%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU772^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 : Wed Feb 25 09:37:04 AM UTC 2026
% Result : Theorem 36.38s 6.84s
% Output : Refutation 36.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 5457 (1465 equ; 0 cnn)
% Maximal formula atoms : 295 ( 88 avg)
% Number of connectives : 3354 ( 196 ~; 187 |; 934 &; 829 @)
% ( 6 <=>;1202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 304 ( 40 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 506 ( 503 usr; 299 con; 0-4 aty)
% Number of variables : 196 ( 0 ^; 148 !; 48 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_348,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_349,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_352,type,
sP4: $i > $i > $i > $i > $o ).
thf(func_def_355,type,
sP7: $i > $i > $o ).
thf(func_def_356,type,
sP8: $i > $o ).
thf(func_def_357,type,
sP9: $i > $i > $o ).
thf(func_def_358,type,
sP10: $i > $i > $o ).
thf(func_def_359,type,
sP11: $i > $o > $i > $i > $o ).
thf(func_def_362,type,
sP14: $i > $i > $i > $o ).
thf(func_def_370,type,
sK22: $i > $o ).
thf(func_def_393,type,
sK45: $i > $i > $o ).
thf(func_def_410,type,
sK62: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_411,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_414,type,
sK66: $i > $o ).
thf(func_def_415,type,
sK67: $i > $o ).
thf(func_def_425,type,
sK77: $i > $i > $i > $i ).
thf(func_def_428,type,
sK80: $i > $o ).
thf(func_def_434,type,
sK86: $i > $i > $o ).
thf(func_def_444,type,
sK96: $i > $o ).
thf(func_def_445,type,
sK97: $i > $o ).
thf(func_def_446,type,
sK98: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_447,type,
sK99: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_449,type,
sK101: $i > $i ).
thf(func_def_463,type,
sK115: ( $i > $o ) > $i > $i ).
thf(func_def_465,type,
sK117: $i > $o ).
thf(func_def_507,type,
sK159: $i > $o ).
thf(func_def_510,type,
sK162: $i > ( $i > $o ) > $i ).
thf(func_def_511,type,
sK163: $i > ( $i > $o ) > $i ).
thf(func_def_532,type,
sK184: $i > $i > $o ).
thf(func_def_536,type,
sK188: $i > $i > $i ).
thf(func_def_587,type,
sK239: $i > $o ).
thf(func_def_590,type,
sK242: $i > ( $i > $o ) > $i ).
thf(func_def_614,type,
sK266: $i > $i > $i > $i > $i ).
thf(func_def_626,type,
sK278: $i > ( $i > $i ) > $i > $i ).
thf(func_def_628,type,
sK280: $i > $i ).
thf(func_def_633,type,
sK285: $o > $i > $i > $i ).
thf(func_def_641,type,
sK293: $i > ( $i > $o ) > $i ).
thf(func_def_642,type,
sK294: $i > $o ).
thf(func_def_649,type,
sK301: $i > $i ).
thf(func_def_651,type,
sK303: $i > ( $i > $i ) > $i > $i ).
thf(func_def_656,type,
sK308: ( $i > $o ) > $i ).
thf(func_def_657,type,
sK309: $i > $o ).
thf(func_def_658,type,
sK310: $i > $i ).
thf(func_def_665,type,
sK317: $i > ( $i > $i ) > $i > $i ).
thf(func_def_667,type,
sK319: $i > $i ).
thf(func_def_669,type,
sK321: ( $i > $o ) > $i > $i ).
thf(func_def_671,type,
sK323: $i > $o ).
thf(func_def_675,type,
sK327: $i > $i > $i ).
thf(func_def_679,type,
sK331: ( $i > $o ) > $i ).
thf(func_def_680,type,
sK332: $i > $o ).
thf(func_def_715,type,
sK367: $i > $i > $i > $i > $i ).
thf(func_def_716,type,
sK368: $i > $i > $i > $i > $i ).
thf(func_def_724,type,
sK376: $i > $i > $i ).
thf(func_def_725,type,
sK377: $i > $i > $i ).
thf(func_def_737,type,
sK389: $i > $o ).
thf(func_def_739,type,
sK391: $i > ( $i > $o ) > $i ).
thf(func_def_741,type,
sK393: $i > ( $i > $o ) > $i ).
thf(func_def_742,type,
sK394: $i > $o ).
thf(func_def_747,type,
sK399: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_748,type,
sK400: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_749,type,
sK401: $i > $o ).
thf(func_def_750,type,
sK402: $i > $o ).
thf(func_def_758,type,
sK410: $i > $i > $i > $i > $i ).
thf(func_def_759,type,
sK411: $i > $i > $i > $i > $i ).
thf(func_def_760,type,
sK412: $i > $i > $i > $i > $i ).
thf(func_def_761,type,
sK413: $i > $i > $i > $i > $i ).
thf(func_def_777,type,
sK429: $i > $i > $o ).
thf(func_def_789,type,
sK441: $i > $i > $i > $i > $i ).
thf(func_def_800,type,
sK452: $i > $i > $o ).
thf(func_def_804,type,
sK456: $i > $i > $i > $i ).
thf(func_def_807,type,
sK459: $i > $o ).
thf(func_def_826,type,
sK478: $i > $i > $o ).
thf(func_def_827,type,
sK479: $i > $i ).
thf(func_def_828,type,
sK480: $i > $i ).
thf(func_def_829,type,
sK481: ( $i > $i > $o ) > $i > $i ).
thf(func_def_830,type,
sK482: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_831,type,
sK483: ( $i > $i > $o ) > $i > $i ).
thf(func_def_842,type,
sK494: $i > $i ).
thf(func_def_855,type,
sK507: $i > $i > $i ).
thf(func_def_856,type,
sK508: $i > $i > $i ).
thf(func_def_857,type,
sK509: $i > $i > $i ).
thf(func_def_858,type,
sK510: $i > $i > $i ).
thf(func_def_859,type,
sK511: $i > $i > $i ).
thf(func_def_860,type,
sK512: $i > $i > $i > $i ).
thf(func_def_861,type,
sK513: $i > $i ).
thf(func_def_862,type,
sK514: $i > $i ).
thf(func_def_863,type,
sK515: $i > $i ).
thf(func_def_864,type,
sK516: $i > $i ).
thf(func_def_865,type,
sK517: $i > $i > $i ).
thf(func_def_866,type,
sK518: $i > $i > $i > $i ).
thf(func_def_867,type,
sK519: $i > $i > $i > $i ).
thf(func_def_868,type,
sK520: $i > $i > $i ).
thf(func_def_869,type,
sK521: $i > $i > $i ).
thf(func_def_871,type,
sK523: $i > $i ).
thf(func_def_872,type,
sK524: $i > $i ).
thf(func_def_873,type,
sK525: $i > $i ).
thf(func_def_877,type,
sK529: $i > $i > $i ).
thf(func_def_887,type,
sK539: $i > $i > $o ).
thf(func_def_891,type,
sK543: $i > $i > $i ).
thf(func_def_895,type,
sK547: $i > $i > $i > $i ).
thf(func_def_896,type,
sK548: $i > $i > $i > $i ).
thf(func_def_913,type,
sK565: $i > $i > $i > $i > $i ).
thf(func_def_916,type,
sK568: $i > $i > $i ).
thf(func_def_924,type,
sK576: $i > $o ).
thf(func_def_932,type,
sK584: $i > $o ).
thf(func_def_934,type,
sK586: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_935,type,
sK587: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_947,type,
sK599: $i > $o ).
thf(func_def_950,type,
sK602: ( $i > $o ) > $i ).
thf(func_def_951,type,
sK603: $i > $o ).
thf(func_def_952,type,
sK604: $i > $i ).
thf(func_def_968,type,
sK620: $i > $o ).
thf(func_def_971,type,
sK623: $i > $o ).
thf(func_def_974,type,
sK626: $i > ( $i > $o ) > $i ).
thf(func_def_980,type,
sK632: $i > $o ).
thf(func_def_989,type,
sK641: $i > $o ).
thf(func_def_994,type,
sK646: $i > $o ).
thf(func_def_1015,type,
sK667: $i > $o ).
thf(func_def_1026,type,
sK678: $i > $o ).
thf(func_def_1029,type,
sK681: $i > ( $i > $o ) > $i ).
thf(func_def_1030,type,
sK682: $i > ( $i > $o ) > $i ).
thf(func_def_1043,type,
sK695: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1044,type,
sK696: $i > $i ).
thf(func_def_1048,type,
sK700: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1051,type,
sK703: $i > $i ).
thf(func_def_1053,type,
sK705: $i > $o ).
thf(func_def_1054,type,
sK706: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1056,type,
sK708: $i > $i ).
thf(func_def_1059,type,
sK711: $i > $o ).
thf(func_def_1087,type,
sK739: $i > $i > $i ).
thf(func_def_1105,type,
sK757: ( $i > $o ) > $i ).
thf(func_def_1106,type,
sK758: ( $i > $o ) > $i ).
thf(func_def_1107,type,
sK759: $i > $o ).
thf(func_def_1111,type,
sK763: $i > $o ).
thf(func_def_1112,type,
sK764: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1118,type,
sK770: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1119,type,
sK771: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1123,type,
sK775: $i > $o ).
thf(func_def_1128,type,
sK780: $i > $i ).
thf(func_def_1131,type,
sK783: $i > $i ).
thf(func_def_1139,type,
sK791: $i > $i > $i > $i ).
thf(func_def_1143,type,
sK795: $i > $i > $i > $i ).
thf(func_def_1154,type,
sK806: $i > $o ).
thf(func_def_1156,type,
sK808: ( $i > $o ) > $i > $i ).
thf(func_def_1157,type,
sK809: $i > $i ).
thf(func_def_1170,type,
sK822: $i > $o ).
thf(func_def_1178,type,
sK830: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1179,type,
sK831: $i > $i > $o ).
thf(func_def_1182,type,
sK834: $i > $i ).
thf(func_def_1199,type,
sK851: $i > $i > $o ).
thf(func_def_1221,type,
sK873: $i > $i ).
thf(func_def_1225,type,
sK877: $i > $o ).
thf(func_def_1227,type,
sK879: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1228,type,
sK880: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1260,type,
sK912: $i > $o ).
thf(func_def_1262,type,
sK914: $i > ( $i > $o ) > $i ).
thf(func_def_1270,type,
sK922: $i > $i > $i ).
thf(func_def_1273,type,
sK925: $i > $i > $o ).
thf(func_def_1284,type,
sK936: $i > $o ).
thf(func_def_1287,type,
sK939: $i > $i > $i ).
thf(func_def_1288,type,
sK940: $i > $i ).
thf(func_def_1295,type,
ph947:
!>[X0: $tType] : X0 ).
thf(f6113,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f5717,f5930,f6077,f6110]) ).
thf(f6110,plain,
( spl946_52
| spl946_69 ),
inference(avatar_split_clause,[status(thm)],[f6109,f6074,f5712]) ).
thf(f5712,definition,
( spl946_52
<=> ! [X2: $i] :
( ( $true
= ( sK459 @ X2 ) )
| ( ( in @ X2 @ sK457 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl946_52])],[avatar_definition]) ).
thf(f6074,definition,
( spl946_69
<=> ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl946_69])],[avatar_definition]) ).
thf(f6109,plain,
( ! [X0: $i] :
( ( ( sK459 @ X0 )
= $true )
| ( ( in @ X0 @ sK457 )
!= $true ) )
| spl946_69 ),
inference(subsumption_resolution,[status(thm)],[f6108,f3480]) ).
thf(f3480,plain,
( ( breln1 @ sK458 @ sK457 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1984]) ).
thf(f1984,plain,
( ( binintersectTELcontra = $true )
& ( woz1_4 = $true )
& ( setukpairinjR12 = $true )
& ( ksndpairEq = $true )
& ( setunionAx = $true )
& ( setOfPairsIsBReln = $true )
& ( ap2apEq1 = $true )
& ( omega0Ax = $true )
& ( setadjoinOr = $true )
& ( setOfPairsIsBReln1 = $true )
& ( kfstpairEq = $true )
& ( binintersectER = $true )
& ( subbreln = $true )
& ( setoftrueEq = $true )
& ( exuE3e = $true )
& ( powersetTE1 = $true )
& ( funcGraphProp1 = $true )
& ( singletonsuniq = $true )
& ( complementTE1 = $true )
& ( contrasubsetT3 = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( binintersectSubset1 = $true )
& ( doubleComplementI1 = $true )
& ( setext = $true )
& ( lam2lamEq = $true )
& ( singletoninpowerset = $true )
& ( cartprodpairmemEL = $true )
& ( emptysetimpfalse = $true )
& ( emptyinunitempty = $true )
& ( woz13rule1 = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinIL = $true )
& ( ex1E1 = $true )
& ( iftrueProp2 = $true )
& ( funcImageSingleton = $true )
& ( singletonsubset = $true )
& ( notdallE = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( setminusILneg = $true )
& ( iffalseProp2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( cartprodfstin = $true )
& ( cartprodmempair = $true )
& ( cartprodpairin = $true )
& ( setminusT_lem = $true )
& ( setunionE2 = $true )
& ( contrasubsetT1 = $true )
& ( demorgan2b2 = $true )
& ( upairequniteq = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndin = $true )
& ( prop2setI = $true )
& ( contrasubsetT2 = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( omegaSAx = $true )
& ( omegaIndAx = $true )
& ( demorgan2a1 = $true )
& ( iftrue = $true )
& ( funcGraphProp2 = $true )
& ( complementTI1 = $true )
& ( subsetTI = $true )
& ( woz1_5 = $true )
& ( prop2set2propI = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( ksndsingleton = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI1 = $true )
& ( setextsub = $true )
& ( exuI2 = $true )
& ( binunionTE = $true )
& ( setminusLsub = $true )
& ( setminusEL = $true )
& ( wellorderingAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjL2 = $true )
& ( woz1_3 = $true )
& ( inCongP = $true )
& ( lamp = $true )
& ( singletonprop = $true )
& ( omega__Cong = $true )
& ( setextT = $true )
& ( binunionEcases = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( funcinfuncset = $true )
& ( nonemptyImpWitness = $true )
& ( funcext = $true )
& ( ap2p = $true )
& ( iftrueProp1 = $true )
& ( brelnall1 = $true )
& ( binintersectT_lem = $true )
& ( binunionTILcontra = $true )
& ( exuI3 = $true )
& ( woz13rule4 = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( demorgan1a = $true )
& ( symdiffE = $true )
& ( inIntersectImpInUnion2 = $true )
& ( woz13rule2 = $true )
& ( powersetI1 = $true )
& ( woz13rule3 = $true )
& ( woz1_1 = $true )
& ( setukpairinjR = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinSub2 = $true )
& ( symdiffIneg2 = $true )
& ( emptyI = $true )
& ( emptysetsubset = $true )
& ( dpsetconstrERa = $true )
& ( setunionI = $true )
& ( symdiffI2 = $true )
& ( setminusSubset1 = $true )
& ( setadjoin__Cong = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetE2 = $true )
& ( kpairiskpair = $true )
& ( lamProp = $true )
& ( setbeta = $true )
& ( binintersectI = $true )
& ( upairsetIL = $true )
& ( demorgan1 = $true )
& ( binintersectSubset2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( cartprodmempaircEq = $true )
& ( binunionTIRcontra = $true )
& ( infuncsetfunc = $true )
& ( setminusER = $true )
& ( sepSubset = $true )
& ( setunionE = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset5 = $true )
& ( demorgan2a = $true )
& ( doubleComplementEq = $true )
& ( kpairp = $true )
& ( dsetconstrI = $true )
& ( breln1all2 = $true )
& ( cartprodfstpairEq = $true )
& ( bs114d = $true )
& ( setadjoinSub = $true )
& ( uniqinunit = $true )
& ( iftrueorfalse = $true )
& ( eta1 = $true )
& ( iffalseProp1 = $true )
& ( demorgan2b = $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK458 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK457 )
!= $true )
| ( $true
= ( sK459 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ sK458 )
!= $true ) )
& ( ( sK459 @ sK460 )
!= $true )
& ( $true
= ( in @ sK460 @ sK457 ) )
& ( ( breln1 @ sK458 @ sK457 )
= $true )
& ( setadjoinAx = $true )
& ( cartprodmempair1 = $true )
& ( ifp = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( complementTnotintersectT = $true )
& ( app = $true )
& ( ubforcartprodlem1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binunionT_lem = $true )
& ( powersetT_lem = $true )
& ( setminusELneg = $true )
& ( symdiffIneg1 = $true )
& ( exuE3u = $true )
& ( setunionsingleton2 = $true )
& ( powersetTI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectLsub = $true )
& ( dpsetconstrEL2 = $true )
& ( beta1 = $true )
& ( binunionE = $true )
& ( complementUnionInPowersetComplement = $true )
& ( quantDeMorgan1 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( setukpairinjL = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectRsub = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectTERcontra = $true )
& ( setukpairinjR11 = $true )
& ( choice2fnsingleton = $true )
& ( setunionsingleton = $true )
& ( binintersectEL = $true )
& ( upairset2E = $true )
& ( binunionLsub = $true )
& ( demorgan1b = $true )
& ( apProp = $true )
& ( dpsetconstrSub = $true )
& ( doubleComplementE1 = $true )
& ( binunionRsub = $true )
& ( woz1_2 = $true )
& ( inPowerset = $true )
& ( setextAx = $true )
& ( doubleComplementSub2 = $true )
& ( beta2 = $true )
& ( complementImpComplementIntersect = $true )
& ( eqbreln = $true )
& ( contraSubsetComplement = $true )
& ( notsubsetI = $true )
& ( exuEu = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( theeq = $true )
& ( cartprodpairmemER = $true )
& ( setminusSubset2 = $true )
& ( dsetconstrER = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL1 = $true )
& ( powerset__Cong = $true )
& ( ex1I2 = $true )
& ( kpairsurjEq = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( demorgan2a2 = $true )
& ( funcGraphProp4 = $true )
& ( lam2p = $true )
& ( binunionTEcontra = $true )
& ( notequalI1 = $true )
& ( setukpairIR = $true )
& ( emptyinPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( foundationAx = $true )
& ( dpsetconstrI = $true )
& ( subset2powerset = $true )
& ( subsetRefl = $true )
& ( breln1SetBreln1 = $true )
& ( disjointsetsI1 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( upairsubunion = $true )
& ( singletoninpowunion = $true )
& ( woz13rule0 = $true )
& ( notinemptyset = $true )
& ( kfstsingleton = $true )
& ( ap2apEq2 = $true )
& ( notdexE = $true )
& ( doubleComplementSub1 = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( funcGraphProp3 = $true )
& ( funcextLem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( nonemptyE1 = $true )
& ( setminusERneg = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( notequalI2 = $true )
& ( demorgan2 = $true )
& ( complementTcontraSubset = $true )
& ( setunion__Cong = $true )
& ( setukpairinjR1 = $true )
& ( subPowSU = $true )
& ( ubforcartprodlem2 = $true )
& ( upairset2IR = $true )
& ( theprop = $true )
& ( emptysetAx = $true )
& ( eqinunit = $true )
& ( subsetE = $true )
& ( emptyInPowerset = $true )
& ( iffalse = $true )
& ( setukpairIL = $true )
& ( complementT_lem = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( powersetsubset = $true )
& ( contrasubsetT = $true )
& ( funcext2 = $true )
& ( ex1I = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR2 = $true )
& ( notinsingleton = $true )
& ( symdiffI1 = $true )
& ( brelnall2 = $true )
& ( eta2 = $true )
& ( powersetI = $true )
& ( ifSingleton = $true )
& ( secondinupair = $true )
& ( subsetTrans = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460])],[f1135,f1983,f1982,f1981]) ).
thf(f1981,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X0 )
= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK458 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK457 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ sK458 )
!= $true ) )
& ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ sK457 )
= $true ) ) )
& ( ( breln1 @ sK458 @ sK457 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1982,plain,
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK458 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK457 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ sK458 )
!= $true ) )
& ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ sK457 )
= $true ) ) )
=> ( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK458 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK457 )
!= $true )
| ( $true
= ( sK459 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ sK458 )
!= $true ) )
& ? [X5: $i] :
( ( ( sK459 @ X5 )
!= $true )
& ( ( in @ X5 @ sK457 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1983,plain,
( ? [X5: $i] :
( ( ( sK459 @ X5 )
!= $true )
& ( ( in @ X5 @ sK457 )
= $true ) )
=> ( ( ( sK459 @ sK460 )
!= $true )
& ( $true
= ( in @ sK460 @ sK457 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1135,plain,
( ( binintersectTELcontra = $true )
& ( woz1_4 = $true )
& ( setukpairinjR12 = $true )
& ( ksndpairEq = $true )
& ( setunionAx = $true )
& ( setOfPairsIsBReln = $true )
& ( ap2apEq1 = $true )
& ( omega0Ax = $true )
& ( setadjoinOr = $true )
& ( setOfPairsIsBReln1 = $true )
& ( kfstpairEq = $true )
& ( binintersectER = $true )
& ( subbreln = $true )
& ( setoftrueEq = $true )
& ( exuE3e = $true )
& ( powersetTE1 = $true )
& ( funcGraphProp1 = $true )
& ( singletonsuniq = $true )
& ( complementTE1 = $true )
& ( contrasubsetT3 = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( binintersectSubset1 = $true )
& ( doubleComplementI1 = $true )
& ( setext = $true )
& ( lam2lamEq = $true )
& ( singletoninpowerset = $true )
& ( cartprodpairmemEL = $true )
& ( emptysetimpfalse = $true )
& ( emptyinunitempty = $true )
& ( woz13rule1 = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinIL = $true )
& ( ex1E1 = $true )
& ( iftrueProp2 = $true )
& ( funcImageSingleton = $true )
& ( singletonsubset = $true )
& ( notdallE = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( setminusILneg = $true )
& ( iffalseProp2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( cartprodfstin = $true )
& ( cartprodmempair = $true )
& ( cartprodpairin = $true )
& ( setminusT_lem = $true )
& ( setunionE2 = $true )
& ( contrasubsetT1 = $true )
& ( demorgan2b2 = $true )
& ( upairequniteq = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndin = $true )
& ( prop2setI = $true )
& ( contrasubsetT2 = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( omegaSAx = $true )
& ( omegaIndAx = $true )
& ( demorgan2a1 = $true )
& ( iftrue = $true )
& ( funcGraphProp2 = $true )
& ( complementTI1 = $true )
& ( subsetTI = $true )
& ( woz1_5 = $true )
& ( prop2set2propI = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( ksndsingleton = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI1 = $true )
& ( setextsub = $true )
& ( exuI2 = $true )
& ( binunionTE = $true )
& ( setminusLsub = $true )
& ( setminusEL = $true )
& ( wellorderingAx = $true )
& ( ubforcartprodlem3 = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjL2 = $true )
& ( woz1_3 = $true )
& ( inCongP = $true )
& ( lamp = $true )
& ( singletonprop = $true )
& ( omega__Cong = $true )
& ( setextT = $true )
& ( binunionEcases = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( funcinfuncset = $true )
& ( nonemptyImpWitness = $true )
& ( funcext = $true )
& ( ap2p = $true )
& ( iftrueProp1 = $true )
& ( brelnall1 = $true )
& ( binintersectT_lem = $true )
& ( binunionTILcontra = $true )
& ( exuI3 = $true )
& ( woz13rule4 = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( demorgan1a = $true )
& ( symdiffE = $true )
& ( inIntersectImpInUnion2 = $true )
& ( woz13rule2 = $true )
& ( powersetI1 = $true )
& ( woz13rule3 = $true )
& ( woz1_1 = $true )
& ( setukpairinjR = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinSub2 = $true )
& ( symdiffIneg2 = $true )
& ( emptyI = $true )
& ( emptysetsubset = $true )
& ( dpsetconstrERa = $true )
& ( setunionI = $true )
& ( symdiffI2 = $true )
& ( setminusSubset1 = $true )
& ( setadjoin__Cong = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subsetE2 = $true )
& ( kpairiskpair = $true )
& ( lamProp = $true )
& ( setbeta = $true )
& ( binintersectI = $true )
& ( upairsetIL = $true )
& ( demorgan1 = $true )
& ( binintersectSubset2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( cartprodmempaircEq = $true )
& ( binunionTIRcontra = $true )
& ( infuncsetfunc = $true )
& ( setminusER = $true )
& ( sepSubset = $true )
& ( setunionE = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectSubset5 = $true )
& ( demorgan2a = $true )
& ( doubleComplementEq = $true )
& ( kpairp = $true )
& ( dsetconstrI = $true )
& ( breln1all2 = $true )
& ( cartprodfstpairEq = $true )
& ( bs114d = $true )
& ( setadjoinSub = $true )
& ( uniqinunit = $true )
& ( iftrueorfalse = $true )
& ( eta1 = $true )
& ( iffalseProp1 = $true )
& ( demorgan2b = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X0 )
= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( setadjoinAx = $true )
& ( cartprodmempair1 = $true )
& ( ifp = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( complementTnotintersectT = $true )
& ( app = $true )
& ( ubforcartprodlem1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binunionT_lem = $true )
& ( powersetT_lem = $true )
& ( setminusELneg = $true )
& ( symdiffIneg1 = $true )
& ( exuE3u = $true )
& ( setunionsingleton2 = $true )
& ( powersetTI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectLsub = $true )
& ( dpsetconstrEL2 = $true )
& ( beta1 = $true )
& ( binunionE = $true )
& ( complementUnionInPowersetComplement = $true )
& ( quantDeMorgan1 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( setukpairinjL = $true )
& ( inIntersectImpInUnion = $true )
& ( binintersectRsub = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectTERcontra = $true )
& ( setukpairinjR11 = $true )
& ( choice2fnsingleton = $true )
& ( setunionsingleton = $true )
& ( binintersectEL = $true )
& ( upairset2E = $true )
& ( binunionLsub = $true )
& ( demorgan1b = $true )
& ( apProp = $true )
& ( dpsetconstrSub = $true )
& ( doubleComplementE1 = $true )
& ( binunionRsub = $true )
& ( woz1_2 = $true )
& ( inPowerset = $true )
& ( setextAx = $true )
& ( doubleComplementSub2 = $true )
& ( beta2 = $true )
& ( complementImpComplementIntersect = $true )
& ( eqbreln = $true )
& ( contraSubsetComplement = $true )
& ( notsubsetI = $true )
& ( exuEu = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( theeq = $true )
& ( cartprodpairmemER = $true )
& ( setminusSubset2 = $true )
& ( dsetconstrER = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL1 = $true )
& ( powerset__Cong = $true )
& ( ex1I2 = $true )
& ( kpairsurjEq = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( demorgan2a2 = $true )
& ( funcGraphProp4 = $true )
& ( lam2p = $true )
& ( binunionTEcontra = $true )
& ( notequalI1 = $true )
& ( setukpairIR = $true )
& ( emptyinPowerset = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( foundationAx = $true )
& ( dpsetconstrI = $true )
& ( subset2powerset = $true )
& ( subsetRefl = $true )
& ( breln1SetBreln1 = $true )
& ( disjointsetsI1 = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( upairsubunion = $true )
& ( singletoninpowunion = $true )
& ( woz13rule0 = $true )
& ( notinemptyset = $true )
& ( kfstsingleton = $true )
& ( ap2apEq2 = $true )
& ( notdexE = $true )
& ( doubleComplementSub1 = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( funcGraphProp3 = $true )
& ( funcextLem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( nonemptyE1 = $true )
& ( setminusERneg = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( notequalI2 = $true )
& ( demorgan2 = $true )
& ( complementTcontraSubset = $true )
& ( setunion__Cong = $true )
& ( setukpairinjR1 = $true )
& ( subPowSU = $true )
& ( ubforcartprodlem2 = $true )
& ( upairset2IR = $true )
& ( theprop = $true )
& ( emptysetAx = $true )
& ( eqinunit = $true )
& ( subsetE = $true )
& ( emptyInPowerset = $true )
& ( iffalse = $true )
& ( setukpairIL = $true )
& ( complementT_lem = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( powersetsubset = $true )
& ( contrasubsetT = $true )
& ( funcext2 = $true )
& ( ex1I = $true )
& ( upairinpowunion = $true )
& ( setukpairinjR2 = $true )
& ( notinsingleton = $true )
& ( symdiffI1 = $true )
& ( brelnall2 = $true )
& ( eta2 = $true )
& ( powersetI = $true )
& ( ifSingleton = $true )
& ( secondinupair = $true )
& ( subsetTrans = $true ) ),
inference(flattening,[status(thm)],[f1134]) ).
thf(f1134,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X0 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f833]) ).
thf(f833,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
=> ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X0 )
= $true )
=> ( $true
= ( X2 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f832]) ).
thf(f832,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X0 )
=> ( X2 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f294]) ).
thf(f294,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X13 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f293]) ).
thf(f293,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X13 )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1jLE4W7LvF/DTF2THF_3370.p',breln1all1) ).
thf(f6108,plain,
( ! [X0: $i] :
( ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( ( in @ X0 @ sK457 )
!= $true ) )
| spl946_69 ),
inference(subsumption_resolution,[status(thm)],[f6104,f3492]) ).
thf(f3492,plain,
breln1all2 = $true,
inference(cnf_transformation,[status(thm)],[f1984]) ).
thf(f6104,plain,
( ! [X0: $i] :
( ( breln1all2 != $true )
| ( ( sK459 @ X0 )
= $true )
| ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( in @ X0 @ sK457 )
!= $true ) )
| spl946_69 ),
inference(trivial_inequality_removal,[status(thm)],[f6101]) ).
thf(f6101,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK457 )
!= $true )
| ( $true != $true )
| ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( breln1all2 != $true ) )
| spl946_69 ),
inference(superposition,[status(thm)],[f6076,f4220]) ).
thf(f4220,plain,
! [X8: $i > $o,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( in @ ( sK879 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( ( in @ X9 @ X7 )
!= $true )
| ( breln1all2 != $true )
| ( $true
= ( X8 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f2653]) ).
thf(f2653,plain,
( ( ( breln1all2 = $true )
| ( ( $true
!= ( sK877 @ sK878 ) )
& ( ( in @ sK878 @ sK876 )
= $true )
& ! [X4: $i] :
( ( ( in @ X4 @ sK875 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ sK875 )
!= $true )
| ( ( sK877 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK876 ) ) ) )
& ( ( breln1 @ sK875 @ sK876 )
= $true ) ) )
& ( ! [X6: $i,X7: $i] :
( ! [X8: $i > $o] :
( ! [X9: $i] :
( ( $true
= ( X8 @ X9 ) )
| ( ( in @ X9 @ X7 )
!= $true ) )
| ( ( $true
= ( in @ ( sK879 @ X8 @ X7 @ X6 ) @ X6 ) )
& ( ( in @ ( sK880 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) ) )
& ( ( in @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true ) ) )
| ( $true
!= ( breln1 @ X6 @ X7 ) ) )
| ( breln1all2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK875,sK876,sK877,sK878,sK879,sK880])],[f2647,f2652,f2651,f2650,f2649,f2648]) ).
thf(f2648,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true ) ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
=> ( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ sK876 ) ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK875 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ sK875 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK876 ) ) ) ) )
& ( ( breln1 @ sK875 @ sK876 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2649,plain,
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( $true
= ( in @ X3 @ sK876 ) ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK875 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ sK875 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK876 ) ) ) ) )
=> ( ? [X3: $i] :
( ( ( sK877 @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ sK876 ) ) )
& ! [X4: $i] :
( ( ( in @ X4 @ sK875 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ sK875 )
!= $true )
| ( ( sK877 @ ( kpair @ X4 @ X5 ) )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK876 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2650,plain,
( ? [X3: $i] :
( ( ( sK877 @ X3 )
!= $true )
& ( $true
= ( in @ X3 @ sK876 ) ) )
=> ( ( $true
!= ( sK877 @ sK878 ) )
& ( ( in @ sK878 @ sK876 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2651,plain,
! [X6: $i,X7: $i,X8: $i > $o] :
( ? [X10: $i] :
( ( $true
= ( in @ X10 @ X6 ) )
& ? [X11: $i] :
( ( ( in @ X11 @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ X10 @ X11 ) ) )
& ( $true
= ( in @ ( kpair @ X10 @ X11 ) @ X7 ) ) ) )
=> ( ( $true
= ( in @ ( sK879 @ X8 @ X7 @ X6 ) @ X6 ) )
& ? [X11: $i] :
( ( ( in @ X11 @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ X11 ) ) )
& ( ( in @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ X11 ) @ X7 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2652,plain,
! [X6: $i,X7: $i,X8: $i > $o] :
( ? [X11: $i] :
( ( ( in @ X11 @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ X11 ) ) )
& ( ( in @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ X11 ) @ X7 )
= $true ) )
=> ( ( ( in @ ( sK880 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) ) )
& ( ( in @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2647,plain,
( ( ( breln1all2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X3: $i] :
( ( $true
!= ( X2 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ! [X5: $i] :
( ( ( in @ X5 @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X4 @ X5 ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X1 )
!= $true ) ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) ) )
& ( ! [X6: $i,X7: $i] :
( ! [X8: $i > $o] :
( ! [X9: $i] :
( ( $true
= ( X8 @ X9 ) )
| ( ( in @ X9 @ X7 )
!= $true ) )
| ? [X10: $i] :
( ( $true
= ( in @ X10 @ X6 ) )
& ? [X11: $i] :
( ( ( in @ X11 @ X6 )
= $true )
& ( $true
!= ( X8 @ ( kpair @ X10 @ X11 ) ) )
& ( $true
= ( in @ ( kpair @ X10 @ X11 ) @ X7 ) ) ) ) )
| ( $true
!= ( breln1 @ X6 @ X7 ) ) )
| ( breln1all2 != $true ) ) ),
inference(rectify,[status(thm)],[f2646]) ).
thf(f2646,plain,
( ( ( breln1all2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i > $o] :
( ? [X5: $i] :
( ( $true
!= ( X2 @ X5 ) )
& ( ( in @ X5 @ X1 )
= $true ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i > $o] :
( ! [X5: $i] :
( ( $true
= ( X2 @ X5 ) )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( $true
!= ( X2 @ ( kpair @ X3 @ X4 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ) ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) )
| ( breln1all2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1226]) ).
thf(f1226,plain,
( ( breln1all2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i > $o] :
( ! [X5: $i] :
( ( $true
= ( X2 @ X5 ) )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ? [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( $true
!= ( X2 @ ( kpair @ X3 @ X4 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ) ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f1225]) ).
thf(f1225,plain,
( ( breln1all2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i > $o] :
( ! [X5: $i] :
( ( $true
= ( X2 @ X5 ) )
| ( ( in @ X5 @ X1 )
!= $true ) )
| ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( X2 @ ( kpair @ X3 @ X4 ) ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( $true
= ( in @ X3 @ X0 ) ) ) )
| ( ( breln1 @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f652]) ).
thf(f652,plain,
( ( breln1all2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
=> ( $true
= ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) ) )
=> ! [X5: $i] :
( ( ( in @ X5 @ X1 )
= $true )
=> ( $true
= ( X2 @ X5 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f651]) ).
thf(f651,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
=> ( X2 @ ( kpair @ X3 @ X4 ) ) ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( X2 @ X5 ) ) ) )
= breln1all2 ),
inference(rectify,[status(thm)],[f289]) ).
thf(f289,axiom,
! [X3: $i,X13: $i] :
( ( ( breln1 @ X3 @ X13 )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( X0 @ ( kpair @ X1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X13 )
=> ( X0 @ X1 ) ) ) )
= breln1all2 ),
file('/export/starexec/sandbox/tmp/tmp.1jLE4W7LvF/DTF2THF_3370.p',breln1all2) ).
thf(f6076,plain,
( ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true )
| spl946_69 ),
inference(avatar_component_clause,[status(thm)],[f6074]) ).
thf(f6077,plain,
( ~ spl946_69
| spl946_52
| ~ spl946_53 ),
inference(avatar_split_clause,[status(thm)],[f6072,f5715,f5712,f6074]) ).
thf(f5715,definition,
( spl946_53
<=> ! [X0: $i] :
( ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl946_53])],[avatar_definition]) ).
