%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP233^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:25:04 AM UTC 2026
% Result : Theorem 68.19s 13.81s
% Output : CNFRefutation 68.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 432 ( 111 unt; 0 typ; 0 def)
% Number of atoms : 3834 (1396 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 2817 ( 563 ~; 989 |; 0 &;1256 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 144 ( 143 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1125 (1122 usr; 69 con; 0-5 aty)
% Number of variables : 399 ( 21 ^; 364 !; 14 ?; 399 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_char,type,
char: $tType ).
thf(tp_complex,type,
complex: $tType ).
thf(tp_extended_enat,type,
extended_enat: $tType ).
thf(tp_filter1242075044329608583at_nat,type,
filter1242075044329608583at_nat: $tType ).
thf(tp_filter_nat,type,
filter_nat: $tType ).
thf(tp_filter_real,type,
filter_real: $tType ).
thf(tp_int,type,
int: $tType ).
thf(tp_list_Extended_enat,type,
list_Extended_enat: $tType ).
thf(tp_list_P2623026923184700063T_real,type,
list_P2623026923184700063T_real: $tType ).
thf(tp_list_P3126845725202233233VEBT_o,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(tp_list_P3521021558325789923at_int,type,
list_P3521021558325789923at_int: $tType ).
thf(tp_list_P3595434254542482545real_o,type,
list_P3595434254542482545real_o: $tType ).
thf(tp_list_P3795440434834930179_o_int,type,
list_P3795440434834930179_o_int: $tType ).
thf(tp_list_P4002435161011370285od_o_o,type,
list_P4002435161011370285od_o_o: $tType ).
thf(tp_list_P4344331454722006975al_int,type,
list_P4344331454722006975al_int: $tType ).
thf(tp_list_P4547456442757143711BT_int,type,
list_P4547456442757143711BT_int: $tType ).
thf(tp_list_P5087981734274514673_int_o,type,
list_P5087981734274514673_int_o: $tType ).
thf(tp_list_P5232166724548748803o_real,type,
list_P5232166724548748803o_real: $tType ).
thf(tp_list_P5647936690300460905T_VEBT,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(tp_list_P5707943133018811711nt_int,type,
list_P5707943133018811711nt_int: $tType ).
thf(tp_list_P6011104703257516679at_nat,type,
list_P6011104703257516679at_nat: $tType ).
thf(tp_list_P6254988961118846195et_nat,type,
list_P6254988961118846195et_nat: $tType ).
thf(tp_list_P6285523579766656935_o_nat,type,
list_P6285523579766656935_o_nat: $tType ).
thf(tp_list_P6356568628958627295d_enat,type,
list_P6356568628958627295d_enat: $tType ).
thf(tp_list_P6834414599653733731al_nat,type,
list_P6834414599653733731al_nat: $tType ).
thf(tp_list_P6863124054624500543t_real,type,
list_P6863124054624500543t_real: $tType ).
thf(tp_list_P7037539587688870467BT_nat,type,
list_P7037539587688870467BT_nat: $tType ).
thf(tp_list_P7413028617227757229T_VEBT,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(tp_list_P7495141550334521929T_VEBT,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(tp_list_P7524865323317820941T_VEBT,type,
list_P7524865323317820941T_VEBT: $tType ).
thf(tp_list_P8198026277950538467nt_nat,type,
list_P8198026277950538467nt_nat: $tType ).
thf(tp_list_P8469869581646625389at_nat,type,
list_P8469869581646625389at_nat: $tType ).
thf(tp_list_P8689742595348180415l_real,type,
list_P8689742595348180415l_real: $tType ).
thf(tp_list_P877281246627933069T_VEBT,type,
list_P877281246627933069T_VEBT: $tType ).
thf(tp_list_VEBT_VEBT,type,
list_VEBT_VEBT: $tType ).
thf(tp_list_complex,type,
list_complex: $tType ).
thf(tp_list_int,type,
list_int: $tType ).
thf(tp_list_list_VEBT_VEBT,type,
list_list_VEBT_VEBT: $tType ).
thf(tp_list_list_int,type,
list_list_int: $tType ).
thf(tp_list_list_nat,type,
list_list_nat: $tType ).
thf(tp_list_nat,type,
list_nat: $tType ).
thf(tp_list_num,type,
list_num: $tType ).
thf(tp_list_o,type,
list_o: $tType ).
thf(tp_list_real,type,
list_real: $tType ).
thf(tp_list_set_nat,type,
list_set_nat: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_num,type,
num: $tType ).
thf(tp_option4927543243414619207at_nat,type,
option4927543243414619207at_nat: $tType ).
thf(tp_option_VEBT_VEBT,type,
option_VEBT_VEBT: $tType ).
thf(tp_option_int,type,
option_int: $tType ).
thf(tp_option_nat,type,
option_nat: $tType ).
thf(tp_option_num,type,
option_num: $tType ).
thf(tp_option_o,type,
option_o: $tType ).
thf(tp_option_real,type,
option_real: $tType ).
thf(tp_option_set_nat,type,
option_set_nat: $tType ).
thf(tp_produc1186641810826059865st_int,type,
produc1186641810826059865st_int: $tType ).
thf(tp_produc1531783533982839933T_VEBT,type,
produc1531783533982839933T_VEBT: $tType ).
thf(tp_produc1828647624359046049st_nat,type,
produc1828647624359046049st_nat: $tType ).
thf(tp_produc2422161461964618553l_real,type,
produc2422161461964618553l_real: $tType ).
thf(tp_produc2504756804600209347T_VEBT,type,
produc2504756804600209347T_VEBT: $tType ).
thf(tp_produc334124729049499915VEBT_o,type,
produc334124729049499915VEBT_o: $tType ).
thf(tp_produc3741383161447143261al_nat,type,
produc3741383161447143261al_nat: $tType ).
thf(tp_produc3757001726724277373T_VEBT,type,
produc3757001726724277373T_VEBT: $tType ).
thf(tp_produc4471711990508489141at_nat,type,
produc4471711990508489141at_nat: $tType ).
thf(tp_produc4894624898956917775BT_int,type,
produc4894624898956917775BT_int: $tType ).
thf(tp_produc5170161368751668367T_real,type,
produc5170161368751668367T_real: $tType ).
thf(tp_produc6392793444374437607at_nat,type,
produc6392793444374437607at_nat: $tType ).
thf(tp_produc679980390762269497t_real,type,
produc679980390762269497t_real: $tType ).
thf(tp_produc7248412053542808358at_nat,type,
produc7248412053542808358at_nat: $tType ).
thf(tp_produc7272778201969148633d_enat,type,
produc7272778201969148633d_enat: $tType ).
thf(tp_produc7819656566062154093et_nat,type,
produc7819656566062154093et_nat: $tType ).
thf(tp_produc8025551001238799321T_VEBT,type,
produc8025551001238799321T_VEBT: $tType ).
thf(tp_produc8243902056947475879T_VEBT,type,
produc8243902056947475879T_VEBT: $tType ).
thf(tp_produc859450856879609959at_nat,type,
produc859450856879609959at_nat: $tType ).
thf(tp_produc8786904178792722361al_int,type,
produc8786904178792722361al_int: $tType ).
thf(tp_produc9072475918466114483BT_nat,type,
produc9072475918466114483BT_nat: $tType ).
thf(tp_produc9211091688327510695T_VEBT,type,
produc9211091688327510695T_VEBT: $tType ).
thf(tp_product_prod_int_int,type,
product_prod_int_int: $tType ).
thf(tp_product_prod_int_nat,type,
product_prod_int_nat: $tType ).
thf(tp_product_prod_int_o,type,
product_prod_int_o: $tType ).
thf(tp_product_prod_nat_int,type,
product_prod_nat_int: $tType ).
thf(tp_product_prod_nat_nat,type,
product_prod_nat_nat: $tType ).
thf(tp_product_prod_o_int,type,
product_prod_o_int: $tType ).
thf(tp_product_prod_o_nat,type,
product_prod_o_nat: $tType ).
thf(tp_product_prod_o_o,type,
product_prod_o_o: $tType ).
thf(tp_product_prod_o_real,type,
product_prod_o_real: $tType ).
thf(tp_product_prod_real_o,type,
product_prod_real_o: $tType ).
thf(tp_product_unit,type,
product_unit: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_Extended_enat,type,
set_Extended_enat: $tType ).
thf(tp_set_Pr1019928272762051225al_int,type,
set_Pr1019928272762051225al_int: $tType ).
thf(tp_set_Pr1261947904930325089at_nat,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(tp_set_Pr1542805901266377927at_nat,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(tp_set_Pr1916528119006554503T_VEBT,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(tp_set_Pr2101469702781467981_o_nat,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(tp_set_Pr2457182780427864761d_enat,type,
set_Pr2457182780427864761d_enat: $tType ).
thf(tp_set_Pr3175402225741728619VEBT_o,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(tp_set_Pr3448869479623346877nt_nat,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(tp_set_Pr3451248702717554689st_nat,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(tp_set_Pr3510011417693777981al_nat,type,
set_Pr3510011417693777981al_nat: $tType ).
thf(tp_set_Pr3538720872664544793t_real,type,
set_Pr3538720872664544793t_real: $tType ).
thf(tp_set_Pr4936984352647145239real_o,type,
set_Pr4936984352647145239real_o: $tType ).
thf(tp_set_Pr5066593544530342725BT_int,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(tp_set_Pr5488025237498180813et_nat,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(tp_set_Pr6019664923565264691T_VEBT,type,
set_Pr6019664923565264691T_VEBT: $tType ).
thf(tp_set_Pr6167073792073659919T_VEBT,type,
set_Pr6167073792073659919T_VEBT: $tType ).
thf(tp_set_Pr6192946355708809607T_VEBT,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(tp_set_Pr6218003697084177305l_real,type,
set_Pr6218003697084177305l_real: $tType ).
thf(tp_set_Pr6573716822653411497o_real,type,
set_Pr6573716822653411497o_real: $tType ).
thf(tp_set_Pr7543698050874017315T_VEBT,type,
set_Pr7543698050874017315T_VEBT: $tType ).
thf(tp_set_Pr7556676689462069481BT_nat,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(tp_set_Pr765067013931698361st_int,type,
set_Pr765067013931698361st_int: $tType ).
thf(tp_set_Pr7765410600122031685T_real,type,
set_Pr7765410600122031685T_real: $tType ).
thf(tp_set_Pr7995236796853374141at_int,type,
set_Pr7995236796853374141at_int: $tType ).
thf(tp_set_Pr8044002425091019955T_VEBT,type,
set_Pr8044002425091019955T_VEBT: $tType ).
thf(tp_set_Pr8693737435421807431at_nat,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(tp_set_Pr8834758594704517033_o_int,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(tp_set_Pr903927857289325719_int_o,type,
set_Pr903927857289325719_int_o: $tType ).
thf(tp_set_Pr958786334691620121nt_int,type,
set_Pr958786334691620121nt_int: $tType ).
thf(tp_set_Product_prod_o_o,type,
set_Product_prod_o_o: $tType ).
thf(tp_set_VEBT_VEBT,type,
set_VEBT_VEBT: $tType ).
thf(tp_set_char,type,
set_char: $tType ).
thf(tp_set_complex,type,
set_complex: $tType ).
thf(tp_set_filter_nat,type,
set_filter_nat: $tType ).
thf(tp_set_int,type,
set_int: $tType ).
thf(tp_set_li5464603477888414924d_enat,type,
set_li5464603477888414924d_enat: $tType ).
thf(tp_set_list_VEBT_VEBT,type,
set_list_VEBT_VEBT: $tType ).
thf(tp_set_list_complex,type,
set_list_complex: $tType ).
thf(tp_set_list_int,type,
set_list_int: $tType ).
thf(tp_set_list_list_nat,type,
set_list_list_nat: $tType ).
thf(tp_set_list_nat,type,
set_list_nat: $tType ).
thf(tp_set_list_set_nat,type,
set_list_set_nat: $tType ).
thf(tp_set_nat,type,
set_nat: $tType ).
thf(tp_set_num,type,
set_num: $tType ).
thf(tp_set_o,type,
set_o: $tType ).
thf(tp_set_real,type,
set_real: $tType ).
thf(tp_set_se7270636423289371942d_enat,type,
set_se7270636423289371942d_enat: $tType ).
thf(tp_set_set_complex,type,
set_set_complex: $tType ).
thf(tp_set_set_int,type,
set_set_int: $tType ).
thf(tp_set_set_list_nat,type,
set_set_list_nat: $tType ).
thf(tp_set_set_nat,type,
set_set_nat: $tType ).
thf(tp_set_set_set_nat,type,
set_set_set_nat: $tType ).
thf(tp_vEBT_VEBT,type,
vEBT_VEBT: $tType ).
thf(tp_abs_Integ,type,
abs_Integ: product_prod_nat_nat > int ).
thf(tp_abs_abs_complex,type,
abs_abs_complex: complex > complex ).
thf(tp_abs_abs_int,type,
abs_abs_int: int > int ).
thf(tp_abs_abs_real,type,
abs_abs_real: real > real ).
thf(tp_accp_P1096762738010456898nt_int,type,
accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
thf(tp_accp_P2887432264394892906BT_nat,type,
accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
thf(tp_accp_P4275260045618599050at_nat,type,
accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(tp_accp_P6183159247885693666d_enat,type,
accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
thf(tp_accp_list_nat,type,
accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
thf(tp_accp_nat,type,
accp_nat: ( nat > nat > $o ) > nat > $o ).
thf(tp_algebr934650988132801477me_nat,type,
algebr934650988132801477me_nat: nat > nat > $o ).
thf(tp_append_int,type,
append_int: list_int > list_int > list_int ).
thf(tp_append_nat,type,
append_nat: list_nat > list_nat > list_nat ).
thf(tp_archim2898591450579166408c_real,type,
archim2898591450579166408c_real: real > real ).
thf(tp_archim6058952711729229775r_real,type,
archim6058952711729229775r_real: real > int ).
thf(tp_archim7802044766580827645g_real,type,
archim7802044766580827645g_real: real > int ).
thf(tp_archim8280529875227126926d_real,type,
archim8280529875227126926d_real: real > int ).
thf(tp_arcosh_real,type,
arcosh_real: real > real ).
thf(tp_arctan,type,
arctan: real > real ).
thf(tp_arg,type,
arg: complex > real ).
thf(tp_arsinh_real,type,
arsinh_real: real > real ).
thf(tp_artanh_real,type,
artanh_real: real > real ).
thf(tp_at_bot_real,type,
at_bot_real: filter_real ).
thf(tp_at_top_nat,type,
at_top_nat: filter_nat ).
thf(tp_at_top_real,type,
at_top_real: filter_real ).
thf(tp_bNF_Ca8459412986667044542atLess,type,
bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
thf(tp_bNF_Ca8665028551170535155natLeq,type,
bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
thf(tp_bNF_We3818239936649020644el_nat,type,
bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
thf(tp_bNF_re2241393799969408733at_nat,type,
bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(tp_bNF_re3099431351363272937at_nat,type,
bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(tp_bNF_re3666534408544137501at_o_o,type,
bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(tp_bNF_re4202695980764964119_nat_o,type,
bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(tp_bNF_re4555766996558763186at_nat,type,
bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
thf(tp_bNF_re6644619430987730960nt_o_o,type,
bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
thf(tp_bNF_re6830278522597306478at_int,type,
bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
thf(tp_bNF_re717283939379294677_int_o,type,
bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
thf(tp_bNF_re7400052026677387805at_int,type,
bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
thf(tp_bNF_re7408651293131936558nt_int,type,
bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
thf(tp_bNF_re8246922863344978751at_nat,type,
bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
thf(tp_basic_1872990034501187214nt_int,type,
basic_1872990034501187214nt_int: ( int > nat ) > ( int > nat ) > product_prod_int_int > nat ).
thf(tp_basic_876126793109182934at_nat,type,
basic_876126793109182934at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > nat ).
thf(tp_bezw,type,
bezw: nat > nat > product_prod_int_int ).
thf(tp_bezw_rel,type,
bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_bi_tot896582865486249351at_int,type,
bi_tot896582865486249351at_int: ( product_prod_nat_nat > int > $o ) > $o ).
thf(tp_bij_be1856998921033663316omplex,type,
bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
thf(tp_bij_betw_nat_complex,type,
bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
thf(tp_bij_betw_nat_nat,type,
bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
thf(tp_binomial,type,
binomial: nat > nat > nat ).
thf(tp_bit0,type,
bit0: num > num ).
thf(tp_bit1,type,
bit1: num > num ).
thf(tp_bit_and_int_rel,type,
bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(tp_bit_concat_bit,type,
bit_concat_bit: nat > int > int > int ).
thf(tp_bit_ri631733984087533419it_int,type,
bit_ri631733984087533419it_int: nat > int > int ).
thf(tp_bit_se1146084159140164899it_int,type,
bit_se1146084159140164899it_int: int > nat > $o ).
thf(tp_bit_se1148574629649215175it_nat,type,
bit_se1148574629649215175it_nat: nat > nat > $o ).
thf(tp_bit_se1409905431419307370or_int,type,
bit_se1409905431419307370or_int: int > int > int ).
thf(tp_bit_se1412395901928357646or_nat,type,
bit_se1412395901928357646or_nat: nat > nat > nat ).
thf(tp_bit_se2000444600071755411sk_int,type,
bit_se2000444600071755411sk_int: nat > int ).
thf(tp_bit_se2002935070580805687sk_nat,type,
bit_se2002935070580805687sk_nat: nat > nat ).
thf(tp_bit_se2159334234014336723it_int,type,
bit_se2159334234014336723it_int: nat > int > int ).
thf(tp_bit_se2161824704523386999it_nat,type,
bit_se2161824704523386999it_nat: nat > nat > nat ).
thf(tp_bit_se2923211474154528505it_int,type,
bit_se2923211474154528505it_int: nat > int > int ).
thf(tp_bit_se2925701944663578781it_nat,type,
bit_se2925701944663578781it_nat: nat > nat > nat ).
thf(tp_bit_se4203085406695923979it_int,type,
bit_se4203085406695923979it_int: nat > int > int ).
thf(tp_bit_se4205575877204974255it_nat,type,
bit_se4205575877204974255it_nat: nat > nat > nat ).
thf(tp_bit_se545348938243370406it_int,type,
bit_se545348938243370406it_int: nat > int > int ).
thf(tp_bit_se547839408752420682it_nat,type,
bit_se547839408752420682it_nat: nat > nat > nat ).
thf(tp_bit_se6526347334894502574or_int,type,
bit_se6526347334894502574or_int: int > int > int ).
thf(tp_bit_se6528837805403552850or_nat,type,
bit_se6528837805403552850or_nat: nat > nat > nat ).
thf(tp_bit_se725231765392027082nd_int,type,
bit_se725231765392027082nd_int: int > int > int ).
thf(tp_bit_se727722235901077358nd_nat,type,
bit_se727722235901077358nd_nat: nat > nat > nat ).
thf(tp_bit_se7879613467334960850it_int,type,
bit_se7879613467334960850it_int: nat > int > int ).
thf(tp_bit_se7882103937844011126it_nat,type,
bit_se7882103937844011126it_nat: nat > nat > nat ).
thf(tp_bit_se8568078237143864401it_int,type,
bit_se8568078237143864401it_int: nat > int > int ).
