TSTP Solution File: ITP219_3 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP219_3 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:24:17 EDT 2024
% Result : Theorem 15.22s 5.17s
% Output : Refutation 15.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 542
% Syntax : Number of formulae : 569 ( 34 unt; 517 typ; 0 def)
% Number of atoms : 80 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 285 ( 11 ~; 0 |; 7 &; 227 @)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 506 ( 505 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 62 ( 0 ^ 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr7057080801110549565et_nat_type,type,
set_Pr7057080801110549565et_nat: $tType ).
thf(produc505541996239113949et_nat_type,type,
produc505541996239113949et_nat: $tType ).
thf(fun_Pr3358449090565925198_nat_o_type,type,
fun_Pr3358449090565925198_nat_o: $tType ).
thf(set_Pr6949033248718891245nteger_type,type,
set_Pr6949033248718891245nteger: $tType ).
thf(produc7379341420752632205nteger_type,type,
produc7379341420752632205nteger: $tType ).
thf(set_Pr3767905878465553991nt_int_type,type,
set_Pr3767905878465553991nt_int: $tType ).
thf(produc881187336974765031nt_int_type,type,
produc881187336974765031nt_int: $tType ).
thf(set_Pr9066344408807579265et_nat_type,type,
set_Pr9066344408807579265et_nat: $tType ).
thf(fun_se177437144654672861at_nat_type,type,
fun_se177437144654672861at_nat: $tType ).
thf(produc8893060842726229537et_nat_type,type,
produc8893060842726229537et_nat: $tType ).
thf(set_Pr3703873761940759199nt_int_type,type,
set_Pr3703873761940759199nt_int: $tType ).
thf(list_P4783563340545138382et_nat_type,type,
list_P4783563340545138382et_nat: $tType ).
thf(set_Pr4040394263813967220et_nat_type,type,
set_Pr4040394263813967220et_nat: $tType ).
thf(fun_Pr1227177680593602867_nat_o_type,type,
fun_Pr1227177680593602867_nat_o: $tType ).
thf(produc3192696172498486335nt_int_type,type,
produc3192696172498486335nt_int: $tType ).
thf(produc4193628355235574503at_nat_type,type,
produc4193628355235574503at_nat: $tType ).
thf(produc3112576180687729086et_nat_type,type,
produc3112576180687729086et_nat: $tType ).
thf(fun_fu2611741329380808165_nat_o_type,type,
fun_fu2611741329380808165_nat_o: $tType ).
thf(produc1319942482725812455at_nat_type,type,
produc1319942482725812455at_nat: $tType ).
thf(list_P6548900253507351021at_nat_type,type,
list_P6548900253507351021at_nat: $tType ).
thf(set_Pr5564308138774400199at_nat_type,type,
set_Pr5564308138774400199at_nat: $tType ).
thf(fun_se6846035212209387651at_nat_type,type,
fun_se6846035212209387651at_nat: $tType ).
thf(produc1906917888121415911at_nat_type,type,
produc1906917888121415911at_nat: $tType ).
thf(list_P2959130015091922598nteger_type,type,
list_P2959130015091922598nteger: $tType ).
thf(fun_Pr5947183769845927726_nat_o_type,type,
fun_Pr5947183769845927726_nat_o: $tType ).
thf(set_Pr3486312109254157132nteger_type,type,
set_Pr3486312109254157132nteger: $tType ).
thf(fun_Pr7015759342434529115eger_o_type,type,
fun_Pr7015759342434529115eger_o: $tType ).
thf(produc9140211490168418807atural_type,type,
produc9140211490168418807atural: $tType ).
thf(produc2453742332425399446nteger_type,type,
produc2453742332425399446nteger: $tType ).
thf(fun_fu7695273699059480439eger_o_type,type,
fun_fu7695273699059480439eger_o: $tType ).
thf(list_P2843741347166045587nt_int_type,type,
list_P2843741347166045587nt_int: $tType ).
thf(fun_Co9168753396221475450atural_type,type,
fun_Co9168753396221475450atural: $tType ).
thf(set_Pr6700895561065273913nt_int_type,type,
set_Pr6700895561065273913nt_int: $tType ).
thf(fun_Pr3540825087398332590_int_o_type,type,
fun_Pr3540825087398332590_int_o: $tType ).
thf(list_P7236803063094035949_nat_o_type,type,
list_P7236803063094035949_nat_o: $tType ).
thf(set_Pr2890355626087285447_nat_o_type,type,
set_Pr2890355626087285447_nat_o: $tType ).
thf(produc3043004577601930755nt_int_type,type,
produc3043004577601930755nt_int: $tType ).
thf(fun_fu6865642474282033866_int_o_type,type,
fun_fu6865642474282033866_int_o: $tType ).
thf(list_P8836981409019564976et_nat_type,type,
list_P8836981409019564976et_nat: $tType ).
thf(set_Pr1312406793078187350et_nat_type,type,
set_Pr1312406793078187350et_nat: $tType ).
thf(fun_Pr2620521676128474833_nat_o_type,type,
fun_Pr2620521676128474833_nat_o: $tType ).
thf(produc6671579610312156647_nat_o_type,type,
produc6671579610312156647_nat_o: $tType ).
thf(fun_fu4164567611050918574at_o_o_type,type,
fun_fu4164567611050918574at_o_o: $tType ).
thf(produc3664700245209686448n_assn_type,type,
produc3664700245209686448n_assn: $tType ).
thf(fun_Co1105491363547889651atural_type,type,
fun_Co1105491363547889651atural: $tType ).
thf(fun_Co1890133979025130057atural_type,type,
fun_Co1890133979025130057atural: $tType ).
thf(produc8799533983703829792et_nat_type,type,
produc8799533983703829792et_nat: $tType ).
thf(fun_fu8419763957888848259_nat_o_type,type,
fun_fu8419763957888848259_nat_o: $tType ).
thf(fun_fu3373238862511017284_nat_o_type,type,
fun_fu3373238862511017284_nat_o: $tType ).
thf(fun_fu5323616038969315652_int_o_type,type,
fun_fu5323616038969315652_int_o: $tType ).
thf(fun_fu4800041728187187127nteger_type,type,
fun_fu4800041728187187127nteger: $tType ).
thf(produc7476732711998919211atural_type,type,
produc7476732711998919211atural: $tType ).
thf(produc7509114972854644512nteger_type,type,
produc7509114972854644512nteger: $tType ).
thf(list_f4306079564415238026e_term_type,type,
list_f4306079564415238026e_term: $tType ).
thf(set_fu8280898353253485872e_term_type,type,
set_fu8280898353253485872e_term: $tType ).
thf(fun_he5234484606919320760it_nat_type,type,
fun_he5234484606919320760it_nat: $tType ).
thf(fun_Pr7769407664385210434atural_type,type,
fun_Pr7769407664385210434atural: $tType ).
thf(fun_Co5709460363461100952atural_type,type,
fun_Co5709460363461100952atural: $tType ).
thf(list_f280343417242313083e_term_type,type,
list_f280343417242313083e_term: $tType ).
thf(fun_Pr285225112257423215e_term_type,type,
fun_Pr285225112257423215e_term: $tType ).
thf(fun_Pr5098669352780829690e_term_type,type,
fun_Pr5098669352780829690e_term: $tType ).
thf(set_fu5653557704672872225e_term_type,type,
set_fu5653557704672872225e_term: $tType ).
thf(fun_se3560235952666129655at_nat_type,type,
fun_se3560235952666129655at_nat: $tType ).