thf(f6072,plain,
( ! [X0: $i] :
( ( ( sK459 @ X0 )
= $true )
| ( ( in @ X0 @ sK457 )
!= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true ) )
| ~ spl946_53 ),
inference(subsumption_resolution,[status(thm)],[f6071,f3480]) ).
thf(f6071,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK457 )
!= $true )
| ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true ) )
| ~ spl946_53 ),
inference(subsumption_resolution,[status(thm)],[f6063,f3492]) ).
thf(f6063,plain,
( ! [X0: $i] :
( ( breln1all2 != $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( ( in @ X0 @ sK457 )
!= $true )
| ( ( breln1 @ sK458 @ sK457 )
!= $true ) )
| ~ spl946_53 ),
inference(trivial_inequality_removal,[status(thm)],[f6062]) ).
thf(f6062,plain,
( ! [X0: $i] :
( ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true )
| ( ( in @ X0 @ sK457 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( $true != $true )
| ( breln1all2 != $true ) )
| ~ spl946_53 ),
inference(duplicate_literal_removal,[status(thm)],[f6061]) ).
thf(f6061,plain,
( ! [X0: $i] :
( ( ( breln1 @ sK458 @ sK457 )
!= $true )
| ( ( in @ X0 @ sK457 )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ sK458 ) @ sK458 )
!= $true )
| ( ( sK459 @ X0 )
= $true )
| ( breln1all2 != $true )
| ( ( breln1 @ sK458 @ sK457 )
!= $true ) )
| ~ spl946_53 ),
inference(superposition,[status(thm)],[f5716,f4219]) ).
thf(f4219,plain,
! [X8: $i > $o,X6: $i,X9: $i,X7: $i] :
( ( ( in @ ( sK880 @ X8 @ X7 @ X6 ) @ X6 )
= $true )
| ( $true
= ( X8 @ X9 ) )
| ( breln1all2 != $true )
| ( ( in @ X9 @ X7 )
!= $true )
| ( $true
!= ( breln1 @ X6 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f2653]) ).
thf(f5716,plain,
( ! [X0: $i] :
( ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true ) )
| ~ spl946_53 ),
inference(avatar_component_clause,[status(thm)],[f5715]) ).
thf(f5930,plain,
~ spl946_52,
inference(avatar_contradiction_clause,[status(thm)],[f5929]) ).
thf(f5929,plain,
( $false
| ~ spl946_52 ),
inference(subsumption_resolution,[status(thm)],[f5923,f3482]) ).
thf(f3482,plain,
( ( sK459 @ sK460 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1984]) ).
thf(f5923,plain,
( ( ( sK459 @ sK460 )
= $true )
| ~ spl946_52 ),
inference(trivial_inequality_removal,[status(thm)],[f5742]) ).
thf(f5742,plain,
( ( $true != $true )
| ( ( sK459 @ sK460 )
= $true )
| ~ spl946_52 ),
inference(superposition,[status(thm)],[f5713,f3481]) ).
thf(f3481,plain,
( $true
= ( in @ sK460 @ sK457 ) ),
inference(cnf_transformation,[status(thm)],[f1984]) ).
thf(f5713,plain,
( ! [X2: $i] :
( ( ( in @ X2 @ sK457 )
!= $true )
| ( $true
= ( sK459 @ X2 ) ) )
| ~ spl946_52 ),
inference(avatar_component_clause,[status(thm)],[f5712]) ).
thf(f5717,plain,
( spl946_52
| spl946_53
| spl946_52 ),
inference(avatar_split_clause,[status(thm)],[f5710,f5712,f5715,f5712]) ).
thf(f5710,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK459 @ X2 ) )
| ( $true
!= ( in @ X1 @ sK457 ) )
| ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( $true
= ( sK459 @ X1 ) )
| ( ( in @ X2 @ sK457 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f5709,f3492]) ).
thf(f5709,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK459 @ X1 ) )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( $true
= ( sK459 @ X2 ) )
| ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true )
| ( ( in @ X2 @ sK457 )
!= $true )
| ( breln1all2 != $true )
| ( $true
!= ( in @ X1 @ sK457 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5708]) ).
thf(f5708,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ sK457 )
!= $true )
| ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true )
| ( $true
= ( sK459 @ X1 ) )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( $true
!= ( in @ X1 @ sK457 ) )
| ( breln1all2 != $true )
| ( $true != $true )
| ( $true
= ( sK459 @ X2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f5705]) ).
thf(f5705,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK459 @ X1 ) )
| ( breln1all2 != $true )
| ( $true != $true )
| ( ( in @ X2 @ sK457 )
!= $true )
| ( ( in @ ( sK880 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true )
| ( $true
= ( sK459 @ X2 ) )
| ( ( in @ ( sK879 @ sK459 @ sK457 @ X0 ) @ sK458 )
!= $true )
| ( ( breln1 @ X0 @ sK457 )
!= $true )
| ( $true
!= ( in @ X1 @ sK457 ) ) ),
inference(superposition,[status(thm)],[f4218,f4559]) ).
thf(f4559,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
= ( sK459 @ ( kpair @ ( sK879 @ X0 @ sK457 @ X1 ) @ ( sK880 @ X0 @ sK457 @ X1 ) ) ) )
| ( $true
!= ( breln1 @ X1 @ sK457 ) )
| ( ( X0 @ X2 )
= $true )
| ( ( in @ X2 @ sK457 )
!= $true )
| ( $true
!= ( in @ ( sK880 @ X0 @ sK457 @ X1 ) @ sK458 ) )
| ( ( in @ ( sK879 @ X0 @ sK457 @ X1 ) @ sK458 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4529,f3492]) ).
thf(f4529,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( $true
!= ( breln1 @ X1 @ sK457 ) )
| ( ( in @ ( sK879 @ X0 @ sK457 @ X1 ) @ sK458 )
!= $true )
| ( ( in @ X2 @ sK457 )
!= $true )
| ( $true
= ( sK459 @ ( kpair @ ( sK879 @ X0 @ sK457 @ X1 ) @ ( sK880 @ X0 @ sK457 @ X1 ) ) ) )
| ( $true
!= ( in @ ( sK880 @ X0 @ sK457 @ X1 ) @ sK458 ) )
| ( breln1all2 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4519]) ).
thf(f4519,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( breln1all2 != $true )
| ( ( in @ X2 @ sK457 )
!= $true )
| ( ( X0 @ X2 )
= $true )
| ( $true
!= ( breln1 @ X1 @ sK457 ) )
| ( ( in @ ( sK879 @ X0 @ sK457 @ X1 ) @ sK458 )
!= $true )
| ( $true
= ( sK459 @ ( kpair @ ( sK879 @ X0 @ sK457 @ X1 ) @ ( sK880 @ X0 @ sK457 @ X1 ) ) ) )
| ( $true
!= ( in @ ( sK880 @ X0 @ sK457 @ X1 ) @ sK458 ) ) ),
inference(superposition,[status(thm)],[f3483,f4217]) ).
thf(f4217,plain,
! [X8: $i > $o,X6: $i,X9: $i,X7: $i] :
( ( ( in @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) @ X7 )
= $true )
| ( ( in @ X9 @ X7 )
!= $true )
| ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( breln1all2 != $true )
| ( $true
= ( X8 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f2653]) ).
thf(f3483,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ sK457 )
!= $true )
| ( ( in @ X3 @ sK458 )
!= $true )
| ( $true
= ( sK459 @ ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X4 @ sK458 ) ) ),
inference(cnf_transformation,[status(thm)],[f1984]) ).
thf(f4218,plain,
! [X8: $i > $o,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( X8 @ ( kpair @ ( sK879 @ X8 @ X7 @ X6 ) @ ( sK880 @ X8 @ X7 @ X6 ) ) ) )
| ( breln1all2 != $true )
| ( $true
= ( X8 @ X9 ) )
| ( ( in @ X9 @ X7 )
!= $true )
| ( $true
!= ( breln1 @ X6 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f2653]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU772^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:33:24 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEU772^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : Binary Relations on a Set
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : (! A:i.! R:i.breln1 A R -> (! phi:i>o.(! x:i.in x A ->
% 0.20/0.47 % (! y:i.in y A -> in (kpair x y) R -> phi (kpair x y))) ->
% 0.20/0.47 % (! x:i.in x R -> phi x)))
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.47 % Source : [Bro08]
% 0.20/0.47 % Names : ZFC274g [Bro08]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 627 ( 292 unt; 334 typ; 292 def)
% 0.20/0.47 % Number of atoms : 1754 ( 421 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 293 ( 5 avg)
% 0.20/0.47 % Number of connectives : 3771 ( 73 ~; 12 |; 46 &;2732 @)
% 0.20/0.47 % ( 14 <=>; 894 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 303 ( 2 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 152 ( 152 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 337 ( 334 usr; 292 con; 0-4 aty)
% 0.20/0.47 % Number of variables : 1009 ( 76 ^; 897 !; 36 ?;1009 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : http://mathgate.info/detsetitem.php?id=330
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(in_type,type,
% 0.20/0.47 in: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu_type,type,
% 0.20/0.47 exu: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu,definition,
% 0.20/0.47 ( exu
% 0.20/0.47 = ( ^ [Xphi: $i > $o] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx_type,type,
% 0.20/0.47 setextAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx,definition,
% 0.20/0.47 ( setextAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 <=> ( in @ Xx @ B ) )
% 0.20/0.47 => ( A = B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset_type,type,
% 0.20/0.47 emptyset: $i ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx_type,type,
% 0.20/0.47 emptysetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx,definition,
% 0.20/0.47 ( emptysetAx
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin_type,type,
% 0.20/0.47 setadjoin: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx_type,type,
% 0.20/0.47 setadjoinAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx,definition,
% 0.20/0.47 ( setadjoinAx
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 <=> ( ( Xy = Xx )
% 0.20/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powerset_type,type,
% 0.20/0.47 powerset: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx_type,type,
% 0.20/0.47 powersetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx,definition,
% 0.20/0.47 ( powersetAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 <=> ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunion_type,type,
% 0.20/0.47 setunion: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setunionAx_type,type,
% 0.20/0.47 setunionAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setunionAx,definition,
% 0.20/0.48 ( setunionAx
% 0.20/0.48 = ( ! [A: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.48 <=> ? [B: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omega_type,type,
% 0.20/0.48 omega: $i ).
% 0.20/0.48
% 0.20/0.48 thf(omega0Ax_type,type,
% 0.20/0.48 omega0Ax: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omega0Ax,definition,
% 0.20/0.48 ( omega0Ax
% 0.20/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omegaSAx_type,type,
% 0.20/0.48 omegaSAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omegaSAx,definition,
% 0.20/0.48 ( omegaSAx
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ omega )
% 0.20/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omegaIndAx_type,type,
% 0.20/0.48 omegaIndAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omegaIndAx,definition,
% 0.20/0.48 ( omegaIndAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ( ( in @ emptyset @ A )
% 0.20/0.48 & ! [Xx: $i] :
% 0.20/0.48 ( ( ( in @ Xx @ omega )
% 0.20/0.48 & ( in @ Xx @ A ) )
% 0.20/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ omega )
% 0.20/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(replAx_type,type,
% 0.20/0.48 replAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(replAx,definition,
% 0.20/0.48 ( replAx
% 0.20/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( exu
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.48 => ? [B: $i] :
% 0.20/0.48 ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 <=> ? [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ A )
% 0.20/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(foundationAx_type,type,
% 0.20/0.48 foundationAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(foundationAx,definition,
% 0.20/0.48 ( foundationAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.48 => ? [B: $i] :
% 0.20/0.48 ( ( in @ B @ A )
% 0.20/0.48 & ~ ? [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(wellorderingAx_type,type,
% 0.20/0.48 wellorderingAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(wellorderingAx,definition,
% 0.20/0.48 ( wellorderingAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ? [B: $i] :
% 0.20/0.48 ( ! [C: $i] :
% 0.20/0.48 ( ( in @ C @ B )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ A ) ) )
% 0.20/0.48 & ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( ( in @ Xx @ A )
% 0.20/0.48 & ( in @ Xy @ A ) )
% 0.20/0.48 => ( ! [C: $i] :
% 0.20/0.48 ( ( in @ C @ B )
% 0.20/0.48 => ( ( in @ Xx @ C )
% 0.20/0.48 <=> ( in @ Xy @ C ) ) )
% 0.20/0.48 => ( Xx = Xy ) ) )
% 0.20/0.48 & ! [C: $i,D: $i] :
% 0.20/0.48 ( ( ( in @ C @ B )
% 0.20/0.48 & ( in @ D @ B ) )
% 0.20/0.48 => ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ D ) )
% 0.20/0.48 | ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ D )
% 0.20/0.48 => ( in @ Xx @ C ) ) ) )
% 0.20/0.48 & ! [C: $i] :
% 0.20/0.48 ( ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ A ) )
% 0.20/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.48 => ? [D: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ D @ B )
% 0.20/0.48 & ( in @ Xx @ C )
% 0.20/0.48 & ~ ? [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ D )
% 0.20/0.48 & ( in @ Xy @ C ) )
% 0.20/0.48 & ! [E: $i] :
% 0.20/0.48 ( ( in @ E @ B )
% 0.20/0.48 => ( ! [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ E )
% 0.20/0.48 => ( in @ Xy @ D ) )
% 0.20/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(descr_type,type,
% 0.20/0.48 descr: ( $i > $o ) > $i ).
% 0.20/0.48
% 0.20/0.48 thf(descrp_type,type,
% 0.20/0.48 descrp: $o ).
% 0.20/0.48
% 0.20/0.48 thf(descrp,definition,
% 0.20/0.48 ( descrp
% 0.20/0.48 = ( ! [Xphi: $i > $o] :
% 0.20/0.48 ( ( exu
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 => ( Xphi
% 0.20/0.48 @ ( descr
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstr_type,type,
% 0.20/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrI_type,type,
% 0.20/0.48 dsetconstrI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrI,definition,
% 0.20/0.48 ( dsetconstrI
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( ( Xphi @ Xx )
% 0.20/0.48 => ( in @ Xx
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrEL_type,type,
% 0.20/0.48 dsetconstrEL: $o ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrEL,definition,
% 0.20/0.48 ( dsetconstrEL
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrER_type,type,
% 0.20/0.48 dsetconstrER: $o ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrER,definition,
% 0.20/0.48 ( dsetconstrER
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(exuE1_type,type,
% 0.20/0.48 exuE1: $o ).
% 0.20/0.48
% 0.20/0.48 thf(exuE1,definition,
% 0.20/0.48 ( exuE1
% 0.20/0.48 = ( ! [Xphi: $i > $o] :
% 0.20/0.48 ( ( exu
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 => ? [Xx: $i] :
% 0.20/0.48 ( ( Xphi @ Xx )
% 0.20/0.48 & ! [Xy: $i] :
% 0.20/0.48 ( ( Xphi @ Xy )
% 0.20/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(prop2set_type,type,
% 0.20/0.48 prop2set: $o > $i ).
% 0.20/0.48
% 0.20/0.48 thf(prop2setE_type,type,
% 0.20/0.48 prop2setE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(prop2setE,definition,
% 0.20/0.48 ( prop2setE
% 0.20/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.48 => Xphi ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetE_type,type,
% 0.20/0.48 emptysetE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetE,definition,
% 0.20/0.48 ( emptysetE
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ emptyset )
% 0.20/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetimpfalse_type,type,
% 0.20/0.48 emptysetimpfalse: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetimpfalse,definition,
% 0.20/0.48 ( emptysetimpfalse
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ emptyset )
% 0.20/0.48 => $false ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(notinemptyset_type,type,
% 0.20/0.48 notinemptyset: $o ).
% 0.20/0.48
% 0.20/0.48 thf(notinemptyset,definition,
% 0.20/0.48 ( notinemptyset
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(exuE3e_type,type,
% 0.20/0.48 exuE3e: $o ).
% 0.20/0.48
% 0.20/0.48 thf(exuE3e,definition,
% 0.20/0.48 ( exuE3e
% 0.20/0.48 = ( ! [Xphi: $i > $o] :
% 0.20/0.48 ( ( exu
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setext_type,type,
% 0.20/0.48 setext: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setext,definition,
% 0.20/0.48 ( setext
% 0.20/0.48 = ( ! [A: $i,B: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( in @ Xx @ B ) )
% 0.20/0.48 => ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 => ( in @ Xx @ A ) )
% 0.20/0.48 => ( A = B ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyI_type,type,
% 0.20/0.48 emptyI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptyI,definition,
% 0.20/0.48 ( emptyI
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ~ ( in @ Xx @ A )
% 0.20/0.48 => ( A = emptyset ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(noeltsimpempty_type,type,
% 0.20/0.48 noeltsimpempty: $o ).
% 0.20/0.48
% 0.20/0.48 thf(noeltsimpempty,definition,
% 0.20/0.48 ( noeltsimpempty
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ~ ( in @ Xx @ A )
% 0.20/0.48 => ( A = emptyset ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setbeta_type,type,
% 0.20/0.48 setbeta: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setbeta,definition,
% 0.20/0.48 ( setbeta
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( ( in @ Xx
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(nonempty_type,type,
% 0.20/0.48 nonempty: $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(nonempty,definition,
% 0.20/0.48 ( nonempty
% 0.20/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyE1_type,type,
% 0.20/0.48 nonemptyE1: $o ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyE1,definition,
% 0.20/0.48 ( nonemptyE1
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ( nonempty @ A )
% 0.20/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyI_type,type,
% 0.20/0.48 nonemptyI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyI,definition,
% 0.20/0.48 ( nonemptyI
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( ( Xphi @ Xx )
% 0.20/0.48 => ( nonempty
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyI1_type,type,
% 0.20/0.48 nonemptyI1: $o ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyI1,definition,
% 0.20/0.48 ( nonemptyI1
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinIL_type,type,
% 0.20/0.48 setadjoinIL: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinIL,definition,
% 0.20/0.48 ( setadjoinIL
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyinunitempty_type,type,
% 0.20/0.48 emptyinunitempty: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptyinunitempty,definition,
% 0.20/0.48 ( emptyinunitempty
% 0.20/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinIR_type,type,
% 0.20/0.48 setadjoinIR: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinIR,definition,
% 0.20/0.48 ( setadjoinIR
% 0.20/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ A )
% 0.20/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinE_type,type,
% 0.20/0.48 setadjoinE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinE,definition,
% 0.20/0.48 ( setadjoinE
% 0.20/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.48 => ! [Xphi: $o] :
% 0.20/0.48 ( ( ( Xy = Xx )
% 0.20/0.48 => Xphi )
% 0.20/0.48 => ( ( ( in @ Xy @ A )
% 0.20/0.48 => Xphi )
% 0.20/0.48 => Xphi ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinOr_type,type,
% 0.20/0.48 setadjoinOr: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinOr,definition,
% 0.20/0.48 ( setadjoinOr
% 0.20/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.48 => ( ( Xy = Xx )
% 0.20/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setoftrueEq_type,type,
% 0.20/0.48 setoftrueEq: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setoftrueEq,definition,
% 0.20/0.48 ( setoftrueEq
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xx: $i] : $true )
% 0.20/0.48 = A ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(powersetI_type,type,
% 0.20/0.48 powersetI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(powersetI,definition,
% 0.20/0.48 ( powersetI
% 0.20/0.48 = ( ! [A: $i,B: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 => ( in @ Xx @ A ) )
% 0.20/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyinPowerset_type,type,
% 0.20/0.48 emptyinPowerset: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptyinPowerset,definition,
% 0.20/0.48 ( emptyinPowerset
% 0.20/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyInPowerset_type,type,
% 0.20/0.48 emptyInPowerset: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptyInPowerset,definition,
% 0.20/0.48 ( emptyInPowerset
% 0.20/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(powersetE_type,type,
% 0.20/0.48 powersetE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(powersetE,definition,
% 0.20/0.48 ( powersetE
% 0.20/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.48 => ( ( in @ Xx @ B )
% 0.20/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setunionI_type,type,
% 0.20/0.48 setunionI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setunionI,definition,
% 0.20/0.48 ( setunionI
% 0.20/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 => ( ( in @ B @ A )
% 0.20/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setunionE_type,type,
% 0.20/0.48 setunionE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setunionE,definition,
% 0.20/0.48 ( setunionE
% 0.20/0.48 = ( ! [A: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.48 => ! [Xphi: $o] :
% 0.20/0.48 ( ! [B: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 => ( ( in @ B @ A )
% 0.20/0.48 => Xphi ) )
% 0.20/0.48 => Xphi ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(subPowSU_type,type,
% 0.20/0.48 subPowSU: $o ).
% 0.20/0.48
% 0.20/0.48 thf(subPowSU,definition,
% 0.20/0.48 ( subPowSU
% 0.20/0.48 = ( ! [A: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(exuE2_type,type,
% 0.20/0.48 exuE2: $o ).
% 0.20/0.48
% 0.20/0.48 thf(exuE2,definition,
% 0.20/0.48 ( exuE2
% 0.20/0.48 = ( ! [Xphi: $i > $o] :
% 0.20/0.48 ( ( exu
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 => ? [Xx: $i] :
% 0.20/0.48 ! [Xy: $i] :
% 0.20/0.48 ( ( Xphi @ Xy )
% 0.20/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyImpWitness_type,type,
% 0.20/0.48 nonemptyImpWitness: $o ).
% 0.20/0.48
% 0.20/0.48 thf(nonemptyImpWitness,definition,
% 0.20/0.48 ( nonemptyImpWitness
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ( nonempty @ A )
% 0.20/0.48 => ? [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 & $true ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(uniqinunit_type,type,
% 0.20/0.48 uniqinunit: $o ).
% 0.20/0.48
% 0.20/0.48 thf(uniqinunit,definition,
% 0.20/0.48 ( uniqinunit
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(notinsingleton_type,type,
% 0.20/0.48 notinsingleton: $o ).
% 0.20/0.48
% 0.20/0.48 thf(notinsingleton,definition,
% 0.20/0.48 ( notinsingleton
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( Xx != Xy )
% 0.20/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(eqinunit_type,type,
% 0.20/0.48 eqinunit: $o ).
% 0.20/0.48
% 0.20/0.48 thf(eqinunit,definition,
% 0.20/0.48 ( eqinunit
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( Xx = Xy )
% 0.20/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(singletonsswitch_type,type,
% 0.20/0.48 singletonsswitch: $o ).
% 0.20/0.48
% 0.20/0.48 thf(singletonsswitch,definition,
% 0.20/0.48 ( singletonsswitch
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetE_type,type,
% 0.20/0.48 upairsetE: $o ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetE,definition,
% 0.20/0.48 ( upairsetE
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.48 => ( ( Xz = Xx )
% 0.20/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetIL_type,type,
% 0.20/0.48 upairsetIL: $o ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetIL,definition,
% 0.20/0.48 ( upairsetIL
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetIR_type,type,
% 0.20/0.48 upairsetIR: $o ).
% 0.20/0.48
% 0.20/0.48 thf(upairsetIR,definition,
% 0.20/0.48 ( upairsetIR
% 0.20/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyE1_type,type,
% 0.20/0.48 emptyE1: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptyE1,definition,
% 0.20/0.48 ( emptyE1
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.48 ( ? [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 & ( Xphi @ Xx ) )
% 0.20/0.48 => ( ( ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 = emptyset )
% 0.20/0.48 => $false ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(vacuousDall_type,type,
% 0.32/0.48 vacuousDall: $o ).
% 0.32/0.48
% 0.32/0.48 thf(vacuousDall,definition,
% 0.32/0.48 ( vacuousDall
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ emptyset )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan1_type,type,
% 0.32/0.48 quantDeMorgan1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan1,definition,
% 0.32/0.48 ( quantDeMorgan1
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan2_type,type,
% 0.32/0.48 quantDeMorgan2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan2,definition,
% 0.32/0.48 ( quantDeMorgan2
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) )
% 0.32/0.48 => ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan3_type,type,
% 0.32/0.48 quantDeMorgan3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan3,definition,
% 0.32/0.48 ( quantDeMorgan3
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan4_type,type,
% 0.32/0.48 quantDeMorgan4: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan4,definition,
% 0.32/0.48 ( quantDeMorgan4
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) )
% 0.32/0.48 => ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setI_type,type,
% 0.32/0.48 prop2setI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setI,definition,
% 0.32/0.48 ( prop2setI
% 0.32/0.48 = ( ! [Xphi: $o] :
% 0.32/0.48 ( Xphi
% 0.32/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(set2prop_type,type,
% 0.32/0.48 set2prop: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2set2propI_type,type,
% 0.32/0.48 prop2set2propI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2set2propI,definition,
% 0.32/0.48 ( prop2set2propI
% 0.32/0.48 = ( ! [Xphi: $o] :
% 0.32/0.48 ( Xphi
% 0.32/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notdexE_type,type,
% 0.32/0.48 notdexE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notdexE,definition,
% 0.32/0.48 ( notdexE
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notdallE_type,type,
% 0.32/0.48 notdallE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notdallE,definition,
% 0.32/0.48 ( notdallE
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI1_type,type,
% 0.32/0.48 exuI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI1,definition,
% 0.32/0.48 ( exuI1
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 & ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI3_type,type,
% 0.32/0.48 exuI3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI3,definition,
% 0.32/0.48 ( exuI3
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.32/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI2_type,type,
% 0.32/0.48 exuI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI2,definition,
% 0.32/0.48 ( exuI2
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 <=> ( Xy = Xx ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(inCongP_type,type,
% 0.32/0.48 inCongP: $o ).
% 0.32/0.48
% 0.32/0.48 thf(inCongP,definition,
% 0.32/0.48 ( inCongP
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(in__Cong_type,type,
% 0.32/0.48 in__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(in__Cong,definition,
% 0.32/0.48 ( in__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3u_type,type,
% 0.32/0.48 exuE3u: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3u,definition,
% 0.32/0.48 ( exuE3u
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exu__Cong_type,type,
% 0.32/0.48 exu__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exu__Cong,definition,
% 0.32/0.48 ( exu__Cong
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 <=> ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset__Cong_type,type,
% 0.32/0.48 emptyset__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset__Cong,definition,
% 0.32/0.48 ( emptyset__Cong
% 0.32/0.48 = ( emptyset = emptyset ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin__Cong_type,type,
% 0.32/0.48 setadjoin__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin__Cong,definition,
% 0.32/0.48 ( setadjoin__Cong
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ! [Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( Xz = Xu )
% 0.32/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.32/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powerset__Cong_type,type,
% 0.32/0.48 powerset__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powerset__Cong,definition,
% 0.32/0.48 ( powerset__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( ( powerset @ A )
% 0.32/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunion__Cong_type,type,
% 0.32/0.48 setunion__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunion__Cong,definition,
% 0.32/0.48 ( setunion__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( ( setunion @ A )
% 0.32/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(omega__Cong_type,type,
% 0.32/0.48 omega__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(omega__Cong,definition,
% 0.32/0.48 ( omega__Cong
% 0.32/0.48 = ( omega = omega ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuEu_type,type,
% 0.32/0.48 exuEu: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuEu,definition,
% 0.32/0.48 ( exuEu
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(descr__Cong_type,type,
% 0.32/0.48 descr__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(descr__Cong,definition,
% 0.32/0.48 ( descr__Cong
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.32/0.48 => ( ( descr
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 = ( descr
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstr__Cong_type,type,
% 0.32/0.48 dsetconstr__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstr__Cong,definition,
% 0.32/0.48 ( dsetconstr__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.32/0.48 => ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 = ( dsetconstr @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subset_type,type,
% 0.32/0.48 subset: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(disjoint_type,type,
% 0.32/0.48 disjoint: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setsmeet_type,type,
% 0.32/0.48 setsmeet: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI1_type,type,
% 0.32/0.48 subsetI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI1,definition,
% 0.32/0.48 ( subsetI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset2_type,type,
% 0.32/0.48 eqimpsubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset2,definition,
% 0.32/0.48 ( eqimpsubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset1_type,type,
% 0.32/0.48 eqimpsubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset1,definition,
% 0.32/0.48 ( eqimpsubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2_type,type,
% 0.32/0.48 subsetI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2,definition,
% 0.32/0.48 ( subsetI2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetsubset_type,type,
% 0.32/0.48 emptysetsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetsubset,definition,
% 0.32/0.48 ( emptysetsubset
% 0.32/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE_type,type,
% 0.32/0.48 subsetE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE,definition,
% 0.32/0.48 ( subsetE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE2_type,type,
% 0.32/0.48 subsetE2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE2,definition,
% 0.32/0.48 ( subsetE2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notsubsetI_type,type,
% 0.32/0.48 notsubsetI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notsubsetI,definition,
% 0.32/0.48 ( notsubsetI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI1_type,type,
% 0.32/0.48 notequalI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI1,definition,
% 0.32/0.48 ( notequalI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ~ ( subset @ A @ B )
% 0.32/0.48 => ( A != B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI2_type,type,
% 0.32/0.48 notequalI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI2,definition,
% 0.32/0.48 ( notequalI2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( A != B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetRefl_type,type,
% 0.32/0.48 subsetRefl: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetRefl,definition,
% 0.32/0.48 ( subsetRefl
% 0.32/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetTrans_type,type,
% 0.32/0.48 subsetTrans: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetTrans,definition,
% 0.32/0.48 ( subsetTrans
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( subset @ B @ C )
% 0.32/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub_type,type,
% 0.32/0.48 setadjoinSub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub,definition,
% 0.32/0.48 ( setadjoinSub
% 0.32/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub2_type,type,
% 0.32/0.48 setadjoinSub2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub2,definition,
% 0.32/0.48 ( setadjoinSub2
% 0.32/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subset2powerset_type,type,
% 0.32/0.48 subset2powerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subset2powerset,definition,
% 0.32/0.48 ( subset2powerset
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setextsub_type,type,
% 0.32/0.48 setextsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setextsub,definition,
% 0.32/0.48 ( setextsub
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( subset @ B @ A )
% 0.32/0.48 => ( A = B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetemptysetimpeq_type,type,
% 0.32/0.48 subsetemptysetimpeq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetemptysetimpeq,definition,
% 0.32/0.48 ( subsetemptysetimpeq
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( subset @ A @ emptyset )
% 0.32/0.48 => ( A = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI1_type,type,
% 0.32/0.48 powersetI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI1,definition,
% 0.32/0.48 ( powersetI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ B @ A )
% 0.32/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE1_type,type,
% 0.32/0.48 powersetE1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE1,definition,
% 0.32/0.48 ( powersetE1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(inPowerset_type,type,
% 0.32/0.48 inPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(inPowerset,definition,
% 0.32/0.48 ( inPowerset
% 0.32/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetsubset_type,type,
% 0.32/0.48 powersetsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetsubset,definition,
% 0.32/0.48 ( powersetsubset
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sepInPowerset_type,type,
% 0.32/0.48 sepInPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(sepInPowerset,definition,
% 0.32/0.48 ( sepInPowerset
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( in
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sepSubset_type,type,
% 0.32/0.48 sepSubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(sepSubset,definition,
% 0.32/0.48 ( sepSubset
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( subset
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunion_type,type,
% 0.32/0.48 binunion: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIL_type,type,
% 0.32/0.48 binunionIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIL,definition,
% 0.32/0.48 ( binunionIL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2IR_type,type,
% 0.32/0.48 upairset2IR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2IR,definition,
% 0.32/0.48 ( upairset2IR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIR_type,type,
% 0.32/0.48 binunionIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIR,definition,
% 0.32/0.48 ( binunionIR
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionEcases_type,type,
% 0.32/0.48 binunionEcases: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionEcases,definition,
% 0.32/0.48 ( binunionEcases
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.32/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/0.48 => ( ( ( in @ Xx @ A )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => ( ( ( in @ Xx @ B )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionE_type,type,
% 0.32/0.48 binunionE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionE,definition,
% 0.32/0.48 ( binunionE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionLsub_type,type,
% 0.32/0.48 binunionLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionLsub,definition,
% 0.32/0.48 ( binunionLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionRsub_type,type,
% 0.32/0.48 binunionRsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionRsub,definition,
% 0.32/0.48 ( binunionRsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersect_type,type,
% 0.32/0.48 binintersect: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectI_type,type,
% 0.32/0.48 binintersectI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectI,definition,
% 0.32/0.48 ( binintersectI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset5_type,type,
% 0.32/0.48 binintersectSubset5: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset5,definition,
% 0.32/0.48 ( binintersectSubset5
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( subset @ C @ A )
% 0.32/0.48 => ( ( subset @ C @ B )
% 0.32/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectEL_type,type,
% 0.32/0.48 binintersectEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectEL,definition,
% 0.32/0.48 ( binintersectEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectLsub_type,type,
% 0.32/0.48 binintersectLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectLsub,definition,
% 0.32/0.48 ( binintersectLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset2_type,type,
% 0.32/0.48 binintersectSubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset2,definition,
% 0.32/0.48 ( binintersectSubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset3_type,type,
% 0.32/0.48 binintersectSubset3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset3,definition,
% 0.32/0.48 ( binintersectSubset3
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( binintersect @ A @ B )
% 0.32/0.48 = B )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectER_type,type,
% 0.32/0.48 binintersectER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectER,definition,
% 0.32/0.48 ( binintersectER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(disjointsetsI1_type,type,
% 0.32/0.48 disjointsetsI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(disjointsetsI1,definition,
% 0.32/0.48 ( disjointsetsI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( in @ Xx @ B ) )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectRsub_type,type,
% 0.32/0.48 binintersectRsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectRsub,definition,
% 0.32/0.48 ( binintersectRsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset4_type,type,
% 0.32/0.48 binintersectSubset4: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset4,definition,
% 0.32/0.48 ( binintersectSubset4
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ B @ A )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset1_type,type,
% 0.32/0.48 binintersectSubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset1,definition,
% 0.32/0.48 ( binintersectSubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( binintersect @ A @ B )
% 0.32/0.48 = A )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(bs114d_type,type,
% 0.32/0.48 bs114d: $o ).
