651817d_enat @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ ( list_u3071683517702156500d_enat @ D @ B @ E ) )
= ( list_u2241885204319820103d_enat @ ( zip_VE7205001627739651817d_enat @ A @ D ) @ B @ ( produc581526299967858633d_enat @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1910_zip__update) ).
thf(132,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_Extended_enat,E: extended_enat] :
( ( zip_VE7205001627739651817d_enat @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ ( list_u3071683517702156500d_enat @ D @ B @ E ) )
= ( list_u2241885204319820103d_enat @ ( zip_VE7205001627739651817d_enat @ A @ D ) @ B @ ( produc581526299967858633d_enat @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_tc) ).
thf(116,plain,
vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_valid__member__both__member__options) ).
thf(74,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: list_VEBT_VEBT,B: nat] :
( ( list_u1324408373059187874T_VEBT @ A @ B @ ( nth_VEBT_VEBT @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list__update__id) ).
thf(102,plain,
! [A: list_VEBT_VEBT,B: nat] :
( ( list_u1324408373059187874T_VEBT @ A @ B @ ( nth_VEBT_VEBT @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [A: produc7272778201969148633d_enat > $o,B: produc7272778201969148633d_enat] :
( ! [C: vEBT_VEBT,D: extended_enat] : ( A @ ( produc581526299967858633d_enat @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1516_prod__cases) ).
thf(60,plain,
! [A: produc7272778201969148633d_enat > $o,B: produc7272778201969148633d_enat] :
( ! [C: vEBT_VEBT,D: extended_enat] : ( A @ ( produc581526299967858633d_enat @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ summary ) @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__C12_C) ).
thf(117,plain,
vEBT_invar_vebt @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ summary ) @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B @ E )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list__update__swap) ).
thf(124,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT,E: vEBT_VEBT] :
( ( A != B )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B @ E )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(12,axiom,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1387_prod_Oinject) ).
thf(77,plain,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
( ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) )
=> ( summary
= ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nsprop) ).
thf(96,plain,
( ~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) )
=> ( summary
= ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ A @ B ) @ ( vEBT_VEBT_low @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bit__split__inv) ).
thf(128,plain,
! [A: nat,B: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ A @ B ) @ ( vEBT_VEBT_low @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
vEBT_invar_vebt @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__C165_C) ).
thf(105,plain,
vEBT_invar_vebt @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1521_Pair__inject) ).
thf(44,plain,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,axiom,
~ ( vEBT_V8194947554948674370ptions @ summary @ i ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__C163_C) ).
thf(118,plain,
~ ( vEBT_V8194947554948674370ptions @ summary @ i ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: produc7272778201969148633d_enat] :
? [B: vEBT_VEBT,C: extended_enat] :
( A
= ( produc581526299967858633d_enat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1511_surj__pair) ).
thf(71,plain,
! [A: produc7272778201969148633d_enat] :
? [B: vEBT_VEBT,C: extended_enat] :
( A
= ( produc581526299967858633d_enat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_min__Null__member) ).
thf(54,plain,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
vEBT_invar_vebt @ summary @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__C1_C) ).
thf(86,plain,
vEBT_invar_vebt @ summary @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B )
= ( nth_VEBT_VEBT @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nth__list__update__neq) ).
thf(140,plain,
! [A: nat,B: nat,C: list_VEBT_VEBT,D: vEBT_VEBT] :
( ( A != B )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ C @ A @ D ) @ B )
= ( nth_VEBT_VEBT @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
=> ( ( member_VEBT_VEBT2 @ C @ B )
=> ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ A @ D @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_set__update__subsetI) ).
thf(91,plain,
! [A: list_VEBT_VEBT,B: set_VEBT_VEBT,C: vEBT_VEBT,D: nat] :
( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ A ) @ B )
=> ( ( member_VEBT_VEBT2 @ C @ B )
=> ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ A @ D @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__C162_C) ).
thf(108,plain,
~ ? [A: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__C11_C) ).
thf(135,plain,
! [A: vEBT_VEBT] :
( ( member_VEBT_VEBT2 @ A @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ) )
=> ( vEBT_invar_vebt @ A @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ ( list_u1324408373059187874T_VEBT @ D @ B @ E ) )
= ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ A @ D ) @ B @ ( produc537772716801021591T_VEBT @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1905_zip__update) ).
thf(80,plain,
! [A: list_VEBT_VEBT,B: nat,C: vEBT_VEBT,D: list_VEBT_VEBT,E: vEBT_VEBT] :
( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ B @ C ) @ ( list_u1324408373059187874T_VEBT @ D @ B @ E ) )
= ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ A @ D ) @ B @ ( produc537772716801021591T_VEBT @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: nat,D: produc8243902056947475879T_VEBT] :
( ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ A @ B ) @ C @ D )
= ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ C @ ( produc6118266651365575811T_VEBT @ D ) ) @ ( list_u1324408373059187874T_VEBT @ B @ C @ ( produc351232539757196229T_VEBT @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8382_update__zip) ).