thf(list_P932735248015874751nt_int_type,type,
list_P932735248015874751nt_int: $tType ).
thf(set_Pr4166680992137330533nt_int_type,type,
set_Pr4166680992137330533nt_int: $tType ).
thf(fun_Pr1196100989263358594_int_o_type,type,
fun_Pr1196100989263358594_int_o: $tType ).
thf(fun_Co1561183069634336733nteger_type,type,
fun_Co1561183069634336733nteger: $tType ).
thf(set_Pr4333006031979791559at_nat_type,type,
set_Pr4333006031979791559at_nat: $tType ).
thf(set_Pr6863447823992824007n_assn_type,type,
set_Pr6863447823992824007n_assn: $tType ).
thf(fun_Pr7763680713840462443e_term_type,type,
fun_Pr7763680713840462443e_term: $tType ).
thf(produc4788131091073775919nt_int_type,type,
produc4788131091073775919nt_int: $tType ).
thf(set_Pr8551490117392284871at_nat_type,type,
set_Pr8551490117392284871at_nat: $tType ).
thf(produc424102278133772007at_nat_type,type,
produc424102278133772007at_nat: $tType ).
thf(produc337509097454979815n_assn_type,type,
produc337509097454979815n_assn: $tType ).
thf(fun_fu2978539155105838238_int_o_type,type,
fun_fu2978539155105838238_int_o: $tType ).
thf(list_s4242580248156217677at_nat_type,type,
list_s4242580248156217677at_nat: $tType ).
thf(fun_li7722483182022397486assn_o_type,type,
fun_li7722483182022397486assn_o: $tType ).
thf(produc6756470014200349799atural_type,type,
produc6756470014200349799atural: $tType ).
thf(fun_Pr3592279944642289454ural_o_type,type,
fun_Pr3592279944642289454ural_o: $tType ).
thf(produc4166570645942440679at_nat_type,type,
produc4166570645942440679at_nat: $tType ).
thf(list_P5464809261938338413at_nat_type,type,
list_P5464809261938338413at_nat: $tType ).
thf(list_P28140577958321773n_assn_type,type,
list_P28140577958321773n_assn: $tType ).
thf(fun_Pr2477239776880934807at_nat_type,type,
fun_Pr2477239776880934807at_nat: $tType ).
thf(fun_Pr1308109350235310159nt_int_type,type,
fun_Pr1308109350235310159nt_int: $tType ).
thf(set_Pr4329608150637261639at_nat_type,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(set_Pr8116311503512020807n_assn_type,type,
set_Pr8116311503512020807n_assn: $tType ).
thf(fun_Pr3059359313727237556_nat_o_type,type,
fun_Pr3059359313727237556_nat_o: $tType ).
thf(fun_Pr5876161306168176259nteger_type,type,
fun_Pr5876161306168176259nteger: $tType ).
thf(fun_Pr1914754426620969278n_assn_type,type,
fun_Pr1914754426620969278n_assn: $tType ).
thf(fun_fu4638078822479986034_int_o_type,type,
fun_fu4638078822479986034_int_o: $tType ).
thf(fun_fu4306744791715064858_rat_o_type,type,
fun_fu4306744791715064858_rat_o: $tType ).
thf(fun_fu6699046866436802030_int_o_type,type,
fun_fu6699046866436802030_int_o: $tType ).
thf(option8956607266484857688it_nat_type,type,
option8956607266484857688it_nat: $tType ).
thf(produc3843707927480180839at_nat_type,type,
produc3843707927480180839at_nat: $tType ).
thf(produc9053633027152450663n_assn_type,type,
produc9053633027152450663n_assn: $tType ).
thf(fun_li8180627568681326368_nat_o_type,type,
fun_li8180627568681326368_nat_o: $tType ).
thf(fun_li197242686306560452_int_o_type,type,
fun_li197242686306560452_int_o: $tType ).
thf(set_Pr457366540195662369at_nat_type,type,
set_Pr457366540195662369at_nat: $tType ).
thf(fun_fu3064074204415222357nt_int_type,type,
fun_fu3064074204415222357nt_int: $tType ).
thf(fun_fu1098312133097393581at_rat_type,type,
fun_fu1098312133097393581at_rat: $tType ).
thf(fun_na1668100129766719005at_nat_type,type,
fun_na1668100129766719005at_nat: $tType ).
thf(fun_se5639961202347202350_nat_o_type,type,
fun_se5639961202347202350_nat_o: $tType ).
thf(fun_Pr5295903952624206638assn_o_type,type,
fun_Pr5295903952624206638assn_o: $tType ).
thf(fun_fu9045186299510176150at_o_o_type,type,
fun_fu9045186299510176150at_o_o: $tType ).
thf(fun_Co2470855966376689427nteger_type,type,
fun_Co2470855966376689427nteger: $tType ).
thf(set_Pr488414391616402044st_nat_type,type,
set_Pr488414391616402044st_nat: $tType ).
thf(set_Pr4898238009683259096st_int_type,type,
set_Pr4898238009683259096st_int: $tType ).
thf(set_Pr7093487733527993602n_assn_type,type,
set_Pr7093487733527993602n_assn: $tType ).
thf(set_Pr4168565316758867366n_assn_type,type,
set_Pr4168565316758867366n_assn: $tType ).
thf(fun_li6524802329284821127st_d_o_type,type,
fun_li6524802329284821127st_d_o: $tType ).
thf(fun_li6977522988354981064st_c_o_type,type,
fun_li6977522988354981064st_c_o: $tType ).
thf(fun_li1100771141684871908_nat_o_type,type,
fun_li1100771141684871908_nat_o: $tType ).
thf(fun_li2340758296164881800_int_o_type,type,
fun_li2340758296164881800_int_o: $tType ).
thf(fun_fu3790787410453625514o_assn_type,type,
fun_fu3790787410453625514o_assn: $tType ).
thf(fun_as3747249873083764768_nat_o_type,type,
fun_as3747249873083764768_nat_o: $tType ).
thf(list_P8469869581646625389at_nat_type,type,
list_P8469869581646625389at_nat: $tType ).
thf(fun_li8250322356051145156st_d_o_type,type,
fun_li8250322356051145156st_d_o: $tType ).
thf(fun_li8703043015121305093st_c_o_type,type,
fun_li8703043015121305093st_c_o: $tType ).
thf(fun_li2130474401912454595st_d_o_type,type,
fun_li2130474401912454595st_d_o: $tType ).
thf(fun_li2583195060982614532st_c_o_type,type,
fun_li2583195060982614532st_c_o: $tType ).