thf(tp_bit_se8570568707652914677it_nat,type,
bit_se8570568707652914677it_nat: nat > nat > nat ).
thf(tp_bit_take_bit_num,type,
bit_take_bit_num: nat > num > option_num ).
thf(tp_bot_bo1565574316222977092_nat_o,type,
bot_bo1565574316222977092_nat_o: vEBT_VEBT > nat > $o ).
thf(tp_bot_bo1642239108664514429BT_nat,type,
bot_bo1642239108664514429BT_nat: set_Pr7556676689462069481BT_nat ).
thf(tp_bot_bo1796632182523588997nt_int,type,
bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
thf(tp_bot_bo2099793752762293965at_nat,type,
bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).
thf(tp_bot_bo2578006069712851624enat_o,type,
bot_bo2578006069712851624enat_o: vEBT_VEBT > extended_enat > $o ).
thf(tp_bot_bo4199563552545308370d_enat,type,
bot_bo4199563552545308370d_enat: extended_enat ).
thf(tp_bot_bo4330027929424010533d_enat,type,
bot_bo4330027929424010533d_enat: set_Pr2457182780427864761d_enat ).
thf(tp_bot_bo4898103413517107610_nat_o,type,
bot_bo4898103413517107610_nat_o: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_bot_bo498966703094740906er_nat,type,
bot_bo498966703094740906er_nat: set_filter_nat ).
thf(tp_bot_bo5327735625951526323at_nat,type,
bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat ).
thf(tp_bot_bo7653980558646680370d_enat,type,
bot_bo7653980558646680370d_enat: set_Extended_enat ).
thf(tp_bot_bo8194388402131092736T_VEBT,type,
bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
thf(tp_bot_bot_filter_nat,type,
bot_bot_filter_nat: filter_nat ).
thf(tp_bot_bot_int_int_o,type,
bot_bot_int_int_o: int > int > $o ).
thf(tp_bot_bot_int_o,type,
bot_bot_int_o: int > $o ).
thf(tp_bot_bot_list_nat_o,type,
bot_bot_list_nat_o: list_nat > $o ).
thf(tp_bot_bot_nat,type,
bot_bot_nat: nat ).
thf(tp_bot_bot_nat_nat_o,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(tp_bot_bot_nat_o,type,
bot_bot_nat_o: nat > $o ).
thf(tp_bot_bot_o,type,
bot_bot_o: $o ).
thf(tp_bot_bot_o_o,type,
bot_bot_o_o: $o > $o ).
thf(tp_bot_bot_real_o,type,
bot_bot_real_o: real > $o ).
thf(tp_bot_bot_set_complex,type,
bot_bot_set_complex: set_complex ).
thf(tp_bot_bot_set_int,type,
bot_bot_set_int: set_int ).
thf(tp_bot_bot_set_list_nat,type,
bot_bot_set_list_nat: set_list_nat ).
thf(tp_bot_bot_set_nat,type,
bot_bot_set_nat: set_nat ).
thf(tp_bot_bot_set_nat_o,type,
bot_bot_set_nat_o: set_nat > $o ).
thf(tp_bot_bot_set_o,type,
bot_bot_set_o: set_o ).
thf(tp_bot_bot_set_real,type,
bot_bot_set_real: set_real ).
thf(tp_bot_bot_set_set_nat,type,
bot_bot_set_set_nat: set_set_nat ).
thf(tp_can_select_VEBT_VEBT,type,
can_select_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT > $o ).
thf(tp_can_select_int,type,
can_select_int: ( int > $o ) > set_int > $o ).
thf(tp_can_select_nat,type,
can_select_nat: ( nat > $o ) > set_nat > $o ).
thf(tp_can_select_o,type,
can_select_o: ( $o > $o ) > set_o > $o ).
thf(tp_can_select_real,type,
can_select_real: ( real > $o ) > set_real > $o ).
thf(tp_can_select_set_nat,type,
can_select_set_nat: ( set_nat > $o ) > set_set_nat > $o ).
thf(tp_case_nat_nat,type,
case_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(tp_case_nat_o,type,
case_nat_o: $o > ( nat > $o ) > nat > $o ).
thf(tp_case_o184042715313410164at_nat,type,
case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
thf(tp_case_o6005452278849405969um_num,type,
case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
thf(tp_case_option_num_num,type,
case_option_num_num: num > ( num > num ) > option_num > num ).
thf(tp_cis,type,
cis: real > complex ).
thf(tp_collec213857154873943460nt_int,type,
collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
thf(tp_collec2260605976452661553d_enat,type,
collec2260605976452661553d_enat: ( set_Extended_enat > $o ) > set_se7270636423289371942d_enat ).
thf(tp_collec3392354462482085612at_nat,type,
collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(tp_collec4429806609662206161d_enat,type,
collec4429806609662206161d_enat: ( extended_enat > $o ) > set_Extended_enat ).
thf(tp_collec5608196760682091941T_VEBT,type,
collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
thf(tp_collec5989764272469232197st_nat,type,
collec5989764272469232197st_nat: ( list_list_nat > $o ) > set_list_list_nat ).
thf(tp_collec8433460942617342167d_enat,type,
collec8433460942617342167d_enat: ( list_Extended_enat > $o ) > set_li5464603477888414924d_enat ).
thf(tp_collect_complex,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(tp_collect_filter_nat,type,
collect_filter_nat: ( filter_nat > $o ) > set_filter_nat ).
thf(tp_collect_int,type,
collect_int: ( int > $o ) > set_int ).
thf(tp_collect_list_complex,type,
collect_list_complex: ( list_complex > $o ) > set_list_complex ).
thf(tp_collect_list_int,type,
collect_list_int: ( list_int > $o ) > set_list_int ).
thf(tp_collect_list_nat,type,
collect_list_nat: ( list_nat > $o ) > set_list_nat ).
thf(tp_collect_list_set_nat,type,
collect_list_set_nat: ( list_set_nat > $o ) > set_list_set_nat ).
thf(tp_collect_nat,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(tp_collect_o,type,
collect_o: ( $o > $o ) > set_o ).
thf(tp_collect_real,type,
collect_real: ( real > $o ) > set_real ).
thf(tp_collect_set_complex,type,
collect_set_complex: ( set_complex > $o ) > set_set_complex ).
thf(tp_collect_set_int,type,
collect_set_int: ( set_int > $o ) > set_set_int ).
thf(tp_collect_set_list_nat,type,
collect_set_list_nat: ( set_list_nat > $o ) > set_set_list_nat ).
thf(tp_collect_set_nat,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(tp_collect_set_set_nat,type,
collect_set_set_nat: ( set_set_nat > $o ) > set_set_set_nat ).
thf(tp_comm_s2602460028002588243omplex,type,
comm_s2602460028002588243omplex: complex > nat > complex ).
thf(tp_comm_s3181272606743183617d_enat,type,
comm_s3181272606743183617d_enat: extended_enat > nat > extended_enat ).
thf(tp_comm_s4660882817536571857er_int,type,
comm_s4660882817536571857er_int: int > nat > int ).
thf(tp_comm_s4663373288045622133er_nat,type,
comm_s4663373288045622133er_nat: nat > nat > nat ).
thf(tp_comm_s629917340098488124ar_nat,type,
comm_s629917340098488124ar_nat: char > nat ).
thf(tp_comm_s7457072308508201937r_real,type,
comm_s7457072308508201937r_real: real > nat > real ).
thf(tp_comp_nat_nat_nat,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(tp_comple2295165028678016749d_enat,type,
comple2295165028678016749d_enat: set_Extended_enat > extended_enat ).
thf(tp_comple4398354569131411667d_enat,type,
comple4398354569131411667d_enat: set_Extended_enat > extended_enat ).
thf(tp_comple7806235888213564991et_nat,type,
comple7806235888213564991et_nat: set_set_nat > set_nat ).
thf(tp_complete_Inf_Inf_nat,type,
complete_Inf_Inf_nat: set_nat > nat ).
thf(tp_complete_Sup_Sup_nat,type,
complete_Sup_Sup_nat: set_nat > nat ).
thf(tp_compow4567540516116640754d_enat,type,
compow4567540516116640754d_enat: nat > ( extended_enat > extended_enat ) > extended_enat > extended_enat ).
thf(tp_compow6801810373992395016omplex,type,
compow6801810373992395016omplex: nat > ( complex > complex ) > complex > complex ).
thf(tp_compow_int_int,type,
compow_int_int: nat > ( int > int ) > int > int ).
thf(tp_compow_nat_nat,type,
compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(tp_compow_real_real,type,
compow_real_real: nat > ( real > real ) > real > real ).
thf(tp_concat_VEBT_VEBT,type,
concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_concat_int,type,
concat_int: list_list_int > list_int ).
thf(tp_concat_nat,type,
concat_nat: list_list_nat > list_nat ).
thf(tp_cons_int,type,
cons_int: int > list_int > list_int ).
thf(tp_cons_nat,type,
cons_nat: nat > list_nat > list_nat ).
thf(tp_cos_coeff,type,
cos_coeff: nat > real ).
thf(tp_cos_complex,type,
cos_complex: complex > complex ).
thf(tp_cos_real,type,
cos_real: real > real ).
thf(tp_cosh_complex,type,
cosh_complex: complex > complex ).
thf(tp_cosh_real,type,
cosh_real: real > real ).
thf(tp_count_101369445342291426d_enat,type,
count_101369445342291426d_enat: list_Extended_enat > extended_enat > nat ).
thf(tp_count_list_VEBT_VEBT,type,
count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
thf(tp_count_list_complex,type,
count_list_complex: list_complex > complex > nat ).
thf(tp_count_list_int,type,
count_list_int: list_int > int > nat ).
thf(tp_count_list_nat,type,
count_list_nat: list_nat > nat > nat ).
thf(tp_count_list_o,type,
count_list_o: list_o > $o > nat ).
thf(tp_count_list_real,type,
count_list_real: list_real > real > nat ).
thf(tp_count_list_set_nat,type,
count_list_set_nat: list_set_nat > set_nat > nat ).
thf(tp_cr_int,type,
cr_int: product_prod_nat_nat > int > $o ).
thf(tp_deg,type,
deg: nat ).
thf(tp_diffs_complex,type,
diffs_complex: ( nat > complex ) > nat > complex ).
thf(tp_diffs_int,type,
diffs_int: ( nat > int ) > nat > int ).
thf(tp_diffs_real,type,
diffs_real: ( nat > real ) > nat > real ).
thf(tp_distin2745374544067255638at_int,type,
distin2745374544067255638at_int: list_P3521021558325789923at_int > $o ).
thf(tp_distin3744728255968310194nt_int,type,
distin3744728255968310194nt_int: list_P5707943133018811711nt_int > $o ).
thf(tp_distin4523846830085650399d_enat,type,
distin4523846830085650399d_enat: list_Extended_enat > $o ).
thf(tp_distin6923225563576452346at_nat,type,
distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o ).
thf(tp_distin7922579275477506902nt_nat,type,
distin7922579275477506902nt_nat: list_P8198026277950538467nt_nat > $o ).
thf(tp_distinct_VEBT_VEBT,type,
distinct_VEBT_VEBT: list_VEBT_VEBT > $o ).
thf(tp_distinct_complex,type,
distinct_complex: list_complex > $o ).
thf(tp_distinct_int,type,
distinct_int: list_int > $o ).
thf(tp_distinct_list_nat,type,
distinct_list_nat: list_list_nat > $o ).
thf(tp_distinct_nat,type,
distinct_nat: list_nat > $o ).
thf(tp_distinct_o,type,
distinct_o: list_o > $o ).
thf(tp_distinct_real,type,
distinct_real: list_real > $o ).
thf(tp_distinct_set_nat,type,
distinct_set_nat: list_set_nat > $o ).
thf(tp_divide1717551699836669952omplex,type,
divide1717551699836669952omplex: complex > complex > complex ).
thf(tp_divide_divide_int,type,
divide_divide_int: int > int > int ).
thf(tp_divide_divide_nat,type,
divide_divide_nat: nat > nat > nat ).
thf(tp_divide_divide_real,type,
divide_divide_real: real > real > real ).
thf(tp_divmod_nat,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(tp_drop_nat,type,
drop_nat: nat > list_nat > list_nat ).
thf(tp_dvd_dv3785147216227455552d_enat,type,
dvd_dv3785147216227455552d_enat: extended_enat > extended_enat > $o ).
thf(tp_dvd_dvd_complex,type,
dvd_dvd_complex: complex > complex > $o ).
thf(tp_dvd_dvd_int,type,
dvd_dvd_int: int > int > $o ).
thf(tp_dvd_dvd_nat,type,
dvd_dvd_nat: nat > nat > $o ).
thf(tp_dvd_dvd_real,type,
dvd_dvd_real: real > real > $o ).
thf(tp_enumerate_VEBT_VEBT,type,
enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(tp_enumerate_int,type,
enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
thf(tp_enumerate_nat,type,
enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
thf(tp_eventu1038000079068216329at_nat,type,
eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
thf(tp_eventually_nat,type,
eventually_nat: ( nat > $o ) > filter_nat > $o ).
thf(tp_exp_complex,type,
exp_complex: complex > complex ).
thf(tp_exp_real,type,
exp_real: real > real ).
thf(tp_extend3600170679010898289d_enat,type,
extend3600170679010898289d_enat: ( nat > extended_enat ) > extended_enat > extended_enat > extended_enat ).
thf(tp_extend5688581933313929465d_enat,type,
extend5688581933313929465d_enat: extended_enat ).
thf(tp_extended_case_enat_o,type,
extended_case_enat_o: ( nat > $o ) > $o > extended_enat > $o ).
thf(tp_extended_eSuc,type,
extended_eSuc: extended_enat > extended_enat ).
thf(tp_extended_enat2,type,
extended_enat2: nat > extended_enat ).
thf(tp_field_5140801741446780682s_real,type,
field_5140801741446780682s_real: set_real ).
thf(tp_field_nat,type,
field_nat: set_Pr1261947904930325089at_nat > set_nat ).
thf(tp_filterlim_nat_nat,type,
filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
thf(tp_filterlim_nat_real,type,
filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
thf(tp_filterlim_real_real,type,
filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
thf(tp_find_P8199882355184865565at_nat,type,
find_P8199882355184865565at_nat: ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > option4927543243414619207at_nat ).
thf(tp_find_VEBT_VEBT,type,
find_VEBT_VEBT: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > option_VEBT_VEBT ).
thf(tp_find_int,type,
find_int: ( int > $o ) > list_int > option_int ).
thf(tp_find_nat,type,
find_nat: ( nat > $o ) > list_nat > option_nat ).
thf(tp_find_num,type,
find_num: ( num > $o ) > list_num > option_num ).
thf(tp_find_o,type,
find_o: ( $o > $o ) > list_o > option_o ).
thf(tp_find_real,type,
find_real: ( real > $o ) > list_real > option_real ).
thf(tp_find_set_nat,type,
find_set_nat: ( set_nat > $o ) > list_set_nat > option_set_nat ).
thf(tp_finite1149291290879098388et_nat,type,
finite1149291290879098388et_nat: set_set_set_nat > nat ).
thf(tp_finite1152437895449049373et_nat,type,
finite1152437895449049373et_nat: set_set_nat > $o ).
thf(tp_finite121521170596916366d_enat,type,
finite121521170596916366d_enat: set_Extended_enat > nat ).
thf(tp_finite1862508098717546133d_enat,type,
finite1862508098717546133d_enat: set_li5464603477888414924d_enat > $o ).
thf(tp_finite2119507909894593271er_nat,type,
finite2119507909894593271er_nat: set_filter_nat > $o ).
thf(tp_finite2364142230527598318st_nat,type,
finite2364142230527598318st_nat: set_set_list_nat > nat ).
thf(tp_finite3004134309566078307T_VEBT,type,
finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
thf(tp_finite3207457112153483333omplex,type,
finite3207457112153483333omplex: set_complex > $o ).
thf(tp_finite3719263829065406702d_enat,type,
finite3719263829065406702d_enat: set_se7270636423289371942d_enat > nat ).
thf(tp_finite3922522038869484883st_int,type,
finite3922522038869484883st_int: set_list_int > $o ).
thf(tp_finite4001608067531595151d_enat,type,
finite4001608067531595151d_enat: set_Extended_enat > $o ).
thf(tp_finite5120063068150530198omplex,type,
finite5120063068150530198omplex: set_list_complex > nat ).
thf(tp_finite5468666774076196335d_enat,type,
finite5468666774076196335d_enat: set_se7270636423289371942d_enat > $o ).
thf(tp_finite5631907774883551598et_nat,type,
finite5631907774883551598et_nat: set_list_set_nat > nat ).
thf(tp_finite5795047828879050333T_VEBT,type,
finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
thf(tp_finite5915292604075114978T_VEBT,type,
finite5915292604075114978T_VEBT: set_list_VEBT_VEBT > nat ).
thf(tp_finite6197958912794628473et_int,type,
finite6197958912794628473et_int: set_set_int > $o ).
thf(tp_finite6551019134538273531omplex,type,
finite6551019134538273531omplex: set_set_complex > $o ).
thf(tp_finite7325466520557071688st_nat,type,
finite7325466520557071688st_nat: set_list_list_nat > nat ).
thf(tp_finite7441382602597825044d_enat,type,
finite7441382602597825044d_enat: set_li5464603477888414924d_enat > nat ).
thf(tp_finite7802652506058667612T_VEBT,type,
finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat ).
thf(tp_finite8100373058378681591st_nat,type,
finite8100373058378681591st_nat: set_list_nat > $o ).
thf(tp_finite8712137658972009173omplex,type,
finite8712137658972009173omplex: set_list_complex > $o ).
thf(tp_finite903997441450111292omplex,type,
finite903997441450111292omplex: set_set_complex > nat ).
thf(tp_finite_card_complex,type,
finite_card_complex: set_complex > nat ).
thf(tp_finite_card_int,type,
finite_card_int: set_int > nat ).
thf(tp_finite_card_list_int,type,
finite_card_list_int: set_list_int > nat ).
thf(tp_finite_card_list_nat,type,
finite_card_list_nat: set_list_nat > nat ).
thf(tp_finite_card_nat,type,
finite_card_nat: set_nat > nat ).
thf(tp_finite_card_o,type,
finite_card_o: set_o > nat ).
thf(tp_finite_card_real,type,
finite_card_real: set_real > nat ).
thf(tp_finite_card_set_int,type,
finite_card_set_int: set_set_int > nat ).
thf(tp_finite_card_set_nat,type,
finite_card_set_nat: set_set_nat > nat ).
thf(tp_finite_finite_int,type,
finite_finite_int: set_int > $o ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: set_nat > $o ).
thf(tp_finite_finite_o,type,
finite_finite_o: set_o > $o ).
thf(tp_finite_finite_real,type,
finite_finite_real: set_real > $o ).
thf(tp_fold_nat_nat,type,
fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
thf(tp_fun_pair_leq,type,
fun_pair_leq: set_Pr8693737435421807431at_nat ).
thf(tp_fun_pair_less,type,
fun_pair_less: set_Pr8693737435421807431at_nat ).
thf(tp_funpow_nat,type,
funpow_nat: nat > ( nat > nat ) > nat > nat ).