% 0.32/0.48
% 0.32/0.48 thf(bs114d,definition,
% 0.32/0.48 ( bs114d
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.32/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(regular_type,type,
% 0.32/0.48 regular: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminus_type,type,
% 0.32/0.48 setminus: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setminusI_type,type,
% 0.32/0.48 setminusI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusI,definition,
% 0.32/0.48 ( setminusI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusEL_type,type,
% 0.32/0.48 setminusEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusEL,definition,
% 0.32/0.48 ( setminusEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusER_type,type,
% 0.32/0.48 setminusER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusER,definition,
% 0.32/0.48 ( setminusER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset2_type,type,
% 0.32/0.48 setminusSubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset2,definition,
% 0.32/0.48 ( setminusSubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( setminus @ A @ B )
% 0.32/0.48 = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusERneg_type,type,
% 0.32/0.48 setminusERneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusERneg,definition,
% 0.32/0.48 ( setminusERneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusELneg_type,type,
% 0.32/0.48 setminusELneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusELneg,definition,
% 0.32/0.48 ( setminusELneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusILneg_type,type,
% 0.32/0.48 setminusILneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusILneg,definition,
% 0.32/0.48 ( setminusILneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusIRneg_type,type,
% 0.32/0.48 setminusIRneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusIRneg,definition,
% 0.32/0.48 ( setminusIRneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusLsub_type,type,
% 0.32/0.48 setminusLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusLsub,definition,
% 0.32/0.48 ( setminusLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset1_type,type,
% 0.32/0.48 setminusSubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset1,definition,
% 0.32/0.48 ( setminusSubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( setminus @ A @ B )
% 0.32/0.48 = emptyset )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiff_type,type,
% 0.32/0.48 symdiff: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffE_type,type,
% 0.32/0.48 symdiffE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffE,definition,
% 0.32/0.48 ( symdiffE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.32/0.48 => ! [Xphi: $o] :
% 0.32/0.48 ( ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => Xphi ) )
% 0.32/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => Xphi ) )
% 0.32/0.48 => Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI1_type,type,
% 0.32/0.48 symdiffI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI1,definition,
% 0.32/0.48 ( symdiffI1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI2_type,type,
% 0.32/0.48 symdiffI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI2,definition,
% 0.32/0.48 ( symdiffI2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg1_type,type,
% 0.32/0.48 symdiffIneg1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg1,definition,
% 0.32/0.48 ( symdiffIneg1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg2_type,type,
% 0.32/0.48 symdiffIneg2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg2,definition,
% 0.32/0.48 ( symdiffIneg2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iskpair_type,type,
% 0.32/0.48 iskpair: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(secondinupair_type,type,
% 0.32/0.48 secondinupair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(secondinupair,definition,
% 0.32/0.48 ( secondinupair
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIL_type,type,
% 0.32/0.48 setukpairIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIL,definition,
% 0.32/0.48 ( setukpairIL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIR_type,type,
% 0.32/0.48 setukpairIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIR,definition,
% 0.32/0.48 ( setukpairIR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpairiskpair_type,type,
% 0.32/0.48 kpairiskpair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairiskpair,definition,
% 0.32/0.48 ( kpairiskpair
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpair_type,type,
% 0.32/0.48 kpair: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(kpairp_type,type,
% 0.32/0.48 kpairp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairp,definition,
% 0.32/0.48 ( kpairp
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprod_type,type,
% 0.32/0.48 cartprod: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsubset_type,type,
% 0.32/0.48 singletonsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsubset,definition,
% 0.32/0.48 ( singletonsubset
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowerset_type,type,
% 0.32/0.48 singletoninpowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowerset,definition,
% 0.32/0.48 ( singletoninpowerset
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowunion_type,type,
% 0.32/0.48 singletoninpowunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowunion,definition,
% 0.32/0.48 ( singletoninpowunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2E_type,type,
% 0.32/0.48 upairset2E: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2E,definition,
% 0.32/0.48 ( upairset2E
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/0.48 => ( ( Xz = Xx )
% 0.32/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairsubunion_type,type,
% 0.32/0.48 upairsubunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsubunion,definition,
% 0.32/0.48 ( upairsubunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairinpowunion_type,type,
% 0.32/0.48 upairinpowunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairinpowunion,definition,
% 0.32/0.48 ( upairinpowunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem1_type,type,
% 0.32/0.48 ubforcartprodlem1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem1,definition,
% 0.32/0.48 ( ubforcartprodlem1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem2_type,type,
% 0.32/0.48 ubforcartprodlem2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem2,definition,
% 0.32/0.48 ( ubforcartprodlem2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem3_type,type,
% 0.32/0.48 ubforcartprodlem3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem3,definition,
% 0.32/0.48 ( ubforcartprodlem3
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairin_type,type,
% 0.32/0.48 cartprodpairin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairin,definition,
% 0.32/0.48 ( cartprodpairin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair1_type,type,
% 0.32/0.48 cartprodmempair1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair1,definition,
% 0.32/0.48 ( cartprodmempair1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ? [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 & ( Xu
% 0.32/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair_type,type,
% 0.32/0.48 cartprodmempair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair,definition,
% 0.32/0.48 ( cartprodmempair
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( iskpair @ Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE2_type,type,
% 0.32/0.48 setunionE2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE2,definition,
% 0.32/0.48 ( setunionE2
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.48 => ? [X: $i] :
% 0.32/0.48 ( ( in @ X @ A )
% 0.32/0.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton1_type,type,
% 0.32/0.48 setunionsingleton1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton1,definition,
% 0.32/0.48 ( setunionsingleton1
% 0.32/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton2_type,type,
% 0.32/0.48 setunionsingleton2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton2,definition,
% 0.32/0.48 ( setunionsingleton2
% 0.32/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton_type,type,
% 0.32/0.48 setunionsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton,definition,
% 0.32/0.48 ( setunionsingleton
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.32/0.48 = Xx ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singleton_type,type,
% 0.32/0.48 singleton: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonprop_type,type,
% 0.32/0.48 singletonprop: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonprop,definition,
% 0.32/0.48 ( singletonprop
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) )
% 0.32/0.48 => ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1_type,type,
% 0.32/0.48 ex1: $i > ( $i > $o ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E1_type,type,
% 0.32/0.48 ex1E1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E1,definition,
% 0.32/0.48 ( ex1E1
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ( ex1 @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I_type,type,
% 0.32/0.48 ex1I: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I,definition,
% 0.32/0.48 ( ex1I
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xy = Xx ) ) )
% 0.32/0.48 => ( ex1 @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I2_type,type,
% 0.32/0.48 ex1I2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I2,definition,
% 0.32/0.48 ( ex1I2
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) )
% 0.32/0.48 => ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ( ex1 @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsuniq_type,type,
% 0.32/0.48 singletonsuniq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsuniq,definition,
% 0.32/0.48 ( singletonsuniq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( ( setadjoin @ Xx @ emptyset )
% 0.32/0.48 = ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(atmost1p_type,type,
% 0.32/0.48 atmost1p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(atleast2p_type,type,
% 0.32/0.48 atleast2p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(atmost2p_type,type,
% 0.32/0.48 atmost2p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetp_type,type,
% 0.32/0.48 upairsetp: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL1_type,type,
% 0.32/0.48 setukpairinjL1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL1,definition,
% 0.32/0.48 ( setukpairinjL1
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kfstsingleton_type,type,
% 0.32/0.48 kfstsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kfstsingleton,definition,
% 0.32/0.48 ( kfstsingleton
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.32/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(theprop_type,type,
% 0.32/0.48 theprop: $o ).
% 0.32/0.48
% 0.32/0.48 thf(theprop,definition,
% 0.32/0.48 ( theprop
% 0.32/0.48 = ( ! [X: $i] :
% 0.32/0.48 ( ( singleton @ X )
% 0.32/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kfst_type,type,
% 0.32/0.48 kfst: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(kfstpairEq_type,type,
% 0.32/0.48 kfstpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kfstpairEq,definition,
% 0.32/0.48 ( kfstpairEq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xx ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstin_type,type,
% 0.32/0.48 cartprodfstin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstin,definition,
% 0.32/0.48 ( cartprodfstin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL2_type,type,
% 0.32/0.48 setukpairinjL2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL2,definition,
% 0.32/0.48 ( setukpairinjL2
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL_type,type,
% 0.32/0.48 setukpairinjL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL,definition,
% 0.32/0.48 ( setukpairinjL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xz @ Xu ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR11_type,type,
% 0.32/0.48 setukpairinjR11: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR11,definition,
% 0.32/0.48 ( setukpairinjR11
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR12_type,type,
% 0.32/0.48 setukpairinjR12: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR12,definition,
% 0.32/0.48 ( setukpairinjR12
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR1_type,type,
% 0.32/0.48 setukpairinjR1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR1,definition,
% 0.32/0.48 ( setukpairinjR1
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( ( Xz = Xu )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairequniteq_type,type,
% 0.32/0.48 upairequniteq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairequniteq,definition,
% 0.32/0.48 ( upairequniteq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR2_type,type,
% 0.32/0.48 setukpairinjR2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR2,definition,
% 0.32/0.48 ( setukpairinjR2
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR_type,type,
% 0.32/0.48 setukpairinjR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR,definition,
% 0.32/0.48 ( setukpairinjR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xz @ Xu ) )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ksndsingleton_type,type,
% 0.32/0.48 ksndsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ksndsingleton,definition,
% 0.32/0.48 ( ksndsingleton
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.32/0.48 @ ^ [Xx: $i] :
% 0.32/0.48 ( Xu
% 0.32/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ksnd_type,type,
% 0.32/0.48 ksnd: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(ksndpairEq_type,type,
% 0.32/0.48 ksndpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ksndpairEq,definition,
% 0.32/0.48 ( ksndpairEq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xy ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpairsurjEq_type,type,
% 0.32/0.48 kpairsurjEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairsurjEq,definition,
% 0.32/0.48 ( kpairsurjEq
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.32/0.48 = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndin_type,type,
% 0.32/0.48 cartprodsndin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndin,definition,
% 0.32/0.48 ( cartprodsndin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemEL_type,type,
% 0.32/0.48 cartprodpairmemEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemEL,definition,
% 0.32/0.48 ( cartprodpairmemEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemER_type,type,
% 0.32/0.48 cartprodpairmemER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemER,definition,
% 0.32/0.48 ( cartprodpairmemER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempaircEq_type,type,
% 0.32/0.48 cartprodmempaircEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempaircEq,definition,
% 0.32/0.48 ( cartprodmempaircEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstpairEq_type,type,
% 0.32/0.48 cartprodfstpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstpairEq,definition,
% 0.32/0.48 ( cartprodfstpairEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndpairEq_type,type,
% 0.32/0.48 cartprodsndpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndpairEq,definition,
% 0.32/0.48 ( cartprodsndpairEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairsurjEq_type,type,
% 0.32/0.48 cartprodpairsurjEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairsurjEq,definition,
% 0.32/0.48 ( cartprodpairsurjEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.32/0.48 = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(breln_type,type,
% 0.32/0.48 breln: $i > $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(breln,definition,
% 0.32/0.48 ( breln
% 0.32/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstr_type,type,
% 0.32/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI_type,type,
% 0.32/0.48 dpsetconstrI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI,definition,
% 0.32/0.48 ( dpsetconstrI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrSub_type,type,
% 0.32/0.48 dpsetconstrSub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrSub,definition,
% 0.32/0.48 ( dpsetconstrSub
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.48 ( subset
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.32/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setOfPairsIsBReln_type,type,
% 0.32/0.48 setOfPairsIsBReln: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setOfPairsIsBReln,definition,
% 0.32/0.48 ( setOfPairsIsBReln
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.48 ( breln @ A @ B
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrERa_type,type,
% 0.32/0.48 dpsetconstrERa: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrERa,definition,
% 0.32/0.48 ( dpsetconstrERa
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL1_type,type,
% 0.32/0.48 dpsetconstrEL1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL1,definition,
% 0.32/0.48 ( dpsetconstrEL1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL2_type,type,
% 0.32/0.48 dpsetconstrEL2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL2,definition,
% 0.32/0.48 ( dpsetconstrEL2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.49 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.49 => ( in @ Xy @ B ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(dpsetconstrER_type,type,
% 0.32/0.49 dpsetconstrER: $o ).
% 0.32/0.49
% 0.32/0.49 thf(dpsetconstrER,definition,
% 0.32/0.49 ( dpsetconstrER
% 0.32/0.49 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.49 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.49 @ ( dpsetconstr @ A @ B
% 0.32/0.49 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.49 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(func_type,type,
% 0.32/0.49 func: $i > $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcSet_type,type,
% 0.32/0.49 funcSet: $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(funcImageSingleton_type,type,
% 0.32/0.49 funcImageSingleton: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcImageSingleton,definition,
% 0.32/0.49 ( funcImageSingleton
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( singleton
% 0.32/0.49 @ ( dsetconstr @ B
% 0.32/0.49 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(apProp_type,type,
% 0.32/0.49 apProp: $o ).
% 0.32/0.49
% 0.32/0.49 thf(apProp,definition,
% 0.32/0.49 ( apProp
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in
% 0.32/0.49 @ ( setunion
% 0.32/0.49 @ ( dsetconstr @ B
% 0.32/0.49 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.32/0.49 @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ap_type,type,
% 0.32/0.49 ap: $i > $i > $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(app_type,type,
% 0.32/0.49 app: $o ).
% 0.32/0.49
% 0.32/0.49 thf(app,definition,
% 0.32/0.49 ( app
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(infuncsetfunc_type,type,
% 0.32/0.49 infuncsetfunc: $o ).
% 0.32/0.49
% 0.32/0.49 thf(infuncsetfunc,definition,
% 0.32/0.49 ( infuncsetfunc
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ap2p_type,type,
% 0.32/0.49 ap2p: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ap2p,definition,
% 0.32/0.49 ( ap2p
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcinfuncset_type,type,
% 0.32/0.49 funcinfuncset: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcinfuncset,definition,
% 0.32/0.49 ( funcinfuncset
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(lamProp_type,type,
% 0.32/0.49 lamProp: $o ).
% 0.32/0.49
% 0.32/0.49 thf(lamProp,definition,
% 0.32/0.49 ( lamProp
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ( func @ A @ B
% 0.32/0.49 @ ( dpsetconstr @ A @ B
% 0.32/0.49 @ ^ [Xx: $i,Xy: $i] :
% 0.32/0.49 ( ( Xf @ Xx )
% 0.32/0.49 = Xy ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(lam_type,type,
% 0.32/0.49 lam: $i > $i > ( $i > $i ) > $i ).
% 0.32/0.49
% 0.32/0.49 thf(lamp_type,type,
% 0.32/0.49 lamp: $o ).
% 0.32/0.49
% 0.32/0.49 thf(lamp,definition,
% 0.32/0.49 ( lamp
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ( func @ A @ B
% 0.32/0.49 @ ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(lam2p_type,type,
% 0.32/0.49 lam2p: $o ).
% 0.32/0.49
% 0.32/0.49 thf(lam2p,definition,
% 0.32/0.49 ( lam2p
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ( in
% 0.32/0.49 @ ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/0.49 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(brelnall1_type,type,
% 0.32/0.49 brelnall1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(brelnall1,definition,
% 0.32/0.49 ( brelnall1
% 0.32/0.49 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(brelnall2_type,type,
% 0.32/0.49 brelnall2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(brelnall2,definition,
% 0.32/0.49 ( brelnall2
% 0.32/0.49 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ex1E2_type,type,
% 0.32/0.49 ex1E2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ex1E2,definition,
% 0.32/0.49 ( ex1E2
% 0.32/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.49 ( ( ex1 @ A
% 0.32/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( Xphi @ Xx )
% 0.32/0.49 => ( ( Xphi @ Xy )
% 0.32/0.49 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp1_type,type,
% 0.32/0.49 funcGraphProp1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp1,definition,
% 0.32/0.49 ( funcGraphProp1
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp3_type,type,
% 0.32/0.49 funcGraphProp3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp3,definition,
% 0.32/0.49 ( funcGraphProp3
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp2_type,type,
% 0.32/0.49 funcGraphProp2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp2,definition,
% 0.32/0.49 ( funcGraphProp2
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = Xy ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcextLem_type,type,
% 0.32/0.49 funcextLem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcextLem,definition,
% 0.32/0.49 ( funcextLem
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xg: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xg )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp4_type,type,
% 0.32/0.49 funcGraphProp4: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcGraphProp4,definition,
% 0.32/0.49 ( funcGraphProp4
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = Xy ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(subbreln_type,type,
% 0.32/0.49 subbreln: $o ).
% 0.32/0.49
% 0.32/0.49 thf(subbreln,definition,
% 0.32/0.49 ( subbreln
% 0.32/0.49 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ S )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.49 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(eqbreln_type,type,
% 0.32/0.49 eqbreln: $o ).
% 0.32/0.49
% 0.32/0.49 thf(eqbreln,definition,
% 0.32/0.49 ( eqbreln
% 0.32/0.49 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln @ A @ B @ S )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.32/0.49 => ( R = S ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcext_type,type,
% 0.32/0.49 funcext: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcext,definition,
% 0.32/0.49 ( funcext
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xg: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xg )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.49 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(funcext2_type,type,
% 0.32/0.49 funcext2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(funcext2,definition,
% 0.32/0.49 ( funcext2
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ! [Xg: $i] :
% 0.32/0.49 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.49 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ap2apEq1_type,type,
% 0.32/0.49 ap2apEq1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ap2apEq1,definition,
% 0.32/0.49 ( ap2apEq1
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ap2apEq2_type,type,
% 0.32/0.49 ap2apEq2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ap2apEq2,definition,
% 0.32/0.49 ( ap2apEq2
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.49 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(beta1_type,type,
% 0.32/0.49 beta1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(beta1,definition,
% 0.32/0.49 ( beta1
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B
% 0.32/0.49 @ ( lam @ A @ B
% 0.32/0.49 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.32/0.49 @ Xx )
% 0.32/0.49 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(eta1_type,type,
% 0.32/0.49 eta1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(eta1,definition,
% 0.32/0.49 ( eta1
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( func @ A @ B @ Xf )
% 0.32/0.49 => ( ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.32/0.49 = Xf ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(lam2lamEq_type,type,
% 0.32/0.49 lam2lamEq: $o ).
% 0.32/0.49
% 0.32/0.49 thf(lam2lamEq,definition,
% 0.32/0.49 ( lam2lamEq
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ( ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/0.49 = ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(beta2_type,type,
% 0.32/0.49 beta2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(beta2,definition,
% 0.32/0.49 ( beta2
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( ap @ A @ B
% 0.32/0.49 @ ( lam @ A @ B
% 0.32/0.49 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.32/0.49 @ Xx )
% 0.32/0.49 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(eta2_type,type,
% 0.32/0.49 eta2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(eta2,definition,
% 0.32/0.49 ( eta2
% 0.32/0.49 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.49 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.49 => ( ( lam @ A @ B
% 0.32/0.49 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.32/0.49 = Xf ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iffalseProp1_type,type,
% 0.32/0.49 iffalseProp1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iffalseProp1,definition,
% 0.32/0.49 ( iffalseProp1
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ~ Xphi
% 0.32/0.49 => ( in @ Xy
% 0.32/0.49 @ ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xz: $i] :
% 0.32/0.49 ( ( Xphi
% 0.32/0.49 & ( Xz = Xx ) )
% 0.32/0.49 | ( ~ Xphi
% 0.32/0.49 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iffalseProp2_type,type,
% 0.32/0.49 iffalseProp2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iffalseProp2,definition,
% 0.32/0.49 ( iffalseProp2
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ~ Xphi
% 0.32/0.49 => ( ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xz: $i] :
% 0.32/0.49 ( ( Xphi
% 0.32/0.49 & ( Xz = Xx ) )
% 0.32/0.49 | ( ~ Xphi
% 0.32/0.49 & ( Xz = Xy ) ) ) )
% 0.32/0.49 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueProp1_type,type,
% 0.32/0.49 iftrueProp1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueProp1,definition,
% 0.32/0.49 ( iftrueProp1
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( Xphi
% 0.32/0.49 => ( in @ Xx
% 0.32/0.49 @ ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xz: $i] :
% 0.32/0.49 ( ( Xphi
% 0.32/0.49 & ( Xz = Xx ) )
% 0.32/0.49 | ( ~ Xphi
% 0.32/0.49 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueProp2_type,type,
% 0.32/0.49 iftrueProp2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueProp2,definition,
% 0.32/0.49 ( iftrueProp2
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( Xphi
% 0.32/0.49 => ( ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xz: $i] :
% 0.32/0.49 ( ( Xphi
% 0.32/0.49 & ( Xz = Xx ) )
% 0.32/0.49 | ( ~ Xphi
% 0.32/0.49 & ( Xz = Xy ) ) ) )
% 0.32/0.49 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(ifSingleton_type,type,
% 0.32/0.49 ifSingleton: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ifSingleton,definition,
% 0.32/0.49 ( ifSingleton
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( singleton
% 0.32/0.49 @ ( dsetconstr @ A
% 0.32/0.49 @ ^ [Xz: $i] :
% 0.32/0.49 ( ( Xphi
% 0.32/0.49 & ( Xz = Xx ) )
% 0.32/0.49 | ( ~ Xphi
% 0.32/0.49 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(if_type,type,
% 0.32/0.49 if: $i > $o > $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(ifp_type,type,
% 0.32/0.49 ifp: $o ).
% 0.32/0.49
% 0.32/0.49 thf(ifp,definition,
% 0.32/0.49 ( ifp
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(theeq_type,type,
% 0.32/0.49 theeq: $o ).
% 0.32/0.49
% 0.32/0.49 thf(theeq,definition,
% 0.32/0.49 ( theeq
% 0.32/0.49 = ( ! [X: $i] :
% 0.32/0.49 ( ( singleton @ X )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ X )
% 0.32/0.49 => ( ( setunion @ X )
% 0.32/0.49 = Xx ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iftrue_type,type,
% 0.32/0.49 iftrue: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iftrue,definition,
% 0.32/0.49 ( iftrue
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( Xphi
% 0.32/0.49 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.32/0.49 = Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iffalse_type,type,
% 0.32/0.49 iffalse: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iffalse,definition,
% 0.32/0.49 ( iffalse
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ~ Xphi
% 0.32/0.49 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.32/0.49 = Xy ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueorfalse_type,type,
% 0.32/0.49 iftrueorfalse: $o ).
% 0.32/0.49
% 0.32/0.49 thf(iftrueorfalse,definition,
% 0.32/0.49 ( iftrueorfalse
% 0.32/0.49 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectT_lem_type,type,
% 0.32/0.49 binintersectT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectT_lem,definition,
% 0.32/0.49 ( binintersectT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionT_lem_type,type,
% 0.32/0.49 binunionT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionT_lem,definition,
% 0.32/0.49 ( binunionT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetT_lem_type,type,
% 0.32/0.49 powersetT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetT_lem,definition,
% 0.32/0.49 ( powersetT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setminusT_lem_type,type,
% 0.32/0.49 setminusT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setminusT_lem,definition,
% 0.32/0.49 ( setminusT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementT_lem_type,type,
% 0.32/0.49 complementT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementT_lem,definition,
% 0.32/0.49 ( complementT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setextT_type,type,
% 0.32/0.49 setextT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setextT,definition,
% 0.32/0.49 ( setextT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ( in @ Xx @ X ) ) )
% 0.32/0.49 => ( X = Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(subsetTI_type,type,
% 0.32/0.49 subsetTI: $o ).
% 0.32/0.49
% 0.32/0.49 thf(subsetTI,definition,
% 0.32/0.49 ( subsetTI
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTI1_type,type,
% 0.32/0.49 powersetTI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTI1,definition,
% 0.32/0.49 ( powersetTI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTE1_type,type,
% 0.32/0.49 powersetTE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTE1,definition,
% 0.32/0.49 ( powersetTE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ X @ ( powerset @ Y ) )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTI1_type,type,
% 0.32/0.49 complementTI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTI1,definition,
% 0.32/0.49 ( complementTI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTE1_type,type,
% 0.32/0.49 complementTE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTE1,definition,
% 0.32/0.49 ( complementTE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTELcontra_type,type,
% 0.32/0.49 binintersectTELcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTELcontra,definition,
% 0.32/0.49 ( binintersectTELcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ X )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTERcontra_type,type,
% 0.32/0.49 binintersectTERcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTERcontra,definition,
% 0.32/0.49 ( binintersectTERcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT_type,type,
% 0.32/0.49 contrasubsetT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT,definition,
% 0.32/0.49 ( contrasubsetT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT1_type,type,
% 0.32/0.49 contrasubsetT1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT1,definition,
% 0.32/0.49 ( contrasubsetT1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT2_type,type,
% 0.32/0.49 contrasubsetT2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT2,definition,
% 0.32/0.49 ( contrasubsetT2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT3_type,type,
% 0.32/0.49 contrasubsetT3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT3,definition,
% 0.32/0.49 ( contrasubsetT3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementI1_type,type,
% 0.32/0.49 doubleComplementI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementI1,definition,
% 0.32/0.49 ( doubleComplementI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementE1_type,type,
% 0.32/0.49 doubleComplementE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementE1,definition,
% 0.32/0.49 ( doubleComplementE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.32/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub1_type,type,
% 0.32/0.49 doubleComplementSub1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub1,definition,
% 0.32/0.49 ( doubleComplementSub1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub2_type,type,
% 0.32/0.49 doubleComplementSub2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub2,definition,
% 0.32/0.49 ( doubleComplementSub2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementEq_type,type,
% 0.32/0.49 doubleComplementEq: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementEq,definition,
% 0.32/0.49 ( doubleComplementEq
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( X
% 0.32/0.49 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTnotintersectT_type,type,
% 0.32/0.49 complementTnotintersectT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTnotintersectT,definition,
% 0.32/0.49 ( complementTnotintersectT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementImpComplementIntersect_type,type,
% 0.32/0.49 complementImpComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementImpComplementIntersect,definition,
% 0.32/0.49 ( complementImpComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementSubsetComplementIntersect_type,type,
% 0.32/0.49 complementSubsetComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementSubsetComplementIntersect,definition,
% 0.32/0.49 ( complementSubsetComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementInPowersetComplementIntersect_type,type,
% 0.32/0.49 complementInPowersetComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementInPowersetComplementIntersect,definition,
% 0.32/0.49 ( complementInPowersetComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contraSubsetComplement_type,type,
% 0.32/0.49 contraSubsetComplement: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contraSubsetComplement,definition,
% 0.32/0.49 ( contraSubsetComplement
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTcontraSubset_type,type,
% 0.32/0.49 complementTcontraSubset: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTcontraSubset,definition,
% 0.32/0.49 ( complementTcontraSubset
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTILcontra_type,type,
% 0.32/0.49 binunionTILcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTILcontra,definition,
% 0.32/0.49 ( binunionTILcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTIRcontra_type,type,
% 0.32/0.49 binunionTIRcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTIRcontra,definition,
% 0.32/0.49 ( binunionTIRcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion_type,type,
% 0.32/0.49 inIntersectImpInUnion: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion,definition,
% 0.32/0.49 ( inIntersectImpInUnion
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion2_type,type,
% 0.32/0.49 inIntersectImpInUnion2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion2,definition,
% 0.32/0.49 ( inIntersectImpInUnion2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInIntersectUnions_type,type,
% 0.32/0.49 inIntersectImpInIntersectUnions: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInIntersectUnions,definition,
% 0.32/0.49 ( inIntersectImpInIntersectUnions
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(intersectInPowersetIntersectUnions_type,type,
% 0.32/0.49 intersectInPowersetIntersectUnions: $o ).
% 0.32/0.49
% 0.32/0.49 thf(intersectInPowersetIntersectUnions,definition,
% 0.32/0.49 ( intersectInPowersetIntersectUnions
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpNotIn1_type,type,
% 0.32/0.49 inComplementUnionImpNotIn1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpNotIn1,definition,
% 0.32/0.49 ( inComplementUnionImpNotIn1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpInComplement1_type,type,
% 0.32/0.49 inComplementUnionImpInComplement1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpInComplement1,definition,
% 0.32/0.49 ( inComplementUnionImpInComplement1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTE_type,type,
% 0.32/0.49 binunionTE: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTE,definition,
% 0.32/0.49 ( binunionTE
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ( ( ( in @ Xx @ X )
% 0.32/0.49 => Xphi )
% 0.32/0.49 => ( ( ( in @ Xx @ Y )
% 0.32/0.49 => Xphi )
% 0.32/0.49 => Xphi ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTEcontra_type,type,
% 0.32/0.49 binunionTEcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTEcontra,definition,
% 0.32/0.49 ( binunionTEcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ X )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a1_type,type,
% 0.32/0.49 demorgan2a1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a1,definition,
% 0.32/0.49 ( demorgan2a1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementUnionInPowersetComplement_type,type,
% 0.32/0.49 complementUnionInPowersetComplement: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementUnionInPowersetComplement,definition,
% 0.32/0.49 ( complementUnionInPowersetComplement
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a2_type,type,
% 0.32/0.49 demorgan2a2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a2,definition,
% 0.32/0.49 ( demorgan2a2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1a_type,type,
% 0.32/0.49 demorgan1a: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1a,definition,
% 0.32/0.49 ( demorgan1a
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1b_type,type,
% 0.32/0.49 demorgan1b: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1b,definition,
% 0.32/0.49 ( demorgan1b
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1_type,type,
% 0.32/0.49 demorgan1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1,definition,
% 0.32/0.49 ( demorgan1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.32/0.49 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a_type,type,
% 0.32/0.49 demorgan2a: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a,definition,
% 0.32/0.49 ( demorgan2a
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b2_type,type,
% 0.32/0.49 demorgan2b2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b2,definition,
% 0.32/0.49 ( demorgan2b2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b_type,type,
% 0.32/0.49 demorgan2b: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b,definition,
% 0.32/0.49 ( demorgan2b
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2_type,type,
% 0.32/0.49 demorgan2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2,definition,
% 0.32/0.49 ( demorgan2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.32/0.49 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule0_type,type,
% 0.32/0.49 woz13rule0: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule0,definition,
% 0.32/0.49 ( woz13rule0
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule1_type,type,
% 0.32/0.49 woz13rule1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule1,definition,
% 0.32/0.49 ( woz13rule1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule2_type,type,
% 0.32/0.49 woz13rule2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule2,definition,
% 0.32/0.49 ( woz13rule2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ Y @ Z )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule3_type,type,
% 0.32/0.49 woz13rule3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule3,definition,
% 0.32/0.49 ( woz13rule3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule4_type,type,
% 0.32/0.49 woz13rule4: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule4,definition,
% 0.32/0.49 ( woz13rule4
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [W: $i] :
% 0.32/0.49 ( ( in @ W @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( ( subset @ Y @ W )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_1_type,type,
% 0.32/0.49 woz1_1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_1,definition,
% 0.32/0.49 ( woz1_1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_2_type,type,
% 0.32/0.49 woz1_2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_2,definition,
% 0.32/0.49 ( woz1_2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [W: $i] :
% 0.32/0.49 ( ( in @ W @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.32/0.49 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_3_type,type,
% 0.32/0.49 woz1_3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_3,definition,
% 0.32/0.49 ( woz1_3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_4_type,type,
% 0.32/0.49 woz1_4: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_4,definition,
% 0.32/0.49 ( woz1_4
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_5_type,type,
% 0.32/0.49 woz1_5: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_5,definition,
% 0.32/0.49 ( woz1_5
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1_type,type,
% 0.32/0.49 breln1: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1,definition,
% 0.32/0.49 ( breln1
% 0.32/0.49 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all2_type,type,
% 0.32/0.49 breln1all2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all2,definition,
% 0.32/0.49 ( breln1all2
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1Set_type,type,
% 0.32/0.49 breln1Set: $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(breln1SetBreln1_type,type,
% 0.32/0.49 breln1SetBreln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1SetBreln1,definition,
% 0.32/0.49 ( breln1SetBreln1
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( in @ R @ ( breln1Set @ A ) )
% 0.32/0.49 => ( breln1 @ A @ R ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(transitive_type,type,
% 0.32/0.49 transitive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(antisymmetric_type,type,
% 0.32/0.49 antisymmetric: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(reflexive_type,type,
% 0.32/0.49 reflexive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(refltransitive_type,type,
% 0.32/0.49 refltransitive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(refllinearorder_type,type,
% 0.32/0.49 refllinearorder: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(reflwellordering_type,type,
% 0.32/0.49 reflwellordering: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(choice2fnsingleton_type,type,
% 0.32/0.49 choice2fnsingleton: $o ).