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(produc8664842809031399944it_nat_type,type,
produc8664842809031399944it_nat: $tType ).
thf(produc732395585841259969at_nat_type,type,
produc732395585841259969at_nat: $tType ).
thf(fun_se320340636488258563at_nat_type,type,
fun_se320340636488258563at_nat: $tType ).
thf(set_Pr1932065953672099015od_o_o_type,type,
set_Pr1932065953672099015od_o_o: $tType ).
thf(produc6654255674790325574st_nat_type,type,
produc6654255674790325574st_nat: $tType ).
thf(produc4164172529858598818st_int_type,type,
produc4164172529858598818st_int: $tType ).
thf(produc2555908794901494476n_assn_type,type,
produc2555908794901494476n_assn: $tType ).
thf(produc8582807064127716720n_assn_type,type,
produc8582807064127716720n_assn: $tType ).
thf(list_f5222602229612168821_nat_o_type,type,
list_f5222602229612168821_nat_o: $tType ).
thf(set_fu3555266933746557007_nat_o_type,type,
set_fu3555266933746557007_nat_o: $tType ).
thf(fun_fu5135969500543783852at_o_o_type,type,
fun_fu5135969500543783852at_o_o: $tType ).
thf(fun_na8713714802964096592at_nat_type,type,
fun_na8713714802964096592at_nat: $tType ).
thf(fun_li3404705325679423581_nat_o_type,type,
fun_li3404705325679423581_nat_o: $tType ).
thf(fun_li3476655817902384897_int_o_type,type,
fun_li3476655817902384897_int_o: $tType ).
thf(fun_li1697075967554290497assn_o_type,type,
fun_li1697075967554290497assn_o: $tType ).
thf(fun_li6324434278616229789assn_o_type,type,
fun_li6324434278616229789assn_o: $tType ).
thf(produc5835291356934675326atural_type,type,
produc5835291356934675326atural: $tType ).
thf(list_f628289730585369423e_term_type,type,
list_f628289730585369423e_term: $tType ).
thf(fun_fu7677565902479959693_rat_o_type,type,
fun_fu7677565902479959693_rat_o: $tType ).
thf(fun_Co6386927884524458043e_term_type,type,
fun_Co6386927884524458043e_term: $tType ).
thf(fun_Co3544761417380347684eger_o_type,type,
fun_Co3544761417380347684eger_o: $tType ).
thf(fun_Co3460408610320954864e_term_type,type,
fun_Co3460408610320954864e_term: $tType ).
thf(set_fu3629540756087427317e_term_type,type,
set_fu3629540756087427317e_term: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(fun_fu8391177546919232046_nat_o_type,type,
fun_fu8391177546919232046_nat_o: $tType ).
thf(fun_fu7503566767892366382_int_o_type,type,
fun_fu7503566767892366382_int_o: $tType ).
thf(fun_Pr2028404973800837934_nat_o_type,type,
fun_Pr2028404973800837934_nat_o: $tType ).
thf(fun_Pr9018117161326028078_int_o_type,type,
fun_Pr9018117161326028078_int_o: $tType ).
thf(produc2934264451710624999od_o_o_type,type,
produc2934264451710624999od_o_o: $tType ).
thf(list_P9062070895058802706et_nat_type,type,
list_P9062070895058802706et_nat: $tType ).
thf(set_Pr3948176798113811640et_nat_type,type,
set_Pr3948176798113811640et_nat: $tType ).
thf(list_P2911967483291296064sn_nat_type,type,
list_P2911967483291296064sn_nat: $tType ).
thf(list_P421884338359569308sn_int_type,type,
list_P421884338359569308sn_int: $tType ).
thf(list_P7711101519850957926n_assn_type,type,
list_P7711101519850957926n_assn: $tType ).
thf(list_P1495281457390866698n_assn_type,type,
list_P1495281457390866698n_assn: $tType ).
thf(fun_Pr6460944699146269935_nat_o_type,type,
fun_Pr6460944699146269935_nat_o: $tType ).
thf(set_Pr4672072672689440998sn_nat_type,type,
set_Pr4672072672689440998sn_nat: $tType ).
thf(set_Pr2181989527757714242sn_int_type,type,
set_Pr2181989527757714242sn_int: $tType ).
thf(set_Pr247834672394327052n_assn_type,type,
set_Pr247834672394327052n_assn: $tType ).
thf(set_Pr3255386646789011632n_assn_type,type,
set_Pr3255386646789011632n_assn: $tType ).
thf(fun_li4463338863320273959_nat_o_type,type,
fun_li4463338863320273959_nat_o: $tType ).
thf(fun_li3597902321612929227_int_o_type,type,
fun_li3597902321612929227_int_o: $tType ).
thf(fun_Pr2676784290456659641t_assn_type,type,
fun_Pr2676784290456659641t_assn: $tType ).
thf(fun_Pr7092578583803811605t_assn_type,type,
fun_Pr7092578583803811605t_assn: $tType ).
thf(fun_na2667955736958379125n_assn_type,type,
fun_na2667955736958379125n_assn: $tType ).
thf(fun_na4143055713577223196at_nat_type,type,
fun_na4143055713577223196at_nat: $tType ).
thf(fun_in2917358019923704601n_assn_type,type,
fun_in2917358019923704601n_assn: $tType ).
thf(fun_in2204242111582549184nt_int_type,type,
fun_in2204242111582549184nt_int: $tType ).
thf(fun_Co6597186368970283863nteger_type,type,
fun_Co6597186368970283863nteger: $tType ).
thf(fun_in5730379987311621695e_term_type,type,
fun_in5730379987311621695e_term: $tType ).
thf(fun_fi7557781610047541018er_nat_type,type,
fun_fi7557781610047541018er_nat: $tType ).
thf(fun_fu9090758901314268781nt_o_o_type,type,
fun_fu9090758901314268781nt_o_o: $tType ).
thf(fun_Pr2118491707810114563at_nat_type,type,
fun_Pr2118491707810114563at_nat: $tType ).
thf(fun_Pr2478283820680522243nt_int_type,type,
fun_Pr2478283820680522243nt_int: $tType ).
thf(fun_li8256078503033673002st_d_o_type,type,
fun_li8256078503033673002st_d_o: $tType ).
thf(fun_li5605408072535077355st_c_o_type,type,
fun_li5605408072535077355st_c_o: $tType ).
thf(fun_li3247565534195299847_nat_o_type,type,
fun_li3247565534195299847_nat_o: $tType ).
thf(fun_li2382128992487955115_int_o_type,type,
fun_li2382128992487955115_int_o: $tType ).
thf(fun_in1425933616158802663n_assn_type,type,
fun_in1425933616158802663n_assn: $tType ).
thf(fun_in4433485590553487243n_assn_type,type,
fun_in4433485590553487243n_assn: $tType ).
thf(fun_na5914473681949881652_nat_o_type,type,
fun_na5914473681949881652_nat_o: $tType ).
thf(produc3658429121746597890et_nat_type,type,
produc3658429121746597890et_nat: $tType ).
thf(list_P5953897101696565392at_nat_type,type,
list_P5953897101696565392at_nat: $tType ).
thf(list_P3463813956764838636at_int_type,type,
list_P3463813956764838636at_int: $tType ).
thf(list_P1909269847677398966at_nat_type,type,
list_P1909269847677398966at_nat: $tType ).
thf(list_P812186867033400410at_nat_type,type,
list_P812186867033400410at_nat: $tType ).
thf(fun_li5638961813688977830_nat_o_type,type,
fun_li5638961813688977830_nat_o: $tType ).
thf(fun_li4773525271981633098_int_o_type,type,
fun_li4773525271981633098_int_o: $tType ).
thf(fun_li1783867155918724199_nat_o_type,type,
fun_li1783867155918724199_nat_o: $tType ).
thf(fun_li918430614211379467_int_o_type,type,
fun_li918430614211379467_int_o: $tType ).
thf(fun_li6882067341086778250st_d_o_type,type,
fun_li6882067341086778250st_d_o: $tType ).
thf(fun_li4231396910588182603st_c_o_type,type,
fun_li4231396910588182603st_c_o: $tType ).
thf(fun_li1868563531609296843st_d_o_type,type,
fun_li1868563531609296843st_d_o: $tType ).
thf(fun_li8441265137965477004st_c_o_type,type,
fun_li8441265137965477004st_c_o: $tType ).
thf(fun_li616801382895168330st_d_o_type,type,
fun_li616801382895168330st_d_o: $tType ).