thf(tp_gbinomial_complex,type,
gbinomial_complex: complex > nat > complex ).
thf(tp_gbinomial_int,type,
gbinomial_int: int > nat > int ).
thf(tp_gbinomial_nat,type,
gbinomial_nat: nat > nat > nat ).
thf(tp_gbinomial_real,type,
gbinomial_real: real > nat > real ).
thf(tp_gcd_Gcd_nat,type,
gcd_Gcd_nat: set_nat > nat ).
thf(tp_gcd_gcd_nat,type,
gcd_gcd_nat: nat > nat > nat ).
thf(tp_gcd_nat_rel,type,
gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_groups1070518202123951855t_real,type,
groups1070518202123951855t_real: ( extended_enat > real ) > set_Extended_enat > real ).
thf(tp_groups129246275422532515t_real,type,
groups129246275422532515t_real: ( nat > real ) > set_nat > real ).
thf(tp_groups1380173120649922871omplex,type,
groups1380173120649922871omplex: ( int > complex ) > complex > list_int > complex ).
thf(tp_groups1523912220035142973t_real,type,
groups1523912220035142973t_real: ( int > real ) > set_int > real ).
thf(tp_groups1549203402269857401d_enat,type,
groups1549203402269857401d_enat: ( nat > extended_enat ) > extended_enat > list_nat > extended_enat ).
thf(tp_groups1681761925125756287l_real,type,
groups1681761925125756287l_real: ( real > real ) > set_real > real ).
thf(tp_groups1705073143266064639nt_int,type,
groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
thf(tp_groups1707563613775114915nt_nat,type,
groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).
thf(tp_groups1752964319039525884d_enat,type,
groups1752964319039525884d_enat: ( complex > extended_enat ) > set_complex > extended_enat ).
thf(tp_groups1931381680841367751omplex,type,
groups1931381680841367751omplex: ( vEBT_VEBT > complex ) > complex > list_VEBT_VEBT > complex ).
thf(tp_groups1932886352136224148al_int,type,
groups1932886352136224148al_int: ( real > int ) > set_real > int ).
thf(tp_groups1935376822645274424al_nat,type,
groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
thf(tp_groups1983926497230936801at_int,type,
groups1983926497230936801at_int: ( nat > int ) > set_nat > int ).
thf(tp_groups1986416967739987077at_nat,type,
groups1986416967739987077at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_groups2025484359314973016at_int,type,
groups2025484359314973016at_int: ( extended_enat > int ) > set_Extended_enat > int ).
thf(tp_groups2027974829824023292at_nat,type,
groups2027974829824023292at_nat: ( extended_enat > nat ) > set_Extended_enat > nat ).
thf(tp_groups2073611262835488442omplex,type,
groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
thf(tp_groups2316167850115554303t_real,type,
groups2316167850115554303t_real: ( int > real ) > set_int > real ).
thf(tp_groups234877984723959775o_real,type,
groups234877984723959775o_real: ( $o > real ) > set_o > real ).
thf(tp_groups2433450451889696826d_enat,type,
groups2433450451889696826d_enat: ( extended_enat > extended_enat ) > set_Extended_enat > extended_enat ).
thf(tp_groups267424677133301183omplex,type,
groups267424677133301183omplex: ( int > complex ) > set_int > complex ).
thf(tp_groups2800946370649118462d_enat,type,
groups2800946370649118462d_enat: ( real > extended_enat ) > set_real > extended_enat ).
thf(tp_groups2878480467620962989at_int,type,
groups2878480467620962989at_int: ( extended_enat > int ) > set_Extended_enat > int ).
thf(tp_groups2880970938130013265at_nat,type,
groups2880970938130013265at_nat: ( extended_enat > nat ) > set_Extended_enat > nat ).
thf(tp_groups2909182065852811199ex_int,type,
groups2909182065852811199ex_int: ( complex > int ) > set_complex > int ).
thf(tp_groups2911672536361861475ex_nat,type,
groups2911672536361861475ex_nat: ( complex > nat ) > set_complex > nat ).
thf(tp_groups2983280209131991357nt_int,type,
groups2983280209131991357nt_int: ( int > int ) > set_int > int ).
thf(tp_groups2985770679641041633nt_nat,type,
groups2985770679641041633nt_nat: ( int > nat ) > set_int > nat ).
thf(tp_groups3049146728041665814omplex,type,
groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
thf(tp_groups3443914341975893411omplex,type,
groups3443914341975893411omplex: ( $o > complex ) > set_o > complex ).
thf(tp_groups3502327434004483295_o_int,type,
groups3502327434004483295_o_int: ( $o > int ) > set_o > int ).
thf(tp_groups3504817904513533571_o_nat,type,
groups3504817904513533571_o_nat: ( $o > nat ) > set_o > nat ).
thf(tp_groups3539618377306564664at_int,type,
groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
thf(tp_groups3542108847815614940at_nat,type,
groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_groups3708469109370488835omplex,type,
groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).
thf(tp_groups3844460828123498381d_enat,type,
groups3844460828123498381d_enat: ( vEBT_VEBT > extended_enat ) > extended_enat > list_VEBT_VEBT > extended_enat ).
thf(tp_groups3901808747961969597al_int,type,
groups3901808747961969597al_int: ( real > int ) > set_real > int ).
thf(tp_groups3904299218471019873al_nat,type,
groups3904299218471019873al_nat: ( real > nat ) > set_real > nat ).
thf(tp_groups404637655443745499omplex,type,
groups404637655443745499omplex: ( nat > complex ) > complex > list_nat > complex ).
thf(tp_groups4075276357253098568at_int,type,
groups4075276357253098568at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > int ).
thf(tp_groups4077766827762148844at_nat,type,
groups4077766827762148844at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).
thf(tp_groups4148127829035722712t_real,type,
groups4148127829035722712t_real: ( extended_enat > real ) > set_Extended_enat > real ).
thf(tp_groups4225252721152677374d_enat,type,
groups4225252721152677374d_enat: ( int > extended_enat ) > set_int > extended_enat ).
thf(tp_groups4395127934049735793omplex,type,
groups4395127934049735793omplex: ( extended_enat > complex ) > set_Extended_enat > complex ).
thf(tp_groups4538972089207619220nt_int,type,
groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
thf(tp_groups4541462559716669496nt_nat,type,
groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
thf(tp_groups4553916814277028129_o_int,type,
groups4553916814277028129_o_int: ( $o > int ) > set_o > int ).
thf(tp_groups4556407284786078405_o_nat,type,
groups4556407284786078405_o_nat: ( $o > nat ) > set_o > nat ).
thf(tp_groups4561878855575611511st_nat,type,
groups4561878855575611511st_nat: list_nat > nat ).
thf(tp_groups4567486121110086003t_real,type,
groups4567486121110086003t_real: ( product_prod_nat_nat > real ) > set_Pr1261947904930325089at_nat > real ).
thf(tp_groups4622424608036095791omplex,type,
groups4622424608036095791omplex: ( extended_enat > complex ) > set_Extended_enat > complex ).
thf(tp_groups4694064378042380927al_int,type,
groups4694064378042380927al_int: ( real > int ) > set_real > int ).
thf(tp_groups4696554848551431203al_nat,type,
groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).
thf(tp_groups4847789403509879791at_int,type,
groups4847789403509879791at_int: ( extended_enat > int ) > set_Extended_enat > int ).
thf(tp_groups4850279874018930067at_nat,type,
groups4850279874018930067at_nat: ( extended_enat > nat ) > set_Extended_enat > nat ).
thf(tp_groups4859619685533338977omplex,type,
groups4859619685533338977omplex: ( $o > complex ) > set_o > complex ).
thf(tp_groups5078248829458667347d_enat,type,
groups5078248829458667347d_enat: ( int > extended_enat ) > set_int > extended_enat ).
thf(tp_groups5107569545109728110t_real,type,
groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
thf(tp_groups5328290441151304332omplex,type,
groups5328290441151304332omplex: ( $o > complex ) > set_o > complex ).
thf(tp_groups5683813829254066239omplex,type,
groups5683813829254066239omplex: ( real > complex ) > set_real > complex ).
thf(tp_groups5690904116761175830ex_int,type,
groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
thf(tp_groups5693394587270226106ex_nat,type,
groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
thf(tp_groups5737402329758386879x_real,type,
groups5737402329758386879x_real: ( complex > real ) > set_complex > real ).
thf(tp_groups5754745047067104278omplex,type,
groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
thf(tp_groups5808333547571424918x_real,type,
groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
thf(tp_groups627172608727702305o_real,type,
groups627172608727702305o_real: ( $o > real ) > set_o > real ).
thf(tp_groups6464643781859351333omplex,type,
groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).
thf(tp_groups6591440286371151544t_real,type,
groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
thf(tp_groups6842663049115397189BT_int,type,
groups6842663049115397189BT_int: ( vEBT_VEBT > int ) > int > list_VEBT_VEBT > int ).
thf(tp_groups6845153519624447465BT_nat,type,
groups6845153519624447465BT_nat: ( vEBT_VEBT > nat ) > nat > list_VEBT_VEBT > nat ).
thf(tp_groups705719431365010083at_int,type,
groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
thf(tp_groups707763781290628081d_enat,type,
groups707763781290628081d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).
thf(tp_groups708209901874060359at_nat,type,
groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_groups7108830773950497114d_enat,type,
groups7108830773950497114d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).
thf(tp_groups713298508707869441omplex,type,
groups713298508707869441omplex: ( real > complex ) > set_real > complex ).
thf(tp_groups7198740251461348360d_enat,type,
groups7198740251461348360d_enat: ( $o > extended_enat ) > set_o > extended_enat ).
thf(tp_groups7440179247065528705omplex,type,
groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).
thf(tp_groups7485877704341954137at_int,type,
groups7485877704341954137at_int: ( nat > int ) > int > list_nat > int ).
thf(tp_groups766887009212190081x_real,type,
groups766887009212190081x_real: ( complex > real ) > set_complex > real ).
thf(tp_groups771621172384141258BT_nat,type,
groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).
thf(tp_groups7754918857620584856omplex,type,
groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
thf(tp_groups783334030178737011d_enat,type,
groups783334030178737011d_enat: ( $o > extended_enat ) > set_o > extended_enat ).
thf(tp_groups7888997386326813469d_enat,type,
groups7888997386326813469d_enat: ( int > extended_enat ) > extended_enat > list_int > extended_enat ).
thf(tp_groups7961826882256487087d_enat,type,
groups7961826882256487087d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).
thf(tp_groups7973222482632965587d_enat,type,
groups7973222482632965587d_enat: ( real > extended_enat ) > set_real > extended_enat ).
thf(tp_groups808145749697022017omplex,type,
groups808145749697022017omplex: ( complex > complex ) > set_complex > complex ).
thf(tp_groups8097168146408367636l_real,type,
groups8097168146408367636l_real: ( real > real ) > set_real > real ).
thf(tp_groups8292507037921071086at_int,type,
groups8292507037921071086at_int: ( set_nat > int ) > set_set_nat > int ).
thf(tp_groups8294997508430121362at_nat,type,
groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
thf(tp_groups8422889724626310577d_enat,type,
groups8422889724626310577d_enat: ( $o > extended_enat ) > set_o > extended_enat ).
thf(tp_groups8485231416243008693nt_int,type,
groups8485231416243008693nt_int: ( int > int ) > int > list_int > int ).
thf(tp_groups8505340233167759370_o_int,type,
groups8505340233167759370_o_int: ( $o > int ) > set_o > int ).
thf(tp_groups8507830703676809646_o_nat,type,
groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).
thf(tp_groups8515261248781899619omplex,type,
groups8515261248781899619omplex: ( nat > complex ) > set_nat > complex ).
thf(tp_groups8560362682196896993t_real,type,
groups8560362682196896993t_real: ( nat > real ) > set_nat > real ).
thf(tp_groups858564598930262913ex_int,type,
groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).
thf(tp_groups861055069439313189ex_nat,type,
groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).
thf(tp_groups8691415230153176458o_real,type,
groups8691415230153176458o_real: ( $o > real ) > set_o > real ).
thf(tp_groups8778361861064173332t_real,type,
groups8778361861064173332t_real: ( int > real ) > set_int > real ).
thf(tp_groups8946708780592123413d_enat,type,
groups8946708780592123413d_enat: ( real > extended_enat ) > set_real > extended_enat ).
thf(tp_groups9116527308978886569_o_int,type,
groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
thf(tp_groups9119017779487936845_o_nat,type,
groups9119017779487936845_o_nat: ( $o > nat ) > nat > list_o > nat ).
thf(tp_groups97031904164794029t_real,type,
groups97031904164794029t_real: ( extended_enat > real ) > set_Extended_enat > real ).
thf(tp_groups977919841031483927at_nat,type,
groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).
thf(tp_groups97945582718554045l_real,type,
groups97945582718554045l_real: ( real > real ) > set_real > real ).
thf(tp_has_fi5821293074295781190e_real,type,
has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
thf(tp_hd_nat,type,
hd_nat: list_nat > nat ).
thf(tp_i,type,
i: nat ).
thf(tp_id_nat,type,
id_nat: nat > nat ).
thf(tp_id_o,type,
id_o: $o > $o ).
thf(tp_if_Extended_enat,type,
if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
thf(tp_if_Pro3027730157355071871nt_int,type,
if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
thf(tp_if_Pro6206227464963214023at_nat,type,
if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_if_VEBT_VEBT,type,
if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(tp_if_complex,type,
if_complex: $o > complex > complex > complex ).
thf(tp_if_filter_nat,type,
if_filter_nat: $o > filter_nat > filter_nat > filter_nat ).
thf(tp_if_int,type,
if_int: $o > int > int > int ).
thf(tp_if_int_int,type,
if_int_int: $o > ( int > int ) > ( int > int ) > int > int ).
thf(tp_if_list_int,type,
if_list_int: $o > list_int > list_int > list_int ).
thf(tp_if_list_nat,type,
if_list_nat: $o > list_nat > list_nat > list_nat ).
thf(tp_if_nat,type,
if_nat: $o > nat > nat > nat ).
thf(tp_if_option_num,type,
if_option_num: $o > option_num > option_num > option_num ).
thf(tp_if_real,type,
if_real: $o > real > real > real ).
thf(tp_if_set_int,type,
if_set_int: $o > set_int > set_int > set_int ).
thf(tp_if_set_nat,type,
if_set_nat: $o > set_nat > set_nat > set_nat ).
thf(tp_image_80655429650038917d_enat,type,
image_80655429650038917d_enat: ( extended_enat > extended_enat ) > set_Extended_enat > set_Extended_enat ).
thf(tp_image_char_nat,type,
image_char_nat: ( char > nat ) > set_char > set_nat ).
thf(tp_image_int_int,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(tp_image_nat_char,type,
image_nat_char: ( nat > char ) > set_nat > set_char ).
thf(tp_image_nat_nat,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(tp_image_nat_set_nat,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(tp_image_real_real,type,
image_real_real: ( real > real ) > set_real > set_real ).
thf(tp_inc,type,
inc: num > num ).
thf(tp_inf_in2572325071724192079at_nat,type,
inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(tp_inf_inf_int,type,
inf_inf_int: int > int > int ).
thf(tp_inf_inf_nat,type,
inf_inf_nat: nat > nat > nat ).
thf(tp_infini8530281810654367211te_nat,type,
infini8530281810654367211te_nat: set_nat > nat > nat ).
thf(tp_inj_on_nat_char,type,
inj_on_nat_char: ( nat > char ) > set_nat > $o ).
thf(tp_inj_on_nat_nat,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(tp_inj_on_real_real,type,
inj_on_real_real: ( real > real ) > set_real > $o ).
thf(tp_insert_Extended_enat,type,
insert_Extended_enat: extended_enat > set_Extended_enat > set_Extended_enat ).
thf(tp_insert_VEBT_VEBT,type,
insert_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_insert_VEBT_VEBT2,type,
insert_VEBT_VEBT2: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(tp_insert_complex,type,
insert_complex: complex > set_complex > set_complex ).
thf(tp_insert_int,type,
insert_int: int > list_int > list_int ).
thf(tp_insert_int2,type,
insert_int2: int > set_int > set_int ).
thf(tp_insert_list_nat,type,
insert_list_nat: list_nat > set_list_nat > set_list_nat ).
thf(tp_insert_nat,type,
insert_nat: nat > list_nat > list_nat ).
thf(tp_insert_nat2,type,
insert_nat2: nat > set_nat > set_nat ).
thf(tp_insert_o,type,
insert_o: $o > list_o > list_o ).
thf(tp_insert_o2,type,
insert_o2: $o > set_o > set_o ).
thf(tp_insert_real,type,
insert_real: real > list_real > list_real ).
thf(tp_insert_real2,type,
insert_real2: real > set_real > set_real ).
thf(tp_insert_set_nat,type,
insert_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(tp_insert_set_nat2,type,
insert_set_nat2: set_nat > set_set_nat > set_set_nat ).
thf(tp_int_ge_less_than,type,
int_ge_less_than: int > set_Pr958786334691620121nt_int ).
thf(tp_int_ge_less_than2,type,
int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
thf(tp_intrel,type,
intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_invers8013647133539491842omplex,type,
invers8013647133539491842omplex: complex > complex ).
thf(tp_inverse_inverse_real,type,
inverse_inverse_real: real > real ).
thf(tp_is_singleton_int,type,
is_singleton_int: set_int > $o ).
thf(tp_is_singleton_nat,type,
is_singleton_nat: set_nat > $o ).
thf(tp_is_singleton_o,type,
is_singleton_o: set_o > $o ).
thf(tp_is_singleton_real,type,
is_singleton_real: set_real > $o ).
thf(tp_is_singleton_set_nat,type,
is_singleton_set_nat: set_set_nat > $o ).
thf(tp_last_nat,type,
last_nat: list_nat > nat ).
thf(tp_lattic1189837152898106425t_real,type,
lattic1189837152898106425t_real: ( extended_enat > real ) > set_Extended_enat > extended_enat ).
thf(tp_lattic1996716550891908761d_enat,type,
lattic1996716550891908761d_enat: ( extended_enat > extended_enat ) > set_Extended_enat > extended_enat ).
thf(tp_lattic2675449441010098035t_real,type,
lattic2675449441010098035t_real: ( int > real ) > set_int > int ).
thf(tp_lattic2775856028456453135_o_nat,type,
lattic2775856028456453135_o_nat: ( $o > nat ) > set_o > $o ).
thf(tp_lattic3845382081240766429at_nat,type,
lattic3845382081240766429at_nat: ( extended_enat > nat ) > set_Extended_enat > extended_enat ).
thf(tp_lattic488527866317076247t_real,type,
lattic488527866317076247t_real: ( nat > real ) > set_nat > nat ).
thf(tp_lattic5055836439445974935al_nat,type,
lattic5055836439445974935al_nat: ( real > nat ) > set_real > real ).
thf(tp_lattic5364784637807008409ex_nat,type,
lattic5364784637807008409ex_nat: ( complex > nat ) > set_complex > complex ).
thf(tp_lattic7446932960582359483at_nat,type,
lattic7446932960582359483at_nat: ( nat > nat ) > set_nat > nat ).