% 0.32/0.49
% 0.32/0.49 thf(choice2fnsingleton,definition,
% 0.32/0.49 ( choice2fnsingleton
% 0.32/0.49 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ? [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 & ( Xphi @ Xx @ Xy ) ) )
% 0.32/0.49 => ! [R: $i] :
% 0.32/0.49 ( ( in @ R @ ( breln1Set @ B ) )
% 0.32/0.49 => ( ( reflwellordering @ B @ R )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( singleton
% 0.32/0.49 @ ( dsetconstr @ B
% 0.32/0.49 @ ^ [Xy: $i] :
% 0.32/0.49 ( ( Xphi @ Xx @ Xy )
% 0.32/0.49 & ! [Xz: $i] :
% 0.32/0.49 ( ( in @ Xz @ B )
% 0.32/0.49 => ( ( Xphi @ Xx @ Xz )
% 0.32/0.49 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setOfPairsIsBReln1_type,type,
% 0.32/0.49 setOfPairsIsBReln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setOfPairsIsBReln1,definition,
% 0.32/0.49 ( setOfPairsIsBReln1
% 0.32/0.49 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.32/0.49 ( breln1 @ A
% 0.32/0.49 @ ( dpsetconstr @ A @ A
% 0.32/0.49 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all1,conjecture,
% 0.32/0.49 ( setextAx
% 0.32/0.49 => ( emptysetAx
% 0.32/0.49 => ( setadjoinAx
% 0.32/0.49 => ( powersetAx
% 0.32/0.49 => ( setunionAx
% 0.32/0.49 => ( omega0Ax
% 0.32/0.49 => ( omegaSAx
% 0.32/0.49 => ( omegaIndAx
% 0.32/0.49 => ( replAx
% 0.32/0.49 => ( foundationAx
% 0.32/0.49 => ( wellorderingAx
% 0.32/0.49 => ( descrp
% 0.32/0.49 => ( dsetconstrI
% 0.32/0.49 => ( dsetconstrEL
% 0.32/0.49 => ( dsetconstrER
% 0.32/0.49 => ( exuE1
% 0.32/0.49 => ( prop2setE
% 0.32/0.49 => ( emptysetE
% 0.32/0.49 => ( emptysetimpfalse
% 0.32/0.49 => ( notinemptyset
% 0.32/0.49 => ( exuE3e
% 0.32/0.49 => ( setext
% 0.32/0.49 => ( emptyI
% 0.32/0.49 => ( noeltsimpempty
% 0.32/0.49 => ( setbeta
% 0.32/0.49 => ( nonemptyE1
% 0.32/0.49 => ( nonemptyI
% 0.32/0.49 => ( nonemptyI1
% 0.32/0.49 => ( setadjoinIL
% 0.32/0.49 => ( emptyinunitempty
% 0.32/0.49 => ( setadjoinIR
% 0.32/0.49 => ( setadjoinE
% 0.32/0.49 => ( setadjoinOr
% 0.32/0.49 => ( setoftrueEq
% 0.32/0.49 => ( powersetI
% 0.32/0.49 => ( emptyinPowerset
% 0.32/0.49 => ( emptyInPowerset
% 0.32/0.49 => ( powersetE
% 0.32/0.49 => ( setunionI
% 0.32/0.49 => ( setunionE
% 0.32/0.49 => ( subPowSU
% 0.32/0.49 => ( exuE2
% 0.32/0.49 => ( nonemptyImpWitness
% 0.32/0.49 => ( uniqinunit
% 0.32/0.49 => ( notinsingleton
% 0.32/0.49 => ( eqinunit
% 0.32/0.49 => ( singletonsswitch
% 0.32/0.49 => ( upairsetE
% 0.32/0.49 => ( upairsetIL
% 0.32/0.49 => ( upairsetIR
% 0.32/0.49 => ( emptyE1
% 0.32/0.49 => ( vacuousDall
% 0.32/0.49 => ( quantDeMorgan1
% 0.32/0.49 => ( quantDeMorgan2
% 0.32/0.49 => ( quantDeMorgan3
% 0.32/0.49 => ( quantDeMorgan4
% 0.32/0.49 => ( prop2setI
% 0.32/0.49 => ( prop2set2propI
% 0.32/0.49 => ( notdexE
% 0.32/0.49 => ( notdallE
% 0.32/0.49 => ( exuI1
% 0.32/0.49 => ( exuI3
% 0.32/0.49 => ( exuI2
% 0.32/0.49 => ( inCongP
% 0.32/0.49 => ( in__Cong
% 0.32/0.49 => ( exuE3u
% 0.32/0.49 => ( exu__Cong
% 0.32/0.49 => ( emptyset__Cong
% 0.32/0.49 => ( setadjoin__Cong
% 0.32/0.49 => ( powerset__Cong
% 0.32/0.49 => ( setunion__Cong
% 0.32/0.49 => ( omega__Cong
% 0.32/0.49 => ( exuEu
% 0.32/0.49 => ( descr__Cong
% 0.32/0.49 => ( dsetconstr__Cong
% 0.32/0.49 => ( subsetI1
% 0.32/0.49 => ( eqimpsubset2
% 0.32/0.49 => ( eqimpsubset1
% 0.32/0.49 => ( subsetI2
% 0.32/0.49 => ( emptysetsubset
% 0.32/0.49 => ( subsetE
% 0.32/0.49 => ( subsetE2
% 0.32/0.49 => ( notsubsetI
% 0.32/0.49 => ( notequalI1
% 0.32/0.49 => ( notequalI2
% 0.32/0.49 => ( subsetRefl
% 0.32/0.49 => ( subsetTrans
% 0.32/0.49 => ( setadjoinSub
% 0.32/0.49 => ( setadjoinSub2
% 0.32/0.49 => ( subset2powerset
% 0.32/0.49 => ( setextsub
% 0.32/0.49 => ( subsetemptysetimpeq
% 0.32/0.49 => ( powersetI1
% 0.32/0.49 => ( powersetE1
% 0.32/0.49 => ( inPowerset
% 0.32/0.49 => ( powersetsubset
% 0.32/0.49 => ( sepInPowerset
% 0.32/0.49 => ( sepSubset
% 0.32/0.49 => ( binunionIL
% 0.32/0.49 => ( upairset2IR
% 0.32/0.49 => ( binunionIR
% 0.32/0.49 => ( binunionEcases
% 0.32/0.49 => ( binunionE
% 0.32/0.49 => ( binunionLsub
% 0.32/0.49 => ( binunionRsub
% 0.32/0.49 => ( binintersectI
% 0.32/0.49 => ( binintersectSubset5
% 0.32/0.49 => ( binintersectEL
% 0.32/0.49 => ( binintersectLsub
% 0.32/0.49 => ( binintersectSubset2
% 0.32/0.49 => ( binintersectSubset3
% 0.32/0.49 => ( binintersectER
% 0.32/0.49 => ( disjointsetsI1
% 0.32/0.49 => ( binintersectRsub
% 0.32/0.49 => ( binintersectSubset4
% 0.32/0.49 => ( binintersectSubset1
% 0.32/0.49 => ( bs114d
% 0.32/0.49 => ( setminusI
% 0.32/0.49 => ( setminusEL
% 0.32/0.49 => ( setminusER
% 0.32/0.49 => ( setminusSubset2
% 0.32/0.49 => ( setminusERneg
% 0.32/0.49 => ( setminusELneg
% 0.32/0.49 => ( setminusILneg
% 0.32/0.49 => ( setminusIRneg
% 0.32/0.49 => ( setminusLsub
% 0.32/0.49 => ( setminusSubset1
% 0.32/0.49 => ( symdiffE
% 0.32/0.49 => ( symdiffI1
% 0.32/0.49 => ( symdiffI2
% 0.32/0.49 => ( symdiffIneg1
% 0.32/0.49 => ( symdiffIneg2
% 0.32/0.49 => ( secondinupair
% 0.32/0.49 => ( setukpairIL
% 0.32/0.49 => ( setukpairIR
% 0.32/0.49 => ( kpairiskpair
% 0.32/0.49 => ( kpairp
% 0.32/0.49 => ( singletonsubset
% 0.32/0.49 => ( singletoninpowerset
% 0.32/0.49 => ( singletoninpowunion
% 0.32/0.49 => ( upairset2E
% 0.32/0.49 => ( upairsubunion
% 0.32/0.49 => ( upairinpowunion
% 0.32/0.49 => ( ubforcartprodlem1
% 0.32/0.49 => ( ubforcartprodlem2
% 0.32/0.49 => ( ubforcartprodlem3
% 0.32/0.49 => ( cartprodpairin
% 0.32/0.49 => ( cartprodmempair1
% 0.32/0.49 => ( cartprodmempair
% 0.32/0.49 => ( setunionE2
% 0.32/0.49 => ( setunionsingleton1
% 0.32/0.49 => ( setunionsingleton2
% 0.32/0.49 => ( setunionsingleton
% 0.32/0.49 => ( singletonprop
% 0.32/0.49 => ( ex1E1
% 0.32/0.49 => ( ex1I
% 0.32/0.49 => ( ex1I2
% 0.32/0.49 => ( singletonsuniq
% 0.32/0.49 => ( setukpairinjL1
% 0.32/0.49 => ( kfstsingleton
% 0.32/0.49 => ( theprop
% 0.32/0.49 => ( kfstpairEq
% 0.32/0.49 => ( cartprodfstin
% 0.32/0.49 => ( setukpairinjL2
% 0.32/0.49 => ( setukpairinjL
% 0.32/0.49 => ( setukpairinjR11
% 0.32/0.49 => ( setukpairinjR12
% 0.32/0.49 => ( setukpairinjR1
% 0.32/0.49 => ( upairequniteq
% 0.32/0.49 => ( setukpairinjR2
% 0.32/0.49 => ( setukpairinjR
% 0.32/0.49 => ( ksndsingleton
% 0.32/0.49 => ( ksndpairEq
% 0.32/0.49 => ( kpairsurjEq
% 0.32/0.49 => ( cartprodsndin
% 0.32/0.49 => ( cartprodpairmemEL
% 0.32/0.49 => ( cartprodpairmemER
% 0.32/0.49 => ( cartprodmempaircEq
% 0.32/0.49 => ( cartprodfstpairEq
% 0.32/0.49 => ( cartprodsndpairEq
% 0.32/0.49 => ( cartprodpairsurjEq
% 0.32/0.49 => ( dpsetconstrI
% 0.32/0.49 => ( dpsetconstrSub
% 0.32/0.49 => ( setOfPairsIsBReln
% 0.32/0.49 => ( dpsetconstrERa
% 0.32/0.49 => ( dpsetconstrEL1
% 0.32/0.49 => ( dpsetconstrEL2
% 0.32/0.49 => ( dpsetconstrER
% 0.32/0.49 => ( funcImageSingleton
% 0.32/0.49 => ( apProp
% 0.32/0.49 => ( app
% 0.32/0.49 => ( infuncsetfunc
% 0.32/0.49 => ( ap2p
% 0.32/0.49 => ( funcinfuncset
% 0.32/0.49 => ( lamProp
% 0.32/0.49 => ( lamp
% 0.32/0.49 => ( lam2p
% 0.32/0.49 => ( brelnall1
% 0.32/0.49 => ( brelnall2
% 0.32/0.49 => ( ex1E2
% 0.32/0.49 => ( funcGraphProp1
% 0.32/0.49 => ( funcGraphProp3
% 0.32/0.49 => ( funcGraphProp2
% 0.32/0.49 => ( funcextLem
% 0.32/0.49 => ( funcGraphProp4
% 0.32/0.49 => ( subbreln
% 0.32/0.49 => ( eqbreln
% 0.32/0.49 => ( funcext
% 0.32/0.49 => ( funcext2
% 0.32/0.49 => ( ap2apEq1
% 0.32/0.49 => ( ap2apEq2
% 0.32/0.49 => ( beta1
% 0.32/0.49 => ( eta1
% 0.32/0.49 => ( lam2lamEq
% 0.32/0.49 => ( beta2
% 0.32/0.49 => ( eta2
% 0.32/0.49 => ( iffalseProp1
% 0.32/0.49 => ( iffalseProp2
% 0.32/0.49 => ( iftrueProp1
% 0.32/0.49 => ( iftrueProp2
% 0.32/0.49 => ( ifSingleton
% 0.32/0.49 => ( ifp
% 0.32/0.49 => ( theeq
% 0.32/0.49 => ( iftrue
% 0.32/0.49 => ( iffalse
% 0.32/0.49 => ( iftrueorfalse
% 0.32/0.49 => ( binintersectT_lem
% 0.32/0.49 => ( binunionT_lem
% 0.32/0.49 => ( powersetT_lem
% 0.32/0.49 => ( setminusT_lem
% 0.32/0.49 => ( complementT_lem
% 0.32/0.49 => ( setextT
% 0.32/0.49 => ( subsetTI
% 0.32/0.49 => ( powersetTI1
% 0.32/0.49 => ( powersetTE1
% 0.32/0.49 => ( complementTI1
% 0.32/0.49 => ( complementTE1
% 0.32/0.49 => ( binintersectTELcontra
% 0.32/0.49 => ( binintersectTERcontra
% 0.32/0.49 => ( contrasubsetT
% 0.32/0.49 => ( contrasubsetT1
% 0.32/0.49 => ( contrasubsetT2
% 0.32/0.49 => ( contrasubsetT3
% 0.32/0.49 => ( doubleComplementI1
% 0.32/0.49 => ( doubleComplementE1
% 0.32/0.49 => ( doubleComplementSub1
% 0.32/0.49 => ( doubleComplementSub2
% 0.32/0.49 => ( doubleComplementEq
% 0.32/0.49 => ( complementTnotintersectT
% 0.32/0.49 => ( complementImpComplementIntersect
% 0.32/0.49 => ( complementSubsetComplementIntersect
% 0.32/0.49 => ( complementInPowersetComplementIntersect
% 0.32/0.49 => ( contraSubsetComplement
% 0.32/0.49 => ( complementTcontraSubset
% 0.32/0.49 => ( binunionTILcontra
% 0.32/0.49 => ( binunionTIRcontra
% 0.32/0.49 => ( inIntersectImpInUnion
% 0.32/0.49 => ( inIntersectImpInUnion2
% 0.32/0.49 => ( inIntersectImpInIntersectUnions
% 0.32/0.49 => ( intersectInPowersetIntersectUnions
% 0.32/0.49 => ( inComplementUnionImpNotIn1
% 0.32/0.49 => ( inComplementUnionImpInComplement1
% 0.32/0.49 => ( binunionTE
% 0.32/0.49 => ( binunionTEcontra
% 0.32/0.49 => ( demorgan2a1
% 0.32/0.49 => ( complementUnionInPowersetComplement
% 0.32/0.49 => ( demorgan2a2
% 0.32/0.49 => ( demorgan1a
% 0.32/0.49 => ( demorgan1b
% 0.32/0.49 => ( demorgan1
% 0.32/0.49 => ( demorgan2a
% 0.32/0.49 => ( demorgan2b2
% 0.32/0.49 => ( demorgan2b
% 0.32/0.49 => ( demorgan2
% 0.32/0.49 => ( woz13rule0
% 0.32/0.49 => ( woz13rule1
% 0.32/0.49 => ( woz13rule2
% 0.32/0.49 => ( woz13rule3
% 0.32/0.49 => ( woz13rule4
% 0.32/0.49 => ( woz1_1
% 0.32/0.49 => ( woz1_2
% 0.32/0.49 => ( woz1_3
% 0.32/0.49 => ( woz1_4
% 0.32/0.49 => ( woz1_5
% 0.32/0.49 => ( breln1all2
% 0.32/0.49 => ( breln1SetBreln1
% 0.32/0.49 => ( choice2fnsingleton
% 0.32/0.49 => ( setOfPairsIsBReln1
% 0.32/0.49 => ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 3.42/1.85 ---- Embedded in THF ---
% 3.42/1.85 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.42/1.85 %%% Generated on Tue Feb 24 12:33:25 EST 2026
% 3.42/1.85 %%% using '$$dhol' embedding, version 1.3.0.
% 3.42/1.85 %%% Logic specification used:
% 3.42/1.85 %%% thf(spec, logic, $$dhol).
% 3.42/1.85
% 3.42/1.85 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1jLE4W7LvF/DTF2DTF3370.p
% See solution above
% 3.42/1.85 ------------------------
% 3.57/1.91 ---- Cleaned THF ---
% 3.57/1.92 thf(in_type,type,
% 3.57/1.92 in: $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(exu_type,type,
% 3.57/1.92 exu: ( $i > $o ) > $o ).
% 3.57/1.92
% 3.57/1.92 thf(exu,definition,
% 3.57/1.92 ( exu
% 3.57/1.92 = ( ^ [Xphi: $i > $o] :
% 3.57/1.92 ? [Xx: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 & ! [Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setextAx_type,type,
% 3.57/1.92 setextAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setextAx,definition,
% 3.57/1.92 ( setextAx
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 <=> ( in @ Xx @ B ) )
% 3.57/1.92 => ( A = B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyset_type,type,
% 3.57/1.92 emptyset: $i ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetAx_type,type,
% 3.57/1.92 emptysetAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetAx,definition,
% 3.57/1.92 ( emptysetAx
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoin_type,type,
% 3.57/1.92 setadjoin: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinAx_type,type,
% 3.57/1.92 setadjoinAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinAx,definition,
% 3.57/1.92 ( setadjoinAx
% 3.57/1.92 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.57/1.92 <=> ( ( Xy = Xx )
% 3.57/1.92 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powerset_type,type,
% 3.57/1.92 powerset: $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(powersetAx_type,type,
% 3.57/1.92 powersetAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetAx,definition,
% 3.57/1.92 ( powersetAx
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( in @ B @ ( powerset @ A ) )
% 3.57/1.92 <=> ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunion_type,type,
% 3.57/1.92 setunion: $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(setunionAx_type,type,
% 3.57/1.92 setunionAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionAx,definition,
% 3.57/1.92 ( setunionAx
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setunion @ A ) )
% 3.57/1.92 <=> ? [B: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 & ( in @ B @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(omega_type,type,
% 3.57/1.92 omega: $i ).
% 3.57/1.92
% 3.57/1.92 thf(omega0Ax_type,type,
% 3.57/1.92 omega0Ax: $o ).
% 3.57/1.92
% 3.57/1.92 thf(omega0Ax,definition,
% 3.57/1.92 ( omega0Ax
% 3.57/1.92 = ( in @ emptyset @ omega ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(omegaSAx_type,type,
% 3.57/1.92 omegaSAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(omegaSAx,definition,
% 3.57/1.92 ( omegaSAx
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ omega )
% 3.57/1.92 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(omegaIndAx_type,type,
% 3.57/1.92 omegaIndAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(omegaIndAx,definition,
% 3.57/1.92 ( omegaIndAx
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ( ( in @ emptyset @ A )
% 3.57/1.92 & ! [Xx: $i] :
% 3.57/1.92 ( ( ( in @ Xx @ omega )
% 3.57/1.92 & ( in @ Xx @ A ) )
% 3.57/1.92 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ omega )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(replAx_type,type,
% 3.57/1.92 replAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(replAx,definition,
% 3.57/1.92 ( replAx
% 3.57/1.92 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( exu
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.57/1.92 => ? [B: $i] :
% 3.57/1.92 ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 <=> ? [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(foundationAx_type,type,
% 3.57/1.92 foundationAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(foundationAx,definition,
% 3.57/1.92 ( foundationAx
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.57/1.92 => ? [B: $i] :
% 3.57/1.92 ( ( in @ B @ A )
% 3.57/1.92 & ~ ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(wellorderingAx_type,type,
% 3.57/1.92 wellorderingAx: $o ).
% 3.57/1.92
% 3.57/1.92 thf(wellorderingAx,definition,
% 3.57/1.92 ( wellorderingAx
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ? [B: $i] :
% 3.57/1.92 ( ! [C: $i] :
% 3.57/1.92 ( ( in @ C @ B )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ C )
% 3.57/1.92 => ( in @ Xx @ A ) ) )
% 3.57/1.92 & ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( ( in @ Xx @ A )
% 3.57/1.92 & ( in @ Xy @ A ) )
% 3.57/1.92 => ( ! [C: $i] :
% 3.57/1.92 ( ( in @ C @ B )
% 3.57/1.92 => ( ( in @ Xx @ C )
% 3.57/1.92 <=> ( in @ Xy @ C ) ) )
% 3.57/1.92 => ( Xx = Xy ) ) )
% 3.57/1.92 & ! [C: $i,D: $i] :
% 3.57/1.92 ( ( ( in @ C @ B )
% 3.57/1.92 & ( in @ D @ B ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ C )
% 3.57/1.92 => ( in @ Xx @ D ) )
% 3.57/1.92 | ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ D )
% 3.57/1.92 => ( in @ Xx @ C ) ) ) )
% 3.57/1.92 & ! [C: $i] :
% 3.57/1.92 ( ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ C )
% 3.57/1.92 => ( in @ Xx @ A ) )
% 3.57/1.92 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.57/1.92 => ? [D: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ D @ B )
% 3.57/1.92 & ( in @ Xx @ C )
% 3.57/1.92 & ~ ? [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ D )
% 3.57/1.92 & ( in @ Xy @ C ) )
% 3.57/1.92 & ! [E: $i] :
% 3.57/1.92 ( ( in @ E @ B )
% 3.57/1.92 => ( ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ E )
% 3.57/1.92 => ( in @ Xy @ D ) )
% 3.57/1.92 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(descr_type,type,
% 3.57/1.92 descr: ( $i > $o ) > $i ).
% 3.57/1.92
% 3.57/1.92 thf(descrp_type,type,
% 3.57/1.92 descrp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(descrp,definition,
% 3.57/1.92 ( descrp
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ( Xphi
% 3.57/1.92 @ ( descr
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstr_type,type,
% 3.57/1.92 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrI_type,type,
% 3.57/1.92 dsetconstrI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrI,definition,
% 3.57/1.92 ( dsetconstrI
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( in @ Xx
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrEL_type,type,
% 3.57/1.92 dsetconstrEL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrEL,definition,
% 3.57/1.92 ( dsetconstrEL
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrER_type,type,
% 3.57/1.92 dsetconstrER: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstrER,definition,
% 3.57/1.92 ( dsetconstrER
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.57/1.92 => ( Xphi @ Xx ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuE1_type,type,
% 3.57/1.92 exuE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuE1,definition,
% 3.57/1.92 ( exuE1
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 & ! [Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(prop2set_type,type,
% 3.57/1.92 prop2set: $o > $i ).
% 3.57/1.92
% 3.57/1.92 thf(prop2setE_type,type,
% 3.57/1.92 prop2setE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(prop2setE,definition,
% 3.57/1.92 ( prop2setE
% 3.57/1.92 = ( ! [Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.57/1.92 => Xphi ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetE_type,type,
% 3.57/1.92 emptysetE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetE,definition,
% 3.57/1.92 ( emptysetE
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ emptyset )
% 3.57/1.92 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetimpfalse_type,type,
% 3.57/1.92 emptysetimpfalse: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetimpfalse,definition,
% 3.57/1.92 ( emptysetimpfalse
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ emptyset )
% 3.57/1.92 => $false ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notinemptyset_type,type,
% 3.57/1.92 notinemptyset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notinemptyset,definition,
% 3.57/1.92 ( notinemptyset
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuE3e_type,type,
% 3.57/1.92 exuE3e: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuE3e,definition,
% 3.57/1.92 ( exuE3e
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setext_type,type,
% 3.57/1.92 setext: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setext,definition,
% 3.57/1.92 ( setext
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ B ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ A ) )
% 3.57/1.92 => ( A = B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyI_type,type,
% 3.57/1.92 emptyI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyI,definition,
% 3.57/1.92 ( emptyI
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ~ ( in @ Xx @ A )
% 3.57/1.92 => ( A = emptyset ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(noeltsimpempty_type,type,
% 3.57/1.92 noeltsimpempty: $o ).
% 3.57/1.92
% 3.57/1.92 thf(noeltsimpempty,definition,
% 3.57/1.92 ( noeltsimpempty
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ~ ( in @ Xx @ A )
% 3.57/1.92 => ( A = emptyset ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setbeta_type,type,
% 3.57/1.92 setbeta: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setbeta,definition,
% 3.57/1.92 ( setbeta
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.57/1.92 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(nonempty_type,type,
% 3.57/1.92 nonempty: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(nonempty,definition,
% 3.57/1.92 ( nonempty
% 3.57/1.92 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyE1_type,type,
% 3.57/1.92 nonemptyE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyE1,definition,
% 3.57/1.92 ( nonemptyE1
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ( nonempty @ A )
% 3.57/1.92 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyI_type,type,
% 3.57/1.92 nonemptyI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyI,definition,
% 3.57/1.92 ( nonemptyI
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( nonempty
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyI1_type,type,
% 3.57/1.92 nonemptyI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyI1,definition,
% 3.57/1.92 ( nonemptyI1
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.57/1.92 => ( nonempty @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinIL_type,type,
% 3.57/1.92 setadjoinIL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinIL,definition,
% 3.57/1.92 ( setadjoinIL
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyinunitempty_type,type,
% 3.57/1.92 emptyinunitempty: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyinunitempty,definition,
% 3.57/1.92 ( emptyinunitempty
% 3.57/1.92 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinIR_type,type,
% 3.57/1.92 setadjoinIR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinIR,definition,
% 3.57/1.92 ( setadjoinIR
% 3.57/1.92 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinE_type,type,
% 3.57/1.92 setadjoinE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinE,definition,
% 3.57/1.92 ( setadjoinE
% 3.57/1.92 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.57/1.92 => ! [Xphi: $o] :
% 3.57/1.92 ( ( ( Xy = Xx )
% 3.57/1.92 => Xphi )
% 3.57/1.92 => ( ( ( in @ Xy @ A )
% 3.57/1.92 => Xphi )
% 3.57/1.92 => Xphi ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinOr_type,type,
% 3.57/1.92 setadjoinOr: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinOr,definition,
% 3.57/1.92 ( setadjoinOr
% 3.57/1.92 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.57/1.92 => ( ( Xy = Xx )
% 3.57/1.92 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setoftrueEq_type,type,
% 3.57/1.92 setoftrueEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setoftrueEq,definition,
% 3.57/1.92 ( setoftrueEq
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : $true )
% 3.57/1.92 = A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetI_type,type,
% 3.57/1.92 powersetI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetI,definition,
% 3.57/1.92 ( powersetI
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ A ) )
% 3.57/1.92 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyinPowerset_type,type,
% 3.57/1.92 emptyinPowerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyinPowerset,definition,
% 3.57/1.92 ( emptyinPowerset
% 3.57/1.92 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyInPowerset_type,type,
% 3.57/1.92 emptyInPowerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyInPowerset,definition,
% 3.57/1.92 ( emptyInPowerset
% 3.57/1.92 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetE_type,type,
% 3.57/1.92 powersetE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetE,definition,
% 3.57/1.92 ( powersetE
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ B @ ( powerset @ A ) )
% 3.57/1.92 => ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionI_type,type,
% 3.57/1.92 setunionI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionI,definition,
% 3.57/1.92 ( setunionI
% 3.57/1.92 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( ( in @ B @ A )
% 3.57/1.92 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionE_type,type,
% 3.57/1.92 setunionE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionE,definition,
% 3.57/1.92 ( setunionE
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setunion @ A ) )
% 3.57/1.92 => ! [Xphi: $o] :
% 3.57/1.92 ( ! [B: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( ( in @ B @ A )
% 3.57/1.92 => Xphi ) )
% 3.57/1.92 => Xphi ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subPowSU_type,type,
% 3.57/1.92 subPowSU: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subPowSU,definition,
% 3.57/1.92 ( subPowSU
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuE2_type,type,
% 3.57/1.92 exuE2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuE2,definition,
% 3.57/1.92 ( exuE2
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ! [Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xy )
% 3.57/1.92 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyImpWitness_type,type,
% 3.57/1.92 nonemptyImpWitness: $o ).
% 3.57/1.92
% 3.57/1.92 thf(nonemptyImpWitness,definition,
% 3.57/1.92 ( nonemptyImpWitness
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ( nonempty @ A )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & $true ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(uniqinunit_type,type,
% 3.57/1.92 uniqinunit: $o ).
% 3.57/1.92
% 3.57/1.92 thf(uniqinunit,definition,
% 3.57/1.92 ( uniqinunit
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notinsingleton_type,type,
% 3.57/1.92 notinsingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notinsingleton,definition,
% 3.57/1.92 ( notinsingleton
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx != Xy )
% 3.57/1.92 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eqinunit_type,type,
% 3.57/1.92 eqinunit: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eqinunit,definition,
% 3.57/1.92 ( eqinunit
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsswitch_type,type,
% 3.57/1.92 singletonsswitch: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsswitch,definition,
% 3.57/1.92 ( singletonsswitch
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.57/1.92 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetE_type,type,
% 3.57/1.92 upairsetE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetE,definition,
% 3.57/1.92 ( upairsetE
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.57/1.92 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.57/1.92 => ( ( Xz = Xx )
% 3.57/1.92 | ( Xz = Xy ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetIL_type,type,
% 3.57/1.92 upairsetIL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetIL,definition,
% 3.57/1.92 ( upairsetIL
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetIR_type,type,
% 3.57/1.92 upairsetIR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetIR,definition,
% 3.57/1.92 ( upairsetIR
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyE1_type,type,
% 3.57/1.92 emptyE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyE1,definition,
% 3.57/1.92 ( emptyE1
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) )
% 3.57/1.92 => ( ( ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 = emptyset )
% 3.57/1.92 => $false ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(vacuousDall_type,type,
% 3.57/1.92 vacuousDall: $o ).
% 3.57/1.92
% 3.57/1.92 thf(vacuousDall,definition,
% 3.57/1.92 ( vacuousDall
% 3.57/1.92 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ emptyset )
% 3.57/1.92 => ( Xphi @ Xx ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan1_type,type,
% 3.57/1.92 quantDeMorgan1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan1,definition,
% 3.57/1.92 ( quantDeMorgan1
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ~ ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan2_type,type,
% 3.57/1.92 quantDeMorgan2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan2,definition,
% 3.57/1.92 ( quantDeMorgan2
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ~ ( Xphi @ Xx ) )
% 3.57/1.92 => ~ ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan3_type,type,
% 3.57/1.92 quantDeMorgan3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan3,definition,
% 3.57/1.92 ( quantDeMorgan3
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ~ ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan4_type,type,
% 3.57/1.92 quantDeMorgan4: $o ).
% 3.57/1.92
% 3.57/1.92 thf(quantDeMorgan4,definition,
% 3.57/1.92 ( quantDeMorgan4
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ~ ( Xphi @ Xx ) )
% 3.57/1.92 => ~ ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(prop2setI_type,type,
% 3.57/1.92 prop2setI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(prop2setI,definition,
% 3.57/1.92 ( prop2setI
% 3.57/1.92 = ( ! [Xphi: $o] :
% 3.57/1.92 ( Xphi
% 3.57/1.92 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(set2prop_type,type,
% 3.57/1.92 set2prop: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(prop2set2propI_type,type,
% 3.57/1.92 prop2set2propI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(prop2set2propI,definition,
% 3.57/1.92 ( prop2set2propI
% 3.57/1.92 = ( ! [Xphi: $o] :
% 3.57/1.92 ( Xphi
% 3.57/1.92 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notdexE_type,type,
% 3.57/1.92 notdexE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notdexE,definition,
% 3.57/1.92 ( notdexE
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ~ ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notdallE_type,type,
% 3.57/1.92 notdallE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notdallE,definition,
% 3.57/1.92 ( notdallE
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ~ ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuI1_type,type,
% 3.57/1.92 exuI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuI1,definition,
% 3.57/1.92 ( exuI1
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ? [Xx: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 & ! [Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) )
% 3.57/1.92 => ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuI3_type,type,
% 3.57/1.92 exuI3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuI3,definition,
% 3.57/1.92 ( exuI3
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.57/1.92 => ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) )
% 3.57/1.92 => ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuI2_type,type,
% 3.57/1.92 exuI2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuI2,definition,
% 3.57/1.92 ( exuI2
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ? [Xx: $i] :
% 3.57/1.92 ! [Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xy )
% 3.57/1.92 <=> ( Xy = Xx ) )
% 3.57/1.92 => ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inCongP_type,type,
% 3.57/1.92 inCongP: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inCongP,definition,
% 3.57/1.92 ( inCongP
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(in__Cong_type,type,
% 3.57/1.92 in__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(in__Cong,definition,
% 3.57/1.92 ( in__Cong
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( in @ Xx @ A )
% 3.57/1.92 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuE3u_type,type,
% 3.57/1.92 exuE3u: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuE3u,definition,
% 3.57/1.92 ( exuE3u
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exu__Cong_type,type,
% 3.57/1.92 exu__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exu__Cong,definition,
% 3.57/1.92 ( exu__Cong
% 3.57/1.92 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 <=> ( Xpsi @ Xy ) ) )
% 3.57/1.92 => ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 <=> ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptyset__Cong_type,type,
% 3.57/1.92 emptyset__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptyset__Cong,definition,
% 3.57/1.92 ( emptyset__Cong
% 3.57/1.92 = ( emptyset = emptyset ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoin__Cong_type,type,
% 3.57/1.92 setadjoin__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoin__Cong,definition,
% 3.57/1.92 ( setadjoin__Cong
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ! [Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( Xz = Xu )
% 3.57/1.92 => ( ( setadjoin @ Xx @ Xz )
% 3.57/1.92 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powerset__Cong_type,type,
% 3.57/1.92 powerset__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powerset__Cong,definition,
% 3.57/1.92 ( powerset__Cong
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ( ( powerset @ A )
% 3.57/1.92 = ( powerset @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunion__Cong_type,type,
% 3.57/1.92 setunion__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunion__Cong,definition,
% 3.57/1.92 ( setunion__Cong
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ( ( setunion @ A )
% 3.57/1.92 = ( setunion @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(omega__Cong_type,type,
% 3.57/1.92 omega__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(omega__Cong,definition,
% 3.57/1.92 ( omega__Cong
% 3.57/1.92 = ( omega = omega ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(exuEu_type,type,
% 3.57/1.92 exuEu: $o ).
% 3.57/1.92
% 3.57/1.92 thf(exuEu,definition,
% 3.57/1.92 ( exuEu
% 3.57/1.92 = ( ! [Xphi: $i > $o] :
% 3.57/1.92 ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(descr__Cong_type,type,
% 3.57/1.92 descr__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(descr__Cong,definition,
% 3.57/1.92 ( descr__Cong
% 3.57/1.92 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 <=> ( Xpsi @ Xy ) ) )
% 3.57/1.92 => ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ( ( exu
% 3.57/1.92 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.57/1.92 => ( ( descr
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 = ( descr
% 3.57/1.92 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstr__Cong_type,type,
% 3.57/1.92 dsetconstr__Cong: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dsetconstr__Cong,definition,
% 3.57/1.92 ( dsetconstr__Cong
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( Xx = Xy )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.57/1.92 => ( ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 = ( dsetconstr @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subset_type,type,
% 3.57/1.92 subset: $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(disjoint_type,type,
% 3.57/1.92 disjoint: $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(setsmeet_type,type,
% 3.57/1.92 setsmeet: $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetI1_type,type,
% 3.57/1.92 subsetI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetI1,definition,
% 3.57/1.92 ( subsetI1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ B ) )
% 3.57/1.92 => ( subset @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eqimpsubset2_type,type,
% 3.57/1.92 eqimpsubset2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eqimpsubset2,definition,
% 3.57/1.92 ( eqimpsubset2
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ( subset @ B @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eqimpsubset1_type,type,
% 3.57/1.92 eqimpsubset1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eqimpsubset1,definition,
% 3.57/1.92 ( eqimpsubset1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( A = B )
% 3.57/1.92 => ( subset @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetI2_type,type,
% 3.57/1.92 subsetI2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetI2,definition,
% 3.57/1.92 ( subsetI2
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ B ) )
% 3.57/1.92 => ( subset @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetsubset_type,type,
% 3.57/1.92 emptysetsubset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(emptysetsubset,definition,
% 3.57/1.92 ( emptysetsubset
% 3.57/1.92 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetE_type,type,
% 3.57/1.92 subsetE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetE,definition,
% 3.57/1.92 ( subsetE
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetE2_type,type,
% 3.57/1.92 subsetE2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetE2,definition,
% 3.57/1.92 ( subsetE2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notsubsetI_type,type,
% 3.57/1.92 notsubsetI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notsubsetI,definition,
% 3.57/1.92 ( notsubsetI
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notequalI1_type,type,
% 3.57/1.92 notequalI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notequalI1,definition,
% 3.57/1.92 ( notequalI1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ~ ( subset @ A @ B )
% 3.57/1.92 => ( A != B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(notequalI2_type,type,
% 3.57/1.92 notequalI2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(notequalI2,definition,
% 3.57/1.92 ( notequalI2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ( A != B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetRefl_type,type,
% 3.57/1.92 subsetRefl: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetRefl,definition,
% 3.57/1.92 ( subsetRefl
% 3.57/1.92 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetTrans_type,type,
% 3.57/1.92 subsetTrans: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetTrans,definition,
% 3.57/1.92 ( subsetTrans
% 3.57/1.92 = ( ! [A: $i,B: $i,C: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ( subset @ B @ C )
% 3.57/1.92 => ( subset @ A @ C ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinSub_type,type,
% 3.57/1.92 setadjoinSub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinSub,definition,
% 3.57/1.92 ( setadjoinSub
% 3.57/1.92 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinSub2_type,type,
% 3.57/1.92 setadjoinSub2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setadjoinSub2,definition,
% 3.57/1.92 ( setadjoinSub2
% 3.57/1.92 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subset2powerset_type,type,
% 3.57/1.92 subset2powerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subset2powerset,definition,
% 3.57/1.92 ( subset2powerset
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setextsub_type,type,
% 3.57/1.92 setextsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setextsub,definition,
% 3.57/1.92 ( setextsub
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ( subset @ B @ A )
% 3.57/1.92 => ( A = B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetemptysetimpeq_type,type,
% 3.57/1.92 subsetemptysetimpeq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetemptysetimpeq,definition,
% 3.57/1.92 ( subsetemptysetimpeq
% 3.57/1.92 = ( ! [A: $i] :
% 3.57/1.92 ( ( subset @ A @ emptyset )
% 3.57/1.92 => ( A = emptyset ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetI1_type,type,
% 3.57/1.92 powersetI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetI1,definition,
% 3.57/1.92 ( powersetI1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ B @ A )
% 3.57/1.92 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetE1_type,type,
% 3.57/1.92 powersetE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetE1,definition,
% 3.57/1.92 ( powersetE1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( in @ B @ ( powerset @ A ) )
% 3.57/1.92 => ( subset @ B @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inPowerset_type,type,
% 3.57/1.92 inPowerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inPowerset,definition,
% 3.57/1.92 ( inPowerset
% 3.57/1.92 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetsubset_type,type,
% 3.57/1.92 powersetsubset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetsubset,definition,
% 3.57/1.92 ( powersetsubset
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(sepInPowerset_type,type,
% 3.57/1.92 sepInPowerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(sepInPowerset,definition,
% 3.57/1.92 ( sepInPowerset
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( in
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 @ ( powerset @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(sepSubset_type,type,
% 3.57/1.92 sepSubset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(sepSubset,definition,
% 3.57/1.92 ( sepSubset
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( subset
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunion_type,type,
% 3.57/1.92 binunion: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(binunionIL_type,type,
% 3.57/1.92 binunionIL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionIL,definition,
% 3.57/1.92 ( binunionIL
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairset2IR_type,type,
% 3.57/1.92 upairset2IR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairset2IR,definition,
% 3.57/1.92 ( upairset2IR
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionIR_type,type,
% 3.57/1.92 binunionIR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionIR,definition,
% 3.57/1.92 ( binunionIR
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionEcases_type,type,
% 3.57/1.92 binunionEcases: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionEcases,definition,
% 3.57/1.92 ( binunionEcases
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.57/1.92 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.57/1.92 => ( ( ( in @ Xx @ A )
% 3.57/1.92 => Xphi )
% 3.57/1.92 => ( ( ( in @ Xx @ B )
% 3.57/1.92 => Xphi )
% 3.57/1.92 => Xphi ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionE_type,type,
% 3.57/1.92 binunionE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionE,definition,
% 3.57/1.92 ( binunionE
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.57/1.92 => ( ( in @ Xx @ A )
% 3.57/1.92 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionLsub_type,type,
% 3.57/1.92 binunionLsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionLsub,definition,
% 3.57/1.92 ( binunionLsub
% 3.57/1.92 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionRsub_type,type,
% 3.57/1.92 binunionRsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionRsub,definition,
% 3.57/1.92 ( binunionRsub
% 3.57/1.92 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersect_type,type,
% 3.57/1.92 binintersect: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectI_type,type,
% 3.57/1.92 binintersectI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectI,definition,
% 3.57/1.92 ( binintersectI
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset5_type,type,
% 3.57/1.92 binintersectSubset5: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset5,definition,
% 3.57/1.92 ( binintersectSubset5
% 3.57/1.92 = ( ! [A: $i,B: $i,C: $i] :
% 3.57/1.92 ( ( subset @ C @ A )
% 3.57/1.92 => ( ( subset @ C @ B )
% 3.57/1.92 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectEL_type,type,
% 3.57/1.92 binintersectEL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectEL,definition,
% 3.57/1.92 ( binintersectEL
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectLsub_type,type,
% 3.57/1.92 binintersectLsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectLsub,definition,
% 3.57/1.92 ( binintersectLsub
% 3.57/1.92 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset2_type,type,
% 3.57/1.92 binintersectSubset2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset2,definition,
% 3.57/1.92 ( binintersectSubset2
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ( binintersect @ A @ B )
% 3.57/1.92 = A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset3_type,type,
% 3.57/1.92 binintersectSubset3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset3,definition,
% 3.57/1.92 ( binintersectSubset3
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( ( binintersect @ A @ B )
% 3.57/1.92 = B )
% 3.57/1.92 => ( subset @ B @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectER_type,type,
% 3.57/1.92 binintersectER: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectER,definition,
% 3.57/1.92 ( binintersectER
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.57/1.92 => ( in @ Xx @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(disjointsetsI1_type,type,
% 3.57/1.92 disjointsetsI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(disjointsetsI1,definition,
% 3.57/1.92 ( disjointsetsI1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ~ ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( in @ Xx @ B ) )
% 3.57/1.92 => ( ( binintersect @ A @ B )
% 3.57/1.92 = emptyset ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectRsub_type,type,
% 3.57/1.92 binintersectRsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectRsub,definition,
% 3.57/1.92 ( binintersectRsub
% 3.57/1.92 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset4_type,type,
% 3.57/1.92 binintersectSubset4: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset4,definition,
% 3.57/1.92 ( binintersectSubset4
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ B @ A )
% 3.57/1.92 => ( ( binintersect @ A @ B )
% 3.57/1.92 = B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset1_type,type,
% 3.57/1.92 binintersectSubset1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectSubset1,definition,
% 3.57/1.92 ( binintersectSubset1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( ( binintersect @ A @ B )
% 3.57/1.92 = A )
% 3.57/1.92 => ( subset @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(bs114d_type,type,
% 3.57/1.92 bs114d: $o ).