thf(fun_li7189502989251348491st_c_o_type,type,
fun_li7189502989251348491st_c_o: $tType ).
thf(set_Pr2539167527615954998at_nat_type,type,
set_Pr2539167527615954998at_nat: $tType ).
thf(set_Pr49084382684228242at_int_type,type,
set_Pr49084382684228242at_int: $tType ).
thf(set_Pr7717912310451564380at_nat_type,type,
set_Pr7717912310451564380at_nat: $tType ).
thf(set_Pr6620829329807565824at_nat_type,type,
set_Pr6620829329807565824at_nat: $tType ).
thf(produc3672657496626091440sn_nat_type,type,
produc3672657496626091440sn_nat: $tType ).
thf(produc8718178513971670540sn_int_type,type,
produc8718178513971670540sn_int: $tType ).
thf(produc1407301962063123414n_assn_type,type,
produc1407301962063123414n_assn: $tType ).
thf(produc3167338625816234618n_assn_type,type,
produc3167338625816234618n_assn: $tType ).
thf(list_f2430256441796990922at_nat_type,type,
list_f2430256441796990922at_nat: $tType ).
thf(produc7317866342734830137st_nat_type,type,
produc7317866342734830137st_nat: $tType ).
thf(produc5262460917026302941st_int_type,type,
produc5262460917026302941st_int: $tType ).
thf(fun_Pr5858031453276514825t_assn_type,type,
fun_Pr5858031453276514825t_assn: $tType ).
thf(fun_Pr1050453709768890981t_assn_type,type,
fun_Pr1050453709768890981t_assn: $tType ).
thf(fun_na5930564906747369413t_assn_type,type,
fun_na5930564906747369413t_assn: $tType ).
thf(fun_in6852455514944667241t_assn_type,type,
fun_in6852455514944667241t_assn: $tType ).
thf(fun_Pr597617920386261747_nat_o_type,type,
fun_Pr597617920386261747_nat_o: $tType ).
thf(fun_Pr7575844989570591639_int_o_type,type,
fun_Pr7575844989570591639_int_o: $tType ).
thf(fun_na1082083995841529399assn_o_type,type,
fun_na1082083995841529399assn_o: $tType ).
thf(fun_in7130107137290581651assn_o_type,type,
fun_in7130107137290581651assn_o: $tType ).
thf(fun_fu7075445697382584196_int_o_type,type,
fun_fu7075445697382584196_int_o: $tType ).
thf(fun_se1909708154429037836et_nat_type,type,
fun_se1909708154429037836et_nat: $tType ).
thf(fun_se6573205548028396576et_int_type,type,
fun_se6573205548028396576et_int: $tType ).
thf(fun_li2045945205358903659st_d_o_type,type,
fun_li2045945205358903659st_d_o: $tType ).
thf(fun_li8618646811715083820st_c_o_type,type,
fun_li8618646811715083820st_c_o: $tType ).
thf(fun_li794183056644775146st_d_o_type,type,
fun_li794183056644775146st_d_o: $tType ).
thf(fun_li7366884663000955307st_c_o_type,type,
fun_li7366884663000955307st_c_o: $tType ).
thf(fun_Co1981900195452921617nteger_type,type,
fun_Co1981900195452921617nteger: $tType ).
thf(set_Pr3451248702717554689st_nat_type,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(set_Pr7861072320784411741st_int_type,type,
set_Pr7861072320784411741st_int: $tType ).
thf(set_Pr5578615432719617117st_nat_type,type,
set_Pr5578615432719617117st_nat: $tType ).
thf(set_Pr765067013931698361st_int_type,type,
set_Pr765067013931698361st_int: $tType ).
thf(list_l6351802567095793725n_assn_type,type,
list_l6351802567095793725n_assn: $tType ).
thf(list_P5578671422887162913nteger_type,type,
list_P5578671422887162913nteger: $tType ).
thf(fun_li2812663585457640420assn_o_type,type,
fun_li2812663585457640420assn_o: $tType ).
thf(fun_Pr3816910165196019820n_assn_type,type,
fun_Pr3816910165196019820n_assn: $tType ).
thf(fun_na4138050610385705875at_nat_type,type,
fun_na4138050610385705875at_nat: $tType ).
thf(fun_in1696471567231710611nt_int_type,type,
fun_in1696471567231710611nt_int: $tType ).
thf(set_Pr4811707699266497531nteger_type,type,
set_Pr4811707699266497531nteger: $tType ).
thf(fun_Pr7211993375558241536eger_o_type,type,
fun_Pr7211993375558241536eger_o: $tType ).
thf(fun_Co1766037875893669450eger_o_type,type,
fun_Co1766037875893669450eger_o: $tType ).
thf(set_Pr3005433631314115148st_nat_type,type,
set_Pr3005433631314115148st_nat: $tType ).
thf(set_Pr7415257249380972200st_int_type,type,
set_Pr7415257249380972200st_int: $tType ).
thf(set_Pr6760183905301009355st_nat_type,type,
set_Pr6760183905301009355st_nat: $tType ).
thf(set_Pr1946635486513090599st_int_type,type,
set_Pr1946635486513090599st_int: $tType ).
thf(set_Pr9082979648927643218list_d_type,type,
set_Pr9082979648927643218list_d: $tType ).
thf(set_Pr2380792130361903057list_c_type,type,
set_Pr2380792130361903057list_c: $tType ).
thf(produc6653097349344004940it_nat_type,type,
produc6653097349344004940it_nat: $tType ).
thf(produc8373899037510109440at_nat_type,type,
produc8373899037510109440at_nat: $tType ).
thf(produc4196048018000912732at_int_type,type,
produc4196048018000912732at_int: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(produc1062882101152166346at_nat_type,type,
produc1062882101152166346at_nat: $tType ).
thf(fun_he4135464443191253079_nat_o_type,type,
fun_he4135464443191253079_nat_o: $tType ).
thf(fun_se4097146774670233028at_nat_type,type,
fun_se4097146774670233028at_nat: $tType ).
thf(fun_na5138202758309126970n_assn_type,type,
fun_na5138202758309126970n_assn: $tType ).
thf(fun_in6898239422062238174n_assn_type,type,
fun_in6898239422062238174n_assn: $tType ).
thf(fun_Pr4738963024209204295_int_o_type,type,
fun_Pr4738963024209204295_int_o: $tType ).
thf(fun_Pr7537129237977221859_rat_o_type,type,
fun_Pr7537129237977221859_rat_o: $tType ).
thf(fun_na3970208099681795815_nat_o_type,type,
fun_na3970208099681795815_nat_o: $tType ).
thf(set_Pr5674772971416283335list_d_type,type,
set_Pr5674772971416283335list_d: $tType ).
thf(set_Pr8195957489705318982list_c_type,type,
set_Pr8195957489705318982list_c: $tType ).
thf(set_Pr8760529213406277896list_d_type,type,
set_Pr8760529213406277896list_d: $tType ).
thf(set_Pr2058341694840537735list_c_type,type,
set_Pr2058341694840537735list_c: $tType ).
thf(produc1828647624359046049st_nat_type,type,
produc1828647624359046049st_nat: $tType ).
thf(produc8561936516282095101st_int_type,type,
produc8561936516282095101st_int: $tType ).
thf(produc3676724955757786621st_nat_type,type,
produc3676724955757786621st_nat: $tType ).
thf(produc1186641810826059865st_int_type,type,
produc1186641810826059865st_int: $tType ).
thf(fun_d_5839661626854366689_d_nat_type,type,
fun_d_5839661626854366689_d_nat: $tType ).