thf(tp_lattic7542187609180611815d_enat,type,
lattic7542187609180611815d_enat: ( $o > extended_enat ) > set_o > $o ).
thf(tp_lattic7796887085614042845d_enat,type,
lattic7796887085614042845d_enat: ( complex > extended_enat ) > set_complex > complex ).
thf(tp_lattic8265883725875713057ax_nat,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
thf(tp_lattic8440615504127631091l_real,type,
lattic8440615504127631091l_real: ( real > real ) > set_real > real ).
thf(tp_lattic8446286672483414039nt_nat,type,
lattic8446286672483414039nt_nat: ( int > nat ) > set_int > int ).
thf(tp_lattic8697145971487455083o_real,type,
lattic8697145971487455083o_real: ( $o > real ) > set_o > $o ).
thf(tp_lattic8794016678065449205x_real,type,
lattic8794016678065449205x_real: ( complex > real ) > set_complex > complex ).
thf(tp_lattic9066027731366277983d_enat,type,
lattic9066027731366277983d_enat: ( real > extended_enat ) > set_real > real ).
thf(tp_lattic921264341876707157d_enat,type,
lattic921264341876707157d_enat: set_Extended_enat > extended_enat ).
thf(tp_less_than,type,
less_than: set_Pr1261947904930325089at_nat ).
thf(tp_linord1735203802627413978nt_int,type,
linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
thf(tp_linord2614967742042102400et_nat,type,
linord2614967742042102400et_nat: set_nat > list_nat ).
thf(tp_linord738340561235409698at_nat,type,
linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
thf(tp_list_ex1_VEBT_VEBT,type,
list_ex1_VEBT_VEBT: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > $o ).
thf(tp_list_ex1_int,type,
list_ex1_int: ( int > $o ) > list_int > $o ).
thf(tp_list_ex1_nat,type,
list_ex1_nat: ( nat > $o ) > list_nat > $o ).
thf(tp_list_ex1_o,type,
list_ex1_o: ( $o > $o ) > list_o > $o ).
thf(tp_list_ex1_real,type,
list_ex1_real: ( real > $o ) > list_real > $o ).
thf(tp_list_ex1_set_nat,type,
list_ex1_set_nat: ( set_nat > $o ) > list_set_nat > $o ).
thf(tp_list_u1324408373059187874T_VEBT,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(tp_list_u2241885204319820103d_enat,type,
list_u2241885204319820103d_enat: list_P6356568628958627295d_enat > nat > produc7272778201969148633d_enat > list_P6356568628958627295d_enat ).
thf(tp_list_u2459188882655168453BT_nat,type,
list_u2459188882655168453BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat > list_P7037539587688870467BT_nat ).
thf(tp_list_u3002344382305578791nt_int,type,
list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int ).
thf(tp_list_u3071683517702156500d_enat,type,
list_u3071683517702156500d_enat: list_Extended_enat > nat > extended_enat > list_Extended_enat ).
thf(tp_list_u5003261594476800725at_nat,type,
list_u5003261594476800725at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat > list_P8469869581646625389at_nat ).
thf(tp_list_u6180841689913720943at_nat,type,
list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
thf(tp_list_u6961636818849549845T_VEBT,type,
list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT ).
thf(tp_list_update_int,type,
list_update_int: list_int > nat > int > list_int ).
thf(tp_list_update_nat,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(tp_list_update_o,type,
list_update_o: list_o > nat > $o > list_o ).
thf(tp_list_update_real,type,
list_update_real: list_real > nat > real > list_real ).
thf(tp_list_update_set_nat,type,
list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
thf(tp_listre4828114922151135584at_nat,type,
listre4828114922151135584at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
thf(tp_listrel1_VEBT_VEBT,type,
listrel1_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(tp_listrel1_int,type,
listrel1_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(tp_listrel1_nat,type,
listrel1_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(tp_listrel1p_int,type,
listrel1p_int: ( int > int > $o ) > list_int > list_int > $o ).
thf(tp_listrel1p_nat,type,
listrel1p_nat: ( nat > nat > $o ) > list_nat > list_nat > $o ).
thf(tp_ln_ln_real,type,
ln_ln_real: real > real ).
thf(tp_log,type,
log: real > real > real ).
thf(tp_m,type,
m: nat ).
thf(tp_ma,type,
ma: nat ).
thf(tp_map_VE8901447254227204932T_VEBT,type,
map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_map_fu2345160673673942751at_nat,type,
map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
thf(tp_map_fu3667384564859982768at_int,type,
map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
thf(tp_map_fu434086159418415080_int_o,type,
map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
thf(tp_map_fu4826362097070443709at_o_o,type,
map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(tp_map_fu4960017516451851995nt_int,type,
map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
thf(tp_map_nat_nat,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(tp_member1627681773268152802al_int,type,
member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o ).
thf(tp_member2056185340421749780T_VEBT,type,
member2056185340421749780T_VEBT: produc1531783533982839933T_VEBT > set_Pr8044002425091019955T_VEBT > $o ).
thf(tp_member216504246829706758nt_nat,type,
member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(tp_member2744130022092475746t_real,type,
member2744130022092475746t_real: produc679980390762269497t_real > set_Pr3538720872664544793t_real > $o ).
thf(tp_member2802428098988154798_o_nat,type,
member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(tp_member2936631157270082147T_VEBT,type,
member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
thf(tp_member3307348790968139188VEBT_o,type,
member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
thf(tp_member373505688050248522BT_nat,type,
member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
thf(tp_member38198578724832770d_enat,type,
member38198578724832770d_enat: produc7272778201969148633d_enat > set_Pr2457182780427864761d_enat > $o ).
thf(tp_member4262671552274231302at_int,type,
member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o ).
thf(tp_member4439316823752958928T_VEBT,type,
member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o ).
thf(tp_member4489920277610959864_int_o,type,
member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o ).
thf(tp_member5262025264175285858nt_int,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(tp_member5419026705395827622BT_int,type,
member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
thf(tp_member5477980866518848620T_VEBT,type,
member5477980866518848620T_VEBT: produc2504756804600209347T_VEBT > set_Pr7543698050874017315T_VEBT > $o ).
thf(tp_member568628332442017744T_VEBT,type,
member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
thf(tp_member5805532792777349510al_nat,type,
member5805532792777349510al_nat: produc3741383161447143261al_nat > set_Pr3510011417693777981al_nat > $o ).
thf(tp_member6693912407220327184at_nat,type,
member6693912407220327184at_nat: produc6392793444374437607at_nat > set_Pr1542805901266377927at_nat > $o ).
thf(tp_member6698963635872716290st_int,type,
member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
thf(tp_member7262085504369356948T_VEBT,type,
member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o ).
thf(tp_member7340969449405702474st_nat,type,
member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o ).
thf(tp_member7400031367953476362o_real,type,
member7400031367953476362o_real: product_prod_o_real > set_Pr6573716822653411497o_real > $o ).
thf(tp_member7466972457876170832od_o_o,type,
member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).
thf(tp_member772602641336174712real_o,type,
member772602641336174712real_o: product_prod_real_o > set_Pr4936984352647145239real_o > $o ).
thf(tp_member7847949116333733898_o_int,type,
member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o ).
thf(tp_member7849222048561428706l_real,type,
member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o ).
thf(tp_member8206827879206165904at_nat,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(tp_member8277197624267554838et_nat,type,
member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
thf(tp_member8440522571783428010at_nat,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(tp_member8549952807677709168T_VEBT,type,
member8549952807677709168T_VEBT: produc8025551001238799321T_VEBT > set_Pr6167073792073659919T_VEBT > $o ).
thf(tp_member8675245146396747942T_real,type,
member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
thf(tp_member_Extended_enat,type,
member_Extended_enat: extended_enat > set_Extended_enat > $o ).
thf(tp_member_VEBT_VEBT,type,
member_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > $o ).
thf(tp_member_VEBT_VEBT2,type,
member_VEBT_VEBT2: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(tp_member_complex,type,
member_complex: complex > set_complex > $o ).
thf(tp_member_filter_nat,type,
member_filter_nat: filter_nat > set_filter_nat > $o ).
thf(tp_member_int,type,
member_int: list_int > int > $o ).
thf(tp_member_int2,type,
member_int2: int > set_int > $o ).
thf(tp_member_list_int,type,
member_list_int: list_int > set_list_int > $o ).
thf(tp_member_list_nat,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(tp_member_nat,type,
member_nat: list_nat > nat > $o ).
thf(tp_member_nat2,type,
member_nat2: nat > set_nat > $o ).
thf(tp_member_num,type,
member_num: num > set_num > $o ).
thf(tp_member_o,type,
member_o: list_o > $o > $o ).
thf(tp_member_o2,type,
member_o2: $o > set_o > $o ).
thf(tp_member_real,type,
member_real: list_real > real > $o ).
thf(tp_member_real2,type,
member_real2: real > set_real > $o ).
thf(tp_member_set_nat,type,
member_set_nat: list_set_nat > set_nat > $o ).
thf(tp_member_set_nat2,type,
member_set_nat2: set_nat > set_set_nat > $o ).
thf(tp_mi,type,
mi: nat ).
thf(tp_minus_2163939370556025621et_nat,type,
minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
thf(tp_minus_3235023915231533773d_enat,type,
minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
thf(tp_minus_5127226145743854075T_VEBT,type,
minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(tp_minus_7954133019191499631st_nat,type,
minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(tp_minus_811609699411566653omplex,type,
minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
thf(tp_minus_925952699566721837d_enat,type,
minus_925952699566721837d_enat: set_Extended_enat > set_Extended_enat > set_Extended_enat ).
thf(tp_minus_minus_complex,type,
minus_minus_complex: complex > complex > complex ).
thf(tp_minus_minus_int,type,
minus_minus_int: int > int > int ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(tp_minus_minus_real,type,
minus_minus_real: real > real > real ).
thf(tp_minus_minus_set_int,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(tp_minus_minus_set_nat,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(tp_minus_minus_set_o,type,
minus_minus_set_o: set_o > set_o > set_o ).
thf(tp_minus_minus_set_real,type,
minus_minus_set_real: set_real > set_real > set_real ).
thf(tp_modulo_modulo_int,type,
modulo_modulo_int: int > int > int ).
thf(tp_modulo_modulo_nat,type,
modulo_modulo_nat: nat > nat > nat ).
thf(tp_n_lists_VEBT_VEBT,type,
n_lists_VEBT_VEBT: nat > list_VEBT_VEBT > list_list_VEBT_VEBT ).
thf(tp_n_lists_int,type,
n_lists_int: nat > list_int > list_list_int ).
thf(tp_n_lists_nat,type,
n_lists_nat: nat > list_nat > list_list_nat ).
thf(tp_na,type,
na: nat ).
thf(tp_nat2,type,
nat2: int > nat ).
thf(tp_nat_list_decode,type,
nat_list_decode: nat > list_nat ).
thf(tp_nat_list_decode_rel,type,
nat_list_decode_rel: nat > nat > $o ).
thf(tp_nat_list_encode,type,
nat_list_encode: list_nat > nat ).
thf(tp_nat_list_encode_rel,type,
nat_list_encode_rel: list_nat > list_nat > $o ).
thf(tp_nat_pr5047031295181774490ux_rel,type,
nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_nat_prod_decode,type,
nat_prod_decode: nat > product_prod_nat_nat ).
thf(tp_nat_prod_decode_aux,type,
nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
thf(tp_nat_prod_encode,type,
nat_prod_encode: product_prod_nat_nat > nat ).
thf(tp_nat_set_decode,type,
nat_set_decode: nat > set_nat ).
thf(tp_nat_set_encode,type,
nat_set_encode: set_nat > nat ).
thf(tp_nat_triangle,type,
nat_triangle: nat > nat ).
thf(tp_neg_nu3811975205180677377ec_int,type,
neg_nu3811975205180677377ec_int: int > int ).
thf(tp_neg_nu6075765906172075777c_real,type,
neg_nu6075765906172075777c_real: real > real ).
thf(tp_neg_nu6511756317524482435omplex,type,
neg_nu6511756317524482435omplex: complex > complex ).
thf(tp_nil_int,type,
nil_int: list_int ).
thf(tp_nil_nat,type,
nil_nat: list_nat ).
thf(tp_none_P5556105721700978146at_nat,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(tp_none_VEBT_VEBT,type,
none_VEBT_VEBT: option_VEBT_VEBT ).
thf(tp_none_int,type,
none_int: option_int ).
thf(tp_none_nat,type,
none_nat: option_nat ).
thf(tp_none_num,type,
none_num: option_num ).
thf(tp_none_o,type,
none_o: option_o ).
thf(tp_none_real,type,
none_real: option_real ).
thf(tp_none_set_nat,type,
none_set_nat: option_set_nat ).
thf(tp_nth_Extended_enat,type,
nth_Extended_enat: list_Extended_enat > nat > extended_enat ).
thf(tp_nth_Pr1791586995822124652BT_nat,type,
nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
thf(tp_nth_Pr3440142176431000676at_int,type,
nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
thf(tp_nth_Pr3474266648193625910T_VEBT,type,
nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT ).
thf(tp_nth_Pr4439495888332055232nt_int,type,
nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
thf(tp_nth_Pr4953567300277697838T_VEBT,type,
nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
thf(tp_nth_Pr6837108013167703752BT_int,type,
nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
thf(tp_nth_Pr744662078594809490T_VEBT,type,
nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
thf(tp_nth_Pr7509392720524132704d_enat,type,
nth_Pr7509392720524132704d_enat: list_P6356568628958627295d_enat > nat > produc7272778201969148633d_enat ).
thf(tp_nth_Pr7617993195940197384at_nat,type,
nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
thf(tp_nth_Pr8617346907841251940nt_nat,type,
nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
thf(tp_nth_VEBT_VEBT,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(tp_nth_int,type,
nth_int: list_int > nat > int ).
thf(tp_nth_nat,type,
nth_nat: list_nat > nat > nat ).
thf(tp_nth_num,type,
nth_num: list_num > nat > num ).
thf(tp_nth_o,type,
nth_o: list_o > nat > $o ).
thf(tp_nth_real,type,
nth_real: list_real > nat > real ).
thf(tp_nth_set_nat,type,
nth_set_nat: list_set_nat > nat > set_nat ).
thf(tp_num_of_nat,type,
num_of_nat: nat > num ).
thf(tp_numera1916890842035813515d_enat,type,
numera1916890842035813515d_enat: num > extended_enat ).
thf(tp_numera6690914467698888265omplex,type,
numera6690914467698888265omplex: num > complex ).
thf(tp_numeral_numeral_int,type,
numeral_numeral_int: num > int ).
thf(tp_numeral_numeral_nat,type,
numeral_numeral_nat: num > nat ).
thf(tp_numeral_numeral_real,type,
numeral_numeral_real: num > real ).
thf(tp_one,type,
one: num ).
thf(tp_one_on7984719198319812577d_enat,type,
one_on7984719198319812577d_enat: extended_enat ).
thf(tp_one_one_complex,type,
one_one_complex: complex ).
thf(tp_one_one_int,type,
one_one_int: int ).
thf(tp_one_one_nat,type,
one_one_nat: nat ).
thf(tp_one_one_real,type,
one_one_real: real ).
thf(tp_ord_Le1955565732374568822d_enat,type,
ord_Le1955565732374568822d_enat: ( extended_enat > $o ) > extended_enat ).
thf(tp_ord_Least_nat,type,
ord_Least_nat: ( nat > $o ) > nat ).
thf(tp_ord_le1182472622972956176_nat_o,type,
ord_le1182472622972956176_nat_o: ( vEBT_VEBT > nat > $o ) > ( vEBT_VEBT > nat > $o ) > $o ).
thf(tp_ord_le1190675801316882794st_nat,type,
ord_le1190675801316882794st_nat: set_list_nat > set_list_nat > $o ).
thf(tp_ord_le211207098394363844omplex,type,
ord_le211207098394363844omplex: set_complex > set_complex > $o ).
thf(tp_ord_le2426478655948331894er_nat,type,
ord_le2426478655948331894er_nat: set_filter_nat > set_filter_nat > $o ).
thf(tp_ord_le2510731241096832064er_nat,type,
ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
thf(tp_ord_le2529575680413868914d_enat,type,
ord_le2529575680413868914d_enat: set_Extended_enat > set_Extended_enat > $o ).
thf(tp_ord_le2646555220125990790_nat_o,type,
ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(tp_ord_le2691948842708570076enat_o,type,
ord_le2691948842708570076enat_o: ( vEBT_VEBT > extended_enat > $o ) > ( vEBT_VEBT > extended_enat > $o ) > $o ).
thf(tp_ord_le2843351958646193337nt_int,type,
ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(tp_ord_le2932123472753598470d_enat,type,
ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
thf(tp_ord_le3000389064537975527at_nat,type,
ord_le3000389064537975527at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(tp_ord_le3146513528884898305at_nat,type,
ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(tp_ord_le3442269383143156041BT_nat,type,
ord_le3442269383143156041BT_nat: set_Pr7556676689462069481BT_nat > set_Pr7556676689462069481BT_nat > $o ).
thf(tp_ord_le3964352015994296041_nat_o,type,
ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
thf(tp_ord_le4337996190870823476T_VEBT,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(tp_ord_le5604493270027003598_nat_o,type,
ord_le5604493270027003598_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(tp_ord_le6045566169113846134st_nat,type,
ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
thf(tp_ord_le6505334834405097322er_nat,type,
ord_le6505334834405097322er_nat: set_filter_nat > set_filter_nat > $o ).
thf(tp_ord_le6741204236512500942_int_o,type,
ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(tp_ord_le6893508408891458716et_nat,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(tp_ord_le7203529160286727270d_enat,type,
ord_le7203529160286727270d_enat: set_Extended_enat > set_Extended_enat > $o ).
thf(tp_ord_le72135733267957522d_enat,type,
ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
thf(tp_ord_le8566326065971749465d_enat,type,
ord_le8566326065971749465d_enat: set_Pr2457182780427864761d_enat > set_Pr2457182780427864761d_enat > $o ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: int > int > $o ).
thf(tp_ord_less_eq_int_o,type,
ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(tp_ord_less_eq_nat_o,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(tp_ord_less_eq_num,type,
ord_less_eq_num: num > num > $o ).
thf(tp_ord_less_eq_o,type,
ord_less_eq_o: $o > $o > $o ).
thf(tp_ord_less_eq_o_o,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_eq_real_o,type,
ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
thf(tp_ord_less_eq_set_int,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(tp_ord_less_eq_set_nat,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_eq_set_o,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(tp_ord_less_eq_set_real,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(tp_ord_less_filter_nat,type,
ord_less_filter_nat: filter_nat > filter_nat > $o ).
thf(tp_ord_less_int,type,
ord_less_int: int > int > $o ).
thf(tp_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(tp_ord_less_num,type,
ord_less_num: num > num > $o ).
thf(tp_ord_less_o,type,
ord_less_o: $o > $o > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_ord_less_set_complex,type,
ord_less_set_complex: set_complex > set_complex > $o ).
thf(tp_ord_less_set_int,type,
ord_less_set_int: set_int > set_int > $o ).
thf(tp_ord_less_set_nat,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(tp_ord_less_set_o,type,
ord_less_set_o: set_o > set_o > $o ).
thf(tp_ord_less_set_real,type,
ord_less_set_real: set_real > set_real > $o ).