% 3.57/1.92
% 3.57/1.92 thf(bs114d,definition,
% 3.57/1.92 ( bs114d
% 3.57/1.92 = ( ! [A: $i,B: $i,C: $i] :
% 3.57/1.92 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.57/1.92 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(regular_type,type,
% 3.57/1.92 regular: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminus_type,type,
% 3.57/1.92 setminus: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(setminusI_type,type,
% 3.57/1.92 setminusI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusI,definition,
% 3.57/1.92 ( setminusI
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusEL_type,type,
% 3.57/1.92 setminusEL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusEL,definition,
% 3.57/1.92 ( setminusEL
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusER_type,type,
% 3.57/1.92 setminusER: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusER,definition,
% 3.57/1.92 ( setminusER
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.57/1.92 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusSubset2_type,type,
% 3.57/1.92 setminusSubset2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusSubset2,definition,
% 3.57/1.92 ( setminusSubset2
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( subset @ A @ B )
% 3.57/1.92 => ( ( setminus @ A @ B )
% 3.57/1.92 = emptyset ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusERneg_type,type,
% 3.57/1.92 setminusERneg: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusERneg,definition,
% 3.57/1.92 ( setminusERneg
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.57/1.92 => ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusELneg_type,type,
% 3.57/1.92 setminusELneg: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusELneg,definition,
% 3.57/1.92 ( setminusELneg
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusILneg_type,type,
% 3.57/1.92 setminusILneg: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusILneg,definition,
% 3.57/1.92 ( setminusILneg
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ~ ( in @ Xx @ A )
% 3.57/1.92 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusIRneg_type,type,
% 3.57/1.92 setminusIRneg: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusIRneg,definition,
% 3.57/1.92 ( setminusIRneg
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ B )
% 3.57/1.92 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusLsub_type,type,
% 3.57/1.92 setminusLsub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusLsub,definition,
% 3.57/1.92 ( setminusLsub
% 3.57/1.92 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusSubset1_type,type,
% 3.57/1.92 setminusSubset1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusSubset1,definition,
% 3.57/1.92 ( setminusSubset1
% 3.57/1.92 = ( ! [A: $i,B: $i] :
% 3.57/1.92 ( ( ( setminus @ A @ B )
% 3.57/1.92 = emptyset )
% 3.57/1.92 => ( subset @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(symdiff_type,type,
% 3.57/1.92 symdiff: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffE_type,type,
% 3.57/1.92 symdiffE: $o ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffE,definition,
% 3.57/1.92 ( symdiffE
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.57/1.92 => ! [Xphi: $o] :
% 3.57/1.92 ( ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => Xphi ) )
% 3.57/1.92 => ( ( ~ ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ B )
% 3.57/1.92 => Xphi ) )
% 3.57/1.92 => Xphi ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffI1_type,type,
% 3.57/1.92 symdiffI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffI1,definition,
% 3.57/1.92 ( symdiffI1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffI2_type,type,
% 3.57/1.92 symdiffI2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffI2,definition,
% 3.57/1.92 ( symdiffI2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ~ ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ B )
% 3.57/1.92 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffIneg1_type,type,
% 3.57/1.92 symdiffIneg1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffIneg1,definition,
% 3.57/1.92 ( symdiffIneg1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ B )
% 3.57/1.92 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffIneg2_type,type,
% 3.57/1.92 symdiffIneg2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(symdiffIneg2,definition,
% 3.57/1.92 ( symdiffIneg2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ~ ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ B )
% 3.57/1.92 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iskpair_type,type,
% 3.57/1.92 iskpair: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(secondinupair_type,type,
% 3.57/1.92 secondinupair: $o ).
% 3.57/1.92
% 3.57/1.92 thf(secondinupair,definition,
% 3.57/1.92 ( secondinupair
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairIL_type,type,
% 3.57/1.92 setukpairIL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairIL,definition,
% 3.57/1.92 ( setukpairIL
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairIR_type,type,
% 3.57/1.92 setukpairIR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairIR,definition,
% 3.57/1.92 ( setukpairIR
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(kpairiskpair_type,type,
% 3.57/1.92 kpairiskpair: $o ).
% 3.57/1.92
% 3.57/1.92 thf(kpairiskpair,definition,
% 3.57/1.92 ( kpairiskpair
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(kpair_type,type,
% 3.57/1.92 kpair: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(kpairp_type,type,
% 3.57/1.92 kpairp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(kpairp,definition,
% 3.57/1.92 ( kpairp
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprod_type,type,
% 3.57/1.92 cartprod: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsubset_type,type,
% 3.57/1.92 singletonsubset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsubset,definition,
% 3.57/1.92 ( singletonsubset
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(singletoninpowerset_type,type,
% 3.57/1.92 singletoninpowerset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletoninpowerset,definition,
% 3.57/1.92 ( singletoninpowerset
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(singletoninpowunion_type,type,
% 3.57/1.92 singletoninpowunion: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletoninpowunion,definition,
% 3.57/1.92 ( singletoninpowunion
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairset2E_type,type,
% 3.57/1.92 upairset2E: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairset2E,definition,
% 3.57/1.92 ( upairset2E
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.57/1.92 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.57/1.92 => ( ( Xz = Xx )
% 3.57/1.92 | ( Xz = Xy ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairsubunion_type,type,
% 3.57/1.92 upairsubunion: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairsubunion,definition,
% 3.57/1.92 ( upairsubunion
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairinpowunion_type,type,
% 3.57/1.92 upairinpowunion: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairinpowunion,definition,
% 3.57/1.92 ( upairinpowunion
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem1_type,type,
% 3.57/1.92 ubforcartprodlem1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem1,definition,
% 3.57/1.92 ( ubforcartprodlem1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem2_type,type,
% 3.57/1.92 ubforcartprodlem2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem2,definition,
% 3.57/1.92 ( ubforcartprodlem2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem3_type,type,
% 3.57/1.92 ubforcartprodlem3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ubforcartprodlem3,definition,
% 3.57/1.92 ( ubforcartprodlem3
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairin_type,type,
% 3.57/1.92 cartprodpairin: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairin,definition,
% 3.57/1.92 ( cartprodpairin
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempair1_type,type,
% 3.57/1.92 cartprodmempair1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempair1,definition,
% 3.57/1.92 ( cartprodmempair1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.57/1.92 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ? [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 & ( Xu
% 3.57/1.92 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempair_type,type,
% 3.57/1.92 cartprodmempair: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempair,definition,
% 3.57/1.92 ( cartprodmempair
% 3.57/1.92 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.57/1.92 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( iskpair @ Xu ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionE2_type,type,
% 3.57/1.92 setunionE2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionE2,definition,
% 3.57/1.92 ( setunionE2
% 3.57/1.92 = ( ! [A: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ ( setunion @ A ) )
% 3.57/1.92 => ? [X: $i] :
% 3.57/1.92 ( ( in @ X @ A )
% 3.57/1.92 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton1_type,type,
% 3.57/1.92 setunionsingleton1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton1,definition,
% 3.57/1.92 ( setunionsingleton1
% 3.57/1.92 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton2_type,type,
% 3.57/1.92 setunionsingleton2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton2,definition,
% 3.57/1.92 ( setunionsingleton2
% 3.57/1.92 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton_type,type,
% 3.57/1.92 setunionsingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setunionsingleton,definition,
% 3.57/1.92 ( setunionsingleton
% 3.57/1.92 = ( ! [Xx: $i] :
% 3.57/1.92 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.57/1.92 = Xx ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(singleton_type,type,
% 3.57/1.92 singleton: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletonprop_type,type,
% 3.57/1.92 singletonprop: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletonprop,definition,
% 3.57/1.92 ( singletonprop
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) )
% 3.57/1.92 => ( ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) )
% 3.57/1.92 => ( singleton
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ex1_type,type,
% 3.57/1.92 ex1: $i > ( $i > $o ) > $o ).
% 3.57/1.92
% 3.57/1.92 thf(ex1E1_type,type,
% 3.57/1.92 ex1E1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ex1E1,definition,
% 3.57/1.92 ( ex1E1
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ( ex1 @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ex1I_type,type,
% 3.57/1.92 ex1I: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ex1I,definition,
% 3.57/1.92 ( ex1I
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xy = Xx ) ) )
% 3.57/1.92 => ( ex1 @ A
% 3.57/1.92 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ex1I2_type,type,
% 3.57/1.92 ex1I2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ex1I2,definition,
% 3.57/1.92 ( ex1I2
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) )
% 3.57/1.92 => ( ? [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 & ( Xphi @ Xx ) )
% 3.57/1.92 => ( ex1 @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsuniq_type,type,
% 3.57/1.92 singletonsuniq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(singletonsuniq,definition,
% 3.57/1.92 ( singletonsuniq
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( ( setadjoin @ Xx @ emptyset )
% 3.57/1.92 = ( setadjoin @ Xy @ emptyset ) )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(atmost1p_type,type,
% 3.57/1.92 atmost1p: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(atleast2p_type,type,
% 3.57/1.92 atleast2p: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(atmost2p_type,type,
% 3.57/1.92 atmost2p: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairsetp_type,type,
% 3.57/1.92 upairsetp: $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL1_type,type,
% 3.57/1.92 setukpairinjL1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL1,definition,
% 3.57/1.92 ( setukpairinjL1
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.57/1.92 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.57/1.92 => ( Xx = Xz ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(kfstsingleton_type,type,
% 3.57/1.92 kfstsingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(kfstsingleton,definition,
% 3.57/1.92 ( kfstsingleton
% 3.57/1.92 = ( ! [Xu: $i] :
% 3.57/1.92 ( ( iskpair @ Xu )
% 3.57/1.92 => ( singleton
% 3.57/1.92 @ ( dsetconstr @ ( setunion @ Xu )
% 3.57/1.92 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(theprop_type,type,
% 3.57/1.92 theprop: $o ).
% 3.57/1.92
% 3.57/1.92 thf(theprop,definition,
% 3.57/1.92 ( theprop
% 3.57/1.92 = ( ! [X: $i] :
% 3.57/1.92 ( ( singleton @ X )
% 3.57/1.92 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(kfst_type,type,
% 3.57/1.92 kfst: $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(kfstpairEq_type,type,
% 3.57/1.92 kfstpairEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(kfstpairEq,definition,
% 3.57/1.92 ( kfstpairEq
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.57/1.92 = Xx ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodfstin_type,type,
% 3.57/1.92 cartprodfstin: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodfstin,definition,
% 3.57/1.92 ( cartprodfstin
% 3.57/1.92 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.57/1.92 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL2_type,type,
% 3.57/1.92 setukpairinjL2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL2,definition,
% 3.57/1.92 ( setukpairinjL2
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.57/1.92 => ( Xx = Xz ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL_type,type,
% 3.57/1.92 setukpairinjL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjL,definition,
% 3.57/1.92 ( setukpairinjL
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( ( kpair @ Xx @ Xy )
% 3.57/1.92 = ( kpair @ Xz @ Xu ) )
% 3.57/1.92 => ( Xx = Xz ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR11_type,type,
% 3.57/1.92 setukpairinjR11: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR11,definition,
% 3.57/1.92 ( setukpairinjR11
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR12_type,type,
% 3.57/1.92 setukpairinjR12: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR12,definition,
% 3.57/1.92 ( setukpairinjR12
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xx = Xy )
% 3.57/1.92 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR1_type,type,
% 3.57/1.92 setukpairinjR1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR1,definition,
% 3.57/1.92 ( setukpairinjR1
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.57/1.92 => ( ( Xz = Xu )
% 3.57/1.92 => ( Xy = Xu ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(upairequniteq_type,type,
% 3.57/1.92 upairequniteq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(upairequniteq,definition,
% 3.57/1.92 ( upairequniteq
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.57/1.92 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ Xz @ emptyset ) )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR2_type,type,
% 3.57/1.92 setukpairinjR2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR2,definition,
% 3.57/1.92 ( setukpairinjR2
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.57/1.92 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.57/1.92 => ( Xy = Xu ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR_type,type,
% 3.57/1.92 setukpairinjR: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setukpairinjR,definition,
% 3.57/1.92 ( setukpairinjR
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.57/1.92 ( ( ( kpair @ Xx @ Xy )
% 3.57/1.92 = ( kpair @ Xz @ Xu ) )
% 3.57/1.92 => ( Xy = Xu ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ksndsingleton_type,type,
% 3.57/1.92 ksndsingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ksndsingleton,definition,
% 3.57/1.92 ( ksndsingleton
% 3.57/1.92 = ( ! [Xu: $i] :
% 3.57/1.92 ( ( iskpair @ Xu )
% 3.57/1.92 => ( singleton
% 3.57/1.92 @ ( dsetconstr @ ( setunion @ Xu )
% 3.57/1.92 @ ^ [Xx: $i] :
% 3.57/1.92 ( Xu
% 3.57/1.92 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ksnd_type,type,
% 3.57/1.92 ksnd: $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(ksndpairEq_type,type,
% 3.57/1.92 ksndpairEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ksndpairEq,definition,
% 3.57/1.92 ( ksndpairEq
% 3.57/1.92 = ( ! [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.57/1.92 = Xy ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(kpairsurjEq_type,type,
% 3.57/1.92 kpairsurjEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(kpairsurjEq,definition,
% 3.57/1.92 ( kpairsurjEq
% 3.57/1.92 = ( ! [Xu: $i] :
% 3.57/1.92 ( ( iskpair @ Xu )
% 3.57/1.92 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.57/1.92 = Xu ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodsndin_type,type,
% 3.57/1.92 cartprodsndin: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodsndin,definition,
% 3.57/1.92 ( cartprodsndin
% 3.57/1.92 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.57/1.92 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairmemEL_type,type,
% 3.57/1.92 cartprodpairmemEL: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairmemEL,definition,
% 3.57/1.92 ( cartprodpairmemEL
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairmemER_type,type,
% 3.57/1.92 cartprodpairmemER: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairmemER,definition,
% 3.57/1.92 ( cartprodpairmemER
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( in @ Xy @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempaircEq_type,type,
% 3.57/1.92 cartprodmempaircEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodmempaircEq,definition,
% 3.57/1.92 ( cartprodmempaircEq
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( kpair @ Xx @ Xy )
% 3.57/1.92 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodfstpairEq_type,type,
% 3.57/1.92 cartprodfstpairEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodfstpairEq,definition,
% 3.57/1.92 ( cartprodfstpairEq
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.57/1.92 = Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodsndpairEq_type,type,
% 3.57/1.92 cartprodsndpairEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodsndpairEq,definition,
% 3.57/1.92 ( cartprodsndpairEq
% 3.57/1.92 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.57/1.92 = Xy ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairsurjEq_type,type,
% 3.57/1.92 cartprodpairsurjEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(cartprodpairsurjEq,definition,
% 3.57/1.92 ( cartprodpairsurjEq
% 3.57/1.92 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.57/1.92 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.57/1.92 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.57/1.92 = Xu ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(breln_type,type,
% 3.57/1.92 breln: $i > $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(breln,definition,
% 3.57/1.92 ( breln
% 3.57/1.92 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstr_type,type,
% 3.57/1.92 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrI_type,type,
% 3.57/1.92 dpsetconstrI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrI,definition,
% 3.57/1.92 ( dpsetconstrI
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( Xphi @ Xx @ Xy )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy )
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrSub_type,type,
% 3.57/1.92 dpsetconstrSub: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrSub,definition,
% 3.57/1.92 ( dpsetconstrSub
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.57/1.92 ( subset
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.57/1.92 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setOfPairsIsBReln_type,type,
% 3.57/1.92 setOfPairsIsBReln: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setOfPairsIsBReln,definition,
% 3.57/1.92 ( setOfPairsIsBReln
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.57/1.92 ( breln @ A @ B
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrERa_type,type,
% 3.57/1.92 dpsetconstrERa: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrERa,definition,
% 3.57/1.92 ( dpsetconstrERa
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.57/1.92 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrEL1_type,type,
% 3.57/1.92 dpsetconstrEL1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrEL1,definition,
% 3.57/1.92 ( dpsetconstrEL1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ ( kpair @ Xx @ Xy )
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.57/1.92 => ( in @ Xx @ A ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrEL2_type,type,
% 3.57/1.92 dpsetconstrEL2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrEL2,definition,
% 3.57/1.92 ( dpsetconstrEL2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ ( kpair @ Xx @ Xy )
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.57/1.92 => ( in @ Xy @ B ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrER_type,type,
% 3.57/1.92 dpsetconstrER: $o ).
% 3.57/1.92
% 3.57/1.92 thf(dpsetconstrER,definition,
% 3.57/1.92 ( dpsetconstrER
% 3.57/1.92 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( in @ ( kpair @ Xx @ Xy )
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.57/1.92 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(func_type,type,
% 3.57/1.92 func: $i > $i > $i > $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcSet_type,type,
% 3.57/1.92 funcSet: $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(funcImageSingleton_type,type,
% 3.57/1.92 funcImageSingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcImageSingleton,definition,
% 3.57/1.92 ( funcImageSingleton
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( singleton
% 3.57/1.92 @ ( dsetconstr @ B
% 3.57/1.92 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(apProp_type,type,
% 3.57/1.92 apProp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(apProp,definition,
% 3.57/1.92 ( apProp
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in
% 3.57/1.92 @ ( setunion
% 3.57/1.92 @ ( dsetconstr @ B
% 3.57/1.92 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.57/1.92 @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ap_type,type,
% 3.57/1.92 ap: $i > $i > $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(app_type,type,
% 3.57/1.92 app: $o ).
% 3.57/1.92
% 3.57/1.92 thf(app,definition,
% 3.57/1.92 ( app
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(infuncsetfunc_type,type,
% 3.57/1.92 infuncsetfunc: $o ).
% 3.57/1.92
% 3.57/1.92 thf(infuncsetfunc,definition,
% 3.57/1.92 ( infuncsetfunc
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ap2p_type,type,
% 3.57/1.92 ap2p: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ap2p,definition,
% 3.57/1.92 ( ap2p
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcinfuncset_type,type,
% 3.57/1.92 funcinfuncset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcinfuncset,definition,
% 3.57/1.92 ( funcinfuncset
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(lamProp_type,type,
% 3.57/1.92 lamProp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(lamProp,definition,
% 3.57/1.92 ( lamProp
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ( func @ A @ B
% 3.57/1.92 @ ( dpsetconstr @ A @ B
% 3.57/1.92 @ ^ [Xx: $i,Xy: $i] :
% 3.57/1.92 ( ( Xf @ Xx )
% 3.57/1.92 = Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(lam_type,type,
% 3.57/1.92 lam: $i > $i > ( $i > $i ) > $i ).
% 3.57/1.92
% 3.57/1.92 thf(lamp_type,type,
% 3.57/1.92 lamp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(lamp,definition,
% 3.57/1.92 ( lamp
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ( func @ A @ B
% 3.57/1.92 @ ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(lam2p_type,type,
% 3.57/1.92 lam2p: $o ).
% 3.57/1.92
% 3.57/1.92 thf(lam2p,definition,
% 3.57/1.92 ( lam2p
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ( in
% 3.57/1.92 @ ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.57/1.92 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(brelnall1_type,type,
% 3.57/1.92 brelnall1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(brelnall1,definition,
% 3.57/1.92 ( brelnall1
% 3.57/1.92 = ( ! [A: $i,B: $i,R: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ R )
% 3.57/1.92 => ! [Xphi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.92 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ R )
% 3.57/1.92 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(brelnall2_type,type,
% 3.57/1.92 brelnall2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(brelnall2,definition,
% 3.57/1.92 ( brelnall2
% 3.57/1.92 = ( ! [A: $i,B: $i,R: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ R )
% 3.57/1.92 => ! [Xphi: $i > $o] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.92 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ R )
% 3.57/1.92 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ex1E2_type,type,
% 3.57/1.92 ex1E2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ex1E2,definition,
% 3.57/1.92 ( ex1E2
% 3.57/1.92 = ( ! [A: $i,Xphi: $i > $o] :
% 3.57/1.92 ( ( ex1 @ A
% 3.57/1.92 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ( Xphi @ Xx )
% 3.57/1.92 => ( ( Xphi @ Xy )
% 3.57/1.92 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp1_type,type,
% 3.57/1.92 funcGraphProp1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp1,definition,
% 3.57/1.92 ( funcGraphProp1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp3_type,type,
% 3.57/1.92 funcGraphProp3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp3,definition,
% 3.57/1.92 ( funcGraphProp3
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp2_type,type,
% 3.57/1.92 funcGraphProp2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp2,definition,
% 3.57/1.92 ( funcGraphProp2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcextLem_type,type,
% 3.57/1.92 funcextLem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcextLem,definition,
% 3.57/1.92 ( funcextLem
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xg: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xg )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp4_type,type,
% 3.57/1.92 funcGraphProp4: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcGraphProp4,definition,
% 3.57/1.92 ( funcGraphProp4
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = Xy ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subbreln_type,type,
% 3.57/1.92 subbreln: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subbreln,definition,
% 3.57/1.92 ( subbreln
% 3.57/1.92 = ( ! [A: $i,B: $i,R: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ R )
% 3.57/1.92 => ! [S: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ S )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.57/1.92 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eqbreln_type,type,
% 3.57/1.92 eqbreln: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eqbreln,definition,
% 3.57/1.92 ( eqbreln
% 3.57/1.92 = ( ! [A: $i,B: $i,R: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ R )
% 3.57/1.92 => ! [S: $i] :
% 3.57/1.92 ( ( breln @ A @ B @ S )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ B )
% 3.57/1.92 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.57/1.92 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.57/1.92 => ( R = S ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcext_type,type,
% 3.57/1.92 funcext: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcext,definition,
% 3.57/1.92 ( funcext
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xg: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xg )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.57/1.92 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(funcext2_type,type,
% 3.57/1.92 funcext2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(funcext2,definition,
% 3.57/1.92 ( funcext2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ! [Xg: $i] :
% 3.57/1.92 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.57/1.92 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ap2apEq1_type,type,
% 3.57/1.92 ap2apEq1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ap2apEq1,definition,
% 3.57/1.92 ( ap2apEq1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ap2apEq2_type,type,
% 3.57/1.92 ap2apEq2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ap2apEq2,definition,
% 3.57/1.92 ( ap2apEq2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.57/1.92 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(beta1_type,type,
% 3.57/1.92 beta1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(beta1,definition,
% 3.57/1.92 ( beta1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B
% 3.57/1.92 @ ( lam @ A @ B
% 3.57/1.92 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.57/1.92 @ Xx )
% 3.57/1.92 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eta1_type,type,
% 3.57/1.92 eta1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eta1,definition,
% 3.57/1.92 ( eta1
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( func @ A @ B @ Xf )
% 3.57/1.92 => ( ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.57/1.92 = Xf ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(lam2lamEq_type,type,
% 3.57/1.92 lam2lamEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(lam2lamEq,definition,
% 3.57/1.92 ( lam2lamEq
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ( ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.57/1.92 = ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(beta2_type,type,
% 3.57/1.92 beta2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(beta2,definition,
% 3.57/1.92 ( beta2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.57/1.92 ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( ap @ A @ B
% 3.57/1.92 @ ( lam @ A @ B
% 3.57/1.92 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.57/1.92 @ Xx )
% 3.57/1.92 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(eta2_type,type,
% 3.57/1.92 eta2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(eta2,definition,
% 3.57/1.92 ( eta2
% 3.57/1.92 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.57/1.92 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.57/1.92 => ( ( lam @ A @ B
% 3.57/1.92 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.57/1.92 = Xf ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iffalseProp1_type,type,
% 3.57/1.92 iffalseProp1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iffalseProp1,definition,
% 3.57/1.92 ( iffalseProp1
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ~ Xphi
% 3.57/1.92 => ( in @ Xy
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xz: $i] :
% 3.57/1.92 ( ( Xphi
% 3.57/1.92 & ( Xz = Xx ) )
% 3.57/1.92 | ( ~ Xphi
% 3.57/1.92 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iffalseProp2_type,type,
% 3.57/1.92 iffalseProp2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iffalseProp2,definition,
% 3.57/1.92 ( iffalseProp2
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ~ Xphi
% 3.57/1.92 => ( ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xz: $i] :
% 3.57/1.92 ( ( Xphi
% 3.57/1.92 & ( Xz = Xx ) )
% 3.57/1.92 | ( ~ Xphi
% 3.57/1.92 & ( Xz = Xy ) ) ) )
% 3.57/1.92 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueProp1_type,type,
% 3.57/1.92 iftrueProp1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueProp1,definition,
% 3.57/1.92 ( iftrueProp1
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( Xphi
% 3.57/1.92 => ( in @ Xx
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xz: $i] :
% 3.57/1.92 ( ( Xphi
% 3.57/1.92 & ( Xz = Xx ) )
% 3.57/1.92 | ( ~ Xphi
% 3.57/1.92 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueProp2_type,type,
% 3.57/1.92 iftrueProp2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueProp2,definition,
% 3.57/1.92 ( iftrueProp2
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( Xphi
% 3.57/1.92 => ( ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xz: $i] :
% 3.57/1.92 ( ( Xphi
% 3.57/1.92 & ( Xz = Xx ) )
% 3.57/1.92 | ( ~ Xphi
% 3.57/1.92 & ( Xz = Xy ) ) ) )
% 3.57/1.92 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(ifSingleton_type,type,
% 3.57/1.92 ifSingleton: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ifSingleton,definition,
% 3.57/1.92 ( ifSingleton
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( singleton
% 3.57/1.92 @ ( dsetconstr @ A
% 3.57/1.92 @ ^ [Xz: $i] :
% 3.57/1.92 ( ( Xphi
% 3.57/1.92 & ( Xz = Xx ) )
% 3.57/1.92 | ( ~ Xphi
% 3.57/1.92 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(if_type,type,
% 3.57/1.92 if: $i > $o > $i > $i > $i ).
% 3.57/1.92
% 3.57/1.92 thf(ifp_type,type,
% 3.57/1.92 ifp: $o ).
% 3.57/1.92
% 3.57/1.92 thf(ifp,definition,
% 3.57/1.92 ( ifp
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(theeq_type,type,
% 3.57/1.92 theeq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(theeq,definition,
% 3.57/1.92 ( theeq
% 3.57/1.92 = ( ! [X: $i] :
% 3.57/1.92 ( ( singleton @ X )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ X )
% 3.57/1.92 => ( ( setunion @ X )
% 3.57/1.92 = Xx ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iftrue_type,type,
% 3.57/1.92 iftrue: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iftrue,definition,
% 3.57/1.92 ( iftrue
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( Xphi
% 3.57/1.92 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.57/1.92 = Xx ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iffalse_type,type,
% 3.57/1.92 iffalse: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iffalse,definition,
% 3.57/1.92 ( iffalse
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( ~ Xphi
% 3.57/1.92 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.57/1.92 = Xy ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueorfalse_type,type,
% 3.57/1.92 iftrueorfalse: $o ).
% 3.57/1.92
% 3.57/1.92 thf(iftrueorfalse,definition,
% 3.57/1.92 ( iftrueorfalse
% 3.57/1.92 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ! [Xy: $i] :
% 3.57/1.92 ( ( in @ Xy @ A )
% 3.57/1.92 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectT_lem_type,type,
% 3.57/1.92 binintersectT_lem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectT_lem,definition,
% 3.57/1.92 ( binintersectT_lem
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionT_lem_type,type,
% 3.57/1.92 binunionT_lem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionT_lem,definition,
% 3.57/1.92 ( binunionT_lem
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetT_lem_type,type,
% 3.57/1.92 powersetT_lem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetT_lem,definition,
% 3.57/1.92 ( powersetT_lem
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setminusT_lem_type,type,
% 3.57/1.92 setminusT_lem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setminusT_lem,definition,
% 3.57/1.92 ( setminusT_lem
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementT_lem_type,type,
% 3.57/1.92 complementT_lem: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementT_lem,definition,
% 3.57/1.92 ( complementT_lem
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(setextT_type,type,
% 3.57/1.92 setextT: $o ).
% 3.57/1.92
% 3.57/1.92 thf(setextT,definition,
% 3.57/1.92 ( setextT
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ( in @ Xx @ Y ) ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ Y )
% 3.57/1.92 => ( in @ Xx @ X ) ) )
% 3.57/1.92 => ( X = Y ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(subsetTI_type,type,
% 3.57/1.92 subsetTI: $o ).
% 3.57/1.92
% 3.57/1.92 thf(subsetTI,definition,
% 3.57/1.92 ( subsetTI
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ( in @ Xx @ Y ) ) )
% 3.57/1.92 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetTI1_type,type,
% 3.57/1.92 powersetTI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetTI1,definition,
% 3.57/1.92 ( powersetTI1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ( in @ Xx @ Y ) ) )
% 3.57/1.92 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(powersetTE1_type,type,
% 3.57/1.92 powersetTE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(powersetTE1,definition,
% 3.57/1.92 ( powersetTE1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ X @ ( powerset @ Y ) )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementTI1_type,type,
% 3.57/1.92 complementTI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementTI1,definition,
% 3.57/1.92 ( complementTI1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementTE1_type,type,
% 3.57/1.92 complementTE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementTE1,definition,
% 3.57/1.92 ( complementTE1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.57/1.92 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectTELcontra_type,type,
% 3.57/1.92 binintersectTELcontra: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectTELcontra,definition,
% 3.57/1.92 ( binintersectTELcontra
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ X )
% 3.57/1.92 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectTERcontra_type,type,
% 3.57/1.92 binintersectTERcontra: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binintersectTERcontra,definition,
% 3.57/1.92 ( binintersectTERcontra
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ Y )
% 3.57/1.92 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT_type,type,
% 3.57/1.92 contrasubsetT: $o ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT,definition,
% 3.57/1.92 ( contrasubsetT
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.57/1.92 => ( ( in @ Xx @ Y )
% 3.57/1.92 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT1_type,type,
% 3.57/1.92 contrasubsetT1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT1,definition,
% 3.57/1.92 ( contrasubsetT1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( subset @ X @ Y )
% 3.57/1.92 => ( ~ ( in @ Xx @ Y )
% 3.57/1.92 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT2_type,type,
% 3.57/1.92 contrasubsetT2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT2,definition,
% 3.57/1.92 ( contrasubsetT2
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ( subset @ X @ Y )
% 3.57/1.92 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT3_type,type,
% 3.57/1.92 contrasubsetT3: $o ).
% 3.57/1.92
% 3.57/1.92 thf(contrasubsetT3,definition,
% 3.57/1.92 ( contrasubsetT3
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.57/1.92 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementI1_type,type,
% 3.57/1.92 doubleComplementI1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementI1,definition,
% 3.57/1.92 ( doubleComplementI1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ X )
% 3.57/1.92 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementE1_type,type,
% 3.57/1.92 doubleComplementE1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementE1,definition,
% 3.57/1.92 ( doubleComplementE1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.57/1.92 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementSub1_type,type,
% 3.57/1.92 doubleComplementSub1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementSub1,definition,
% 3.57/1.92 ( doubleComplementSub1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementSub2_type,type,
% 3.57/1.92 doubleComplementSub2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementSub2,definition,
% 3.57/1.92 ( doubleComplementSub2
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementEq_type,type,
% 3.57/1.92 doubleComplementEq: $o ).
% 3.57/1.92
% 3.57/1.92 thf(doubleComplementEq,definition,
% 3.57/1.92 ( doubleComplementEq
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ( X
% 3.57/1.92 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementTnotintersectT_type,type,
% 3.57/1.92 complementTnotintersectT: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementTnotintersectT,definition,
% 3.57/1.92 ( complementTnotintersectT
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.57/1.92 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementImpComplementIntersect_type,type,
% 3.57/1.92 complementImpComplementIntersect: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementImpComplementIntersect,definition,
% 3.57/1.92 ( complementImpComplementIntersect
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.57/1.92 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementSubsetComplementIntersect_type,type,
% 3.57/1.92 complementSubsetComplementIntersect: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementSubsetComplementIntersect,definition,
% 3.57/1.92 ( complementSubsetComplementIntersect
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementInPowersetComplementIntersect_type,type,
% 3.57/1.92 complementInPowersetComplementIntersect: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementInPowersetComplementIntersect,definition,
% 3.57/1.92 ( complementInPowersetComplementIntersect
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(contraSubsetComplement_type,type,
% 3.57/1.92 contraSubsetComplement: $o ).
% 3.57/1.92
% 3.57/1.92 thf(contraSubsetComplement,definition,
% 3.57/1.92 ( contraSubsetComplement
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ Y )
% 3.57/1.92 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(complementTcontraSubset_type,type,
% 3.57/1.92 complementTcontraSubset: $o ).
% 3.57/1.92
% 3.57/1.92 thf(complementTcontraSubset,definition,
% 3.57/1.92 ( complementTcontraSubset
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.57/1.92 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionTILcontra_type,type,
% 3.57/1.92 binunionTILcontra: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionTILcontra,definition,
% 3.57/1.92 ( binunionTILcontra
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.57/1.92 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(binunionTIRcontra_type,type,
% 3.57/1.92 binunionTIRcontra: $o ).
% 3.57/1.92
% 3.57/1.92 thf(binunionTIRcontra,definition,
% 3.57/1.92 ( binunionTIRcontra
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.57/1.92 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInUnion_type,type,
% 3.57/1.92 inIntersectImpInUnion: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInUnion,definition,
% 3.57/1.92 ( inIntersectImpInUnion
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Z: $i] :
% 3.57/1.92 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.57/1.92 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInUnion2_type,type,
% 3.57/1.92 inIntersectImpInUnion2: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInUnion2,definition,
% 3.57/1.92 ( inIntersectImpInUnion2
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Z: $i] :
% 3.57/1.92 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.57/1.92 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInIntersectUnions_type,type,
% 3.57/1.92 inIntersectImpInIntersectUnions: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inIntersectImpInIntersectUnions,definition,
% 3.57/1.92 ( inIntersectImpInIntersectUnions
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Z: $i] :
% 3.57/1.92 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.57/1.92 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(intersectInPowersetIntersectUnions_type,type,
% 3.57/1.92 intersectInPowersetIntersectUnions: $o ).
% 3.57/1.92
% 3.57/1.92 thf(intersectInPowersetIntersectUnions,definition,
% 3.57/1.92 ( intersectInPowersetIntersectUnions
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Z: $i] :
% 3.57/1.92 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.92 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inComplementUnionImpNotIn1_type,type,
% 3.57/1.92 inComplementUnionImpNotIn1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inComplementUnionImpNotIn1,definition,
% 3.57/1.92 ( inComplementUnionImpNotIn1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.57/1.92 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.57/1.92
% 3.57/1.92 thf(inComplementUnionImpInComplement1_type,type,
% 3.57/1.92 inComplementUnionImpInComplement1: $o ).