thf(fun_d_2234230340994827929_d_int_type,type,
fun_d_2234230340994827929_d_int: $tType ).
thf(fun_c_1789499241325163999_c_nat_type,type,
fun_c_1789499241325163999_c_nat: $tType ).
thf(fun_c_7407439992320401047_c_int_type,type,
fun_c_7407439992320401047_c_int: $tType ).
thf(fun_na5312369548907571267_nat_d_type,type,
fun_na5312369548907571267_nat_d: $tType ).
thf(fun_na3893605480571770689_nat_c_type,type,
fun_na3893605480571770689_nat_c: $tType ).
thf(list_s1210847774152347623at_nat_type,type,
list_s1210847774152347623at_nat: $tType ).
thf(list_P8527749157015355191n_assn_type,type,
list_P8527749157015355191n_assn: $tType ).
thf(fun_Pr6640091470896217020t_assn_type,type,
fun_Pr6640091470896217020t_assn: $tType ).
thf(fun_li1025265955262268170_nat_o_type,type,
fun_li1025265955262268170_nat_o: $tType ).
thf(fun_li1097216447485229486_int_o_type,type,
fun_li1097216447485229486_int_o: $tType ).
thf(fun_li1262843096912843182_nat_o_type,type,
fun_li1262843096912843182_nat_o: $tType ).
thf(fun_li1334793589135804498_int_o_type,type,
fun_li1334793589135804498_int_o: $tType ).
thf(set_se7855581050983116737at_nat_type,type,
set_se7855581050983116737at_nat: $tType ).
thf(set_Pr5949110396991348497n_assn_type,type,
set_Pr5949110396991348497n_assn: $tType ).
thf(produc7822875418678951345atural_type,type,
produc7822875418678951345atural: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(fun_se4782206882984618170_nat_o_type,type,
fun_se4782206882984618170_nat_o: $tType ).
thf(fun_Pr3571187171380813162assn_o_type,type,
fun_Pr3571187171380813162assn_o: $tType ).
thf(fun_as3983628580203722482n_assn_type,type,
fun_as3983628580203722482n_assn: $tType ).
thf(produc2433097559162738582st_nat_type,type,
produc2433097559162738582st_nat: $tType ).
thf(produc9166386451085787634st_int_type,type,
produc9166386451085787634st_int: $tType ).
thf(produc1766198083622830229st_nat_type,type,
produc1766198083622830229st_nat: $tType ).
thf(produc8499486975545879281st_int_type,type,
produc8499486975545879281st_int: $tType ).
thf(produc1726512871120090780list_d_type,type,
produc1726512871120090780list_d: $tType ).
thf(produc1655478831073744795list_c_type,type,
produc1655478831073744795list_c: $tType ).
thf(fun_Co2081214437782444048eger_o_type,type,
fun_Co2081214437782444048eger_o: $tType ).
thf(fun_fu7564235448449272366at_o_o_type,type,
fun_fu7564235448449272366at_o_o: $tType ).
thf(fun_se2621318847353125966_set_o_type,type,
fun_se2621318847353125966_set_o: $tType ).
thf(multis2468970476368604999at_nat_type,type,
multis2468970476368604999at_nat: $tType ).
thf(fun_li3172987763358990349_nat_o_type,type,
fun_li3172987763358990349_nat_o: $tType ).
thf(fun_li3244938255581951665_int_o_type,type,
fun_li3244938255581951665_int_o: $tType ).
thf(fun_li6181769218026185550_nat_o_type,type,
fun_li6181769218026185550_nat_o: $tType ).
thf(fun_li6253719710249146866_int_o_type,type,
fun_li6253719710249146866_int_o: $tType ).
thf(fun_li3700998088691485681st_d_o_type,type,
fun_li3700998088691485681st_d_o: $tType ).
thf(fun_li4336647089296472370st_c_o_type,type,
fun_li4336647089296472370st_c_o: $tType ).
thf(fun_li6714305004359949901st_d_o_type,type,
fun_li6714305004359949901st_d_o: $tType ).
thf(fun_li7349954004964936590st_c_o_type,type,
fun_li7349954004964936590st_c_o: $tType ).
thf(fun_fi2406938933853765693er_nat_type,type,
fun_fi2406938933853765693er_nat: $tType ).
thf(fun_ra4503298312962071866nt_int_type,type,
fun_ra4503298312962071866nt_int: $tType ).
thf(fun_Pr7647638413817135296at_int_type,type,
fun_Pr7647638413817135296at_int: $tType ).
thf(fun_Pr1652463973008025892nt_rat_type,type,
fun_Pr1652463973008025892nt_rat: $tType ).
thf(fun_na1476630412504255114at_nat_type,type,
fun_na1476630412504255114at_nat: $tType ).
thf(fun_in4514472496968388910at_nat_type,type,
fun_in4514472496968388910at_nat: $tType ).
thf(fun_in4211310926729683942nt_int_type,type,
fun_in4211310926729683942nt_int: $tType ).
thf(produc2783776724613635559list_d_type,type,
produc2783776724613635559list_d: $tType ).
thf(produc2712742684567289574list_c_type,type,
produc2712742684567289574list_c: $tType ).
thf(produc8056257125849822888list_d_type,type,
produc8056257125849822888list_d: $tType ).
thf(produc7985223085803476903list_c_type,type,
produc7985223085803476903list_c: $tType ).
thf(filter1242075044329608583at_nat_type,type,
filter1242075044329608583at_nat: $tType ).
thf(fun_d_3518232967345404797od_d_d_type,type,
fun_d_3518232967345404797od_d_d: $tType ).
thf(fun_d_7375468105587134781od_d_c_type,type,
fun_d_7375468105587134781od_d_c: $tType ).
thf(fun_c_8225647604158478269od_c_d_type,type,
fun_c_8225647604158478269od_c_d: $tType ).
thf(fun_c_2859510705545432445od_c_c_type,type,
fun_c_2859510705545432445od_c_c: $tType ).
thf(fun_na7928631014926962227_nat_o_type,type,
fun_na7928631014926962227_nat_o: $tType ).
thf(fun_li2716627548323645870st_d_o_type,type,
fun_li2716627548323645870st_d_o: $tType ).
thf(fun_li3352276548928632559st_c_o_type,type,
fun_li3352276548928632559st_c_o: $tType ).
thf(fun_li454908266862867629st_d_o_type,type,
fun_li454908266862867629st_d_o: $tType ).
thf(fun_li1090557267467854318st_c_o_type,type,
fun_li1090557267467854318st_c_o: $tType ).
thf(list_P6011104703257516679at_nat_type,type,
list_P6011104703257516679at_nat: $tType ).
thf(list_P3521021558325789923at_int_type,type,
list_P3521021558325789923at_int: $tType ).
thf(list_P8198026277950538467nt_nat_type,type,
list_P8198026277950538467nt_nat: $tType ).
thf(list_P5707943133018811711nt_int_type,type,
list_P5707943133018811711nt_int: $tType ).
thf(fun_na1795394851323331405_d_nat_type,type,
fun_na1795394851323331405_d_nat: $tType ).
thf(fun_na5422548272989976524_c_nat_type,type,
fun_na5422548272989976524_c_nat: $tType ).
thf(fun_in5852856594745477125_d_int_type,type,
fun_in5852856594745477125_d_int: $tType ).
thf(fun_in256637979557346436_c_int_type,type,
fun_in256637979557346436_c_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr7995236796853374141at_int_type,type,
set_Pr7995236796853374141at_int: $tType ).