thf(tp_ord_less_set_set_nat,type,
ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
thf(tp_ord_ma741700101516333627d_enat,type,
ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
thf(tp_ord_max_filter_nat,type,
ord_max_filter_nat: filter_nat > filter_nat > filter_nat ).
thf(tp_ord_max_int,type,
ord_max_int: int > int > int ).
thf(tp_ord_max_nat,type,
ord_max_nat: nat > nat > nat ).
thf(tp_ord_max_real,type,
ord_max_real: real > real > real ).
thf(tp_ord_max_set_int,type,
ord_max_set_int: set_int > set_int > set_int ).
thf(tp_ord_max_set_nat,type,
ord_max_set_nat: set_nat > set_nat > set_nat ).
thf(tp_ord_max_set_o,type,
ord_max_set_o: set_o > set_o > set_o ).
thf(tp_ord_max_set_real,type,
ord_max_set_real: set_real > set_real > set_real ).
thf(tp_ord_min_int,type,
ord_min_int: int > int > int ).
thf(tp_ord_min_nat,type,
ord_min_nat: nat > nat > nat ).
thf(tp_order_2888998067076097458on_nat,type,
order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(tp_order_5726023648592871131at_nat,type,
order_5726023648592871131at_nat: ( nat > nat ) > $o ).
thf(tp_order_Greatest_nat,type,
order_Greatest_nat: ( nat > $o ) > nat ).
thf(tp_order_mono_nat_nat,type,
order_mono_nat_nat: ( nat > nat ) > $o ).
thf(tp_order_underS_nat,type,
order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
thf(tp_ordering_top_nat,type,
ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
thf(tp_pcr_int,type,
pcr_int: product_prod_nat_nat > int > $o ).
thf(tp_pi,type,
pi: real ).
thf(tp_plus_p3455044024723400733d_enat,type,
plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
thf(tp_plus_plus_complex,type,
plus_plus_complex: complex > complex > complex ).
thf(tp_plus_plus_int,type,
plus_plus_int: int > int > int ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: nat > nat > nat ).
thf(tp_plus_plus_num,type,
plus_plus_num: num > num > num ).
thf(tp_plus_plus_real,type,
plus_plus_real: real > real > real ).
thf(tp_pow_nat,type,
pow_nat: set_nat > set_set_nat ).
thf(tp_power_8040749407984259932d_enat,type,
power_8040749407984259932d_enat: extended_enat > nat > extended_enat ).
thf(tp_power_power_complex,type,
power_power_complex: complex > nat > complex ).
thf(tp_power_power_int,type,
power_power_int: int > nat > int ).
thf(tp_power_power_nat,type,
power_power_nat: nat > nat > nat ).
thf(tp_power_power_real,type,
power_power_real: real > nat > real ).
thf(tp_powr_real,type,
powr_real: real > real > real ).
thf(tp_pred,type,
pred: nat > nat ).
thf(tp_pred_nat,type,
pred_nat: set_Pr1261947904930325089at_nat ).
thf(tp_pred_numeral,type,
pred_numeral: num > nat ).
thf(tp_prod_filter_nat_nat,type,
prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
thf(tp_produc1206667027950169146enat_o,type,
produc1206667027950169146enat_o: ( vEBT_VEBT > extended_enat > $o ) > produc7272778201969148633d_enat > $o ).
thf(tp_produc162892877563308318_set_o,type,
produc162892877563308318_set_o: ( vEBT_VEBT > nat > set_o ) > produc9072475918466114483BT_nat > set_o ).
thf(tp_produc1678900780639429121T_VEBT,type,
produc1678900780639429121T_VEBT: produc1531783533982839933T_VEBT > vEBT_VEBT ).
thf(tp_produc1703576794950452218t_real,type,
produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
thf(tp_produc1917071388513777916omplex,type,
produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
thf(tp_produc2011625207790711856et_int,type,
produc2011625207790711856et_int: ( nat > nat > set_int ) > product_prod_nat_nat > set_int ).
thf(tp_produc2081412961586463171T_VEBT,type,
produc2081412961586463171T_VEBT: produc1531783533982839933T_VEBT > int ).
thf(tp_produc2626176000494625587at_nat,type,
produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_produc2645369811736392845BT_nat,type,
produc2645369811736392845BT_nat: ( vEBT_VEBT > nat > produc9072475918466114483BT_nat ) > produc9072475918466114483BT_nat > produc9072475918466114483BT_nat ).
thf(tp_produc2676513652042109336d_enat,type,
produc2676513652042109336d_enat: ( nat > nat > extended_enat ) > product_prod_nat_nat > extended_enat ).
thf(tp_produc2694037385005941721st_nat,type,
produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).
thf(tp_produc27273713700761075at_nat,type,
produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_produc2761476792215241774st_nat,type,
produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
thf(tp_produc2982872950893828659T_VEBT,type,
produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
thf(tp_produc3179012173361985393al_int,type,
produc3179012173361985393al_int: real > int > produc8786904178792722361al_int ).
thf(tp_produc3181502643871035669al_nat,type,
produc3181502643871035669al_nat: real > nat > produc3741383161447143261al_nat ).
thf(tp_produc3209952032786966637at_nat,type,
produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
thf(tp_produc3213797794245857475at_nat,type,
produc3213797794245857475at_nat: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(tp_produc3329399203697025711T_VEBT,type,
produc3329399203697025711T_VEBT: int > vEBT_VEBT > produc1531783533982839933T_VEBT ).
thf(tp_produc351232539757196229T_VEBT,type,
produc351232539757196229T_VEBT: produc8243902056947475879T_VEBT > vEBT_VEBT ).
thf(tp_produc364263696895485585st_int,type,
produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
thf(tp_produc3668448655016342576t_real,type,
produc3668448655016342576t_real: ( nat > nat > set_real ) > product_prod_nat_nat > set_real ).
thf(tp_produc3897820843166775703T_VEBT,type,
produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT ).
thf(tp_produc4174022389229927035d_enat,type,
produc4174022389229927035d_enat: ( vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ) > produc7272778201969148633d_enat > produc7272778201969148633d_enat ).
thf(tp_produc4245557441103728435nt_int,type,
produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(tp_produc4257766111578684402_set_o,type,
produc4257766111578684402_set_o: ( int > int > set_o ) > product_prod_int_int > set_o ).
thf(tp_produc4370036051912753340t_real,type,
produc4370036051912753340t_real: ( vEBT_VEBT > nat > set_real ) > produc9072475918466114483BT_nat > set_real ).
thf(tp_produc4511245868158468465l_real,type,
produc4511245868158468465l_real: real > real > produc2422161461964618553l_real ).
thf(tp_produc4532415448927165861et_nat,type,
produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
thf(tp_produc457027306803732586at_nat,type,
produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
thf(tp_produc4601227381281490620et_int,type,
produc4601227381281490620et_int: ( vEBT_VEBT > nat > set_int ) > produc9072475918466114483BT_nat > set_int ).
thf(tp_produc4743750530478302277T_VEBT,type,
produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(tp_produc487386426758144856at_nat,type,
produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
thf(tp_produc4894985897562121079d_enat,type,
produc4894985897562121079d_enat: list_VEBT_VEBT > list_Extended_enat > list_P6356568628958627295d_enat ).
thf(tp_produc4947309494688390418_int_o,type,
produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(tp_produc522021263368680183d_enat,type,
produc522021263368680183d_enat: produc7272778201969148633d_enat > extended_enat ).
thf(tp_produc537772716801021591T_VEBT,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(tp_produc581526299967858633d_enat,type,
produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
thf(tp_produc5943733680697469783at_nat,type,
produc5943733680697469783at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > produc6392793444374437607at_nat ).
thf(tp_produc599794634098209291T_VEBT,type,
produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
thf(tp_produc59986286002894506_set_o,type,
produc59986286002894506_set_o: ( nat > nat > set_o ) > product_prod_nat_nat > set_o ).
thf(tp_produc6081775807080527818_nat_o,type,
produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(tp_produc6118266651365575811T_VEBT,type,
produc6118266651365575811T_VEBT: produc8243902056947475879T_VEBT > vEBT_VEBT ).
thf(tp_produc6161850002892822231at_nat,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(tp_produc6189476227299908564et_nat,type,
produc6189476227299908564et_nat: ( nat > nat > set_nat ) > product_prod_nat_nat > set_nat ).
thf(tp_produc6408287024330202629at_nat,type,
produc6408287024330202629at_nat: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(tp_produc6452406959799940328t_real,type,
produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
thf(tp_produc6590410687421337004_nat_o,type,
produc6590410687421337004_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc859450856879609959at_nat > $o ).
thf(tp_produc662631939642741121T_VEBT,type,
produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
thf(tp_produc6744312701629110395at_nat,type,
produc6744312701629110395at_nat: ( product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ) > produc859450856879609959at_nat > produc859450856879609959at_nat ).
thf(tp_produc6840382203811409530at_int,type,
produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
thf(tp_produc6842872674320459806at_nat,type,
produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(tp_produc6931449550656315951T_VEBT,type,
produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT ).
thf(tp_produc7156399406898700509T_VEBT,type,
produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(tp_produc7292646706713671643BT_int,type,
produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
thf(tp_produc7295137177222721919BT_nat,type,
produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
thf(tp_produc736041933913180425BT_int,type,
produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
thf(tp_produc738532404422230701BT_nat,type,
produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
thf(tp_produc7574032145190910526_nat_o,type,
produc7574032145190910526_nat_o: ( vEBT_VEBT > nat > $o ) > produc9072475918466114483BT_nat > $o ).
thf(tp_produc801115645435158769t_real,type,
produc801115645435158769t_real: int > real > produc679980390762269497t_real ).
thf(tp_produc8117437818029410057T_real,type,
produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real ).
thf(tp_produc8172668247895388509T_VEBT,type,
produc8172668247895388509T_VEBT: produc8025551001238799321T_VEBT > vEBT_VEBT ).
thf(tp_produc8308915547710359643BT_int,type,
produc8308915547710359643BT_int: produc4894624898956917775BT_int > int ).
thf(tp_produc8311406018219409919BT_nat,type,
produc8311406018219409919BT_nat: produc9072475918466114483BT_nat > nat ).
thf(tp_produc8575180428842422559T_VEBT,type,
produc8575180428842422559T_VEBT: produc8025551001238799321T_VEBT > nat ).
thf(tp_produc8711427728657393693BT_int,type,
produc8711427728657393693BT_int: produc4894624898956917775BT_int > vEBT_VEBT ).
thf(tp_produc8713918199166443969BT_nat,type,
produc8713918199166443969BT_nat: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(tp_produc8721562602347293563VEBT_o,type,
produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
thf(tp_produc8739625826339149834_nat_o,type,
produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(tp_produc8779078400790687328et_nat,type,
produc8779078400790687328et_nat: ( vEBT_VEBT > nat > set_nat ) > produc9072475918466114483BT_nat > set_nat ).
thf(tp_produc967593531271825845d_enat,type,
produc967593531271825845d_enat: produc7272778201969148633d_enat > vEBT_VEBT ).
thf(tp_product_Abs_unit,type,
product_Abs_unit: $o > product_unit ).
thf(tp_product_Pair_int_int,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(tp_product_Pair_int_nat,type,
product_Pair_int_nat: int > nat > product_prod_int_nat ).
thf(tp_product_Pair_int_o,type,
product_Pair_int_o: int > $o > product_prod_int_o ).
thf(tp_product_Pair_nat_int,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(tp_product_Pair_nat_nat,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(tp_product_Pair_o_int,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(tp_product_Pair_o_nat,type,
product_Pair_o_nat: $o > nat > product_prod_o_nat ).
thf(tp_product_Pair_o_o,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(tp_product_Pair_o_real,type,
product_Pair_o_real: $o > real > product_prod_o_real ).
thf(tp_product_Pair_real_o,type,
product_Pair_real_o: real > $o > product_prod_real_o ).
thf(tp_product_Rep_unit,type,
product_Rep_unit: product_unit > $o ).
thf(tp_product_fst_int_int,type,
product_fst_int_int: product_prod_int_int > int ).
thf(tp_product_fst_int_nat,type,
product_fst_int_nat: product_prod_int_nat > int ).
thf(tp_product_fst_nat_int,type,
product_fst_nat_int: product_prod_nat_int > nat ).
thf(tp_product_fst_nat_nat,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(tp_product_int_int,type,
product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
thf(tp_product_int_nat,type,
product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
thf(tp_product_nat_int,type,
product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
thf(tp_product_nat_nat,type,
product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
thf(tp_product_snd_int_int,type,
product_snd_int_int: product_prod_int_int > int ).
thf(tp_product_snd_int_nat,type,
product_snd_int_nat: product_prod_int_nat > nat ).
thf(tp_product_snd_nat_int,type,
product_snd_nat_int: product_prod_nat_int > int ).
thf(tp_product_snd_nat_nat,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(tp_quotie1194848508323700631at_int,type,
quotie1194848508323700631at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int ) > ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int > $o ) > $o ).
thf(tp_real_V1022390504157884413omplex,type,
real_V1022390504157884413omplex: complex > real ).
thf(tp_real_V1485227260804924795R_real,type,
real_V1485227260804924795R_real: real > real > real ).
thf(tp_real_V1803761363581548252l_real,type,
real_V1803761363581548252l_real: real > real ).
thf(tp_real_V2046097035970521341omplex,type,
real_V2046097035970521341omplex: real > complex > complex ).
thf(tp_real_V4546457046886955230omplex,type,
real_V4546457046886955230omplex: real > complex ).
thf(tp_real_V7735802525324610683m_real,type,
real_V7735802525324610683m_real: real > real ).
thf(tp_remdups_nat,type,
remdups_nat: list_nat > list_nat ).
thf(tp_remove1_VEBT_VEBT,type,
remove1_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_remove1_int,type,
remove1_int: int > list_int > list_int ).
thf(tp_remove1_nat,type,
remove1_nat: nat > list_nat > list_nat ).
thf(tp_remove1_o,type,
remove1_o: $o > list_o > list_o ).
thf(tp_remove1_real,type,
remove1_real: real > list_real > list_real ).
thf(tp_remove1_set_nat,type,
remove1_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(tp_rep_Integ,type,
rep_Integ: int > product_prod_nat_nat ).
thf(tp_replicate_VEBT_VEBT,type,
replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(tp_replicate_int,type,
replicate_int: nat > int > list_int ).
thf(tp_replicate_nat,type,
replicate_nat: nat > nat > list_nat ).
thf(tp_replicate_o,type,
replicate_o: nat > $o > list_o ).
thf(tp_replicate_real,type,
replicate_real: nat > real > list_real ).
thf(tp_replicate_set_nat,type,
replicate_set_nat: nat > set_nat > list_set_nat ).
thf(tp_ring_17405671764205052669omplex,type,
ring_17405671764205052669omplex: int > complex ).
thf(tp_ring_1_of_int_int,type,
ring_1_of_int_int: int > int ).
thf(tp_ring_1_of_int_real,type,
ring_1_of_int_real: int > real ).
thf(tp_root,type,
root: nat > real > real ).
thf(tp_rotate1_VEBT_VEBT,type,
rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_rotate1_int,type,
rotate1_int: list_int > list_int ).
thf(tp_rotate1_nat,type,
rotate1_nat: list_nat > list_nat ).
thf(tp_sK1_SY42,type,
sK1_SY42: vEBT_VEBT > nat ).
thf(tp_semila1623282765462674594er_nat,type,
semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(tp_semiri1314217659103216013at_int,type,
semiri1314217659103216013at_int: nat > int ).
thf(tp_semiri1316708129612266289at_nat,type,
semiri1316708129612266289at_nat: nat > nat ).
thf(tp_semiri1406184849735516958ct_int,type,
semiri1406184849735516958ct_int: nat > int ).
thf(tp_semiri1408675320244567234ct_nat,type,
semiri1408675320244567234ct_nat: nat > nat ).
thf(tp_semiri2265585572941072030t_real,type,
semiri2265585572941072030t_real: nat > real ).
thf(tp_semiri2816024913162550771omplex,type,
semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
thf(tp_semiri4216267220026989637d_enat,type,
semiri4216267220026989637d_enat: nat > extended_enat ).
thf(tp_semiri4449623510593786356d_enat,type,
semiri4449623510593786356d_enat: nat > extended_enat ).
thf(tp_semiri5044797733671781792omplex,type,
semiri5044797733671781792omplex: nat > complex ).
thf(tp_semiri5074537144036343181t_real,type,
semiri5074537144036343181t_real: nat > real ).
thf(tp_semiri7260567687927622513x_real,type,
semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
thf(tp_semiri8010041392384452111omplex,type,
semiri8010041392384452111omplex: nat > complex ).
thf(tp_semiri8420488043553186161ux_int,type,
semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
thf(tp_semiri8422978514062236437ux_nat,type,
semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
thf(tp_semiri8563196900006977889d_enat,type,
semiri8563196900006977889d_enat: ( extended_enat > extended_enat ) > nat > extended_enat > extended_enat ).
thf(tp_semiring_1_Nats_int,type,
semiring_1_Nats_int: set_int ).
thf(tp_set_Extended_enat2,type,
set_Extended_enat2: list_Extended_enat > set_Extended_enat ).
thf(tp_set_Pr1087130671499945274T_real,type,
set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real ).
thf(tp_set_Pr112895574167722958t_real,type,
set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real ).
thf(tp_set_Pr1470767568048878706at_int,type,
set_Pr1470767568048878706at_int: list_P3521021558325789923at_int > set_Pr7995236796853374141at_int ).
thf(tp_set_Pr2470121279949933262nt_int,type,
set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(tp_set_Pr2600826154070092190o_real,type,
set_Pr2600826154070092190o_real: list_P5232166724548748803o_real > set_Pr6573716822653411497o_real ).
thf(tp_set_Pr2828948584524939422_o_int,type,
set_Pr2828948584524939422_o_int: list_P3795440434834930179_o_int > set_Pr8834758594704517033_o_int ).
thf(tp_set_Pr2853735649769556538BT_int,type,
set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int ).
thf(tp_set_Pr3174298344852596722al_nat,type,
set_Pr3174298344852596722al_nat: list_P6834414599653733731al_nat > set_Pr3510011417693777981al_nat ).
thf(tp_set_Pr4712219556205076590d_enat,type,
set_Pr4712219556205076590d_enat: list_P6356568628958627295d_enat > set_Pr2457182780427864761d_enat ).
thf(tp_set_Pr5196769464307566348real_o,type,
set_Pr5196769464307566348real_o: list_P3595434254542482545real_o > set_Pr4936984352647145239real_o ).
thf(tp_set_Pr5518436109238095868at_nat,type,
set_Pr5518436109238095868at_nat: list_P8469869581646625389at_nat > set_Pr8693737435421807431at_nat ).
thf(tp_set_Pr5648618587558075414at_nat,type,
set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
thf(tp_set_Pr5984661752051438084T_VEBT,type,
set_Pr5984661752051438084T_VEBT: list_P5647936690300460905T_VEBT > set_Pr6167073792073659919T_VEBT ).
thf(tp_set_Pr5999470521830281550l_real,type,
set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real ).