% 3.57/1.92
% 3.57/1.92 thf(inComplementUnionImpInComplement1,definition,
% 3.57/1.92 ( inComplementUnionImpInComplement1
% 3.57/1.92 = ( ! [A: $i,X: $i] :
% 3.57/1.92 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.92 => ! [Y: $i] :
% 3.57/1.92 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.92 => ! [Xx: $i] :
% 3.57/1.92 ( ( in @ Xx @ A )
% 3.57/1.92 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.57/1.92 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(binunionTE_type,type,
% 3.57/1.93 binunionTE: $o ).
% 3.57/1.93
% 3.57/1.93 thf(binunionTE,definition,
% 3.57/1.93 ( binunionTE
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xphi: $o,Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.57/1.93 => ( ( ( in @ Xx @ X )
% 3.57/1.93 => Xphi )
% 3.57/1.93 => ( ( ( in @ Xx @ Y )
% 3.57/1.93 => Xphi )
% 3.57/1.93 => Xphi ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(binunionTEcontra_type,type,
% 3.57/1.93 binunionTEcontra: $o ).
% 3.57/1.93
% 3.57/1.93 thf(binunionTEcontra,definition,
% 3.57/1.93 ( binunionTEcontra
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ~ ( in @ Xx @ X )
% 3.57/1.93 => ( ~ ( in @ Xx @ Y )
% 3.57/1.93 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a1_type,type,
% 3.57/1.93 demorgan2a1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a1,definition,
% 3.57/1.93 ( demorgan2a1
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(complementUnionInPowersetComplement_type,type,
% 3.57/1.93 complementUnionInPowersetComplement: $o ).
% 3.57/1.93
% 3.57/1.93 thf(complementUnionInPowersetComplement,definition,
% 3.57/1.93 ( complementUnionInPowersetComplement
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a2_type,type,
% 3.57/1.93 demorgan2a2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a2,definition,
% 3.57/1.93 ( demorgan2a2
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1a_type,type,
% 3.57/1.93 demorgan1a: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1a,definition,
% 3.57/1.93 ( demorgan1a
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1b_type,type,
% 3.57/1.93 demorgan1b: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1b,definition,
% 3.57/1.93 ( demorgan1b
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1_type,type,
% 3.57/1.93 demorgan1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan1,definition,
% 3.57/1.93 ( demorgan1
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.57/1.93 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a_type,type,
% 3.57/1.93 demorgan2a: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2a,definition,
% 3.57/1.93 ( demorgan2a
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2b2_type,type,
% 3.57/1.93 demorgan2b2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2b2,definition,
% 3.57/1.93 ( demorgan2b2
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.57/1.93 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.57/1.93 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2b_type,type,
% 3.57/1.93 demorgan2b: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2b,definition,
% 3.57/1.93 ( demorgan2b
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.57/1.93 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2_type,type,
% 3.57/1.93 demorgan2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(demorgan2,definition,
% 3.57/1.93 ( demorgan2
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.57/1.93 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule0_type,type,
% 3.57/1.93 woz13rule0: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule0,definition,
% 3.57/1.93 ( woz13rule0
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.57/1.93 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule1_type,type,
% 3.57/1.93 woz13rule1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule1,definition,
% 3.57/1.93 ( woz13rule1
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ( ( subset @ X @ Z )
% 3.57/1.93 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule2_type,type,
% 3.57/1.93 woz13rule2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule2,definition,
% 3.57/1.93 ( woz13rule2
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ( ( subset @ Y @ Z )
% 3.57/1.93 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule3_type,type,
% 3.57/1.93 woz13rule3: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule3,definition,
% 3.57/1.93 ( woz13rule3
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ( ( subset @ X @ Y )
% 3.57/1.93 => ( ( subset @ X @ Z )
% 3.57/1.93 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule4_type,type,
% 3.57/1.93 woz13rule4: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz13rule4,definition,
% 3.57/1.93 ( woz13rule4
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ! [W: $i] :
% 3.57/1.93 ( ( in @ W @ ( powerset @ A ) )
% 3.57/1.93 => ( ( subset @ X @ Z )
% 3.57/1.93 => ( ( subset @ Y @ W )
% 3.57/1.93 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_1_type,type,
% 3.57/1.93 woz1_1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_1,definition,
% 3.57/1.93 ( woz1_1
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_2_type,type,
% 3.57/1.93 woz1_2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_2,definition,
% 3.57/1.93 ( woz1_2
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ! [W: $i] :
% 3.57/1.93 ( ( in @ W @ ( powerset @ A ) )
% 3.57/1.93 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.57/1.93 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_3_type,type,
% 3.57/1.93 woz1_3: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_3,definition,
% 3.57/1.93 ( woz1_3
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ! [Z: $i] :
% 3.57/1.93 ( ( in @ Z @ ( powerset @ A ) )
% 3.57/1.93 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_4_type,type,
% 3.57/1.93 woz1_4: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_4,definition,
% 3.57/1.93 ( woz1_4
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.57/1.93 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_5_type,type,
% 3.57/1.93 woz1_5: $o ).
% 3.57/1.93
% 3.57/1.93 thf(woz1_5,definition,
% 3.57/1.93 ( woz1_5
% 3.57/1.93 = ( ! [A: $i,X: $i] :
% 3.57/1.93 ( ( in @ X @ ( powerset @ A ) )
% 3.57/1.93 => ! [Y: $i] :
% 3.57/1.93 ( ( in @ Y @ ( powerset @ A ) )
% 3.57/1.93 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(breln1_type,type,
% 3.57/1.93 breln1: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(breln1,definition,
% 3.57/1.93 ( breln1
% 3.57/1.93 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(breln1all2_type,type,
% 3.57/1.93 breln1all2: $o ).
% 3.57/1.93
% 3.57/1.93 thf(breln1all2,definition,
% 3.57/1.93 ( breln1all2
% 3.57/1.93 = ( ! [A: $i,R: $i] :
% 3.57/1.93 ( ( breln1 @ A @ R )
% 3.57/1.93 => ! [Xphi: $i > $o] :
% 3.57/1.93 ( ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ! [Xy: $i] :
% 3.57/1.93 ( ( in @ Xy @ A )
% 3.57/1.93 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.93 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ R )
% 3.57/1.93 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(breln1Set_type,type,
% 3.57/1.93 breln1Set: $i > $i ).
% 3.57/1.93
% 3.57/1.93 thf(breln1SetBreln1_type,type,
% 3.57/1.93 breln1SetBreln1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(breln1SetBreln1,definition,
% 3.57/1.93 ( breln1SetBreln1
% 3.57/1.93 = ( ! [A: $i,R: $i] :
% 3.57/1.93 ( ( in @ R @ ( breln1Set @ A ) )
% 3.57/1.93 => ( breln1 @ A @ R ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(transitive_type,type,
% 3.57/1.93 transitive: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(antisymmetric_type,type,
% 3.57/1.93 antisymmetric: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(reflexive_type,type,
% 3.57/1.93 reflexive: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(refltransitive_type,type,
% 3.57/1.93 refltransitive: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(refllinearorder_type,type,
% 3.57/1.93 refllinearorder: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(reflwellordering_type,type,
% 3.57/1.93 reflwellordering: $i > $i > $o ).
% 3.57/1.93
% 3.57/1.93 thf(choice2fnsingleton_type,type,
% 3.57/1.93 choice2fnsingleton: $o ).
% 3.57/1.93
% 3.57/1.93 thf(choice2fnsingleton,definition,
% 3.57/1.93 ( choice2fnsingleton
% 3.57/1.93 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.57/1.93 ( ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ? [Xy: $i] :
% 3.57/1.93 ( ( in @ Xy @ B )
% 3.57/1.93 & ( Xphi @ Xx @ Xy ) ) )
% 3.57/1.93 => ! [R: $i] :
% 3.57/1.93 ( ( in @ R @ ( breln1Set @ B ) )
% 3.57/1.93 => ( ( reflwellordering @ B @ R )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ( singleton
% 3.57/1.93 @ ( dsetconstr @ B
% 3.57/1.93 @ ^ [Xy: $i] :
% 3.57/1.93 ( ( Xphi @ Xx @ Xy )
% 3.57/1.93 & ! [Xz: $i] :
% 3.57/1.93 ( ( in @ Xz @ B )
% 3.57/1.93 => ( ( Xphi @ Xx @ Xz )
% 3.57/1.93 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(setOfPairsIsBReln1_type,type,
% 3.57/1.93 setOfPairsIsBReln1: $o ).
% 3.57/1.93
% 3.57/1.93 thf(setOfPairsIsBReln1,definition,
% 3.57/1.93 ( setOfPairsIsBReln1
% 3.57/1.93 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.57/1.93 ( breln1 @ A
% 3.57/1.93 @ ( dpsetconstr @ A @ A
% 3.57/1.93 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.57/1.93
% 3.57/1.93 thf(breln1all1,conjecture,
% 3.57/1.93 ( setextAx
% 3.57/1.93 => ( emptysetAx
% 3.57/1.93 => ( setadjoinAx
% 3.57/1.93 => ( powersetAx
% 3.57/1.93 => ( setunionAx
% 3.57/1.93 => ( omega0Ax
% 3.57/1.93 => ( omegaSAx
% 3.57/1.93 => ( omegaIndAx
% 3.57/1.93 => ( replAx
% 3.57/1.93 => ( foundationAx
% 3.57/1.93 => ( wellorderingAx
% 3.57/1.93 => ( descrp
% 3.57/1.93 => ( dsetconstrI
% 3.57/1.93 => ( dsetconstrEL
% 3.57/1.93 => ( dsetconstrER
% 3.57/1.93 => ( exuE1
% 3.57/1.93 => ( prop2setE
% 3.57/1.93 => ( emptysetE
% 3.57/1.93 => ( emptysetimpfalse
% 3.57/1.93 => ( notinemptyset
% 3.57/1.93 => ( exuE3e
% 3.57/1.93 => ( setext
% 3.57/1.93 => ( emptyI
% 3.57/1.93 => ( noeltsimpempty
% 3.57/1.93 => ( setbeta
% 3.57/1.93 => ( nonemptyE1
% 3.57/1.93 => ( nonemptyI
% 3.57/1.93 => ( nonemptyI1
% 3.57/1.93 => ( setadjoinIL
% 3.57/1.93 => ( emptyinunitempty
% 3.57/1.93 => ( setadjoinIR
% 3.57/1.93 => ( setadjoinE
% 3.57/1.93 => ( setadjoinOr
% 3.57/1.93 => ( setoftrueEq
% 3.57/1.93 => ( powersetI
% 3.57/1.93 => ( emptyinPowerset
% 3.57/1.93 => ( emptyInPowerset
% 3.57/1.93 => ( powersetE
% 3.57/1.93 => ( setunionI
% 3.57/1.93 => ( setunionE
% 3.57/1.93 => ( subPowSU
% 3.57/1.93 => ( exuE2
% 3.57/1.93 => ( nonemptyImpWitness
% 3.57/1.93 => ( uniqinunit
% 3.57/1.93 => ( notinsingleton
% 3.57/1.93 => ( eqinunit
% 3.57/1.93 => ( singletonsswitch
% 3.57/1.93 => ( upairsetE
% 3.57/1.93 => ( upairsetIL
% 3.57/1.93 => ( upairsetIR
% 3.57/1.93 => ( emptyE1
% 3.57/1.93 => ( vacuousDall
% 3.57/1.93 => ( quantDeMorgan1
% 3.57/1.93 => ( quantDeMorgan2
% 3.57/1.93 => ( quantDeMorgan3
% 3.57/1.93 => ( quantDeMorgan4
% 3.57/1.93 => ( prop2setI
% 3.57/1.93 => ( prop2set2propI
% 3.57/1.93 => ( notdexE
% 3.57/1.93 => ( notdallE
% 3.57/1.93 => ( exuI1
% 3.57/1.93 => ( exuI3
% 3.57/1.93 => ( exuI2
% 3.57/1.93 => ( inCongP
% 3.57/1.93 => ( in__Cong
% 3.57/1.93 => ( exuE3u
% 3.57/1.93 => ( exu__Cong
% 3.57/1.93 => ( emptyset__Cong
% 3.57/1.93 => ( setadjoin__Cong
% 3.57/1.93 => ( powerset__Cong
% 3.57/1.93 => ( setunion__Cong
% 3.57/1.93 => ( omega__Cong
% 3.57/1.93 => ( exuEu
% 3.57/1.93 => ( descr__Cong
% 3.57/1.93 => ( dsetconstr__Cong
% 3.57/1.93 => ( subsetI1
% 3.57/1.93 => ( eqimpsubset2
% 3.57/1.93 => ( eqimpsubset1
% 3.57/1.93 => ( subsetI2
% 3.57/1.93 => ( emptysetsubset
% 3.57/1.93 => ( subsetE
% 3.57/1.93 => ( subsetE2
% 3.57/1.93 => ( notsubsetI
% 3.57/1.93 => ( notequalI1
% 3.57/1.93 => ( notequalI2
% 3.57/1.93 => ( subsetRefl
% 3.57/1.93 => ( subsetTrans
% 3.57/1.93 => ( setadjoinSub
% 3.57/1.93 => ( setadjoinSub2
% 3.57/1.93 => ( subset2powerset
% 3.57/1.93 => ( setextsub
% 3.57/1.93 => ( subsetemptysetimpeq
% 3.57/1.93 => ( powersetI1
% 3.57/1.93 => ( powersetE1
% 3.57/1.93 => ( inPowerset
% 3.57/1.93 => ( powersetsubset
% 3.57/1.93 => ( sepInPowerset
% 3.57/1.93 => ( sepSubset
% 3.57/1.93 => ( binunionIL
% 3.57/1.93 => ( upairset2IR
% 3.57/1.93 => ( binunionIR
% 3.57/1.93 => ( binunionEcases
% 3.57/1.93 => ( binunionE
% 3.57/1.93 => ( binunionLsub
% 3.57/1.93 => ( binunionRsub
% 3.57/1.93 => ( binintersectI
% 3.57/1.93 => ( binintersectSubset5
% 3.57/1.93 => ( binintersectEL
% 3.57/1.93 => ( binintersectLsub
% 3.57/1.93 => ( binintersectSubset2
% 3.57/1.93 => ( binintersectSubset3
% 3.57/1.93 => ( binintersectER
% 3.57/1.93 => ( disjointsetsI1
% 3.57/1.93 => ( binintersectRsub
% 3.57/1.93 => ( binintersectSubset4
% 3.57/1.93 => ( binintersectSubset1
% 3.57/1.93 => ( bs114d
% 3.57/1.93 => ( setminusI
% 3.57/1.93 => ( setminusEL
% 3.57/1.93 => ( setminusER
% 3.57/1.93 => ( setminusSubset2
% 3.57/1.93 => ( setminusERneg
% 3.57/1.93 => ( setminusELneg
% 3.57/1.93 => ( setminusILneg
% 3.57/1.93 => ( setminusIRneg
% 3.57/1.93 => ( setminusLsub
% 3.57/1.93 => ( setminusSubset1
% 3.57/1.93 => ( symdiffE
% 3.57/1.93 => ( symdiffI1
% 3.57/1.93 => ( symdiffI2
% 3.57/1.93 => ( symdiffIneg1
% 3.57/1.93 => ( symdiffIneg2
% 3.57/1.93 => ( secondinupair
% 3.57/1.93 => ( setukpairIL
% 3.57/1.93 => ( setukpairIR
% 3.57/1.93 => ( kpairiskpair
% 3.57/1.93 => ( kpairp
% 3.57/1.93 => ( singletonsubset
% 3.57/1.93 => ( singletoninpowerset
% 3.57/1.93 => ( singletoninpowunion
% 3.57/1.93 => ( upairset2E
% 3.57/1.93 => ( upairsubunion
% 3.57/1.93 => ( upairinpowunion
% 3.57/1.93 => ( ubforcartprodlem1
% 3.57/1.93 => ( ubforcartprodlem2
% 3.57/1.93 => ( ubforcartprodlem3
% 3.57/1.93 => ( cartprodpairin
% 3.57/1.93 => ( cartprodmempair1
% 3.57/1.93 => ( cartprodmempair
% 3.57/1.93 => ( setunionE2
% 3.57/1.93 => ( setunionsingleton1
% 3.57/1.93 => ( setunionsingleton2
% 3.57/1.93 => ( setunionsingleton
% 3.57/1.93 => ( singletonprop
% 3.57/1.93 => ( ex1E1
% 3.57/1.93 => ( ex1I
% 3.57/1.93 => ( ex1I2
% 3.57/1.93 => ( singletonsuniq
% 3.57/1.93 => ( setukpairinjL1
% 3.57/1.93 => ( kfstsingleton
% 3.57/1.93 => ( theprop
% 3.57/1.93 => ( kfstpairEq
% 3.57/1.93 => ( cartprodfstin
% 3.57/1.93 => ( setukpairinjL2
% 3.57/1.93 => ( setukpairinjL
% 3.57/1.93 => ( setukpairinjR11
% 3.57/1.93 => ( setukpairinjR12
% 3.57/1.93 => ( setukpairinjR1
% 3.57/1.93 => ( upairequniteq
% 3.57/1.93 => ( setukpairinjR2
% 3.57/1.93 => ( setukpairinjR
% 3.57/1.93 => ( ksndsingleton
% 3.57/1.93 => ( ksndpairEq
% 3.57/1.93 => ( kpairsurjEq
% 3.57/1.93 => ( cartprodsndin
% 3.57/1.93 => ( cartprodpairmemEL
% 3.57/1.93 => ( cartprodpairmemER
% 3.57/1.93 => ( cartprodmempaircEq
% 3.57/1.93 => ( cartprodfstpairEq
% 3.57/1.93 => ( cartprodsndpairEq
% 3.57/1.93 => ( cartprodpairsurjEq
% 3.57/1.93 => ( dpsetconstrI
% 3.57/1.93 => ( dpsetconstrSub
% 3.57/1.93 => ( setOfPairsIsBReln
% 3.57/1.93 => ( dpsetconstrERa
% 3.57/1.93 => ( dpsetconstrEL1
% 3.57/1.93 => ( dpsetconstrEL2
% 3.57/1.93 => ( dpsetconstrER
% 3.57/1.93 => ( funcImageSingleton
% 3.57/1.93 => ( apProp
% 3.57/1.93 => ( app
% 3.57/1.93 => ( infuncsetfunc
% 3.57/1.93 => ( ap2p
% 3.57/1.93 => ( funcinfuncset
% 3.57/1.93 => ( lamProp
% 3.57/1.93 => ( lamp
% 3.57/1.93 => ( lam2p
% 3.57/1.93 => ( brelnall1
% 3.57/1.93 => ( brelnall2
% 3.57/1.93 => ( ex1E2
% 3.57/1.93 => ( funcGraphProp1
% 3.57/1.93 => ( funcGraphProp3
% 3.57/1.93 => ( funcGraphProp2
% 3.57/1.93 => ( funcextLem
% 3.57/1.93 => ( funcGraphProp4
% 3.57/1.93 => ( subbreln
% 3.57/1.93 => ( eqbreln
% 3.57/1.93 => ( funcext
% 3.57/1.93 => ( funcext2
% 3.57/1.93 => ( ap2apEq1
% 3.57/1.93 => ( ap2apEq2
% 3.57/1.93 => ( beta1
% 3.57/1.93 => ( eta1
% 3.57/1.93 => ( lam2lamEq
% 3.57/1.93 => ( beta2
% 3.57/1.93 => ( eta2
% 3.57/1.93 => ( iffalseProp1
% 3.57/1.93 => ( iffalseProp2
% 3.57/1.93 => ( iftrueProp1
% 3.57/1.93 => ( iftrueProp2
% 3.57/1.93 => ( ifSingleton
% 3.57/1.93 => ( ifp
% 3.57/1.93 => ( theeq
% 3.57/1.93 => ( iftrue
% 3.57/1.93 => ( iffalse
% 3.57/1.93 => ( iftrueorfalse
% 3.57/1.93 => ( binintersectT_lem
% 3.57/1.93 => ( binunionT_lem
% 3.57/1.93 => ( powersetT_lem
% 3.57/1.93 => ( setminusT_lem
% 3.57/1.93 => ( complementT_lem
% 3.57/1.93 => ( setextT
% 3.57/1.93 => ( subsetTI
% 3.57/1.93 => ( powersetTI1
% 3.57/1.93 => ( powersetTE1
% 3.57/1.93 => ( complementTI1
% 3.57/1.93 => ( complementTE1
% 3.57/1.93 => ( binintersectTELcontra
% 3.57/1.93 => ( binintersectTERcontra
% 3.57/1.93 => ( contrasubsetT
% 3.57/1.93 => ( contrasubsetT1
% 3.57/1.93 => ( contrasubsetT2
% 3.57/1.93 => ( contrasubsetT3
% 3.57/1.93 => ( doubleComplementI1
% 3.57/1.93 => ( doubleComplementE1
% 3.57/1.93 => ( doubleComplementSub1
% 3.57/1.93 => ( doubleComplementSub2
% 3.57/1.93 => ( doubleComplementEq
% 3.57/1.93 => ( complementTnotintersectT
% 3.57/1.93 => ( complementImpComplementIntersect
% 3.57/1.93 => ( complementSubsetComplementIntersect
% 3.57/1.93 => ( complementInPowersetComplementIntersect
% 3.57/1.93 => ( contraSubsetComplement
% 3.57/1.93 => ( complementTcontraSubset
% 3.57/1.93 => ( binunionTILcontra
% 3.57/1.93 => ( binunionTIRcontra
% 3.57/1.93 => ( inIntersectImpInUnion
% 3.57/1.93 => ( inIntersectImpInUnion2
% 3.57/1.93 => ( inIntersectImpInIntersectUnions
% 3.57/1.93 => ( intersectInPowersetIntersectUnions
% 3.57/1.93 => ( inComplementUnionImpNotIn1
% 3.57/1.93 => ( inComplementUnionImpInComplement1
% 3.57/1.93 => ( binunionTE
% 3.57/1.93 => ( binunionTEcontra
% 3.57/1.93 => ( demorgan2a1
% 3.57/1.93 => ( complementUnionInPowersetComplement
% 3.57/1.93 => ( demorgan2a2
% 3.57/1.93 => ( demorgan1a
% 3.57/1.93 => ( demorgan1b
% 3.57/1.93 => ( demorgan1
% 3.57/1.93 => ( demorgan2a
% 3.57/1.93 => ( demorgan2b2
% 3.57/1.93 => ( demorgan2b
% 3.57/1.93 => ( demorgan2
% 3.57/1.93 => ( woz13rule0
% 3.57/1.93 => ( woz13rule1
% 3.57/1.93 => ( woz13rule2
% 3.57/1.93 => ( woz13rule3
% 3.57/1.93 => ( woz13rule4
% 3.57/1.93 => ( woz1_1
% 3.57/1.93 => ( woz1_2
% 3.57/1.93 => ( woz1_3
% 3.57/1.93 => ( woz1_4
% 3.57/1.93 => ( woz1_5
% 3.57/1.93 => ( breln1all2
% 3.57/1.93 => ( breln1SetBreln1
% 3.57/1.93 => ( choice2fnsingleton
% 3.57/1.93 => ( setOfPairsIsBReln1
% 3.57/1.93 => ! [A: $i,R: $i] :
% 3.57/1.93 ( ( breln1 @ A @ R )
% 3.57/1.93 => ! [Xphi: $i > $o] :
% 3.57/1.93 ( ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ A )
% 3.57/1.93 => ! [Xy: $i] :
% 3.57/1.93 ( ( in @ Xy @ A )
% 3.57/1.93 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.57/1.93 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.57/1.93 => ! [Xx: $i] :
% 3.57/1.93 ( ( in @ Xx @ R )
% 3.57/1.93 => ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.57/1.93 ------------------------
% 3.57/1.97 % (3529)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/18Mi)
% 3.57/1.97 % (3528)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/275Mi)
% 3.57/1.97 % (3526)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/2Mi)
% 3.57/1.97 % (3527)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/2Mi)
% 3.57/1.97 % (3524)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/4Mi)
% 3.57/1.97 % (3523)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/183Mi)
% 3.57/1.97 % (3526)Instruction limit reached!
% 3.57/1.97 % (3526)------------------------------
% 3.57/1.97 % (3526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.97 % (3526)Termination reason: Unknown
% 3.57/1.97 % (3526)Termination phase: shuffling
% 3.57/1.97 % (3527)Instruction limit reached!
% 3.57/1.97 % (3527)------------------------------
% 3.57/1.97 % (3527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.97 % (3527)Termination reason: Unknown
% 3.57/1.97 % (3527)Termination phase: shuffling
% 3.57/1.97
% 3.57/1.97 % (3527)Memory used [KB]: 1535
% 3.57/1.97 % (3527)Time elapsed: 0.003 s
% 3.57/1.97 % (3527)Instructions burned: 3 (million)
% 3.57/1.97 % (3527)------------------------------
% 3.57/1.97 % (3527)------------------------------
% 3.57/1.97
% 3.57/1.97 % (3526)Memory used [KB]: 1535
% 3.57/1.97 % (3526)Time elapsed: 0.003 s
% 3.57/1.97 % (3526)Instructions burned: 3 (million)
% 3.57/1.97 % (3526)------------------------------
% 3.57/1.97 % (3526)------------------------------
% 3.57/1.97 % (3525)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/27Mi)
% 3.57/1.97 % (3524)Instruction limit reached!
% 3.57/1.97 % (3524)------------------------------
% 3.57/1.97 % (3524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.97 % (3524)Termination reason: Unknown
% 3.57/1.97 % (3524)Termination phase: shuffling
% 3.57/1.97
% 3.57/1.97 % (3524)Memory used [KB]: 1535
% 3.57/1.97 % (3524)Time elapsed: 0.004 s
% 3.57/1.97 % (3524)Instructions burned: 5 (million)
% 3.57/1.97 % (3524)------------------------------
% 3.57/1.97 % (3524)------------------------------
% 3.57/1.98 % (3529)Instruction limit reached!
% 3.57/1.98 % (3529)------------------------------
% 3.57/1.98 % (3529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.98 % (3529)Termination reason: Unknown
% 3.57/1.98 % (3529)Termination phase: shuffling
% 3.57/1.98
% 3.57/1.98 % (3529)Memory used [KB]: 1918
% 3.57/1.98 % (3529)Time elapsed: 0.011 s
% 3.57/1.98 % (3529)Instructions burned: 18 (million)
% 3.57/1.98 % (3529)------------------------------
% 3.57/1.98 % (3529)------------------------------
% 3.57/1.99 % (3525)Instruction limit reached!
% 3.57/1.99 % (3525)------------------------------
% 3.57/1.99 % (3525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.99 % (3525)Termination reason: Unknown
% 3.57/1.99 % (3525)Termination phase: shuffling
% 3.57/1.99
% 3.57/1.99 % (3525)Memory used [KB]: 2046
% 3.57/1.99 % (3525)Time elapsed: 0.015 s
% 3.57/1.99 % (3525)Instructions burned: 28 (million)
% 3.57/1.99 % (3525)------------------------------
% 3.57/1.99 % (3525)------------------------------
% 3.57/1.99 % (3531)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/37Mi)
% 3.57/1.99 % (3530)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/3Mi)
% 3.57/1.99 % (3532)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/15Mi)
% 3.57/1.99 % (3530)Instruction limit reached!
% 3.57/1.99 % (3530)------------------------------
% 3.57/1.99 % (3530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/1.99 % (3530)Termination reason: Unknown
% 3.57/1.99 % (3530)Termination phase: shuffling
% 3.57/1.99
% 3.57/1.99 % (3530)Memory used [KB]: 1535
% 3.57/1.99 % (3530)Time elapsed: 0.004 s
% 3.57/1.99 % (3530)Instructions burned: 4 (million)
% 3.57/1.99 % (3530)------------------------------
% 3.57/1.99 % (3530)------------------------------
% 3.57/2.00 % (3533)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/3Mi)
% 3.57/2.00 % (3532)Instruction limit reached!
% 3.57/2.00 % (3532)------------------------------
% 3.57/2.00 % (3532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.00 % (3532)Termination reason: Unknown
% 3.57/2.00 % (3532)Termination phase: shuffling
% 3.57/2.00
% 3.57/2.00 % (3532)Memory used [KB]: 1791
% 3.57/2.00 % (3532)Time elapsed: 0.009 s
% 3.57/2.00 % (3532)Instructions burned: 15 (million)
% 3.57/2.00 % (3532)------------------------------
% 3.57/2.00 % (3532)------------------------------
% 3.57/2.00 % (3533)Instruction limit reached!
% 3.57/2.00 % (3533)------------------------------
% 3.57/2.00 % (3533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.00 % (3533)Termination reason: Unknown
% 3.57/2.00 % (3533)Termination phase: shuffling
% 3.57/2.00
% 3.57/2.00 % (3533)Memory used [KB]: 1535
% 3.57/2.00 % (3533)Time elapsed: 0.004 s
% 3.57/2.00 % (3533)Instructions burned: 4 (million)
% 3.57/2.00 % (3533)------------------------------
% 3.57/2.00 % (3533)------------------------------
% 3.57/2.00 % (3534)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/1041Mi)
% 3.57/2.01 % (3531)Instruction limit reached!
% 3.57/2.01 % (3531)------------------------------
% 3.57/2.01 % (3531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.01 % (3531)Termination reason: Unknown
% 3.57/2.01 % (3531)Termination phase: shuffling
% 3.57/2.01
% 3.57/2.01 % (3531)Memory used [KB]: 2302
% 3.57/2.01 % (3531)Time elapsed: 0.018 s
% 3.57/2.01 % (3531)Instructions burned: 37 (million)
% 3.57/2.01 % (3531)------------------------------
% 3.57/2.01 % (3531)------------------------------
% 3.57/2.01 % (3535)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/7Mi)
% 3.57/2.01 % (3535)Instruction limit reached!
% 3.57/2.01 % (3535)------------------------------
% 3.57/2.01 % (3535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.01 % (3535)Termination reason: Unknown
% 3.57/2.01 % (3535)Termination phase: shuffling
% 3.57/2.01
% 3.57/2.01 % (3535)Memory used [KB]: 1663
% 3.57/2.01 % (3535)Time elapsed: 0.006 s
% 3.57/2.01 % (3535)Instructions burned: 8 (million)
% 3.57/2.01 % (3535)------------------------------
% 3.57/2.01 % (3535)------------------------------
% 3.57/2.02 % (3536)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/16Mi)
% 3.57/2.02 % (3537)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/3Mi)
% 3.57/2.02 % (3537)Instruction limit reached!
% 3.57/2.02 % (3537)------------------------------
% 3.57/2.02 % (3537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.02 % (3537)Termination reason: Unknown
% 3.57/2.02 % (3537)Termination phase: shuffling
% 3.57/2.02
% 3.57/2.02 % (3537)Memory used [KB]: 1535
% 3.57/2.02 % (3537)Time elapsed: 0.004 s
% 3.57/2.02 % (3537)Instructions burned: 4 (million)
% 3.57/2.02 % (3537)------------------------------
% 3.57/2.02 % (3537)------------------------------
% 3.57/2.02 % (3536)Instruction limit reached!
% 3.57/2.02 % (3536)------------------------------
% 3.57/2.02 % (3536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.02 % (3536)Termination reason: Unknown
% 3.57/2.02 % (3536)Termination phase: shuffling
% 3.57/2.02
% 3.57/2.02 % (3536)Memory used [KB]: 1791
% 3.57/2.02 % (3536)Time elapsed: 0.010 s
% 3.57/2.02 % (3536)Instructions burned: 17 (million)
% 3.57/2.02 % (3536)------------------------------
% 3.57/2.02 % (3536)------------------------------
% 3.57/2.02 % (3538)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/3Mi)
% 3.57/2.03 % (3538)Instruction limit reached!
% 3.57/2.03 % (3538)------------------------------
% 3.57/2.03 % (3538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.57/2.03 % (3538)Termination reason: Unknown
% 3.57/2.03 % (3538)Termination phase: shuffling
% 3.57/2.03
% 3.57/2.03 % (3538)Memory used [KB]: 1535
% 3.57/2.03 % (3538)Time elapsed: 0.004 s
% 3.57/2.03 % (3538)Instructions burned: 4 (million)
% 3.57/2.03 % (3538)------------------------------
% 3.57/2.03 % (3538)------------------------------
% 4.04/2.03 % (3539)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/7Mi)
% 4.04/2.03 % (3539)Instruction limit reached!
% 4.04/2.03 % (3539)------------------------------
% 4.04/2.03 % (3539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.03 % (3539)Termination reason: Unknown
% 4.04/2.03 % (3539)Termination phase: shuffling
% 4.04/2.03
% 4.04/2.03 % (3539)Memory used [KB]: 1663
% 4.04/2.03 % (3539)Time elapsed: 0.006 s
% 4.04/2.03 % (3539)Instructions burned: 8 (million)
% 4.04/2.03 % (3539)------------------------------
% 4.04/2.03 % (3539)------------------------------
% 4.04/2.04 % (3540)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/3Mi)
% 4.04/2.04 % (3540)Instruction limit reached!
% 4.04/2.04 % (3540)------------------------------
% 4.04/2.04 % (3540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.04 % (3540)Termination reason: Unknown
% 4.04/2.04 % (3540)Termination phase: shuffling
% 4.04/2.04
% 4.04/2.04 % (3540)Memory used [KB]: 1535
% 4.04/2.04 % (3540)Time elapsed: 0.003 s
% 4.04/2.04 % (3540)Instructions burned: 3 (million)
% 4.04/2.04 % (3540)------------------------------
% 4.04/2.04 % (3540)------------------------------
% 4.04/2.04 % (3541)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/4Mi)
% 4.04/2.04 % (3541)Instruction limit reached!
% 4.04/2.04 % (3541)------------------------------
% 4.04/2.04 % (3541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.04 % (3541)Termination reason: Unknown
% 4.04/2.04 % (3541)Termination phase: shuffling
% 4.04/2.04
% 4.04/2.04 % (3541)Memory used [KB]: 1535
% 4.04/2.04 % (3541)Time elapsed: 0.004 s
% 4.04/2.04 % (3541)Instructions burned: 4 (million)
% 4.04/2.04 % (3541)------------------------------
% 4.04/2.04 % (3541)------------------------------
% 4.04/2.04 % (3542)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/18Mi)
% 4.04/2.05 % (3543)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/710Mi)
% 4.04/2.05 % (3542)Instruction limit reached!
% 4.04/2.05 % (3542)------------------------------
% 4.04/2.05 % (3542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.05 % (3542)Termination reason: Unknown
% 4.04/2.05 % (3542)Termination phase: shuffling
% 4.04/2.05
% 4.04/2.05 % (3542)Memory used [KB]: 1918
% 4.04/2.05 % (3542)Time elapsed: 0.010 s
% 4.04/2.05 % (3542)Instructions burned: 18 (million)
% 4.04/2.05 % (3542)------------------------------
% 4.04/2.05 % (3542)------------------------------
% 4.04/2.05 % (3544)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3370 for (2999ds/6Mi)
% 4.04/2.06 % (3523)Instruction limit reached!
% 4.04/2.06 % (3523)------------------------------
% 4.04/2.06 % (3523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.06 % (3523)Termination reason: Unknown
% 4.04/2.06 % (3523)Termination phase: Saturation
% 4.04/2.06
% 4.04/2.06 % (3523)Memory used [KB]: 7419
% 4.04/2.06 % (3523)Time elapsed: 0.085 s
% 4.04/2.06 % (3523)Instructions burned: 185 (million)
% 4.04/2.06 % (3523)------------------------------
% 4.04/2.06 % (3523)------------------------------
% 4.04/2.06 % (3544)Instruction limit reached!
% 4.04/2.06 % (3544)------------------------------
% 4.04/2.06 % (3544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.06 % (3544)Termination reason: Unknown
% 4.04/2.06 % (3544)Termination phase: shuffling
% 4.04/2.06
% 4.04/2.06 % (3544)Memory used [KB]: 1535
% 4.04/2.06 % (3544)Time elapsed: 0.005 s
% 4.04/2.06 % (3544)Instructions burned: 6 (million)
% 4.04/2.06 % (3544)------------------------------
% 4.04/2.06 % (3544)------------------------------
% 4.04/2.06 % (3545)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/902Mi)
% 4.04/2.07 % (3546)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/21Mi)
% 4.04/2.07 % (3547)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/5Mi)
% 4.04/2.07 % (3548)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/6Mi)
% 4.04/2.07 % (3547)Instruction limit reached!