thf(set_Pr3448869479623346877nt_nat_type,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(produc6575502325842934193n_assn_type,type,
produc6575502325842934193n_assn: $tType ).
thf(fun_Pr4796943543331071514_nat_o_type,type,
fun_Pr4796943543331071514_nat_o: $tType ).
thf(fun_Pr3238374608701176162_int_o_type,type,
fun_Pr3238374608701176162_int_o: $tType ).
thf(fun_set_nat_set_nat_type,type,
fun_set_nat_set_nat: $tType ).
thf(fun_set_int_set_int_type,type,
fun_set_int_set_int: $tType ).
thf(fun_nat_fun_nat_assn_type,type,
fun_nat_fun_nat_assn: $tType ).
thf(fun_nat_fun_int_assn_type,type,
fun_nat_fun_int_assn: $tType ).
thf(fun_int_fun_nat_assn_type,type,
fun_int_fun_nat_assn: $tType ).
thf(fun_int_fun_int_assn_type,type,
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thf(fun_Co8499238673658658103nteger_type,type,
fun_Co8499238673658658103nteger: $tType ).
thf(fun_assn_fun_assn_o_type,type,
fun_assn_fun_assn_o: $tType ).
thf(fun_filter_nat_assn_type,type,
fun_filter_nat_assn: $tType ).
thf(fun_assn_filter_nat_type,type,
fun_assn_filter_nat: $tType ).
thf(list_P1934797086108301456_d_nat_type,type,
list_P1934797086108301456_d_nat: $tType ).
thf(list_P8668085978031350508_d_int_type,type,
list_P8668085978031350508_d_int: $tType ).
thf(list_P5561950507774946575_c_nat_type,type,
list_P5561950507774946575_c_nat: $tType ).
thf(list_P3071867362843219819_c_int_type,type,
list_P3071867362843219819_c_int: $tType ).
thf(list_P3064893870870525238_nat_d_type,type,
list_P3064893870870525238_nat_d: $tType ).
thf(list_P2993859830824179253_nat_c_type,type,
list_P2993859830824179253_nat_c: $tType ).
thf(fun_d_3823435825767679546_nat_d_type,type,
fun_d_3823435825767679546_nat_d: $tType ).
thf(fun_c_5868829843711808568_nat_c_type,type,
fun_c_5868829843711808568_nat_c: $tType ).
thf(set_Pr3276347184212964150_d_nat_type,type,
set_Pr3276347184212964150_d_nat: $tType ).
thf(set_Pr786264039281237394_d_int_type,type,
set_Pr786264039281237394_d_int: $tType ).
thf(set_Pr6903500605879609269_c_nat_type,type,
set_Pr6903500605879609269_c_nat: $tType ).
thf(set_Pr4413417460947882513_c_int_type,type,
set_Pr4413417460947882513_c_int: $tType ).
thf(set_Pr4406443968975187932_nat_d_type,type,
set_Pr4406443968975187932_nat_d: $tType ).
thf(set_Pr4335409928928841947_nat_c_type,type,
set_Pr4335409928928841947_nat_c: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(fun_d_fun_nat_assn_type,type,
fun_d_fun_nat_assn: $tType ).
thf(fun_d_fun_int_assn_type,type,
fun_d_fun_int_assn: $tType ).
thf(fun_c_fun_nat_assn_type,type,
fun_c_fun_nat_assn: $tType ).
thf(fun_c_fun_int_assn_type,type,
fun_c_fun_int_assn: $tType ).
thf(fun_nat_fun_d_assn_type,type,
fun_nat_fun_d_assn: $tType ).
thf(fun_nat_fun_c_assn_type,type,
fun_nat_fun_c_assn: $tType ).
thf(fun_rat_fun_rat_rat_type,type,
fun_rat_fun_rat_rat: $tType ).
thf(fun_nat_fun_nat_nat_type,type,
fun_nat_fun_nat_nat: $tType ).
thf(fun_nat_fun_nat_int_type,type,
fun_nat_fun_nat_int: $tType ).
thf(fun_nat_fun_int_nat_type,type,
fun_nat_fun_int_nat: $tType ).
thf(fun_nat_fun_int_int_type,type,
fun_nat_fun_int_int: $tType ).
thf(fun_int_fun_nat_nat_type,type,
fun_int_fun_nat_nat: $tType ).
thf(fun_int_fun_nat_int_type,type,
fun_int_fun_nat_int: $tType ).
thf(fun_int_fun_int_rat_type,type,
fun_int_fun_int_rat: $tType ).
thf(fun_int_fun_int_nat_type,type,
fun_int_fun_int_nat: $tType ).
thf(fun_int_fun_int_int_type,type,
fun_int_fun_int_int: $tType ).
thf(fun_Co4490034186337852034r_assn_type,type,
fun_Co4490034186337852034r_assn: $tType ).
thf(fun_as9138348466139350018nteger_type,type,
fun_as9138348466139350018nteger: $tType ).
thf(heap_T5738788834812785303t_unit_type,type,
heap_T5738788834812785303t_unit: $tType ).
thf(list_P8926467638345140077od_d_d_type,type,
list_P8926467638345140077od_d_d: $tType ).
thf(list_P8855433598298794092od_d_c_type,type,
list_P8855433598298794092od_d_c: $tType ).
thf(list_P338744602095350958od_c_d_type,type,
list_P338744602095350958od_c_d: $tType ).
thf(list_P267710562049004973od_c_c_type,type,
list_P267710562049004973od_c_c: $tType ).
thf(fun_d_620910671289397097od_d_d_type,type,
fun_d_620910671289397097od_d_d: $tType ).
thf(fun_d_1256559671894383786od_c_d_type,type,
fun_d_1256559671894383786od_c_d: $tType ).
thf(fun_c_1189316931574867241od_d_c_type,type,
fun_c_1189316931574867241od_d_c: $tType ).
thf(fun_c_1824965932179853930od_c_c_type,type,
fun_c_1824965932179853930od_c_c: $tType ).
thf(fun_Pr6626665806141890376t_assn_type,type,
fun_Pr6626665806141890376t_assn: $tType ).
thf(set_Product_prod_d_d_type,type,
set_Product_prod_d_d: $tType ).
thf(set_Product_prod_d_c_type,type,
set_Product_prod_d_c: $tType ).
thf(set_Product_prod_c_d_type,type,
set_Product_prod_c_d: $tType ).
thf(set_Product_prod_c_c_type,type,
set_Product_prod_c_c: $tType ).
thf(heap_e7401611519738050253t_unit_type,type,
heap_e7401611519738050253t_unit: $tType ).
thf(product_prod_num_num_type,type,
product_prod_num_num: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_nat_int_type,type,
product_prod_nat_int: $tType ).
thf(product_prod_int_nat_type,type,
product_prod_int_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(fun_d_fun_d_assn_type,type,
fun_d_fun_d_assn: $tType ).
thf(fun_d_fun_c_assn_type,type,
fun_d_fun_c_assn: $tType ).
thf(fun_c_fun_d_assn_type,type,
fun_c_fun_d_assn: $tType ).
thf(fun_c_fun_c_assn_type,type,
fun_c_fun_c_assn: $tType ).
thf(list_fun_nat_nat_type,type,
list_fun_nat_nat: $tType ).
thf(set_Product_prod_o_o_type,type,
set_Product_prod_o_o: $tType ).
thf(fun_num_Code_integer_type,type,
fun_num_Code_integer: $tType ).
thf(fun_nat_set_nat_type,type,
fun_nat_set_nat: $tType ).