thf(tp_set_Pr655345902815428824T_VEBT,type,
set_Pr655345902815428824T_VEBT: list_P7495141550334521929T_VEBT > set_Pr7543698050874017315T_VEBT ).
thf(tp_set_Pr6647972299459129970nt_nat,type,
set_Pr6647972299459129970nt_nat: list_P8198026277950538467nt_nat > set_Pr3448869479623346877nt_nat ).
thf(tp_set_Pr7006799604034136130_o_nat,type,
set_Pr7006799604034136130_o_nat: list_P6285523579766656935_o_nat > set_Pr2101469702781467981_o_nat ).
thf(tp_set_Pr7031586669278753246BT_nat,type,
set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat ).
thf(tp_set_Pr7708085864119495200VEBT_o,type,
set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o ).
thf(tp_set_Pr8219819362198175822al_int,type,
set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int ).
thf(tp_set_Pr8694291782656941196_int_o,type,
set_Pr8694291782656941196_int_o: list_P5087981734274514673_int_o > set_Pr903927857289325719_int_o ).
thf(tp_set_Pr8714266321650254504T_VEBT,type,
set_Pr8714266321650254504T_VEBT: list_P7524865323317820941T_VEBT > set_Pr8044002425091019955T_VEBT ).
thf(tp_set_Pr8897343066327330088T_VEBT,type,
set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT ).
thf(tp_set_Pr9040384385603167362et_nat,type,
set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat ).
thf(tp_set_Pr9182192707038809660T_VEBT,type,
set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT ).
thf(tp_set_Product_prod_o_o2,type,
set_Product_prod_o_o2: list_P4002435161011370285od_o_o > set_Product_prod_o_o ).
thf(tp_set_VEBT_VEBT2,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(tp_set_complex2,type,
set_complex2: list_complex > set_complex ).
thf(tp_set_fo1517530859248394432omplex,type,
set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
thf(tp_set_fo2538466533108834004d_enat,type,
set_fo2538466533108834004d_enat: ( nat > extended_enat > extended_enat ) > nat > nat > extended_enat > extended_enat ).
thf(tp_set_fo2581907887559384638at_int,type,
set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
thf(tp_set_fo2584398358068434914at_nat,type,
set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
thf(tp_set_fo3111899725591712190t_real,type,
set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
thf(tp_set_int2,type,
set_int2: list_int > set_int ).
thf(tp_set_list_VEBT_VEBT2,type,
set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
thf(tp_set_list_int2,type,
set_list_int2: list_list_int > set_list_int ).
thf(tp_set_list_nat2,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(tp_set_nat2,type,
set_nat2: list_nat > set_nat ).
thf(tp_set_num2,type,
set_num2: list_num > set_num ).
thf(tp_set_o2,type,
set_o2: list_o > set_o ).
thf(tp_set_or1210151606488870762an_nat,type,
set_or1210151606488870762an_nat: nat > set_nat ).
thf(tp_set_or1222579329274155063t_real,type,
set_or1222579329274155063t_real: real > real > set_real ).
thf(tp_set_or1266510415728281911st_int,type,
set_or1266510415728281911st_int: int > int > set_int ).
thf(tp_set_or1269000886237332187st_nat,type,
set_or1269000886237332187st_nat: nat > nat > set_nat ).
thf(tp_set_or1633881224788618240n_real,type,
set_or1633881224788618240n_real: real > real > set_real ).
thf(tp_set_or1773934645810362255er_nat,type,
set_or1773934645810362255er_nat: filter_nat > filter_nat > set_filter_nat ).
thf(tp_set_or1955772592623580779er_nat,type,
set_or1955772592623580779er_nat: filter_nat > filter_nat > set_filter_nat ).
thf(tp_set_or3540276404033026485et_nat,type,
set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat ).
thf(tp_set_or4236626031148496127et_nat,type,
set_or4236626031148496127et_nat: set_nat > set_set_nat ).
thf(tp_set_or4374356025156299511d_enat,type,
set_or4374356025156299511d_enat: extended_enat > extended_enat > set_Extended_enat ).
thf(tp_set_or4548717258645045905et_nat,type,
set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
thf(tp_set_or4662586982721622107an_int,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(tp_set_or4665077453230672383an_nat,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(tp_set_or5403411693681687835d_enat,type,
set_or5403411693681687835d_enat: extended_enat > extended_enat > set_Extended_enat ).
thf(tp_set_or5832277885323065728an_int,type,
set_or5832277885323065728an_int: int > int > set_int ).
thf(tp_set_or5834768355832116004an_nat,type,
set_or5834768355832116004an_nat: nat > nat > set_nat ).
thf(tp_set_or5984915006950818249n_real,type,
set_or5984915006950818249n_real: real > set_real ).
thf(tp_set_or6656581121297822940st_int,type,
set_or6656581121297822940st_int: int > int > set_int ).
thf(tp_set_or6659071591806873216st_nat,type,
set_or6659071591806873216st_nat: nat > nat > set_nat ).
thf(tp_set_or66887138388493659n_real,type,
set_or66887138388493659n_real: real > real > set_real ).
thf(tp_set_or7139685690850216873Than_o,type,
set_or7139685690850216873Than_o: $o > $o > set_o ).
thf(tp_set_or8332593352340944941d_enat,type,
set_or8332593352340944941d_enat: extended_enat > set_Extended_enat ).
thf(tp_set_or8419480210114673929d_enat,type,
set_or8419480210114673929d_enat: extended_enat > set_Extended_enat ).
thf(tp_set_or890127255671739683et_nat,type,
set_or890127255671739683et_nat: set_nat > set_set_nat ).
thf(tp_set_or8904488021354931149Most_o,type,
set_or8904488021354931149Most_o: $o > $o > set_o ).
thf(tp_set_or9144418160755794905er_nat,type,
set_or9144418160755794905er_nat: filter_nat > set_filter_nat ).
thf(tp_set_ord_atLeast_nat,type,
set_ord_atLeast_nat: nat > set_nat ).
thf(tp_set_ord_atMost_int,type,
set_ord_atMost_int: int > set_int ).
thf(tp_set_ord_atMost_nat,type,
set_ord_atMost_nat: nat > set_nat ).
thf(tp_set_ord_atMost_o,type,
set_ord_atMost_o: $o > set_o ).
thf(tp_set_ord_atMost_real,type,
set_ord_atMost_real: real > set_real ).
thf(tp_set_ord_lessThan_int,type,
set_ord_lessThan_int: int > set_int ).
thf(tp_set_ord_lessThan_nat,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(tp_set_ord_lessThan_o,type,
set_ord_lessThan_o: $o > set_o ).
thf(tp_set_real2,type,
set_real2: list_real > set_real ).
thf(tp_set_set_nat2,type,
set_set_nat2: list_set_nat > set_set_nat ).
thf(tp_sgn_sgn_complex,type,
sgn_sgn_complex: complex > complex ).
thf(tp_sgn_sgn_int,type,
sgn_sgn_int: int > int ).
thf(tp_sgn_sgn_real,type,
sgn_sgn_real: real > real ).
thf(tp_sin_coeff,type,
sin_coeff: nat > real ).
thf(tp_sin_complex,type,
sin_complex: complex > complex ).
thf(tp_sin_real,type,
sin_real: real > real ).
thf(tp_sinh_complex,type,
sinh_complex: complex > complex ).
thf(tp_sinh_real,type,
sinh_real: real > real ).
thf(tp_size_list_VEBT_VEBT,type,
size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
thf(tp_size_list_int,type,
size_list_int: ( int > nat ) > list_int > nat ).
thf(tp_size_list_nat,type,
size_list_nat: ( nat > nat ) > list_nat > nat ).
thf(tp_size_list_o,type,
size_list_o: ( $o > nat ) > list_o > nat ).
thf(tp_size_list_real,type,
size_list_real: ( real > nat ) > list_real > nat ).
thf(tp_size_list_set_nat,type,
size_list_set_nat: ( set_nat > nat ) > list_set_nat > nat ).
thf(tp_size_num,type,
size_num: num > nat ).
thf(tp_size_o8335143837870341156at_nat,type,
size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
thf(tp_size_option_num,type,
size_option_num: ( num > nat ) > option_num > nat ).
thf(tp_size_s170228958280169651at_nat,type,
size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
thf(tp_size_s2970893825323803983at_int,type,
size_s2970893825323803983at_int: list_P3521021558325789923at_int > nat ).
thf(tp_size_s3023201423986296836st_nat,type,
size_s3023201423986296836st_nat: list_list_nat > nat ).
thf(tp_size_s3254054031482475050et_nat,type,
size_s3254054031482475050et_nat: list_set_nat > nat ).
thf(tp_size_s3451745648224563538omplex,type,
size_s3451745648224563538omplex: list_complex > nat ).
thf(tp_size_s3661962791536183091BT_int,type,
size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
thf(tp_size_s3941691890525107288d_enat,type,
size_s3941691890525107288d_enat: list_Extended_enat > nat ).
thf(tp_size_s4762443039079500285T_VEBT,type,
size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
thf(tp_size_s5157815400016825771nt_int,type,
size_s5157815400016825771nt_int: list_P5707943133018811711nt_int > nat ).
thf(tp_size_s533118279054570080st_int,type,
size_s533118279054570080st_int: list_list_int > nat ).
thf(tp_size_s5460976970255530739at_nat,type,
size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
thf(tp_size_s6152045936467909847BT_nat,type,
size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
thf(tp_size_s6639371672096860321T_VEBT,type,
size_s6639371672096860321T_VEBT: list_P7524865323317820941T_VEBT > nat ).
thf(tp_size_s6755466524823107622T_VEBT,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(tp_size_s7466405169056248089T_VEBT,type,
size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
thf(tp_size_s7647898544948552527nt_nat,type,
size_s7647898544948552527nt_nat: list_P8198026277950538467nt_nat > nat ).
thf(tp_size_s8217280938318005548T_VEBT,type,
size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
thf(tp_size_size_VEBT_VEBT,type,
size_size_VEBT_VEBT: vEBT_VEBT > nat ).
thf(tp_size_size_list_int,type,
size_size_list_int: list_int > nat ).
thf(tp_size_size_list_nat,type,
size_size_list_nat: list_nat > nat ).
thf(tp_size_size_list_num,type,
size_size_list_num: list_num > nat ).
thf(tp_size_size_list_o,type,
size_size_list_o: list_o > nat ).
thf(tp_size_size_list_real,type,
size_size_list_real: list_real > nat ).
thf(tp_size_size_num,type,
size_size_num: num > nat ).
thf(tp_size_size_option_num,type,
size_size_option_num: option_num > nat ).
thf(tp_some_P7363390416028606310at_nat,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(tp_some_VEBT_VEBT,type,
some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT ).
thf(tp_some_int,type,
some_int: int > option_int ).
thf(tp_some_nat,type,
some_nat: nat > option_nat ).
thf(tp_some_num,type,
some_num: num > option_num ).
thf(tp_sorted_wrt_int,type,
sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
thf(tp_sorted_wrt_nat,type,
sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
thf(tp_strict1292158309912662752at_nat,type,
strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
thf(tp_subseqs_VEBT_VEBT,type,
subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
thf(tp_subseqs_int,type,
subseqs_int: list_int > list_list_int ).
thf(tp_subseqs_nat,type,
subseqs_nat: list_nat > list_list_nat ).
thf(tp_suc,type,
suc: nat > nat ).
thf(tp_suminf_complex,type,
suminf_complex: ( nat > complex ) > complex ).
thf(tp_suminf_int,type,
suminf_int: ( nat > int ) > int ).
thf(tp_suminf_nat,type,
suminf_nat: ( nat > nat ) > nat ).
thf(tp_suminf_real,type,
suminf_real: ( nat > real ) > real ).
thf(tp_summable_complex,type,
summable_complex: ( nat > complex ) > $o ).
thf(tp_summable_int,type,
summable_int: ( nat > int ) > $o ).
thf(tp_summable_nat,type,
summable_nat: ( nat > nat ) > $o ).
thf(tp_summable_real,type,
summable_real: ( nat > real ) > $o ).
thf(tp_summary,type,
summary: vEBT_VEBT ).
thf(tp_sums_complex,type,
sums_complex: ( nat > complex ) > complex > $o ).
thf(tp_sums_int,type,
sums_int: ( nat > int ) > int > $o ).
thf(tp_sums_nat,type,
sums_nat: ( nat > nat ) > nat > $o ).
thf(tp_sums_real,type,
sums_real: ( nat > real ) > real > $o ).
thf(tp_sup_sup_int,type,
sup_sup_int: int > int > int ).
thf(tp_sup_sup_nat,type,
sup_sup_nat: nat > nat > nat ).
thf(tp_sup_sup_set_nat,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(tp_take_VEBT_VEBT,type,
take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(tp_take_nat,type,
take_nat: nat > list_nat > list_nat ).
thf(tp_tan_complex,type,
tan_complex: complex > complex ).
thf(tp_tan_real,type,
tan_real: real > real ).
thf(tp_tanh_complex,type,
tanh_complex: complex > complex ).
thf(tp_tanh_real,type,
tanh_real: real > real ).
thf(tp_the_elem_int,type,
the_elem_int: set_int > int ).
thf(tp_the_elem_nat,type,
the_elem_nat: set_nat > nat ).
thf(tp_the_elem_o,type,
the_elem_o: set_o > $o ).
thf(tp_the_elem_real,type,
the_elem_real: set_real > real ).
thf(tp_the_in5290026491893676941l_real,type,
the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
thf(tp_times_7803423173614009249d_enat,type,
times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
thf(tp_times_times_complex,type,
times_times_complex: complex > complex > complex ).
thf(tp_times_times_int,type,
times_times_int: int > int > int ).
thf(tp_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(tp_times_times_real,type,
times_times_real: real > real > real ).
thf(tp_tl_nat,type,
tl_nat: list_nat > list_nat ).
thf(tp_top_top_set_char,type,
top_top_set_char: set_char ).
thf(tp_top_top_set_int,type,
top_top_set_int: set_int ).
thf(tp_top_top_set_nat,type,
top_top_set_nat: set_nat ).
thf(tp_top_top_set_o,type,
top_top_set_o: set_o ).
thf(tp_top_top_set_real,type,
top_top_set_real: set_real ).
thf(tp_topolo2177554685111907308n_real,type,
topolo2177554685111907308n_real: real > set_real > filter_real ).
thf(tp_topolo2815343760600316023s_real,type,
topolo2815343760600316023s_real: real > filter_real ).
thf(tp_topolo4055970368930404560y_real,type,
topolo4055970368930404560y_real: ( nat > real ) > $o ).
thf(tp_topolo4899668324122417113eq_int,type,
topolo4899668324122417113eq_int: ( nat > int ) > $o ).
thf(tp_topolo4902158794631467389eq_nat,type,
topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
thf(tp_topolo6427056007704750605er_nat,type,
topolo6427056007704750605er_nat: ( nat > filter_nat ) > $o ).
thf(tp_topolo6517432010174082258omplex,type,
topolo6517432010174082258omplex: ( nat > complex ) > $o ).
thf(tp_topolo6980174941875973593q_real,type,
topolo6980174941875973593q_real: ( nat > real ) > $o ).
thf(tp_topolo7278393974255667507et_nat,type,
topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
thf(tp_transi2905341329935302413cl_nat,type,
transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(tp_transi6264000038957366511cl_nat,type,
transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(tp_treeList,type,
treeList: list_VEBT_VEBT ).
thf(tp_type_d6188575255521822967unit_o,type,
type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).
thf(tp_uminus1482373934393186551omplex,type,
uminus1482373934393186551omplex: complex > complex ).
thf(tp_uminus1532241313380277803et_int,type,
uminus1532241313380277803et_int: set_int > set_int ).
thf(tp_uminus5710092332889474511et_nat,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(tp_uminus612125837232591019t_real,type,
uminus612125837232591019t_real: set_real > set_real ).
thf(tp_uminus613421341184616069et_nat,type,
uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
thf(tp_uminus_uminus_int,type,
uminus_uminus_int: int > int ).
thf(tp_uminus_uminus_real,type,
uminus_uminus_real: real > real ).
thf(tp_uminus_uminus_set_o,type,
uminus_uminus_set_o: set_o > set_o ).
thf(tp_union_int,type,
union_int: list_int > list_int > list_int ).
thf(tp_union_nat,type,
union_nat: list_nat > list_nat > list_nat ).
thf(tp_unique3096191561947761185of_nat,type,
unique3096191561947761185of_nat: nat > char ).
thf(tp_unique5024387138958732305ep_int,type,
unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
thf(tp_unique5026877609467782581ep_nat,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(tp_unique5052692396658037445od_int,type,
unique5052692396658037445od_int: num > num > product_prod_int_int ).
thf(tp_unique5055182867167087721od_nat,type,
unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
thf(tp_unique6319869463603278526ux_int,type,
unique6319869463603278526ux_int: product_prod_int_int > $o ).
thf(tp_unique6322359934112328802ux_nat,type,
unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
thf(tp_upt,type,
upt: nat > nat > list_nat ).
thf(tp_upto,type,
upto: int > int > list_int ).
thf(tp_upto_aux,type,
upto_aux: int > int > list_int > list_int ).
thf(tp_upto_rel,type,
upto_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(tp_vEBT_Leaf,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
thf(tp_vEBT_Node,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(tp_vEBT_V312737461966249ad_rel,type,
vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
thf(tp_vEBT_V4351362008482014158ma_rel,type,
vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(tp_vEBT_V5719532721284313246member,type,
vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_V5765760719290551771er_rel,type,
vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(tp_vEBT_V5917875025757280293ildren,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
thf(tp_vEBT_V8194947554948674370ptions,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_VEBT_bit_concat,type,
vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
thf(tp_vEBT_VEBT_elim_dead,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(tp_vEBT_VEBT_high,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(tp_vEBT_VEBT_low,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(tp_vEBT_VEBT_membermima,type,
vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_VEBT_minNull,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(tp_vEBT_VEBT_set_vebt,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(tp_vEBT_VEBT_valid,type,
vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_VEBT_valid_rel,type,
vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(tp_vEBT_invar_vebt,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_set_vebt,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(tp_vEBT_size_VEBT,type,
vEBT_size_VEBT: vEBT_VEBT > nat ).
thf(tp_vEBT_v4011308405150292612up_rel,type,
vEBT_v4011308405150292612up_rel: nat > nat > $o ).
thf(tp_vEBT_vebt_buildup,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(tp_vEBT_vebt_insert,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(tp_vEBT_vebt_insert_rel,type,
vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(tp_vEBT_vebt_member,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(tp_vEBT_vebt_member_rel,type,
vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(tp_vimage_nat_nat,type,
vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(tp_wf_int,type,
wf_int: set_Pr958786334691620121nt_int > $o ).
thf(tp_wf_nat,type,
wf_nat: set_Pr1261947904930325089at_nat > $o ).
thf(tp_xa,type,
xa: nat ).
thf(tp_zero_n1046097342994218471d_enat,type,
zero_n1046097342994218471d_enat: $o > extended_enat ).
thf(tp_zero_n1201886186963655149omplex,type,
zero_n1201886186963655149omplex: $o > complex ).
thf(tp_zero_n2684676970156552555ol_int,type,
zero_n2684676970156552555ol_int: $o > int ).
thf(tp_zero_n2687167440665602831ol_nat,type,
zero_n2687167440665602831ol_nat: $o > nat ).