thf(99,plain,
! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,C: nat,D: produc8243902056947475879T_VEBT] :
( ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ A @ B ) @ C @ D )
= ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ A @ C @ ( produc6118266651365575811T_VEBT @ D ) ) @ ( list_u1324408373059187874T_VEBT @ B @ C @ ( produc351232539757196229T_VEBT @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [A: produc7272778201969148633d_enat] :
~ ! [B: vEBT_VEBT,C: extended_enat] :
( A
!= ( produc581526299967858633d_enat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1506_old_Oprod_Oexhaust) ).
thf(87,plain,
! [A: produc7272778201969148633d_enat] :
~ ! [B: vEBT_VEBT,C: extended_enat] :
( A
!= ( produc581526299967858633d_enat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
~ ? [A: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C161_C) ).
thf(111,plain,
~ ? [A: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31,axiom,
( i
= ( vEBT_VEBT_high @ xa @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
thf(122,plain,
( i
= ( vEBT_VEBT_high @ xa @ na ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(14,axiom,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1382_old_Oprod_Oinject) ).
thf(83,plain,
! [A: vEBT_VEBT,B: extended_enat,C: vEBT_VEBT,D: extended_enat] :
( ( ( produc581526299967858633d_enat @ A @ B )
= ( produc581526299967858633d_enat @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(144,plain,
$false,
inference(e,[status(thm)],[69,120,57,106,137,65,41,39,114,94,131,132,116,74,102,60,117,124,77,96,128,105,44,118,71,54,86,140,91,108,135,80,99,87,111,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP233^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.11 % 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
% 0.21/0.32 % Computer : n003.cluster.edu
% 0.21/0.32 % Model : x86_64 x86_64
% 0.21/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.32 % Memory : 8046.5625MB
% 0.21/0.32 % OS : Linux 6.8.0-71-generic
% 0.21/0.32 % CPULimit : 300
% 0.21/0.32 % WCLimit : 300
% 0.21/0.32 % DateTime : Tue Sep 29 20:26:44 UTC 2026
% 0.21/0.32 % CPUTime :
% 0.21/0.32 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
% 1.11/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 9.51/3.24 % [INFO] Parsing done (2206ms).
% 9.51/3.27 % [INFO] Running in sequential loop mode.
% 10.42/3.71 % [INFO] eprover registered as external prover.
% 10.42/3.72 % [INFO] Scanning for conjecture ...
% 13.37/4.55 % [INFO] Found a conjecture (or negated_conjecture) and 9117 axioms. Running axiom selection ...
% 14.44/4.87 % [INFO] Axiom selection finished. Selected 36 axioms (removed 9081 axioms).
% 14.78/4.96 % [INFO] Problem is higher-order (TPTP THF).
% 14.78/4.98 % [INFO] Type checking passed.
% 14.78/4.98 % [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 ...
% 19.69/6.33 % External prover 'e' found a proof!
% 19.69/6.33 % [INFO] Killing All external provers ...
% 19.69/6.33 % Time passed: 5810ms (effective reasoning time: 3056ms)
% 19.69/6.33 % 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)>
% 19.69/6.34 % Axioms used in derivation (36): fact_28__C0_C, fact_23_min__Null__member, fact_18_not__min__Null__member, fact_1511_surj__pair, fact_16__C163_C, fact_19_nsprop, fact_1382_old_Oprod_Oinject, fact_21_list__update__swap, fact_15_nth__list__update__neq, fact_33__C12_C, fact_9__C165_C, fact_1387_prod_Oinject, fact_20__C11_C, fact_3__C164_C, fact_2_bit__split__inv, fact_1516_prod__cases, fact_4__C162_C, fact_1521_Pair__inject, fact_1__C166_C, fact_17_list__update__overwrite, fact_6_tc, fact_30__C1_C, fact_8382_update__zip, fact_44_in__set__member, fact_7_in__children__def, fact_5_insprop, fact_1910_zip__update, fact_1905_zip__update, fact_165_set__update__subsetI, fact_156_subset__code_I1_J, fact_24_valid__member__both__member__options, fact_0_True, fact_8__C161_C, fact_1506_old_Oprod_Oexhaust, fact_25_both__member__options__equiv__member, fact_12_list__update__id
% 19.69/6.34 % No. of inferences in proof: 76
% 19.69/6.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5810 ms resp. 3056 ms w/o parsing
% 20.18/6.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.18/6.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------