thf(fun_nat_Code_integer_type,type,
fun_nat_Code_integer: $tType ).
thf(fun_int_Code_integer_type,type,
fun_int_Code_integer: $tType ).
thf(fun_Code_integer_num_type,type,
fun_Code_integer_num: $tType ).
thf(fun_Code_integer_nat_type,type,
fun_Code_integer_nat: $tType ).
thf(fun_Code_integer_int_type,type,
fun_Code_integer_int: $tType ).
thf(fun_assn_assn_type,type,
fun_assn_assn: $tType ).
thf(fun_fun_rat_rat_o_type,type,
fun_fun_rat_rat_o: $tType ).
thf(fun_fun_int_int_o_type,type,
fun_fun_int_int_o: $tType ).
thf(fun_num_fun_num_o_type,type,
fun_num_fun_num_o: $tType ).
thf(fun_nat_fun_nat_o_type,type,
fun_nat_fun_nat_o: $tType ).
thf(fun_nat_fun_int_o_type,type,
fun_nat_fun_int_o: $tType ).
thf(fun_int_fun_nat_o_type,type,
fun_int_fun_nat_o: $tType ).
thf(fun_int_fun_int_o_type,type,
fun_int_fun_int_o: $tType ).
thf(fun_set_o_set_o_type,type,
fun_set_o_set_o: $tType ).
thf(filter_set_nat_type,type,
filter_set_nat: $tType ).
thf(product_prod_d_nat_type,type,
product_prod_d_nat: $tType ).
thf(product_prod_d_int_type,type,
product_prod_d_int: $tType ).
thf(product_prod_c_nat_type,type,
product_prod_c_nat: $tType ).
thf(product_prod_c_int_type,type,
product_prod_c_int: $tType ).
thf(product_prod_nat_d_type,type,
product_prod_nat_d: $tType ).
thf(product_prod_nat_c_type,type,
product_prod_nat_c: $tType ).
thf(list_list_nat_type,type,
list_list_nat: $tType ).
thf(list_list_int_type,type,
list_list_int: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(list_set_int_type,type,
list_set_int: $tType ).
thf(list_Code_integer_type,type,
list_Code_integer: $tType ).
thf(fun_list_nat_o_type,type,
fun_list_nat_o: $tType ).
thf(fun_list_int_o_type,type,
fun_list_int_o: $tType ).
thf(fun_d_fun_nat_o_type,type,
fun_d_fun_nat_o: $tType ).
thf(fun_c_fun_nat_o_type,type,
fun_c_fun_nat_o: $tType ).
thf(fun_num_assn_type,type,
fun_num_assn: $tType ).
thf(fun_nat_fun_d_o_type,type,
fun_nat_fun_d_o: $tType ).
thf(fun_nat_fun_c_o_type,type,
fun_nat_fun_c_o: $tType ).
thf(fun_nat_assn_type,type,
fun_nat_assn: $tType ).
thf(fun_int_assn_type,type,
fun_int_assn: $tType ).
thf(fun_assn_num_type,type,
fun_assn_num: $tType ).
thf(fun_assn_nat_type,type,
fun_assn_nat: $tType ).
thf(fun_assn_int_type,type,
fun_assn_int: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(fun_Code_integer_o_type,type,
fun_Code_integer_o: $tType ).
thf(product_prod_d_d_type,type,
product_prod_d_d: $tType ).
thf(product_prod_d_c_type,type,
product_prod_d_c: $tType ).
thf(product_prod_c_d_type,type,
product_prod_c_d: $tType ).
thf(product_prod_c_c_type,type,
product_prod_c_c: $tType ).
thf(fun_list_d_o_type,type,
fun_list_d_o: $tType ).
thf(fun_list_c_o_type,type,
fun_list_c_o: $tType ).
thf(list_assn_type,type,
list_assn: $tType ).
thf(fun_d_fun_d_o_type,type,
fun_d_fun_d_o: $tType ).
thf(fun_d_assn_type,type,
fun_d_assn: $tType ).
thf(fun_c_fun_c_o_type,type,
fun_c_fun_c_o: $tType ).
thf(fun_c_assn_type,type,
fun_c_assn: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(list_set_o_type,type,
list_set_o: $tType ).
thf(fun_rat_rat_type,type,
fun_rat_rat: $tType ).
thf(fun_num_num_type,type,
fun_num_num: $tType ).
thf(fun_nat_num_type,type,
fun_nat_num: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_int_type,type,
fun_nat_int: $tType ).
thf(fun_int_rat_type,type,
fun_int_rat: $tType ).
thf(fun_int_num_type,type,
fun_int_num: $tType ).
thf(fun_int_nat_type,type,
fun_int_nat: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(set_assn_type,type,
set_assn: $tType ).
thf(fun_assn_o_type,type,
fun_assn_o: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(fun_o_fun_o_o_type,type,
fun_o_fun_o_o: $tType ).
thf(list_rat_type,type,
list_rat: $tType ).
thf(list_num_type,type,
list_num: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_natural_type,type,
code_natural: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(fun_rat_o_type,type,
fun_rat_o: $tType ).
thf(fun_num_o_type,type,
fun_num_o: $tType ).
thf(fun_nat_o_type,type,
fun_nat_o: $tType ).
thf(fun_int_o_type,type,
fun_int_o: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(list_d_type,type,
list_d: $tType ).
thf(list_c_type,type,
list_c: $tType ).
thf(set_d_type,type,
set_d: $tType ).
thf(set_c_type,type,
set_c: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(fun_d_o_type,type,
fun_d_o: $tType ).
thf(fun_c_o_type,type,
fun_c_o: $tType ).
thf(assn_type,type,
assn: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(fun_o_o_type,type,
fun_o_o: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(d_type,type,
d: $tType ).
thf(c_type,type,
c: $tType ).
thf(entails_type,type,
entails: fun_assn_fun_assn_o ).
thf(entailst_type,type,
entailst: assn > fun_assn_o ).
thf(pure_assn_type,type,
pure_assn: $o > assn ).
thf(fI_QUERY_type,type,
fI_QUERY: assn > assn > fun_assn_o ).
thf(fI_RESULT_type,type,
fI_RESULT: list_P8527749157015355191n_assn > assn > assn > fun_assn_o ).
thf(one_one_assn_type,type,
one_one_assn: assn ).
thf(bot_bot_assn_type,type,
bot_bot_assn: assn ).
thf(top_top_assn_type,type,
top_top_assn: assn ).
thf(aa_assn_o_type,type,
aa_assn_o: fun_assn_o > assn > $o ).
thf(aa_assn_fun_assn_o_type,type,
aa_assn_fun_assn_o: fun_assn_fun_assn_o > assn > fun_assn_o ).
thf(p_type,type,
p: assn ).
thf(q_type,type,
q: assn ).
thf(10,axiom,
! [A: list_P8527749157015355191n_assn,B: assn] : ( aa_assn_o @ ( fI_RESULT @ A @ B @ one_one_assn ) @ top_top_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5200_entails__solve__finalize_I1_J) ).
thf(52,plain,
! [A: list_P8527749157015355191n_assn,B: assn] : ( aa_assn_o @ ( fI_RESULT @ A @ B @ one_one_assn ) @ top_top_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $o] :
( ( ( pure_assn @ A )
= bot_bot_assn )
<=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_pure__assn__eq__false__iff) ).
thf(78,plain,
! [A: $o] :
( ( ( ( pure_assn @ A )
= bot_bot_assn )
=> ~ A )
& ( ~ A
=> ( ( pure_assn @ A )
= bot_bot_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( fI_QUERY @ A @ B ) @ one_one_assn )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_entails__solve__init_I2_J) ).