thf(tp_zero_n3304061248610475627l_real,type,
zero_n3304061248610475627l_real: $o > real ).
thf(tp_zero_z5237406670263579293d_enat,type,
zero_z5237406670263579293d_enat: extended_enat ).
thf(tp_zero_zero_complex,type,
zero_zero_complex: complex ).
thf(tp_zero_zero_int,type,
zero_zero_int: int ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(tp_zip_Pr4664179122662387191at_nat,type,
zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
thf(tp_zip_VE537291747668921783T_VEBT,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(tp_zip_VE7205001627739651817d_enat,type,
zip_VE7205001627739651817d_enat: list_VEBT_VEBT > list_Extended_enat > list_P6356568628958627295d_enat ).
thf(tp_zip_VEBT_VEBT_int,type,
zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
thf(tp_zip_VEBT_VEBT_nat,type,
zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
thf(tp_zip_VEBT_VEBT_o,type,
zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
thf(tp_zip_VEBT_VEBT_real,type,
zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
thf(tp_zip_int_VEBT_VEBT,type,
zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
thf(tp_zip_int_int,type,
zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
thf(tp_zip_int_nat,type,
zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
thf(tp_zip_int_o,type,
zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
thf(tp_zip_int_real,type,
zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
thf(tp_zip_nat_VEBT_VEBT,type,
zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(tp_zip_nat_int,type,
zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
thf(tp_zip_nat_nat,type,
zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
thf(tp_zip_o_VEBT_VEBT,type,
zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
thf(tp_zip_o_int,type,
zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
thf(tp_zip_o_nat,type,
zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
thf(tp_zip_o_o,type,
zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
thf(tp_zip_o_real,type,
zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
thf(tp_zip_real_VEBT_VEBT,type,
zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
thf(tp_zip_real_int,type,
zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
thf(tp_zip_real_nat,type,
zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
thf(tp_zip_real_o,type,
zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
thf(tp_zip_real_real,type,
zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
thf(tp_zip_set_nat_set_nat,type,
zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
thf(3,axiom,
! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T) ).
thf(7707,axiom,
! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
= ( size_s6755466524823107622T_VEBT @ Xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1410_length__list__update) ).
thf(9096,axiom,
! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X4: vEBT_VEBT] :
( ( I != I2 )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I2 @ X4 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X4 ) @ I @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_list__update__swap) ).
thf(9099,axiom,
! [T: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ T )
=> ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_not__min__Null__member) ).
thf(9100,axiom,
! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
= ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__update__overwrite) ).
thf(9101,axiom,
~ ( vEBT_V8194947554948674370ptions @ summary @ i ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__C163_C) ).
thf(9102,axiom,
! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
( ( I != J )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
= ( nth_VEBT_VEBT @ Xs @ J ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nth__list__update__neq) ).
thf(9105,axiom,
! [Xs: list_VEBT_VEBT,I: nat] :
( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
= Xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_list__update__id) ).
thf(9108,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(9109,axiom,
~ ? [X_1: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C161_C) ).
thf(9110,axiom,
( vEBT_V5917875025757280293ildren
= ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__children__def) ).
thf(9111,axiom,
vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_tc) ).
thf(9112,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(9113,axiom,
~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__C162_C) ).
thf(9114,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(9115,axiom,
! [X: nat,D: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bit__split__inv) ).
thf(9116,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(9117,axiom,
( i
= ( vEBT_VEBT_high @ xa @ na ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
thf(9118,conjecture,
? [Y4: 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 ) @ Y4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(9119,negated_conjecture,
( ( ? [Y4: 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 ) @ Y4 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[9118]) ).
thf(9120,plain,
( ( ? [Y4: 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 ) @ Y4 ) )
= $false ),
inference(unfold_def,[status(thm)],[9119]) ).
thf(9121,plain,
( ( ! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(9122,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
= ( size_s6755466524823107622T_VEBT @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7707]) ).
thf(9123,plain,
( ( ! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X4: vEBT_VEBT] :
( ( I != I2 )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I2 @ X4 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X4 ) @ I @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9096]) ).
thf(9124,plain,
( ( ! [T: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ T )
=> ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9099]) ).
thf(9125,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
= ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9100]) ).
thf(9126,plain,
( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ i ) )
= $true ),
inference(unfold_def,[status(thm)],[9101]) ).
thf(9127,plain,
( ( ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
( ( I != J )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
= ( nth_VEBT_VEBT @ Xs @ J ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9102]) ).
thf(9128,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat] :
( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
= Xs ) )
= $true ),
inference(unfold_def,[status(thm)],[9105]) ).
thf(9129,plain,
( ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na )
= $true ),
inference(unfold_def,[status(thm)],[9108]) ).
thf(9130,plain,
( ( ~ ? [X_1: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9109]) ).
thf(9131,plain,
( ( vEBT_V5917875025757280293ildren
= ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9110]) ).
thf(9132,plain,
( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9111]) ).
thf(9133,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9112]) ).
thf(9134,plain,
( ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9113]) ).
thf(9135,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9114]) ).
thf(9136,plain,
( ( ! [X: nat,D: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9115]) ).
thf(9137,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 ) )
= $true ),
inference(unfold_def,[status(thm)],[9116]) ).
thf(9138,plain,
( ( i
= ( vEBT_VEBT_high @ xa @ na ) )
= $true ),
inference(unfold_def,[status(thm)],[9117]) ).
thf(9139,plain,
( ( ~ ? [Y4: 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 ) @ Y4 ) )
= $true ),
inference(polarity_switch,[status(thm)],[9120]) ).
thf(9140,plain,
( ( i
= ( vEBT_VEBT_high @ xa @ na ) )
= $true ),
inference(copy,[status(thm)],[9138]) ).
thf(9141,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 ) )
= $true ),
inference(copy,[status(thm)],[9137]) ).
thf(9142,plain,
( ( ! [X: nat,D: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
= X ) )
= $true ),
inference(copy,[status(thm)],[9136]) ).
thf(9143,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 ) ) )
= $true ),
inference(copy,[status(thm)],[9135]) ).
thf(9144,plain,
( ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ) )
= $true ),
inference(copy,[status(thm)],[9134]) ).
thf(9145,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 ) ) )
= $true ),
inference(copy,[status(thm)],[9133]) ).
thf(9146,plain,
( ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) )
= $true ),
inference(copy,[status(thm)],[9132]) ).
thf(9147,plain,
( ( vEBT_V5917875025757280293ildren
= ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[9131]) ).
thf(9148,plain,
( ( ~ ? [X_1: nat] : ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X_1 ) )
= $true ),
inference(copy,[status(thm)],[9130]) ).
thf(9149,plain,
( ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na )
= $true ),
inference(copy,[status(thm)],[9129]) ).
thf(9150,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat] :
( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
= Xs ) )
= $true ),
inference(copy,[status(thm)],[9128]) ).
thf(9151,plain,
( ( ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
( ( I != J )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
= ( nth_VEBT_VEBT @ Xs @ J ) ) ) )
= $true ),
inference(copy,[status(thm)],[9127]) ).
thf(9152,plain,
( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ i ) )
= $true ),
inference(copy,[status(thm)],[9126]) ).
thf(9153,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
= ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[9125]) ).
thf(9154,plain,
( ( ! [T: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ T )
=> ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) )
= $true ),
inference(copy,[status(thm)],[9124]) ).
thf(9155,plain,
( ( ! [I: nat,I2: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X4: vEBT_VEBT] :
( ( I != I2 )
=> ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I2 @ X4 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X4 ) @ I @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[9123]) ).
thf(9156,plain,
( ( ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
= ( size_s6755466524823107622T_VEBT @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[9122]) ).
thf(9157,plain,
( ( ! [P2: $o] :
( ( P2 = $true )
| ( P2 = $false ) ) )
= $true ),
inference(copy,[status(thm)],[9121]) ).
thf(9158,plain,
( ( ~ ? [Y4: 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 ) @ Y4 ) )
= $true ),
inference(copy,[status(thm)],[9139]) ).
thf(9159,plain,
( ( ! [SX0: nat,SX1: nat,SX2: list_VEBT_VEBT,SX3: vEBT_VEBT,SX4: vEBT_VEBT] :
( ~ ( ( SX0 != SX1 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX0 @ SX3 ) @ SX1 @ SX4 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX1 @ SX4 ) @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9155]) ).
thf(9160,plain,
( ( ~ ~ ! [SX0: 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 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9158]) ).
thf(9161,plain,
( ( ! [SX0: vEBT_VEBT] :
( ~ ~ ( vEBT_VEBT_minNull @ SX0 )
| ~ ! [SX1: nat] :
~ ( vEBT_V8194947554948674370ptions @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9154]) ).
thf(9162,plain,
( ( ~ ~ ! [SX0: nat] :
~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9148]) ).
thf(9163,plain,
( ( ! [SX0: nat,SX1: nat,SX2: list_VEBT_VEBT,SX3: vEBT_VEBT] :
( ~ ( ( SX0 != SX1 ) )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX0 @ SX3 ) @ SX1 )
= ( nth_VEBT_VEBT @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9151]) ).
thf(9164,plain,
( ( ~ ~ ! [SX0: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9144]) ).
thf(9165,plain,
! [SV1: nat] :
( ( ! [SY29: nat] :
( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ SV1 @ SY29 ) @ ( vEBT_VEBT_low @ SV1 @ SY29 ) @ SY29 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9142]) ).
thf(9166,plain,
( ( ! [SV2: nat] :
( ( vEBT_V5917875025757280293ildren @ SV2 )
= ( ^ [SY30: list_VEBT_VEBT,SY31: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SY30 @ ( vEBT_VEBT_high @ SY31 @ SV2 ) ) @ ( vEBT_VEBT_low @ SY31 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9147]) ).
thf(9167,plain,
( ( vEBT_V5917875025757280293ildren
= ( ^ [N: nat,TreeList: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ N ) ) @ ( vEBT_VEBT_low @ X2 @ N ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9147]) ).
thf(9168,plain,
! [SV3: list_VEBT_VEBT] :
( ( ! [SY32: nat] :
( ( list_u1324408373059187874T_VEBT @ SV3 @ SY32 @ ( nth_VEBT_VEBT @ SV3 @ SY32 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9150]) ).
thf(9169,plain,
( ( vEBT_V8194947554948674370ptions @ summary @ i )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9152]) ).
thf(9170,plain,
! [SV4: list_VEBT_VEBT] :
( ( ! [SY33: nat,SY34: vEBT_VEBT,SY35: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV4 @ SY33 @ SY34 ) @ SY33 @ SY35 )
= ( list_u1324408373059187874T_VEBT @ SV4 @ SY33 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9153]) ).
thf(9171,plain,
! [SV5: list_VEBT_VEBT] :
( ( ! [SY36: nat,SY37: vEBT_VEBT] :
( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV5 @ SY36 @ SY37 ) )
= ( size_s6755466524823107622T_VEBT @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9156]) ).
thf(9172,plain,
! [SV6: $o] :
( ( ( SV6 = $true )
| ( SV6 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9157]) ).
thf(9173,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9157]) ).
thf(9174,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9157]) ).
thf(9175,plain,
! [SV7: nat] :
( ( ! [SY38: nat,SY39: list_VEBT_VEBT,SY40: vEBT_VEBT,SY41: vEBT_VEBT] :
( ~ ( ( SV7 != SY38 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY39 @ SV7 @ SY40 ) @ SY38 @ SY41 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY39 @ SY38 @ SY41 ) @ SV7 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9159]) ).
thf(9176,plain,
( ( ~ ! [SX0: 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 ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9160]) ).
thf(9177,plain,
! [SV8: vEBT_VEBT] :
( ( ~ ~ ( vEBT_VEBT_minNull @ SV8 )
| ~ ! [SY42: nat] :
~ ( vEBT_V8194947554948674370ptions @ SV8 @ SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9161]) ).
thf(9178,plain,
( ( ~ ! [SX0: nat] :
~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9162]) ).
thf(9179,plain,
! [SV9: nat] :
( ( ! [SY43: nat,SY44: list_VEBT_VEBT,SY45: vEBT_VEBT] :
( ~ ( ( SV9 != SY43 ) )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SY44 @ SV9 @ SY45 ) @ SY43 )
= ( nth_VEBT_VEBT @ SY44 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9163]) ).
thf(9180,plain,
( ( ~ ! [SX0: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9164]) ).
thf(9181,plain,
! [SV10: nat,SV1: nat] :
( ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ SV1 @ SV10 ) @ ( vEBT_VEBT_low @ SV1 @ SV10 ) @ SV10 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9165]) ).
thf(9182,plain,
! [SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 )
= ( ^ [SY46: list_VEBT_VEBT,SY47: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SY46 @ ( vEBT_VEBT_high @ SY47 @ SV11 ) ) @ ( vEBT_VEBT_low @ SY47 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9166]) ).
thf(9183,plain,
! [SV12: nat,SV3: list_VEBT_VEBT] :
( ( ( list_u1324408373059187874T_VEBT @ SV3 @ SV12 @ ( nth_VEBT_VEBT @ SV3 @ SV12 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9168]) ).
thf(9184,plain,
! [SV13: nat,SV4: list_VEBT_VEBT] :
( ( ! [SY48: vEBT_VEBT,SY49: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SY48 ) @ SV13 @ SY49 )
= ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9170]) ).
thf(9185,plain,
! [SV14: nat,SV5: list_VEBT_VEBT] :
( ( ! [SY50: vEBT_VEBT] :
( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV5 @ SV14 @ SY50 ) )
= ( size_s6755466524823107622T_VEBT @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9171]) ).
thf(9186,plain,
! [SV6: $o] :
( ( ( SV6 = $true )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9172]) ).
thf(9187,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9173]) ).
thf(9188,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9174]) ).
thf(9189,plain,
! [SV15: nat,SV7: nat] :
( ( ! [SY51: list_VEBT_VEBT,SY52: vEBT_VEBT,SY53: vEBT_VEBT] :
( ~ ( ( SV7 != SV15 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY51 @ SV7 @ SY52 ) @ SV15 @ SY53 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY51 @ SV15 @ SY53 ) @ SV7 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9175]) ).
thf(9190,plain,
( ( ! [SX0: 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 ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9176]) ).
thf(9191,plain,
! [SV8: vEBT_VEBT] :
( ( ( ~ ~ ( vEBT_VEBT_minNull @ SV8 ) )
= $true )
| ( ( ~ ! [SY42: nat] :
~ ( vEBT_V8194947554948674370ptions @ SV8 @ SY42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9177]) ).
thf(9192,plain,
( ( ! [SX0: nat] :
~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9178]) ).
thf(9193,plain,
! [SV16: nat,SV9: nat] :
( ( ! [SY54: list_VEBT_VEBT,SY55: vEBT_VEBT] :
( ~ ( ( SV9 != SV16 ) )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SY54 @ SV9 @ SY55 ) @ SV16 )
= ( nth_VEBT_VEBT @ SY54 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9179]) ).
thf(9194,plain,
( ( ! [SX0: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9180]) ).
thf(9195,plain,
! [SV11: nat] :
( ( ! [SV17: list_VEBT_VEBT] :
( ( vEBT_V5917875025757280293ildren @ SV11 @ SV17 )
= ( ^ [SY56: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV17 @ ( vEBT_VEBT_high @ SY56 @ SV11 ) ) @ ( vEBT_VEBT_low @ SY56 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9182]) ).
thf(9196,plain,
! [SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 )
= ( ^ [SY46: list_VEBT_VEBT,SY47: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SY46 @ ( vEBT_VEBT_high @ SY47 @ SV11 ) ) @ ( vEBT_VEBT_low @ SY47 @ SV11 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9182]) ).
thf(9197,plain,
! [SV18: vEBT_VEBT,SV13: nat,SV4: list_VEBT_VEBT] :
( ( ! [SY57: vEBT_VEBT] :
( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SV18 ) @ SV13 @ SY57 )
= ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9184]) ).
thf(9198,plain,
! [SV19: vEBT_VEBT,SV14: nat,SV5: list_VEBT_VEBT] :
( ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV5 @ SV14 @ SV19 ) )
= ( size_s6755466524823107622T_VEBT @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9185]) ).
thf(9199,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $true )
| ~ ( ~ SV6
| ~ $true ) )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9186]) ).
thf(9200,plain,
! [SV6: $o] :
( ( ( SV6 = $true )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9186]) ).
thf(9201,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9187]) ).
thf(9202,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9187]) ).
thf(9203,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9188]) ).
thf(9204,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9188]) ).
thf(9205,plain,
! [SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ! [SY58: vEBT_VEBT,SY59: vEBT_VEBT] :
( ~ ( ( SV7 != SV15 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SY58 ) @ SV15 @ SY59 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SY59 ) @ SV7 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9189]) ).
thf(9206,plain,
! [SV21: 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 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9190]) ).
thf(9207,plain,
! [SV8: vEBT_VEBT] :
( ( ( ~ ( vEBT_VEBT_minNull @ SV8 ) )
= $false )
| ( ( ~ ! [SY42: nat] :
~ ( vEBT_V8194947554948674370ptions @ SV8 @ SY42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9191]) ).
thf(9208,plain,
! [SV22: nat] :
( ( ~ ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9192]) ).
thf(9209,plain,
! [SV23: list_VEBT_VEBT,SV16: nat,SV9: nat] :
( ( ! [SY60: vEBT_VEBT] :
( ~ ( ( SV9 != SV16 ) )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV23 @ SV9 @ SY60 ) @ SV16 )
= ( nth_VEBT_VEBT @ SV23 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9193]) ).
thf(9210,plain,
! [SV24: nat] :
( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9194]) ).
thf(9211,plain,
! [SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 )
= ( ^ [SY61: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SY61 @ SV11 ) ) @ ( vEBT_VEBT_low @ SY61 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9195]) ).
thf(9212,plain,
! [SV26: vEBT_VEBT,SV18: vEBT_VEBT,SV13: nat,SV4: list_VEBT_VEBT] :
( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SV18 ) @ SV13 @ SV26 )
= ( list_u1324408373059187874T_VEBT @ SV4 @ SV13 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9197]) ).
thf(9213,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $true ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $true ) )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9199]) ).
thf(9214,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false )
| ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9200]) ).
thf(9215,plain,
! [SV6: $o] :
( ( ( SV6 = $false )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9200]) ).
thf(9216,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9201]) ).
thf(9217,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9202]) ).
thf(9218,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9202]) ).
thf(9219,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9203]) ).
thf(9220,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9204]) ).
thf(9221,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9204]) ).
thf(9222,plain,
! [SV27: vEBT_VEBT,SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ! [SY62: vEBT_VEBT] :
( ~ ( ( SV7 != SV15 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SV27 ) @ SV15 @ SY62 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SY62 ) @ SV7 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9205]) ).
thf(9223,plain,
! [SV21: 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 ) @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9206]) ).
thf(9224,plain,
! [SV8: vEBT_VEBT] :
( ( ( vEBT_VEBT_minNull @ SV8 )
= $true )
| ( ( ~ ! [SY42: nat] :
~ ( vEBT_V8194947554948674370ptions @ SV8 @ SY42 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9207]) ).
thf(9225,plain,
! [SV22: nat] :
( ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SV22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9208]) ).