% 4.04/2.07 % (3547)------------------------------
% 4.04/2.07 % (3547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.07 % (3547)Termination reason: Unknown
% 4.04/2.07 % (3547)Termination phase: shuffling
% 4.04/2.07
% 4.04/2.07 % (3547)Memory used [KB]: 1535
% 4.04/2.07 % (3547)Time elapsed: 0.004 s
% 4.04/2.07 % (3547)Instructions burned: 5 (million)
% 4.04/2.07 % (3547)------------------------------
% 4.04/2.07 % (3547)------------------------------
% 4.04/2.08 % (3548)Instruction limit reached!
% 4.04/2.08 % (3548)------------------------------
% 4.04/2.08 % (3548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.08 % (3548)Termination reason: Unknown
% 4.04/2.08 % (3548)Termination phase: shuffling
% 4.04/2.08
% 4.04/2.08 % (3548)Memory used [KB]: 1663
% 4.04/2.08 % (3548)Time elapsed: 0.005 s
% 4.04/2.08 % (3548)Instructions burned: 7 (million)
% 4.04/2.08 % (3548)------------------------------
% 4.04/2.08 % (3548)------------------------------
% 4.04/2.08 % (3546)Instruction limit reached!
% 4.04/2.08 % (3546)------------------------------
% 4.04/2.08 % (3546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.08 % (3546)Termination reason: Unknown
% 4.04/2.08 % (3546)Termination phase: shuffling
% 4.04/2.08
% 4.04/2.08 % (3546)Memory used [KB]: 1918
% 4.04/2.08 % (3546)Time elapsed: 0.012 s
% 4.04/2.08 % (3546)Instructions burned: 21 (million)
% 4.04/2.08 % (3546)------------------------------
% 4.04/2.08 % (3546)------------------------------
% 4.04/2.09 % (3549)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/377Mi)
% 4.04/2.09 % (3550)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/779Mi)
% 4.04/2.09 % (3551)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/19Mi)
% 4.04/2.10 % (3551)Instruction limit reached!
% 4.04/2.10 % (3551)------------------------------
% 4.04/2.10 % (3551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.10 % (3551)Termination reason: Unknown
% 4.04/2.10 % (3551)Termination phase: shuffling
% 4.04/2.10
% 4.04/2.10 % (3551)Memory used [KB]: 1791
% 4.04/2.10 % (3551)Time elapsed: 0.010 s
% 4.04/2.10 % (3551)Instructions burned: 19 (million)
% 4.04/2.10 % (3551)------------------------------
% 4.04/2.10 % (3551)------------------------------
% 4.04/2.10 % (3528)Instruction limit reached!
% 4.04/2.10 % (3528)------------------------------
% 4.04/2.10 % (3528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.04/2.10 % (3528)Termination reason: Unknown
% 4.04/2.10 % (3528)Termination phase: Saturation
% 4.04/2.10
% 4.04/2.10 % (3528)Memory used [KB]: 10106
% 4.04/2.10 % (3528)Time elapsed: 0.132 s
% 4.04/2.10 % (3528)Instructions burned: 275 (million)
% 4.04/2.10 % (3528)------------------------------
% 4.04/2.10 % (3528)------------------------------
% 4.04/2.12 % (3552)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/879Mi)
% 4.04/2.12 % (3553)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/17Mi)
% 4.51/2.13 % (3553)Instruction limit reached!
% 4.51/2.13 % (3553)------------------------------
% 4.51/2.13 % (3553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.51/2.13 % (3553)Termination reason: Unknown
% 4.51/2.13 % (3553)Termination phase: shuffling
% 4.51/2.13
% 4.51/2.13 % (3553)Memory used [KB]: 1791
% 4.51/2.13 % (3553)Time elapsed: 0.010 s
% 4.51/2.13 % (3553)Instructions burned: 18 (million)
% 4.51/2.13 % (3553)------------------------------
% 4.51/2.13 % (3553)------------------------------
% 4.51/2.15 % (3554)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/3Mi)
% 4.51/2.15 % (3554)Instruction limit reached!
% 4.51/2.15 % (3554)------------------------------
% 4.51/2.15 % (3554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.51/2.15 % (3554)Termination reason: Unknown
% 4.51/2.15 % (3554)Termination phase: shuffling
% 4.51/2.15
% 4.51/2.15 % (3554)Memory used [KB]: 1535
% 4.51/2.15 % (3554)Time elapsed: 0.004 s
% 4.51/2.15 % (3554)Instructions burned: 3 (million)
% 4.51/2.15 % (3554)------------------------------
% 4.51/2.15 % (3554)------------------------------
% 4.51/2.17 % (3555)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3370 for (2998ds/30Mi)
% 4.51/2.18 % (3555)Instruction limit reached!
% 4.51/2.18 % (3555)------------------------------
% 4.51/2.18 % (3555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.51/2.18 % (3555)Termination reason: Unknown
% 4.51/2.18 % (3555)Termination phase: shuffling
% 4.51/2.18
% 4.51/2.18 % (3555)Memory used [KB]: 2046
% 4.51/2.18 % (3555)Time elapsed: 0.017 s
% 4.51/2.18 % (3555)Instructions burned: 31 (million)
% 4.51/2.18 % (3555)------------------------------
% 4.51/2.18 % (3555)------------------------------
% 4.65/2.20 % (3556)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3370 for (2997ds/127Mi)
% 4.65/2.25 % (3556)Instruction limit reached!
% 4.65/2.25 % (3556)------------------------------
% 4.65/2.25 % (3556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.65/2.25 % (3556)Termination reason: Unknown
% 4.65/2.25 % (3556)Termination phase: Property scanning
% 4.65/2.25
% 4.65/2.25 % (3556)Memory used [KB]: 2814
% 4.65/2.25 % (3556)Time elapsed: 0.057 s
% 4.65/2.25 % (3556)Instructions burned: 129 (million)
% 4.65/2.25 % (3556)------------------------------
% 4.65/2.25 % (3556)------------------------------
% 4.65/2.26 % (3549)Instruction limit reached!
% 4.65/2.26 % (3549)------------------------------
% 4.65/2.26 % (3549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.65/2.26 % (3549)Termination reason: Unknown
% 4.65/2.26 % (3549)Termination phase: Saturation
% 4.65/2.26
% 4.65/2.26 % (3549)Memory used [KB]: 9466
% 4.65/2.26 % (3549)Time elapsed: 0.172 s
% 4.65/2.26 % (3549)Instructions burned: 377 (million)
% 4.65/2.26 % (3549)------------------------------
% 4.65/2.26 % (3549)------------------------------
% 4.65/2.27 % (3557)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3370 for (2996ds/100Mi)
% 4.65/2.28 % (3558)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3370 for (2996ds/3Mi)
% 4.65/2.28 % (3558)Instruction limit reached!
% 4.65/2.28 % (3558)------------------------------
% 4.65/2.28 % (3558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.65/2.28 % (3558)Termination reason: Unknown
% 4.65/2.28 % (3558)Termination phase: shuffling
% 4.65/2.28
% 4.65/2.28 % (3558)Memory used [KB]: 1535
% 4.65/2.28 % (3558)Time elapsed: 0.003 s
% 4.65/2.28 % (3558)Instructions burned: 3 (million)
% 4.65/2.28 % (3558)------------------------------
% 4.65/2.28 % (3558)------------------------------
% 5.03/2.30 % (3559)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3370 for (2996ds/20Mi)
% 5.03/2.31 % (3559)Instruction limit reached!
% 5.03/2.31 % (3559)------------------------------
% 5.03/2.31 % (3559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.31 % (3559)Termination reason: Unknown
% 5.03/2.31 % (3559)Termination phase: shuffling
% 5.03/2.31
% 5.03/2.31 % (3559)Memory used [KB]: 1791
% 5.03/2.31 % (3559)Time elapsed: 0.013 s
% 5.03/2.31 % (3559)Instructions burned: 21 (million)
% 5.03/2.31 % (3559)------------------------------
% 5.03/2.31 % (3559)------------------------------
% 5.03/2.31 % (3557)Instruction limit reached!
% 5.03/2.31 % (3557)------------------------------
% 5.03/2.31 % (3557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.31 % (3557)Termination reason: Unknown
% 5.03/2.31 % (3557)Termination phase: Property scanning
% 5.03/2.31
% 5.03/2.31 % (3557)Memory used [KB]: 2686
% 5.03/2.31 % (3557)Time elapsed: 0.047 s
% 5.03/2.31 % (3557)Instructions burned: 101 (million)
% 5.03/2.31 % (3557)------------------------------
% 5.03/2.31 % (3557)------------------------------
% 5.03/2.33 % (3560)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3370 for (2996ds/86Mi)
% 5.03/2.33 % (3561)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3370 for (2996ds/107Mi)
% 5.03/2.36 % (3560)Instruction limit reached!
% 5.03/2.36 % (3560)------------------------------
% 5.03/2.36 % (3560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.36 % (3560)Termination reason: Unknown
% 5.03/2.36 % (3560)Termination phase: Property scanning
% 5.03/2.36
% 5.03/2.36 % (3560)Memory used [KB]: 2558
% 5.03/2.36 % (3560)Time elapsed: 0.040 s
% 5.03/2.36 % (3560)Instructions burned: 86 (million)
% 5.03/2.36 % (3560)------------------------------
% 5.03/2.36 % (3560)------------------------------
% 5.03/2.38 % (3561)Instruction limit reached!
% 5.03/2.38 % (3561)------------------------------
% 5.03/2.38 % (3561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.03/2.38 % (3561)Termination reason: Unknown
% 5.03/2.38 % (3561)Termination phase: SInE selection
% 5.03/2.38
% 5.03/2.38 % (3561)Memory used [KB]: 2558
% 5.03/2.38 % (3561)Time elapsed: 0.048 s
% 5.03/2.38 % (3561)Instructions burned: 108 (million)
% 5.03/2.38 % (3561)------------------------------
% 5.03/2.38 % (3561)------------------------------
% 5.03/2.38 % (3562)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/39Mi)
% 5.03/2.39 % (3563)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/448Mi)
% 5.33/2.40 % (3562)Instruction limit reached!
% 5.33/2.40 % (3562)------------------------------
% 5.33/2.40 % (3562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.40 % (3562)Termination reason: Unknown
% 5.33/2.40 % (3562)Termination phase: shuffling
% 5.33/2.40
% 5.33/2.40 % (3562)Memory used [KB]: 2302
% 5.33/2.40 % (3562)Time elapsed: 0.019 s
% 5.33/2.40 % (3562)Instructions burned: 39 (million)
% 5.33/2.40 % (3562)------------------------------
% 5.33/2.40 % (3562)------------------------------
% 5.33/2.40 % (3543)Instruction limit reached!
% 5.33/2.40 % (3543)------------------------------
% 5.33/2.40 % (3543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.40 % (3543)Termination reason: Unknown
% 5.33/2.40 % (3543)Termination phase: Saturation
% 5.33/2.40
% 5.33/2.40 % (3543)Memory used [KB]: 11001
% 5.33/2.40 % (3543)Time elapsed: 0.353 s
% 5.33/2.40 % (3543)Instructions burned: 711 (million)
% 5.33/2.40 % (3543)------------------------------
% 5.33/2.40 % (3543)------------------------------
% 5.33/2.40 % (3550)Instruction limit reached!
% 5.33/2.40 % (3550)------------------------------
% 5.33/2.40 % (3550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.40 % (3550)Termination reason: Unknown
% 5.33/2.40 % (3550)Termination phase: Saturation
% 5.33/2.40
% 5.33/2.40 % (3550)Memory used [KB]: 7675
% 5.33/2.40 % (3550)Time elapsed: 0.311 s
% 5.33/2.40 % (3550)Instructions burned: 780 (million)
% 5.33/2.40 % (3550)------------------------------
% 5.33/2.40 % (3550)------------------------------
% 5.33/2.41 % (3534)Instruction limit reached!
% 5.33/2.41 % (3534)------------------------------
% 5.33/2.41 % (3534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.41 % (3534)Termination reason: Unknown
% 5.33/2.41 % (3534)Termination phase: Saturation
% 5.33/2.41
% 5.33/2.41 % (3534)Memory used [KB]: 16119
% 5.33/2.41 % (3534)Time elapsed: 0.407 s
% 5.33/2.41 % (3534)Instructions burned: 1043 (million)
% 5.33/2.41 % (3534)------------------------------
% 5.33/2.41 % (3534)------------------------------
% 5.33/2.42 % (3564)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/46Mi)
% 5.33/2.42 % (3565)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/98Mi)
% 5.33/2.42 % (3566)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/507Mi)
% 5.33/2.43 % (3567)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3370 for (2995ds/149Mi)
% 5.33/2.44 % (3564)Instruction limit reached!
% 5.33/2.44 % (3564)------------------------------
% 5.33/2.44 % (3564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.44 % (3564)Termination reason: Unknown
% 5.33/2.44 % (3564)Termination phase: shuffling
% 5.33/2.44
% 5.33/2.44 % (3564)Memory used [KB]: 2430
% 5.33/2.44 % (3564)Time elapsed: 0.024 s
% 5.33/2.44 % (3564)Instructions burned: 47 (million)
% 5.33/2.44 % (3564)------------------------------
% 5.33/2.44 % (3564)------------------------------
% 5.33/2.45 % (3568)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/39Mi)
% 5.33/2.46 % (3565)Instruction limit reached!
% 5.33/2.46 % (3565)------------------------------
% 5.33/2.46 % (3565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.46 % (3565)Termination reason: Unknown
% 5.33/2.46 % (3565)Termination phase: Property scanning
% 5.33/2.46
% 5.33/2.46 % (3565)Memory used [KB]: 2558
% 5.33/2.46 % (3565)Time elapsed: 0.046 s
% 5.33/2.46 % (3565)Instructions burned: 99 (million)
% 5.33/2.46 % (3565)------------------------------
% 5.33/2.46 % (3565)------------------------------
% 5.33/2.47 % (3568)Instruction limit reached!
% 5.33/2.47 % (3568)------------------------------
% 5.33/2.47 % (3568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.47 % (3568)Termination reason: Unknown
% 5.33/2.47 % (3568)Termination phase: shuffling
% 5.33/2.47
% 5.33/2.47 % (3568)Memory used [KB]: 2302
% 5.33/2.47 % (3568)Time elapsed: 0.020 s
% 5.33/2.47 % (3568)Instructions burned: 40 (million)
% 5.33/2.47 % (3568)------------------------------
% 5.33/2.47 % (3568)------------------------------
% 5.33/2.48 % (3569)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/6Mi)
% 5.33/2.48 % (3569)Instruction limit reached!
% 5.33/2.48 % (3569)------------------------------
% 5.33/2.48 % (3569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.48 % (3569)Termination reason: Unknown
% 5.33/2.48 % (3569)Termination phase: shuffling
% 5.33/2.48
% 5.33/2.48 % (3569)Memory used [KB]: 1535
% 5.33/2.48 % (3569)Time elapsed: 0.004 s
% 5.33/2.48 % (3569)Instructions burned: 6 (million)
% 5.33/2.48 % (3569)------------------------------
% 5.33/2.48 % (3569)------------------------------
% 5.33/2.49 % (3570)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/1087Mi)
% 5.33/2.49 % (3567)Instruction limit reached!
% 5.33/2.49 % (3567)------------------------------
% 5.33/2.49 % (3567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.33/2.49 % (3567)Termination reason: Unknown
% 5.33/2.49 % (3567)Termination phase: Twee Goal Transformation
% 5.33/2.49
% 5.33/2.49 % (3567)Memory used [KB]: 3070
% 5.33/2.49 % (3567)Time elapsed: 0.068 s
% 5.33/2.49 % (3567)Instructions burned: 150 (million)
% 5.33/2.49 % (3567)------------------------------
% 5.33/2.49 % (3567)------------------------------
% 6.33/2.50 % (3571)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/47Mi)
% 6.33/2.50 % (3545)Instruction limit reached!
% 6.33/2.50 % (3545)------------------------------
% 6.33/2.50 % (3545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.50 % (3545)Termination reason: Unknown
% 6.33/2.50 % (3545)Termination phase: Saturation
% 6.33/2.50
% 6.33/2.50 % (3545)Memory used [KB]: 12537
% 6.33/2.50 % (3545)Time elapsed: 0.444 s
% 6.33/2.50 % (3545)Instructions burned: 903 (million)
% 6.33/2.50 % (3545)------------------------------
% 6.33/2.50 % (3545)------------------------------
% 6.33/2.51 % (3572)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/44Mi)
% 6.33/2.52 % (3573)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/432Mi)
% 6.33/2.52 % (3571)Instruction limit reached!
% 6.33/2.52 % (3571)------------------------------
% 6.33/2.52 % (3571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.52 % (3571)Termination reason: Unknown
% 6.33/2.52 % (3571)Termination phase: shuffling
% 6.33/2.52
% 6.33/2.52 % (3571)Memory used [KB]: 2430
% 6.33/2.52 % (3571)Time elapsed: 0.024 s
% 6.33/2.52 % (3571)Instructions burned: 48 (million)
% 6.33/2.52 % (3571)------------------------------
% 6.33/2.52 % (3571)------------------------------
% 6.33/2.53 % (3572)Instruction limit reached!
% 6.33/2.53 % (3572)------------------------------
% 6.33/2.53 % (3572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.53 % (3572)Termination reason: Unknown
% 6.33/2.53 % (3572)Termination phase: shuffling
% 6.33/2.53
% 6.33/2.53 % (3572)Memory used [KB]: 2430
% 6.33/2.53 % (3572)Time elapsed: 0.022 s
% 6.33/2.53 % (3572)Instructions burned: 45 (million)
% 6.33/2.53 % (3572)------------------------------
% 6.33/2.53 % (3572)------------------------------
% 6.33/2.54 % (3574)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/62Mi)
% 6.33/2.54 % (3552)Instruction limit reached!
% 6.33/2.54 % (3552)------------------------------
% 6.33/2.54 % (3552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.54 % (3552)Termination reason: Unknown
% 6.33/2.54 % (3552)Termination phase: Saturation
% 6.33/2.54
% 6.33/2.54 % (3552)Memory used [KB]: 10106
% 6.33/2.54 % (3552)Time elapsed: 0.423 s
% 6.33/2.54 % (3552)Instructions burned: 879 (million)
% 6.33/2.54 % (3552)------------------------------
% 6.33/2.54 % (3552)------------------------------
% 6.33/2.55 % (3575)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3370 for (2994ds/31Mi)
% 6.33/2.56 % (3576)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/96Mi)
% 6.33/2.56 % (3575)Instruction limit reached!
% 6.33/2.56 % (3575)------------------------------
% 6.33/2.56 % (3575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.56 % (3575)Termination reason: Unknown
% 6.33/2.56 % (3575)Termination phase: shuffling
% 6.33/2.56
% 6.33/2.56 % (3575)Memory used [KB]: 2174
% 6.33/2.56 % (3575)Time elapsed: 0.016 s
% 6.33/2.56 % (3575)Instructions burned: 32 (million)
% 6.33/2.56 % (3575)------------------------------
% 6.33/2.56 % (3575)------------------------------
% 6.33/2.57 % (3574)Instruction limit reached!
% 6.33/2.57 % (3574)------------------------------
% 6.33/2.57 % (3574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.57 % (3574)Termination reason: Unknown
% 6.33/2.57 % (3574)Termination phase: Property scanning
% 6.33/2.57
% 6.33/2.57 % (3574)Memory used [KB]: 2558
% 6.33/2.57 % (3574)Time elapsed: 0.030 s
% 6.33/2.57 % (3574)Instructions burned: 62 (million)
% 6.33/2.57 % (3574)------------------------------
% 6.33/2.57 % (3574)------------------------------
% 6.33/2.58 % (3577)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/453Mi)
% 6.33/2.58 % (3563)Instruction limit reached!
% 6.33/2.58 % (3563)------------------------------
% 6.33/2.58 % (3563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.58 % (3563)Termination reason: Unknown
% 6.33/2.58 % (3563)Termination phase: Saturation
% 6.33/2.58
% 6.33/2.58 % (3563)Memory used [KB]: 7547
% 6.33/2.58 % (3563)Time elapsed: 0.188 s
% 6.33/2.58 % (3563)Instructions burned: 448 (million)
% 6.33/2.58 % (3563)------------------------------
% 6.33/2.58 % (3563)------------------------------
% 6.33/2.58 % (3578)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/71Mi)
% 7.59/2.60 % (3579)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/83Mi)
% 7.59/2.60 % (3576)Instruction limit reached!
% 7.59/2.60 % (3576)------------------------------
% 7.59/2.60 % (3576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.60 % (3576)Termination reason: Unknown
% 7.59/2.60 % (3576)Termination phase: Property scanning
% 7.59/2.60
% 7.59/2.60 % (3576)Memory used [KB]: 2686
% 7.59/2.60 % (3576)Time elapsed: 0.045 s
% 7.59/2.60 % (3576)Instructions burned: 96 (million)
% 7.59/2.60 % (3576)------------------------------
% 7.59/2.60 % (3576)------------------------------
% 7.59/2.61 % (3578)Instruction limit reached!
% 7.59/2.61 % (3578)------------------------------
% 7.59/2.61 % (3578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.61 % (3578)Termination reason: Unknown
% 7.59/2.61 % (3578)Termination phase: Property scanning
% 7.59/2.61
% 7.59/2.61 % (3578)Memory used [KB]: 2558
% 7.59/2.61 % (3578)Time elapsed: 0.034 s
% 7.59/2.61 % (3578)Instructions burned: 72 (million)
% 7.59/2.61 % (3578)------------------------------
% 7.59/2.61 % (3578)------------------------------
% 7.59/2.62 % (3580)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/11Mi)
% 7.59/2.62 % (3580)Instruction limit reached!
% 7.59/2.62 % (3580)------------------------------
% 7.59/2.62 % (3580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.62 % (3580)Termination reason: Unknown
% 7.59/2.62 % (3580)Termination phase: shuffling
% 7.59/2.62
% 7.59/2.62 % (3580)Memory used [KB]: 1791
% 7.59/2.62 % (3580)Time elapsed: 0.007 s
% 7.59/2.62 % (3580)Instructions burned: 12 (million)
% 7.59/2.62 % (3580)------------------------------
% 7.59/2.62 % (3580)------------------------------
% 7.59/2.63 % (3581)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/41Mi)
% 7.59/2.64 % (3579)Instruction limit reached!
% 7.59/2.64 % (3579)------------------------------
% 7.59/2.64 % (3579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.64 % (3579)Termination reason: Unknown
% 7.59/2.64 % (3579)Termination phase: Property scanning
% 7.59/2.64
% 7.59/2.64 % (3579)Memory used [KB]: 2558
% 7.59/2.64 % (3579)Time elapsed: 0.039 s
% 7.59/2.64 % (3579)Instructions burned: 83 (million)
% 7.59/2.64 % (3579)------------------------------
% 7.59/2.64 % (3579)------------------------------
% 7.59/2.64 % (3582)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/6Mi)
% 7.59/2.64 % (3582)Instruction limit reached!
% 7.59/2.64 % (3582)------------------------------
% 7.59/2.64 % (3582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.64 % (3582)Termination reason: Unknown
% 7.59/2.64 % (3582)Termination phase: shuffling
% 7.59/2.64
% 7.59/2.64 % (3582)Memory used [KB]: 1535
% 7.59/2.64 % (3582)Time elapsed: 0.005 s
% 7.59/2.64 % (3582)Instructions burned: 7 (million)
% 7.59/2.64 % (3582)------------------------------
% 7.59/2.64 % (3582)------------------------------
% 7.59/2.65 % (3581)Instruction limit reached!
% 7.59/2.65 % (3581)------------------------------
% 7.59/2.65 % (3581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.65 % (3581)Termination reason: Unknown
% 7.59/2.65 % (3581)Termination phase: shuffling
% 7.59/2.65
% 7.59/2.65 % (3581)Memory used [KB]: 2302
% 7.59/2.65 % (3581)Time elapsed: 0.021 s
% 7.59/2.65 % (3581)Instructions burned: 42 (million)
% 7.59/2.65 % (3581)------------------------------
% 7.59/2.65 % (3581)------------------------------
% 7.59/2.65 % (3583)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/150Mi)
% 7.59/2.66 % (3566)Instruction limit reached!
% 7.59/2.66 % (3566)------------------------------
% 7.59/2.66 % (3566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.59/2.66 % (3566)Termination reason: Unknown
% 7.59/2.66 % (3566)Termination phase: Saturation
% 7.59/2.66
% 7.59/2.66 % (3566)Memory used [KB]: 8187
% 7.59/2.66 % (3566)Time elapsed: 0.239 s
% 7.59/2.66 % (3566)Instructions burned: 509 (million)
% 7.59/2.66 % (3566)------------------------------
% 7.59/2.66 % (3566)------------------------------
% 7.59/2.66 % (3584)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3370 for (2993ds/343Mi)
% 7.59/2.67 % (3585)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_3370 for (2992ds/109Mi)
% 7.59/2.67 % (3586)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_3370 for (2992ds/253Mi)
% 8.09/2.70 % (3573)Instruction limit reached!
% 8.09/2.70 % (3573)------------------------------
% 8.09/2.70 % (3573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.70 % (3573)Termination reason: Unknown
% 8.09/2.70 % (3573)Termination phase: Saturation
% 8.09/2.70
% 8.09/2.70 % (3573)Memory used [KB]: 3070
% 8.09/2.70 % (3573)Time elapsed: 0.180 s
% 8.09/2.70 % (3573)Instructions burned: 434 (million)
% 8.09/2.70 % (3573)------------------------------
% 8.09/2.70 % (3573)------------------------------
% 8.09/2.71 % (3585)Instruction limit reached!
% 8.09/2.71 % (3585)------------------------------
% 8.09/2.71 % (3585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.71 % (3585)Termination reason: Unknown
% 8.09/2.71 % (3585)Termination phase: SInE selection
% 8.09/2.71
% 8.09/2.71 % (3585)Memory used [KB]: 2558
% 8.09/2.71 % (3585)Time elapsed: 0.049 s
% 8.09/2.71 % (3585)Instructions burned: 109 (million)
% 8.09/2.71 % (3585)------------------------------
% 8.09/2.71 % (3585)------------------------------
% 8.09/2.71 % (3587)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3370 for (2992ds/140Mi)
% 8.09/2.73 % (3583)Instruction limit reached!
% 8.09/2.73 % (3583)------------------------------
% 8.09/2.73 % (3583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.73 % (3583)Termination reason: Unknown
% 8.09/2.73 % (3583)Termination phase: Property scanning
% 8.09/2.73
% 8.09/2.73 % (3583)Memory used [KB]: 4989
% 8.09/2.73 % (3583)Time elapsed: 0.076 s
% 8.09/2.73 % (3583)Instructions burned: 151 (million)
% 8.09/2.73 % (3583)------------------------------
% 8.09/2.73 % (3583)------------------------------
% 8.09/2.73 % (3588)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_3370 for (2992ds/614Mi)
% 8.09/2.74 % (3589)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_3370 for (2992ds/202Mi)
% 8.09/2.77 % (3577)Instruction limit reached!
% 8.09/2.77 % (3577)------------------------------
% 8.09/2.77 % (3577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.77 % (3577)Termination reason: Unknown
% 8.09/2.77 % (3577)Termination phase: Saturation
% 8.09/2.77
% 8.09/2.77 % (3577)Memory used [KB]: 7547
% 8.09/2.77 % (3577)Time elapsed: 0.188 s
% 8.09/2.77 % (3577)Instructions burned: 454 (million)
% 8.09/2.77 % (3577)------------------------------
% 8.09/2.77 % (3577)------------------------------
% 8.09/2.78 % (3587)Instruction limit reached!
% 8.09/2.78 % (3587)------------------------------
% 8.09/2.78 % (3587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.78 % (3587)Termination reason: Unknown
% 8.09/2.78 % (3587)Termination phase: Function definition elimination
% 8.09/2.78
% 8.09/2.78 % (3587)Memory used [KB]: 2814
% 8.09/2.78 % (3587)Time elapsed: 0.063 s
% 8.09/2.78 % (3587)Instructions burned: 142 (million)
% 8.09/2.78 % (3587)------------------------------
% 8.09/2.78 % (3587)------------------------------
% 8.09/2.78 % (3590)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_3370 for (2991ds/339Mi)
% 8.09/2.79 % (3586)Instruction limit reached!
% 8.09/2.79 % (3586)------------------------------
% 8.09/2.79 % (3586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.79 % (3586)Termination reason: Unknown
% 8.09/2.79 % (3586)Termination phase: Saturation
% 8.09/2.79
% 8.09/2.79 % (3586)Memory used [KB]: 5628
% 8.09/2.79 % (3586)Time elapsed: 0.121 s
% 8.09/2.79 % (3586)Instructions burned: 254 (million)
% 8.09/2.79 % (3586)------------------------------
% 8.09/2.79 % (3586)------------------------------
% 8.09/2.79 % (3591)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_3370 for (2991ds/283Mi)
% 8.85/2.81 % (3584)Instruction limit reached!
% 8.85/2.81 % (3584)------------------------------
% 8.85/2.81 % (3584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.81 % (3584)Termination reason: Unknown
% 8.85/2.81 % (3584)Termination phase: Saturation
% 8.85/2.81
% 8.85/2.81 % (3584)Memory used [KB]: 8315
% 8.85/2.81 % (3584)Time elapsed: 0.152 s
% 8.85/2.81 % (3584)Instructions burned: 344 (million)
% 8.85/2.81 % (3584)------------------------------
% 8.85/2.81 % (3584)------------------------------
% 8.85/2.81 % (3592)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3370 for (2991ds/134Mi)
% 8.85/2.83 % (3593)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3370 for (2991ds/298Mi)
% 8.85/2.84 % (3589)Instruction limit reached!
% 8.85/2.84 % (3589)------------------------------
% 8.85/2.84 % (3589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.84 % (3589)Termination reason: Unknown
% 8.85/2.84 % (3589)Termination phase: Property scanning
% 8.85/2.84
% 8.85/2.84 % (3589)Memory used [KB]: 5117
% 8.85/2.84 % (3589)Time elapsed: 0.098 s
% 8.85/2.84 % (3589)Instructions burned: 203 (million)
% 8.85/2.84 % (3589)------------------------------
% 8.85/2.84 % (3589)------------------------------
% 8.85/2.86 % (3594)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3370 for (2991ds/192Mi)
% 8.85/2.87 % (3592)Instruction limit reached!
% 8.85/2.87 % (3592)------------------------------
% 8.85/2.87 % (3592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.87 % (3592)Termination reason: Unknown
% 8.85/2.87 % (3592)Termination phase: Function definition elimination
% 8.85/2.87
% 8.85/2.87 % (3592)Memory used [KB]: 2814
% 8.85/2.87 % (3592)Time elapsed: 0.062 s
% 8.85/2.87 % (3592)Instructions burned: 136 (million)
% 8.85/2.87 % (3592)------------------------------
% 8.85/2.87 % (3592)------------------------------
% 8.85/2.89 % (3595)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_3370 for (2990ds/258Mi)
% 9.21/2.91 % (3591)Instruction limit reached!
% 9.21/2.91 % (3591)------------------------------
% 9.21/2.91 % (3591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.91 % (3591)Termination reason: Unknown
% 9.21/2.91 % (3591)Termination phase: Saturation
% 9.21/2.91
% 9.21/2.91 % (3591)Memory used [KB]: 7547
% 9.21/2.91 % (3591)Time elapsed: 0.121 s
% 9.21/2.91 % (3591)Instructions burned: 284 (million)
% 9.21/2.91 % (3591)------------------------------
% 9.21/2.91 % (3591)------------------------------
% 9.21/2.93 % (3596)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3370 for (2990ds/90Mi)
% 9.21/2.93 % (3590)Instruction limit reached!
% 9.21/2.93 % (3590)------------------------------
% 9.21/2.93 % (3590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.93 % (3590)Termination reason: Unknown
% 9.21/2.93 % (3590)Termination phase: Saturation
% 9.21/2.93
% 9.21/2.93 % (3590)Memory used [KB]: 7931
% 9.21/2.93 % (3590)Time elapsed: 0.153 s
% 9.21/2.93 % (3590)Instructions burned: 341 (million)
% 9.21/2.93 % (3590)------------------------------
% 9.21/2.93 % (3590)------------------------------
% 9.21/2.94 % (3594)Instruction limit reached!
% 9.21/2.94 % (3594)------------------------------
% 9.21/2.94 % (3594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.94 % (3594)Termination reason: Unknown
% 9.21/2.94 % (3594)Termination phase: Saturation
% 9.21/2.94
% 9.21/2.94 % (3594)Memory used [KB]: 7547
% 9.21/2.94 % (3594)Time elapsed: 0.088 s
% 9.21/2.94 % (3594)Instructions burned: 192 (million)
% 9.21/2.94 % (3594)------------------------------
% 9.21/2.94 % (3594)------------------------------
% 9.21/2.95 % (3593)Instruction limit reached!
% 9.21/2.95 % (3593)------------------------------
% 9.21/2.95 % (3593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.95 % (3593)Termination reason: Unknown
% 9.21/2.95 % (3593)Termination phase: Saturation
% 9.21/2.95
% 9.21/2.95 % (3593)Memory used [KB]: 7547
% 9.21/2.95 % (3593)Time elapsed: 0.126 s
% 9.21/2.95 % (3593)Instructions burned: 298 (million)
% 9.21/2.95 % (3593)------------------------------
% 9.21/2.95 % (3593)------------------------------
% 9.21/2.95 % (3597)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/231Mi)
% 9.21/2.96 % (3598)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/458Mi)
% 9.21/2.97 % (3599)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/31Mi)
% 9.21/2.97 % (3596)Instruction limit reached!
% 9.21/2.97 % (3596)------------------------------
% 9.21/2.97 % (3596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.97 % (3596)Termination reason: Unknown
% 9.21/2.97 % (3596)Termination phase: Preprocessing 2
% 9.21/2.97
% 9.21/2.97 % (3596)Memory used [KB]: 2558
% 9.21/2.97 % (3596)Time elapsed: 0.042 s
% 9.21/2.97 % (3596)Instructions burned: 90 (million)
% 9.21/2.97 % (3596)------------------------------
% 9.21/2.97 % (3596)------------------------------
% 9.21/2.98 % (3599)Instruction limit reached!
% 9.21/2.98 % (3599)------------------------------
% 9.21/2.98 % (3599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/2.98 % (3599)Termination reason: Unknown
% 9.21/2.98 % (3599)Termination phase: shuffling
% 9.21/2.98
% 9.21/2.98 % (3599)Memory used [KB]: 2046
% 9.21/2.98 % (3599)Time elapsed: 0.016 s
% 9.21/2.98 % (3599)Instructions burned: 31 (million)
% 9.21/2.98 % (3599)------------------------------
% 9.21/2.98 % (3599)------------------------------
% 9.21/2.99 % (3600)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/297Mi)
% 9.21/3.00 % (3601)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/987Mi)
% 9.21/3.00 % (3595)Instruction limit reached!
% 9.21/3.00 % (3595)------------------------------
% 9.21/3.00 % (3595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/3.00 % (3595)Termination reason: Unknown
% 9.21/3.00 % (3595)Termination phase: Saturation
% 9.21/3.00
% 9.21/3.00 % (3595)Memory used [KB]: 7931
% 9.21/3.00 % (3595)Time elapsed: 0.115 s
% 9.21/3.00 % (3595)Instructions burned: 259 (million)
% 9.21/3.00 % (3595)------------------------------
% 9.21/3.00 % (3595)------------------------------
% 9.21/3.02 % (3602)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/182Mi)
% 9.21/3.02 % (3588)Instruction limit reached!