thf(85,plain,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( fI_QUERY @ A @ B ) @ one_one_assn )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: list_P8527749157015355191n_assn] : ( aa_assn_o @ ( fI_RESULT @ A @ one_one_assn @ one_one_assn ) @ one_one_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5202_entails__solve__finalize_I2_J) ).
thf(28,plain,
! [A: list_P8527749157015355191n_assn] : ( aa_assn_o @ ( fI_RESULT @ A @ one_one_assn @ one_one_assn ) @ one_one_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ent__refl) ).
thf(109,plain,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(23,axiom,
! [A: assn,B: assn,C: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ B ) @ C )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_ent__trans) ).
thf(105,plain,
! [A: assn,B: assn,C: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ B ) @ C )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ p ) @ q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ p ) @ q ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ p ) @ q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: assn] :
( ( one_one_assn = A )
<=> ( A = one_one_assn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_one__reorient) ).
thf(54,plain,
! [A: assn] :
( ( ( one_one_assn = A )
=> ( A = one_one_assn ) )
& ( ( A = one_one_assn )
=> ( one_one_assn = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ top_top_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5136_entt__true) ).
thf(50,plain,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ top_top_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ B ) @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ent__iffI) ).
thf(87,plain,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ B ) @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
bot_bot_assn != one_one_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_assn__basic__inequalities_I3_J) ).
thf(75,plain,
bot_bot_assn != one_one_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: list_P8527749157015355191n_assn,B: assn] : ( aa_assn_o @ ( fI_RESULT @ A @ B @ one_one_assn ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5201_frame__inference__finalize) ).
thf(30,plain,
! [A: list_P8527749157015355191n_assn,B: assn] : ( aa_assn_o @ ( fI_RESULT @ A @ B @ one_one_assn ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: assn,B: assn,C: assn] :
( ( aa_assn_o @ ( entailst @ A ) @ B )
=> ( ( aa_assn_o @ ( entailst @ B ) @ C )
=> ( aa_assn_o @ ( entailst @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_entt__trans) ).
thf(69,plain,
! [A: assn,B: assn,C: assn] :
( ( aa_assn_o @ ( entailst @ A ) @ B )
=> ( ( aa_assn_o @ ( entailst @ B ) @ C )
=> ( aa_assn_o @ ( entailst @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( aa_assn_o @ ( entailst @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ent__imp__entt) ).
thf(101,plain,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( aa_assn_o @ ( entailst @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [A: $o,B: $o] :
( ( ( pure_assn @ A )
= ( pure_assn @ B ) )
<=> ( A
<=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_pure__assn__eq__conv) ).
thf(32,plain,
! [A: $o,B: $o] :
( ( ( ( pure_assn @ A )
= ( pure_assn @ B ) )
=> ( ( A
=> B )
& ( B
=> A ) ) )
& ( ( ( A
=> B )
& ( B
=> A ) )
=> ( ( pure_assn @ A )
= ( pure_assn @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_entt__refl) ).
thf(45,plain,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ top_top_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5141_ent__true) ).
thf(103,plain,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ top_top_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(20,axiom,
! [A: $o,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ ( pure_assn @ A ) ) @ B )
<=> ( A
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ one_one_assn ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_ent__pure__pre__iff__sng) ).
thf(91,plain,
! [A: $o,B: assn] :
( ( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ ( pure_assn @ A ) ) @ B )
=> ( A
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ one_one_assn ) @ B ) ) )
& ( ( A
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ one_one_assn ) @ B ) )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ ( pure_assn @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [A: assn,B: assn] :
( ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B )
=> ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_is__entails) ).
thf(108,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
top_top_assn != one_one_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5135_assn__basic__inequalities_I1_J) ).
thf(72,plain,
top_top_assn != one_one_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ one_one_assn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_entt__emp) ).
thf(43,plain,
! [A: assn] : ( aa_assn_o @ ( entailst @ A ) @ one_one_assn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
top_top_assn != bot_bot_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5137_assn__basic__inequalities_I5_J) ).
thf(47,plain,
top_top_assn != bot_bot_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $o] :
( ( ( pure_assn @ A )
= one_one_assn )
<=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_pure__assn__eq__emp__iff) ).
thf(62,plain,
! [A: $o] :
( ( ( ( pure_assn @ A )
= one_one_assn )
=> A )
& ( A
=> ( ( pure_assn @ A )
= one_one_assn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ p ) @ bot_bot_assn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062P_A_092_060Longrightarrow_062_092_060_094sub_062A_Afalse_092_060close_062) ).
thf(90,plain,
aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ p ) @ bot_bot_assn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ bot_bot_assn ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ent__false) ).
thf(111,plain,
! [A: assn] : ( aa_assn_o @ ( aa_assn_fun_assn_o @ entails @ bot_bot_assn ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(113,plain,
$false,
inference(cvc4,[status(thm)],[52,78,85,28,109,105,27,54,50,87,75,30,69,101,32,45,103,91,108,72,43,47,62,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ITP219_3 : TPTP v8.2.0. Released v8.0.0.
% 0.13/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n032.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sat May 18 18:07:39 EDT 2024
% 0.17/0.39 % CPUTime :
% 1.30/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.40/2.49 % [INFO] Parsing done (1264ms).
% 6.56/2.51 % [INFO] Running in sequential loop mode.
% 7.83/3.00 % [INFO] eprover registered as external prover.
% 7.83/3.01 % [INFO] cvc4 registered as external prover.
% 7.83/3.02 % [INFO] Scanning for conjecture ...
% 10.36/3.76 % [INFO] Found a conjecture (or negated_conjecture) and 5835 axioms. Running axiom selection ...
% 11.27/3.97 % [INFO] Axiom selection finished. Selected 24 axioms (removed 5811 axioms).
% 11.27/4.01 % [INFO] Problem is typed first-order (TPTP TFF).
% 11.27/4.02 % [INFO] Type checking passed.
% 11.27/4.03 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 15.22/5.16 % External prover 'cvc4' found a proof!
% 15.22/5.16 % [INFO] Killing All external provers ...
% 15.22/5.16 % Time passed: 4584ms (effective reasoning time: 2647ms)
% 15.22/5.16 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 15.22/5.17 % Axioms used in derivation (24): fact_5202_entails__solve__finalize_I2_J, fact_1051_assn__basic__inequalities_I3_J, fact_15_entt__refl, fact_3_ent__iffI, fact_1044_entt__emp, fact_1110_entails__solve__init_I2_J, fact_1056_one__reorient, fact_5141_ent__true, fact_826_pure__assn__eq__conv, fact_5135_assn__basic__inequalities_I1_J, fact_5200_entails__solve__finalize_I1_J, fact_1054_ent__pure__pre__iff__sng, fact_7_ent__false, fact_6_is__entails, fact_5136_entt__true, fact_1__092_060open_062P_A_092_060Longrightarrow_062_092_060_094sub_062A_Afalse_092_060close_062, fact_1043_pure__assn__eq__emp__iff, fact_5137_assn__basic__inequalities_I5_J, fact_5201_frame__inference__finalize, fact_5_ent__trans, fact_24_entt__trans, fact_13_ent__imp__entt, fact_834_pure__assn__eq__false__iff, fact_4_ent__refl
% 15.22/5.17 % No. of inferences in proof: 52
% 15.22/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4584 ms resp. 2647 ms w/o parsing
% 15.46/5.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.66/5.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------