thf(9226,plain,
! [SV28: vEBT_VEBT,SV23: list_VEBT_VEBT,SV16: nat,SV9: nat] :
( ( ~ ( ( SV9 != SV16 ) )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV23 @ SV9 @ SV28 ) @ SV16 )
= ( nth_VEBT_VEBT @ SV23 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9209]) ).
thf(9227,plain,
! [SV24: nat] :
( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ SV24 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9210]) ).
thf(9228,plain,
! [SV25: list_VEBT_VEBT,SV11: nat] :
( ( ! [SV29: nat] :
( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV29 )
= ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV29 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV29 @ SV11 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9211]) ).
thf(9229,plain,
! [SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 )
= ( ^ [SY61: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SY61 @ SV11 ) ) @ ( vEBT_VEBT_low @ SY61 @ SV11 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9211]) ).
thf(9230,plain,
! [SV6: $o] :
( ( ( SV6
| $true )
= $false )
| ( ( ~ ( ~ SV6
| ~ $true ) )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9213]) ).
thf(9231,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9214]) ).
thf(9232,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9216]) ).
thf(9233,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9217]) ).
thf(9234,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9219]) ).
thf(9235,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9220]) ).
thf(9236,plain,
! [SV30: vEBT_VEBT,SV27: vEBT_VEBT,SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ~ ( ( SV7 != SV15 ) )
| ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SV27 ) @ SV15 @ SV30 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SV30 ) @ SV7 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9222]) ).
thf(9237,plain,
! [SV8: vEBT_VEBT] :
( ( ( ! [SY42: nat] :
~ ( vEBT_V8194947554948674370ptions @ SV8 @ SY42 ) )
= $false )
| ( ( vEBT_VEBT_minNull @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9224]) ).
thf(9238,plain,
! [SV28: vEBT_VEBT,SV23: list_VEBT_VEBT,SV16: nat,SV9: nat] :
( ( ( ~ ( ( SV9 != SV16 ) ) )
= $true )
| ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV23 @ SV9 @ SV28 ) @ SV16 )
= ( nth_VEBT_VEBT @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9226]) ).
thf(9239,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9228]) ).
thf(9240,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $true ) )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9230]) ).
thf(9241,plain,
! [SV6: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV6
| ~ $true ) )
= $true )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9230]) ).
thf(9242,plain,
! [SV6: $o] :
( ( ( SV6
| $false )
= $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9231]) ).
thf(9243,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9232]) ).
thf(9244,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9232]) ).
thf(9245,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9233]) ).
thf(9246,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9234]) ).
thf(9247,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9234]) ).
thf(9248,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9235]) ).
thf(9249,plain,
! [SV30: vEBT_VEBT,SV27: vEBT_VEBT,SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ( ~ ( ( SV7 != SV15 ) ) )
= $true )
| ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SV27 ) @ SV15 @ SV30 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SV30 ) @ SV7 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9236]) ).
thf(9250,plain,
! [SV8: vEBT_VEBT] :
( ( ( ~ ( vEBT_V8194947554948674370ptions @ SV8 @ ( sK1_SY42 @ SV8 ) ) )
= $false )
| ( ( vEBT_VEBT_minNull @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[9237]) ).
thf(9251,plain,
! [SV28: vEBT_VEBT,SV23: list_VEBT_VEBT,SV16: nat,SV9: nat] :
( ( ( SV9 != SV16 )
= $false )
| ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV23 @ SV9 @ SV28 ) @ SV16 )
= ( nth_VEBT_VEBT @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9238]) ).
thf(9252,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ~ ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
| ~ ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9239]) ).
thf(9253,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[9239]) ).
thf(9254,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $true )
= $false )
| ( SV6 = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9240]) ).
thf(9255,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9241]) ).
thf(9256,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9242]) ).
thf(9257,plain,
! [SV6: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9242]) ).
thf(9258,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9243]) ).
thf(9259,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9244]) ).
thf(9260,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9245]) ).
thf(9261,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9245]) ).
thf(9262,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9246]) ).
thf(9263,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9247]) ).
thf(9264,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9248]) ).
thf(9265,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9248]) ).
thf(9266,plain,
! [SV30: vEBT_VEBT,SV27: vEBT_VEBT,SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ( SV7 != SV15 )
= $false )
| ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SV27 ) @ SV15 @ SV30 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SV30 ) @ SV7 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9249]) ).
thf(9267,plain,
! [SV8: vEBT_VEBT] :
( ( ( vEBT_V8194947554948674370ptions @ SV8 @ ( sK1_SY42 @ SV8 ) )
= $true )
| ( ( vEBT_VEBT_minNull @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9250]) ).
thf(9268,plain,
! [SV28: vEBT_VEBT,SV23: list_VEBT_VEBT,SV16: nat,SV9: nat] :
( ( ( SV9 = SV16 )
= $true )
| ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV23 @ SV9 @ SV28 ) @ SV16 )
= ( nth_VEBT_VEBT @ SV23 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9251]) ).
thf(9269,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ~ ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true )
| ( ( ~ ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9252]) ).
thf(9270,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9254]) ).
thf(9271,plain,
! [SV6: $o] :
( ( ( ~ $true ) = $false )
| ( SV6 = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9254]) ).
thf(9272,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $true = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9255]) ).
thf(9273,plain,
! [SV6: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9255]) ).
thf(9274,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( SV6 = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9256]) ).
thf(9275,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9257]) ).
thf(9276,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9258]) ).
thf(9277,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9258]) ).
thf(9278,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9259]) ).
thf(9279,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9259]) ).
thf(9280,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9260]) ).
thf(9281,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9261]) ).
thf(9282,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9262]) ).
thf(9283,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9262]) ).
thf(9284,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9263]) ).
thf(9285,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9263]) ).
thf(9286,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9264]) ).
thf(9287,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9265]) ).
thf(9288,plain,
! [SV30: vEBT_VEBT,SV27: vEBT_VEBT,SV20: list_VEBT_VEBT,SV15: nat,SV7: nat] :
( ( ( SV7 = SV15 )
= $true )
| ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV7 @ SV27 ) @ SV15 @ SV30 )
= ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV20 @ SV15 @ SV30 ) @ SV7 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9266]) ).
thf(9289,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[9269]) ).
thf(9290,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9270]) ).
thf(9291,plain,
! [SV6: $o] :
( ( $true = $true )
| ( SV6 = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9271]) ).
thf(9292,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $true = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9272]) ).
thf(9293,plain,
! [SV6: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV6 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9273]) ).
thf(9294,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9274]) ).
thf(9295,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( SV6 = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9274]) ).
thf(9296,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $false = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9275]) ).
thf(9297,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9275]) ).
thf(9298,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9276]) ).
thf(9299,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9277]) ).
thf(9300,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9278]) ).
thf(9301,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9279]) ).
thf(9302,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9280]) ).
thf(9303,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9280]) ).
thf(9304,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9281]) ).
thf(9305,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9281]) ).
thf(9306,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9282]) ).
thf(9307,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9283]) ).
thf(9308,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9284]) ).
thf(9309,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9285]) ).
thf(9310,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9286]) ).
thf(9311,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9286]) ).
thf(9312,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9287]) ).
thf(9313,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9287]) ).
thf(9314,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false )
| ( ( ~ ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9289]) ).
thf(9315,plain,
! [SV11: nat,SV31: nat,SV25: list_VEBT_VEBT] :
( ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[9289]) ).
thf(9316,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false )
| ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9290]) ).
thf(9317,plain,
! [SV6: $o] :
( ( ( SV6 = $false )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9290]) ).
thf(9318,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false )
| ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9291]) ).
thf(9319,plain,
! [SV6: $o] :
( ( ( SV6 = $false )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9291]) ).
thf(9320,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false )
| ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9292]) ).
thf(9321,plain,
! [SV6: $o] :
( ( ( SV6 = $false )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9292]) ).
thf(9322,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false )
| ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9293]) ).
thf(9323,plain,
! [SV6: $o] :
( ( ( SV6 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9293]) ).
thf(9324,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9294]) ).
thf(9325,plain,
! [SV6: $o] :
( ( $false = $true )
| ( SV6 = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9295]) ).
thf(9326,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $false = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9296]) ).
thf(9327,plain,
! [SV6: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV6 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9297]) ).
thf(9328,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9298]) ).
thf(9329,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9298]) ).
thf(9330,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9299]) ).
thf(9331,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9299]) ).
thf(9332,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9300]) ).
thf(9333,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9300]) ).
thf(9334,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9301]) ).
thf(9335,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9301]) ).
thf(9336,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9302]) ).
thf(9337,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9303]) ).
thf(9338,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9304]) ).
thf(9339,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9305]) ).
thf(9340,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9306]) ).
thf(9341,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9306]) ).
thf(9342,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9307]) ).
thf(9343,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9307]) ).
thf(9344,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9308]) ).
thf(9345,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9308]) ).
thf(9346,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9309]) ).
thf(9347,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[9309]) ).
thf(9348,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9310]) ).
thf(9349,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9311]) ).
thf(9350,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9312]) ).
thf(9351,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[9313]) ).
thf(9352,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $false )
| ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[9314]) ).
thf(9353,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
| ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $false )
| ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[9315]) ).
thf(9354,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9316]) ).
thf(9355,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9318]) ).
thf(9356,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9320]) ).
thf(9357,plain,
! [SV6: $o] :
( ( ( ~ ( SV6
| $false ) )
= $true )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9322]) ).
thf(9358,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9328]) ).
thf(9359,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9330]) ).
thf(9360,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9332]) ).
thf(9361,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9334]) ).
thf(9362,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9340]) ).
thf(9363,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9342]) ).
thf(9364,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9344]) ).
thf(9365,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[9346]) ).
thf(9366,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 ) )
= $false )
| ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[9352]) ).
thf(9367,plain,
! [SV11: nat,SV31: nat,SV25: list_VEBT_VEBT] :
( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $false )
| ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[9352]) ).
thf(9368,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( ~ ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 ) )
= $false )
| ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[9353]) ).
thf(9369,plain,
! [SV11: nat,SV31: nat,SV25: list_VEBT_VEBT] :
( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) ) )
= $false )
| ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[9353]) ).
thf(9370,plain,
! [SV6: $o] :
( ( ( SV6
| $false )
= $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9354]) ).
thf(9371,plain,
! [SV6: $o] :
( ( ( SV6
| $false )
= $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9355]) ).
thf(9372,plain,
! [SV6: $o] :
( ( ( SV6
| $false )
= $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9356]) ).
thf(9373,plain,
! [SV6: $o] :
( ( ( SV6
| $false )
= $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9357]) ).
thf(9374,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9358]) ).
thf(9375,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9359]) ).
thf(9376,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9360]) ).
thf(9377,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9361]) ).
thf(9378,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9362]) ).
thf(9379,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9363]) ).
thf(9380,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9364]) ).
thf(9381,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9365]) ).
thf(9382,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $true )
| ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[9366]) ).
thf(9383,plain,
! [SV11: nat,SV31: nat,SV25: list_VEBT_VEBT] :
( ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $true )
| ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[9367]) ).
thf(9384,plain,
! [SV31: nat,SV25: list_VEBT_VEBT,SV11: nat] :
( ( ( vEBT_V5917875025757280293ildren @ SV11 @ SV25 @ SV31 )
= $true )
| ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[9368]) ).
thf(9385,plain,
! [SV11: nat,SV31: nat,SV25: list_VEBT_VEBT] :
( ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $true )
| ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ SV25 @ ( vEBT_VEBT_high @ SV31 @ SV11 ) ) @ ( vEBT_VEBT_low @ SV31 @ SV11 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[9369]) ).
thf(9386,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9370]) ).
thf(9387,plain,
! [SV6: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9370]) ).
thf(9388,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9371]) ).
thf(9389,plain,
! [SV6: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9371]) ).
thf(9390,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9372]) ).
thf(9391,plain,
! [SV6: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9372]) ).
thf(9392,plain,
! [SV6: $o] :
( ( SV6 = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9373]) ).
thf(9393,plain,
! [SV6: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV6
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9373]) ).
thf(9394,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9374]) ).
thf(9395,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9374]) ).
thf(9396,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9375]) ).
thf(9397,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9375]) ).
thf(9398,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9376]) ).
thf(9399,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9376]) ).
thf(9400,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9377]) ).
thf(9401,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9377]) ).
thf(9402,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9378]) ).
thf(9403,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9378]) ).
thf(9404,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9379]) ).
thf(9405,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9379]) ).
thf(9406,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9380]) ).
thf(9407,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9380]) ).
thf(9408,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9381]) ).
thf(9409,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9381]) ).
thf(9410,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9386]) ).
thf(9411,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( $false = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9387]) ).
thf(9412,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9388]) ).
thf(9413,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( $false = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9389]) ).
thf(9414,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( SV6 = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9390]) ).
thf(9415,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9391]) ).
thf(9416,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( SV6 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9392]) ).
thf(9417,plain,
! [SV6: $o] :
( ( ( ~ SV6
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9393]) ).
thf(9418,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9394]) ).
thf(9419,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9395]) ).
thf(9420,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9396]) ).
thf(9421,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9397]) ).
thf(9422,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9398]) ).
thf(9423,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9399]) ).
thf(9424,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9400]) ).
thf(9425,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9401]) ).
thf(9426,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9402]) ).
thf(9427,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9403]) ).
thf(9428,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9404]) ).
thf(9429,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9405]) ).
thf(9430,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9406]) ).
thf(9431,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9407]) ).
thf(9432,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9408]) ).
thf(9433,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[9409]) ).
thf(9434,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9410]) ).
thf(9435,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9410]) ).
thf(9436,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $false = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9411]) ).
thf(9437,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9411]) ).
thf(9438,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9412]) ).
thf(9439,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( SV6 = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9412]) ).
thf(9440,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $false = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9413]) ).
thf(9441,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9413]) ).
thf(9442,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9414]) ).
thf(9443,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( SV6 = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9414]) ).
thf(9444,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9415]) ).
thf(9445,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9415]) ).
thf(9446,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( SV6 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9416]) ).
thf(9447,plain,
! [SV6: $o] :
( ( ( ~ $false ) = $false )
| ( SV6 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9416]) ).
thf(9448,plain,
! [SV6: $o] :
( ( ( ~ SV6 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9417]) ).
thf(9449,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9417]) ).
thf(9450,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9418]) ).
thf(9451,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9418]) ).
thf(9452,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9419]) ).
thf(9453,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9419]) ).
thf(9454,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9420]) ).
thf(9455,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9420]) ).
thf(9456,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9421]) ).
thf(9457,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9421]) ).
thf(9458,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9422]) ).
thf(9459,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9422]) ).
thf(9460,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9423]) ).
thf(9461,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9423]) ).
thf(9462,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9424]) ).
thf(9463,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9424]) ).
thf(9464,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9425]) ).
thf(9465,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9425]) ).
thf(9466,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9426]) ).
thf(9467,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9426]) ).
thf(9468,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9427]) ).
thf(9469,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9427]) ).
thf(9470,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9428]) ).
thf(9471,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9428]) ).
thf(9472,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9429]) ).
thf(9473,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9429]) ).
thf(9474,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9430]) ).
thf(9475,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9430]) ).
thf(9476,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9431]) ).
thf(9477,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9431]) ).
thf(9478,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9432]) ).
thf(9479,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9432]) ).
thf(9480,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9433]) ).
thf(9481,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[9433]) ).
thf(9482,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9434]) ).
thf(9483,plain,
! [SV6: $o] :
( ( $false = $true )
| ( SV6 = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9435]) ).
thf(9484,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $false = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9436]) ).
thf(9485,plain,
! [SV6: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV6 = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9437]) ).
thf(9486,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9438]) ).
thf(9487,plain,
! [SV6: $o] :
( ( $false = $true )
| ( SV6 = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9439]) ).
thf(9488,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $false = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9440]) ).
thf(9489,plain,
! [SV6: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV6 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9441]) ).
thf(9490,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9442]) ).
thf(9491,plain,
! [SV6: $o] :
( ( $false = $true )
| ( SV6 = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9443]) ).
thf(9492,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9444]) ).
thf(9493,plain,
! [SV6: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV6 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9445]) ).
thf(9494,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( SV6 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9446]) ).
thf(9495,plain,
! [SV6: $o] :
( ( $false = $true )
| ( SV6 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9447]) ).
thf(9496,plain,
! [SV6: $o] :
( ( SV6 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9448]) ).
thf(9497,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9449]) ).
thf(9498,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9450]) ).
thf(9499,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9451]) ).
thf(9500,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9452]) ).
thf(9501,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9453]) ).
thf(9502,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9454]) ).
thf(9503,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9455]) ).
thf(9504,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9456]) ).
thf(9505,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9457]) ).
thf(9506,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9458]) ).
thf(9507,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9459]) ).
thf(9508,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9460]) ).
thf(9509,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9461]) ).
thf(9510,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9462]) ).
thf(9511,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9463]) ).
thf(9512,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9464]) ).
thf(9513,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9465]) ).
thf(9514,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9466]) ).
thf(9515,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9467]) ).
thf(9516,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9468]) ).
thf(9517,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9469]) ).
thf(9518,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9470]) ).
thf(9519,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9471]) ).
thf(9520,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9472]) ).
thf(9521,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9473]) ).
thf(9522,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9474]) ).
thf(9523,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9475]) ).
thf(9524,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9476]) ).
thf(9525,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9477]) ).
thf(9526,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9478]) ).
thf(9527,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9479]) ).
thf(9528,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9480]) ).
thf(9529,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[9481]) ).
thf(9530,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[9140,9529,9528,9527,9526,9525,9524,9523,9522,9521,9520,9519,9518,9517,9516,9515,9514,9513,9512,9511,9510,9509,9508,9507,9506,9505,9504,9503,9502,9501,9500,9499,9498,9497,9496,9495,9494,9493,9492,9491,9490,9489,9488,9487,9486,9485,9484,9483,9482,9385,9384,9383,9382,9351,9350,9349,9348,9347,9345,9343,9341,9339,9338,9337,9336,9335,9333,9331,9329,9327,9326,9325,9324,9323,9321,9319,9317,9288,9268,9267,9253,9229,9227,9225,9223,9221,9218,9215,9212,9198,9196,9183,9181,9169,9167,9149,9146,9145,9143,9141]) ).
thf(9531,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[9530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP233^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 11:23:25 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.19/13.81 ....................................................................
% 68.19/13.81
% 68.19/13.81 No.of.Axioms: 18
% 68.19/13.81
% 68.19/13.81 Length.of.Defs: 0
% 68.19/13.81
% 68.19/13.81 Contains.Choice.Funs: true
% 68.19/13.81 ...........................................................................
% 68.19/13.81
% 68.19/13.81 ********************************
% 68.19/13.81 * All subproblems solved! *
% 68.19/13.81 ********************************
% 68.19/13.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:18,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:9530,loop_count:0,foatp_calls:1,translation:fof_full)
% 68.19/13.81
% 68.19/13.81 %**** Beginning of derivation protocol ****
% 68.19/13.81 % SZS output start CNFRefutation
% See solution above
% 68.19/13.82
% 68.19/13.82 %**** End of derivation protocol ****
% 68.19/13.82 %**** no. of clauses in derivation: 432 ****
% 68.19/13.82 %**** clause counter: 9530 ****
% 68.19/13.82
% 68.19/13.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:18,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:9530,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------