% 9.21/3.02 % (3588)------------------------------
% 9.21/3.02 % (3588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.21/3.02 % (3588)Termination reason: Unknown
% 9.21/3.02 % (3588)Termination phase: Saturation
% 9.21/3.02
% 9.21/3.02 % (3588)Memory used [KB]: 10106
% 9.21/3.02 % (3588)Time elapsed: 0.290 s
% 9.21/3.02 % (3588)Instructions burned: 616 (million)
% 9.21/3.02 % (3588)------------------------------
% 9.21/3.02 % (3588)------------------------------
% 11.03/3.04 % (3603)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_3370 for (2989ds/182Mi)
% 11.03/3.04 % (3570)Instruction limit reached!
% 11.03/3.04 % (3570)------------------------------
% 11.03/3.04 % (3570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.04 % (3570)Termination reason: Unknown
% 11.03/3.04 % (3570)Termination phase: Saturation
% 11.03/3.04
% 11.03/3.04 % (3570)Memory used [KB]: 12025
% 11.03/3.04 % (3570)Time elapsed: 0.552 s
% 11.03/3.04 % (3570)Instructions burned: 1088 (million)
% 11.03/3.04 % (3570)------------------------------
% 11.03/3.04 % (3570)------------------------------
% 11.03/3.05 % (3597)Instruction limit reached!
% 11.03/3.05 % (3597)------------------------------
% 11.03/3.05 % (3597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.05 % (3597)Termination reason: Unknown
% 11.03/3.05 % (3597)Termination phase: Saturation
% 11.03/3.05
% 11.03/3.05 % (3597)Memory used [KB]: 8443
% 11.03/3.05 % (3597)Time elapsed: 0.104 s
% 11.03/3.05 % (3597)Instructions burned: 231 (million)
% 11.03/3.05 % (3597)------------------------------
% 11.03/3.05 % (3597)------------------------------
% 11.03/3.06 % (3604)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/154Mi)
% 11.03/3.07 % (3605)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/79Mi)
% 11.03/3.10 % (3602)Instruction limit reached!
% 11.03/3.10 % (3602)------------------------------
% 11.03/3.10 % (3602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.10 % (3602)Termination reason: Unknown
% 11.03/3.10 % (3602)Termination phase: Saturation
% 11.03/3.10
% 11.03/3.10 % (3602)Memory used [KB]: 7419
% 11.03/3.10 % (3602)Time elapsed: 0.082 s
% 11.03/3.10 % (3602)Instructions burned: 183 (million)
% 11.03/3.10 % (3602)------------------------------
% 11.03/3.10 % (3602)------------------------------
% 11.03/3.11 % (3605)Instruction limit reached!
% 11.03/3.11 % (3605)------------------------------
% 11.03/3.11 % (3605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.11 % (3605)Termination reason: Unknown
% 11.03/3.11 % (3605)Termination phase: Property scanning
% 11.03/3.11
% 11.03/3.11 % (3605)Memory used [KB]: 2558
% 11.03/3.11 % (3605)Time elapsed: 0.038 s
% 11.03/3.11 % (3605)Instructions burned: 80 (million)
% 11.03/3.11 % (3605)------------------------------
% 11.03/3.11 % (3605)------------------------------
% 11.03/3.11 % (3600)Instruction limit reached!
% 11.03/3.11 % (3600)------------------------------
% 11.03/3.11 % (3600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.11 % (3600)Termination reason: Unknown
% 11.03/3.11 % (3600)Termination phase: Saturation
% 11.03/3.11
% 11.03/3.11 % (3600)Memory used [KB]: 7547
% 11.03/3.11 % (3600)Time elapsed: 0.126 s
% 11.03/3.11 % (3600)Instructions burned: 297 (million)
% 11.03/3.11 % (3600)------------------------------
% 11.03/3.11 % (3600)------------------------------
% 11.03/3.11 % (3606)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/216Mi)
% 11.03/3.12 % (3603)Instruction limit reached!
% 11.03/3.12 % (3603)------------------------------
% 11.03/3.12 % (3603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.12 % (3603)Termination reason: Unknown
% 11.03/3.12 % (3603)Termination phase: Property scanning
% 11.03/3.12
% 11.03/3.12 % (3603)Memory used [KB]: 5117
% 11.03/3.12 % (3603)Time elapsed: 0.087 s
% 11.03/3.12 % (3603)Instructions burned: 183 (million)
% 11.03/3.12 % (3603)------------------------------
% 11.03/3.12 % (3603)------------------------------
% 11.03/3.12 % (3607)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/114Mi)
% 11.03/3.13 % (3604)Instruction limit reached!
% 11.03/3.13 % (3604)------------------------------
% 11.03/3.13 % (3604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.03/3.13 % (3604)Termination reason: Unknown
% 11.03/3.13 % (3604)Termination phase: Property scanning
% 11.03/3.13
% 11.03/3.13 % (3604)Memory used [KB]: 2686
% 11.03/3.13 % (3604)Time elapsed: 0.069 s
% 11.03/3.13 % (3604)Instructions burned: 156 (million)
% 11.03/3.13 % (3604)------------------------------
% 11.03/3.13 % (3604)------------------------------
% 11.67/3.13 % (3608)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/922Mi)
% 11.67/3.14 % (3609)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/182Mi)
% 11.67/3.14 % (3610)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3370 for (2988ds/164Mi)
% 11.67/3.17 % (3598)Instruction limit reached!
% 11.67/3.17 % (3598)------------------------------
% 11.67/3.17 % (3598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.67/3.17 % (3598)Termination reason: Unknown
% 11.67/3.17 % (3598)Termination phase: Saturation
% 11.67/3.17
% 11.67/3.17 % (3598)Memory used [KB]: 9722
% 11.67/3.17 % (3598)Time elapsed: 0.212 s
% 11.67/3.17 % (3598)Instructions burned: 459 (million)
% 11.67/3.17 % (3598)------------------------------
% 11.67/3.17 % (3598)------------------------------
% 11.67/3.18 % (3607)Instruction limit reached!
% 11.67/3.18 % (3607)------------------------------
% 11.67/3.18 % (3607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.67/3.18 % (3607)Termination reason: Unknown
% 11.67/3.18 % (3607)Termination phase: Property scanning
% 11.67/3.18
% 11.67/3.18 % (3607)Memory used [KB]: 2686
% 11.67/3.18 % (3607)Time elapsed: 0.053 s
% 11.67/3.18 % (3607)Instructions burned: 114 (million)
% 11.67/3.18 % (3607)------------------------------
% 11.67/3.18 % (3607)------------------------------
% 11.67/3.19 % (3611)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/50Mi)
% 11.67/3.19 % (3612)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/368Mi)
% 11.96/3.20 % (3606)Instruction limit reached!
% 11.96/3.20 % (3606)------------------------------
% 11.96/3.20 % (3606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.20 % (3606)Termination reason: Unknown
% 11.96/3.20 % (3606)Termination phase: Property scanning
% 11.96/3.20
% 11.96/3.20 % (3606)Memory used [KB]: 2686
% 11.96/3.20 % (3606)Time elapsed: 0.092 s
% 11.96/3.20 % (3606)Instructions burned: 216 (million)
% 11.96/3.21 % (3606)------------------------------
% 11.96/3.21 % (3606)------------------------------
% 11.96/3.21 % (3611)Instruction limit reached!
% 11.96/3.21 % (3611)------------------------------
% 11.96/3.21 % (3611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.21 % (3611)Termination reason: Unknown
% 11.96/3.21 % (3611)Termination phase: shuffling
% 11.96/3.21
% 11.96/3.21 % (3611)Memory used [KB]: 2430
% 11.96/3.21 % (3611)Time elapsed: 0.026 s
% 11.96/3.21 % (3611)Instructions burned: 52 (million)
% 11.96/3.21 % (3611)------------------------------
% 11.96/3.21 % (3611)------------------------------
% 11.96/3.21 % (3610)Instruction limit reached!
% 11.96/3.21 % (3610)------------------------------
% 11.96/3.21 % (3610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.21 % (3610)Termination reason: Unknown
% 11.96/3.21 % (3610)Termination phase: Function definition elimination
% 11.96/3.21
% 11.96/3.21 % (3610)Memory used [KB]: 2814
% 11.96/3.21 % (3610)Time elapsed: 0.073 s
% 11.96/3.21 % (3610)Instructions burned: 165 (million)
% 11.96/3.21 % (3610)------------------------------
% 11.96/3.21 % (3610)------------------------------
% 11.96/3.22 % (3609)Instruction limit reached!
% 11.96/3.22 % (3609)------------------------------
% 11.96/3.22 % (3609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.22 % (3609)Termination reason: Unknown
% 11.96/3.22 % (3609)Termination phase: Saturation
% 11.96/3.22
% 11.96/3.22 % (3609)Memory used [KB]: 7547
% 11.96/3.22 % (3609)Time elapsed: 0.082 s
% 11.96/3.22 % (3609)Instructions burned: 183 (million)
% 11.96/3.22 % (3609)------------------------------
% 11.96/3.22 % (3609)------------------------------
% 11.96/3.22 % (3613)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/1021Mi)
% 11.96/3.23 % (3615)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/204Mi)
% 11.96/3.23 % (3614)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/267Mi)
% 11.96/3.24 % (3616)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3370 for (2987ds/26Mi)
% 11.96/3.25 % (3616)Instruction limit reached!
% 11.96/3.25 % (3616)------------------------------
% 11.96/3.25 % (3616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.25 % (3616)Termination reason: Unknown
% 11.96/3.25 % (3616)Termination phase: shuffling
% 11.96/3.25
% 11.96/3.25 % (3616)Memory used [KB]: 1918
% 11.96/3.25 % (3616)Time elapsed: 0.014 s
% 11.96/3.25 % (3616)Instructions burned: 27 (million)
% 11.96/3.25 % (3616)------------------------------
% 11.96/3.25 % (3616)------------------------------
% 11.96/3.26 % (3617)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3370 for (2986ds/53Mi)
% 11.96/3.29 % (3617)Instruction limit reached!
% 11.96/3.29 % (3617)------------------------------
% 11.96/3.29 % (3617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.96/3.29 % (3617)Termination reason: Unknown
% 11.96/3.29 % (3617)Termination phase: shuffling
% 11.96/3.29
% 11.96/3.29 % (3617)Memory used [KB]: 2558
% 11.96/3.29 % (3617)Time elapsed: 0.026 s
% 11.96/3.29 % (3617)Instructions burned: 54 (million)
% 11.96/3.29 % (3617)------------------------------
% 11.96/3.29 % (3617)------------------------------
% 12.46/3.31 % (3618)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3370 for (2986ds/4436Mi)
% 12.46/3.32 % (3615)Instruction limit reached!
% 12.46/3.32 % (3615)------------------------------
% 12.46/3.32 % (3615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.32 % (3615)Termination reason: Unknown
% 12.46/3.32 % (3615)Termination phase: Property scanning
% 12.46/3.32
% 12.46/3.32 % (3615)Memory used [KB]: 2814
% 12.46/3.32 % (3615)Time elapsed: 0.089 s
% 12.46/3.32 % (3615)Instructions burned: 205 (million)
% 12.46/3.32 % (3615)------------------------------
% 12.46/3.32 % (3615)------------------------------
% 12.46/3.33 % (3619)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3370 for (2986ds/1539Mi)
% 12.46/3.33 % (3614)Instruction limit reached!
% 12.46/3.33 % (3614)------------------------------
% 12.46/3.33 % (3614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.33 % (3614)Termination reason: Unknown
% 12.46/3.33 % (3614)Termination phase: Saturation
% 12.46/3.33
% 12.46/3.33 % (3614)Memory used [KB]: 7547
% 12.46/3.33 % (3614)Time elapsed: 0.107 s
% 12.46/3.33 % (3614)Instructions burned: 269 (million)
% 12.46/3.33 % (3614)------------------------------
% 12.46/3.33 % (3614)------------------------------
% 12.46/3.35 % (3620)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3370 for (2986ds/408Mi)
% 12.46/3.36 % (3612)Instruction limit reached!
% 12.46/3.36 % (3612)------------------------------
% 12.46/3.36 % (3612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.36 % (3612)Termination reason: Unknown
% 12.46/3.36 % (3612)Termination phase: Saturation
% 12.46/3.36
% 12.46/3.36 % (3612)Memory used [KB]: 9338
% 12.46/3.36 % (3612)Time elapsed: 0.167 s
% 12.46/3.36 % (3612)Instructions burned: 368 (million)
% 12.46/3.36 % (3612)------------------------------
% 12.46/3.36 % (3612)------------------------------
% 12.46/3.37 % (3601)Instruction limit reached!
% 12.46/3.37 % (3601)------------------------------
% 12.46/3.37 % (3601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.37 % (3601)Termination reason: Unknown
% 12.46/3.37 % (3601)Termination phase: Saturation
% 12.46/3.37
% 12.46/3.37 % (3601)Memory used [KB]: 16502
% 12.46/3.37 % (3601)Time elapsed: 0.378 s
% 12.46/3.37 % (3601)Instructions burned: 988 (million)
% 12.46/3.37 % (3601)------------------------------
% 12.46/3.37 % (3601)------------------------------
% 12.46/3.38 % (3621)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3370 for (2985ds/5205Mi)
% 12.46/3.39 % (3622)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3370 for (2985ds/1913Mi)
% 12.95/3.56 % (3620)Instruction limit reached!
% 12.95/3.56 % (3620)------------------------------
% 12.95/3.56 % (3620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.56 % (3620)Termination reason: Unknown
% 12.95/3.56 % (3620)Termination phase: Saturation
% 12.95/3.56
% 12.95/3.56 % (3620)Memory used [KB]: 11385
% 12.95/3.56 % (3620)Time elapsed: 0.208 s
% 12.95/3.56 % (3620)Instructions burned: 409 (million)
% 12.95/3.56 % (3620)------------------------------
% 12.95/3.56 % (3620)------------------------------
% 12.95/3.58 % (3623)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3370 for (2983ds/4350Mi)
% 12.95/3.59 % (3608)Instruction limit reached!
% 12.95/3.59 % (3608)------------------------------
% 12.95/3.59 % (3608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.59 % (3608)Termination reason: Unknown
% 12.95/3.59 % (3608)Termination phase: Saturation
% 12.95/3.59
% 12.95/3.59 % (3608)Memory used [KB]: 12153
% 12.95/3.59 % (3608)Time elapsed: 0.460 s
% 12.95/3.59 % (3608)Instructions burned: 922 (million)
% 12.95/3.59 % (3608)------------------------------
% 12.95/3.59 % (3608)------------------------------
% 13.65/3.60 % (3624)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3370 for (2983ds/68Mi)
% 13.65/3.63 % (3624)Instruction limit reached!
% 13.65/3.63 % (3624)------------------------------
% 13.65/3.63 % (3624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.65/3.63 % (3624)Termination reason: Unknown
% 13.65/3.63 % (3624)Termination phase: Property scanning
% 13.65/3.63
% 13.65/3.63 % (3624)Memory used [KB]: 2558
% 13.65/3.63 % (3624)Time elapsed: 0.033 s
% 13.65/3.63 % (3624)Instructions burned: 69 (million)
% 13.65/3.63 % (3624)------------------------------
% 13.65/3.63 % (3624)------------------------------
% 13.65/3.65 % (3625)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3370 for (2983ds/358Mi)
% 13.69/3.73 % (3613)Instruction limit reached!
% 13.69/3.73 % (3613)------------------------------
% 13.69/3.73 % (3613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.73 % (3613)Termination reason: Unknown
% 13.69/3.73 % (3613)Termination phase: Saturation
% 13.69/3.73
% 13.69/3.73 % (3613)Memory used [KB]: 12792
% 13.69/3.73 % (3613)Time elapsed: 0.513 s
% 13.69/3.73 % (3613)Instructions burned: 1022 (million)
% 13.69/3.73 % (3613)------------------------------
% 13.69/3.73 % (3613)------------------------------
% 13.69/3.75 % (3626)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3370 for (2982ds/31Mi)
% 13.69/3.77 % (3626)Instruction limit reached!
% 13.69/3.77 % (3626)------------------------------
% 13.69/3.77 % (3626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.77 % (3626)Termination reason: Unknown
% 13.69/3.77 % (3626)Termination phase: shuffling
% 13.69/3.77
% 13.69/3.77 % (3626)Memory used [KB]: 2046
% 13.69/3.77 % (3626)Time elapsed: 0.016 s
% 13.69/3.77 % (3626)Instructions burned: 31 (million)
% 13.69/3.77 % (3626)------------------------------
% 13.69/3.77 % (3626)------------------------------
% 13.69/3.78 % (3627)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3370 for (2981ds/279Mi)
% 14.25/3.81 % (3625)Instruction limit reached!
% 14.25/3.81 % (3625)------------------------------
% 14.25/3.81 % (3625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.25/3.81 % (3625)Termination reason: Unknown
% 14.25/3.81 % (3625)Termination phase: Saturation
% 14.25/3.81
% 14.25/3.81 % (3625)Memory used [KB]: 8571
% 14.25/3.81 % (3625)Time elapsed: 0.159 s
% 14.25/3.81 % (3625)Instructions burned: 358 (million)
% 14.25/3.81 % (3625)------------------------------
% 14.25/3.81 % (3625)------------------------------
% 14.25/3.83 % (3628)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3370 for (2981ds/258Mi)
% 14.44/3.90 % (3627)Instruction limit reached!
% 14.44/3.90 % (3627)------------------------------
% 14.44/3.90 % (3627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.90 % (3627)Termination reason: Unknown
% 14.44/3.90 % (3627)Termination phase: Saturation
% 14.44/3.90
% 14.44/3.90 % (3627)Memory used [KB]: 7547
% 14.44/3.90 % (3627)Time elapsed: 0.121 s
% 14.44/3.90 % (3627)Instructions burned: 280 (million)
% 14.44/3.90 % (3627)------------------------------
% 14.44/3.90 % (3627)------------------------------
% 14.44/3.92 % (3629)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3370 for (2980ds/26Mi)
% 14.44/3.93 % (3629)Instruction limit reached!
% 14.44/3.93 % (3629)------------------------------
% 14.44/3.93 % (3629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.93 % (3629)Termination reason: Unknown
% 14.44/3.93 % (3629)Termination phase: shuffling
% 14.44/3.93
% 14.44/3.93 % (3629)Memory used [KB]: 2046
% 14.44/3.93 % (3629)Time elapsed: 0.014 s
% 14.44/3.93 % (3629)Instructions burned: 26 (million)
% 14.44/3.93 % (3629)------------------------------
% 14.44/3.93 % (3629)------------------------------
% 14.44/3.94 % (3628)Instruction limit reached!
% 14.44/3.94 % (3628)------------------------------
% 14.44/3.94 % (3628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.94 % (3628)Termination reason: Unknown
% 14.44/3.94 % (3628)Termination phase: Saturation
% 14.44/3.94
% 14.44/3.94 % (3628)Memory used [KB]: 8187
% 14.44/3.94 % (3628)Time elapsed: 0.119 s
% 14.44/3.94 % (3628)Instructions burned: 259 (million)
% 14.44/3.94 % (3628)------------------------------
% 14.44/3.94 % (3628)------------------------------
% 14.44/3.95 % (3630)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3370 for (2979ds/995Mi)
% 14.44/3.96 % (3631)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3370 for (2979ds/373Mi)
% 18.03/4.09 % (3619)Instruction limit reached!
% 18.03/4.09 % (3619)------------------------------
% 18.03/4.09 % (3619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.03/4.09 % (3619)Termination reason: Unknown
% 18.03/4.09 % (3619)Termination phase: Saturation
% 18.03/4.09
% 18.03/4.09 % (3619)Memory used [KB]: 11001
% 18.03/4.09 % (3619)Time elapsed: 0.762 s
% 18.03/4.09 % (3619)Instructions burned: 1540 (million)
% 18.03/4.09 % (3619)------------------------------
% 18.03/4.09 % (3619)------------------------------
% 18.03/4.11 % (3632)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3370 for (2978ds/253Mi)
% 18.03/4.12 % (3631)Instruction limit reached!
% 18.03/4.12 % (3631)------------------------------
% 18.03/4.12 % (3631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.03/4.12 % (3631)Termination reason: Unknown
% 18.03/4.12 % (3631)Termination phase: Saturation
% 18.03/4.12
% 18.03/4.12 % (3631)Memory used [KB]: 9466
% 18.03/4.12 % (3631)Time elapsed: 0.166 s
% 18.03/4.12 % (3631)Instructions burned: 373 (million)
% 18.03/4.12 % (3631)------------------------------
% 18.03/4.12 % (3631)------------------------------
% 18.58/4.14 % (3633)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3370 for (2978ds/832Mi)
% 19.10/4.22 % (3632)Instruction limit reached!
% 19.10/4.22 % (3632)------------------------------
% 19.10/4.22 % (3632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.10/4.22 % (3632)Termination reason: Unknown
% 19.10/4.22 % (3632)Termination phase: Saturation
% 19.10/4.22
% 19.10/4.22 % (3632)Memory used [KB]: 7547
% 19.10/4.22 % (3632)Time elapsed: 0.108 s
% 19.10/4.22 % (3632)Instructions burned: 254 (million)
% 19.10/4.22 % (3632)------------------------------
% 19.10/4.22 % (3632)------------------------------
% 19.10/4.24 % (3634)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3370 for (2977ds/668Mi)
% 19.72/4.32 % (3622)Instruction limit reached!
% 19.72/4.32 % (3622)------------------------------
% 19.72/4.32 % (3622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.32 % (3622)Termination reason: Unknown
% 19.72/4.32 % (3622)Termination phase: Saturation
% 19.72/4.32
% 19.72/4.32 % (3622)Memory used [KB]: 6268
% 19.72/4.32 % (3622)Time elapsed: 0.948 s
% 19.72/4.32 % (3622)Instructions burned: 1914 (million)
% 19.72/4.32 % (3622)------------------------------
% 19.72/4.32 % (3622)------------------------------
% 19.72/4.33 % (3630)Instruction limit reached!
% 19.72/4.33 % (3630)------------------------------
% 19.72/4.33 % (3630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.33 % (3630)Termination reason: Unknown
% 19.72/4.33 % (3630)Termination phase: Saturation
% 19.72/4.33
% 19.72/4.33 % (3635)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3370 for (2976ds/40Mi)
% 19.72/4.33 % (3630)Memory used [KB]: 16119
% 19.72/4.33 % (3630)Time elapsed: 0.386 s
% 19.72/4.33 % (3630)Instructions burned: 996 (million)
% 19.72/4.33 % (3630)------------------------------
% 19.72/4.33 % (3630)------------------------------
% 19.72/4.35 % (3635)Instruction limit reached!
% 19.72/4.35 % (3635)------------------------------
% 19.72/4.35 % (3635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.35 % (3635)Termination reason: Unknown
% 19.72/4.35 % (3635)Termination phase: shuffling
% 19.72/4.35
% 19.72/4.35 % (3635)Memory used [KB]: 2302
% 19.72/4.35 % (3635)Time elapsed: 0.020 s
% 19.72/4.35 % (3635)Instructions burned: 40 (million)
% 19.72/4.35 % (3635)------------------------------
% 19.72/4.35 % (3635)------------------------------
% 19.72/4.36 % (3636)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3370 for (2975ds/294Mi)
% 19.72/4.37 % (3637)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3370 for (2975ds/187Mi)
% 20.15/4.46 % (3637)Instruction limit reached!
% 20.15/4.46 % (3637)------------------------------
% 20.15/4.46 % (3637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.15/4.46 % (3637)Termination reason: Unknown
% 20.15/4.46 % (3637)Termination phase: Saturation
% 20.15/4.46
% 20.15/4.46 % (3637)Memory used [KB]: 7419
% 20.15/4.46 % (3637)Time elapsed: 0.087 s
% 20.15/4.46 % (3637)Instructions burned: 188 (million)
% 20.15/4.46 % (3637)------------------------------
% 20.15/4.46 % (3637)------------------------------
% 20.15/4.48 % (3638)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3370 for (2974ds/371Mi)
% 20.15/4.48 % (3636)Instruction limit reached!
% 20.15/4.48 % (3636)------------------------------
% 20.15/4.48 % (3636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.15/4.48 % (3636)Termination reason: Unknown
% 20.15/4.48 % (3636)Termination phase: Saturation
% 20.15/4.48
% 20.15/4.48 % (3636)Memory used [KB]: 7547
% 20.15/4.48 % (3636)Time elapsed: 0.125 s
% 20.15/4.48 % (3636)Instructions burned: 295 (million)
% 20.15/4.48 % (3636)------------------------------
% 20.15/4.48 % (3636)------------------------------
% 20.69/4.50 % (3639)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3370 for (2974ds/1827Mi)
% 20.69/4.50 % (3634)Instruction limit reached!
% 20.69/4.50 % (3634)------------------------------
% 20.69/4.50 % (3634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.50 % (3634)Termination reason: Unknown
% 20.69/4.50 % (3634)Termination phase: Saturation
% 20.69/4.50
% 20.69/4.50 % (3634)Memory used [KB]: 15607
% 20.69/4.50 % (3634)Time elapsed: 0.268 s
% 20.69/4.50 % (3634)Instructions burned: 670 (million)
% 20.69/4.50 % (3634)------------------------------
% 20.69/4.50 % (3634)------------------------------
% 20.69/4.52 % (3640)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3370 for (2974ds/70Mi)
% 20.69/4.54 % (3633)Instruction limit reached!
% 20.69/4.54 % (3633)------------------------------
% 20.69/4.54 % (3633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.54 % (3633)Termination reason: Unknown
% 20.69/4.54 % (3633)Termination phase: Saturation
% 20.69/4.54
% 20.69/4.54 % (3633)Memory used [KB]: 11641
% 20.69/4.54 % (3633)Time elapsed: 0.401 s
% 20.69/4.54 % (3633)Instructions burned: 832 (million)
% 20.69/4.54 % (3633)------------------------------
% 20.69/4.54 % (3633)------------------------------
% 20.69/4.55 % (3640)Instruction limit reached!
% 20.69/4.55 % (3640)------------------------------
% 20.69/4.55 % (3640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.69/4.55 % (3640)Termination reason: Unknown
% 20.69/4.55 % (3640)Termination phase: Property scanning
% 20.69/4.55
% 20.69/4.55 % (3640)Memory used [KB]: 2558
% 20.69/4.55 % (3640)Time elapsed: 0.032 s
% 20.69/4.55 % (3640)Instructions burned: 71 (million)
% 20.69/4.55 % (3640)------------------------------
% 20.69/4.55 % (3640)------------------------------
% 20.69/4.56 % (3641)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3370 for (2973ds/316Mi)
% 20.69/4.57 % (3642)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3370 for (2973ds/932Mi)
% 21.74/4.64 % (3638)Instruction limit reached!
% 21.74/4.64 % (3638)------------------------------
% 21.74/4.64 % (3638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.74/4.64 % (3638)Termination reason: Unknown
% 21.74/4.64 % (3638)Termination phase: Saturation
% 21.74/4.64
% 21.74/4.64 % (3638)Memory used [KB]: 9210
% 21.74/4.64 % (3638)Time elapsed: 0.166 s
% 21.74/4.64 % (3638)Instructions burned: 372 (million)
% 21.74/4.64 % (3638)------------------------------
% 21.74/4.64 % (3638)------------------------------
% 21.74/4.66 % (3643)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3370 for (2972ds/4714Mi)
% 21.74/4.69 % (3641)Instruction limit reached!
% 21.74/4.69 % (3641)------------------------------
% 21.74/4.69 % (3641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.74/4.69 % (3641)Termination reason: Unknown
% 21.74/4.69 % (3641)Termination phase: Saturation
% 21.74/4.69
% 21.74/4.69 % (3641)Memory used [KB]: 7547
% 21.74/4.69 % (3641)Time elapsed: 0.136 s
% 21.74/4.69 % (3641)Instructions burned: 316 (million)
% 21.74/4.69 % (3641)------------------------------
% 21.74/4.69 % (3641)------------------------------
% 22.37/4.71 % (3644)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3370 for (2972ds/8250Mi)
% 22.67/4.89 % (3642)Instruction limit reached!
% 22.67/4.89 % (3642)------------------------------
% 22.67/4.89 % (3642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.89 % (3642)Termination reason: Unknown
% 22.67/4.89 % (3642)Termination phase: Saturation
% 22.67/4.89
% 22.67/4.89 % (3642)Memory used [KB]: 16247
% 22.67/4.89 % (3642)Time elapsed: 0.322 s
% 22.67/4.89 % (3642)Instructions burned: 934 (million)
% 22.67/4.89 % (3642)------------------------------
% 22.67/4.89 % (3642)------------------------------
% 23.29/4.90 % (3645)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3370 for (2970ds/770Mi)
% 25.65/5.15 % (3645)Instruction limit reached!
% 25.65/5.15 % (3645)------------------------------
% 25.65/5.15 % (3645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.65/5.15 % (3645)Termination reason: Unknown
% 25.65/5.15 % (3645)Termination phase: Saturation
% 25.65/5.15
% 25.65/5.15 % (3645)Memory used [KB]: 7803
% 25.65/5.15 % (3645)Time elapsed: 0.265 s
% 25.65/5.15 % (3645)Instructions burned: 772 (million)
% 25.65/5.15 % (3645)------------------------------
% 25.65/5.15 % (3645)------------------------------
% 25.65/5.17 % (3646)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3370 for (2967ds/794Mi)
% 26.17/5.28 % (3621)Instruction limit reached!
% 26.17/5.28 % (3621)------------------------------
% 26.17/5.28 % (3621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.17/5.28 % (3621)Termination reason: Unknown
% 26.17/5.28 % (3621)Termination phase: Saturation
% 26.17/5.28
% 26.17/5.28 % (3621)Memory used [KB]: 17142
% 26.17/5.28 % (3621)Time elapsed: 1.902 s
% 26.17/5.28 % (3621)Instructions burned: 5205 (million)
% 26.17/5.28 % (3621)------------------------------
% 26.17/5.28 % (3621)------------------------------
% 26.17/5.29 % (3647)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3370 for (2966ds/464Mi)
% 26.77/5.33 % (3639)Instruction limit reached!
% 26.77/5.33 % (3639)------------------------------
% 26.77/5.33 % (3639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/5.33 % (3639)Termination reason: Unknown
% 26.77/5.33 % (3639)Termination phase: Saturation
% 26.77/5.33
% 26.77/5.33 % (3639)Memory used [KB]: 20980
% 26.77/5.33 % (3639)Time elapsed: 0.834 s
% 26.77/5.33 % (3639)Instructions burned: 1827 (million)
% 26.77/5.33 % (3639)------------------------------
% 26.77/5.33 % (3639)------------------------------
% 26.77/5.35 % (3648)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3370 for (2966ds/1376Mi)
% 27.62/5.50 % (3647)Instruction limit reached!
% 27.62/5.50 % (3647)------------------------------
% 27.62/5.50 % (3647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.62/5.50 % (3647)Termination reason: Unknown
% 27.62/5.50 % (3647)Termination phase: Saturation
% 27.62/5.50
% 27.62/5.50 % (3647)Memory used [KB]: 9594
% 27.62/5.50 % (3647)Time elapsed: 0.212 s
% 27.62/5.50 % (3647)Instructions burned: 465 (million)
% 27.62/5.50 % (3647)------------------------------
% 27.62/5.50 % (3647)------------------------------
% 27.62/5.52 % (3649)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3370 for (2964ds/906Mi)
% 27.62/5.53 % (3618)Instruction limit reached!
% 27.62/5.53 % (3618)------------------------------
% 27.62/5.53 % (3618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.62/5.53 % (3618)Termination reason: Unknown
% 27.62/5.53 % (3618)Termination phase: Saturation
% 27.62/5.53
% 27.62/5.53 % (3618)Memory used [KB]: 15095
% 27.62/5.53 % (3618)Time elapsed: 2.228 s
% 27.62/5.53 % (3618)Instructions burned: 4436 (million)
% 27.62/5.53 % (3618)------------------------------
% 27.62/5.53 % (3618)------------------------------
% 27.62/5.55 % (3646)Instruction limit reached!
% 27.62/5.55 % (3646)------------------------------
% 27.62/5.55 % (3646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.62/5.55 % (3646)Termination reason: Unknown
% 27.62/5.55 % (3646)Termination phase: Saturation
% 27.62/5.55
% 27.62/5.55 % (3646)Memory used [KB]: 6012
% 27.62/5.55 % (3646)Time elapsed: 0.404 s
% 27.62/5.55 % (3646)Instructions burned: 794 (million)
% 27.62/5.55 % (3646)------------------------------
% 27.62/5.55 % (3646)------------------------------
% 27.62/5.55 % (3650)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3370 for (2964ds/434Mi)
% 27.62/5.57 % (3651)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3370 for (2963ds/865Mi)
% 28.90/5.72 % (3623)Instruction limit reached!
% 28.90/5.72 % (3623)------------------------------
% 28.90/5.72 % (3623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.90/5.72 % (3623)Termination reason: Unknown
% 28.90/5.72 % (3623)Termination phase: Saturation
% 28.90/5.72
% 28.90/5.72 % (3623)Memory used [KB]: 13688
% 28.90/5.72 % (3623)Time elapsed: 2.156 s
% 28.90/5.72 % (3623)Instructions burned: 4350 (million)
% 28.90/5.72 % (3623)------------------------------
% 28.90/5.72 % (3623)------------------------------
% 28.90/5.74 % (3652)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3370 for (2962ds/593Mi)
% 28.90/5.76 % (3650)Instruction limit reached!
% 28.90/5.76 % (3650)------------------------------
% 28.90/5.76 % (3650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.90/5.76 % (3650)Termination reason: Unknown
% 28.90/5.76 % (3650)Termination phase: Saturation
% 28.90/5.76
% 28.90/5.76 % (3650)Memory used [KB]: 11385
% 28.90/5.76 % (3650)Time elapsed: 0.230 s
% 28.90/5.76 % (3650)Instructions burned: 435 (million)
% 28.90/5.76 % (3650)------------------------------
% 28.90/5.76 % (3650)------------------------------
% 28.90/5.78 % (3653)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3370 for (2961ds/443Mi)
% 29.57/5.90 % (3648)Instruction limit reached!
% 29.57/5.90 % (3648)------------------------------
% 29.57/5.90 % (3648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.57/5.90 % (3648)Termination reason: Unknown
% 29.57/5.90 % (3648)Termination phase: Saturation
% 29.57/5.90
% 29.57/5.90 % (3648)Memory used [KB]: 9850
% 29.57/5.90 % (3648)Time elapsed: 0.547 s
% 29.57/5.90 % (3648)Instructions burned: 1378 (million)
% 29.57/5.90 % (3648)------------------------------
% 29.57/5.90 % (3648)------------------------------
% 29.57/5.92 % (3654)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3370 for (2960ds/594Mi)
% 29.57/5.97 % (3649)Instruction limit reached!
% 29.57/5.97 % (3649)------------------------------
% 29.57/5.97 % (3649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.57/5.97 % (3649)Termination reason: Unknown
% 29.57/5.97 % (3649)Termination phase: Saturation
% 29.57/5.97
% 29.57/5.97 % (3649)Memory used [KB]: 11385
% 29.57/5.97 % (3649)Time elapsed: 0.467 s
% 29.57/5.97 % (3649)Instructions burned: 907 (million)
% 29.57/5.97 % (3649)------------------------------
% 29.57/5.97 % (3649)------------------------------
% 29.57/5.97 % (3653)Instruction limit reached!
% 29.57/5.97 % (3653)------------------------------
% 29.57/5.97 % (3653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.57/5.97 % (3653)Termination reason: Unknown
% 29.57/5.97 % (3653)Termination phase: Saturation
% 29.57/5.97
% 29.57/5.97 % (3653)Memory used [KB]: 9594
% 29.57/5.97 % (3653)Time elapsed: 0.196 s
% 29.57/5.97 % (3653)Instructions burned: 443 (million)
% 29.57/5.97 % (3653)------------------------------
% 29.57/5.97 % (3653)------------------------------
% 29.57/5.97 % (3652)Instruction limit reached!
% 29.57/5.97 % (3652)------------------------------
% 29.57/5.97 % (3652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.57/5.97 % (3652)Termination reason: Unknown
% 29.57/5.97 % (3652)Termination phase: Saturation
% 29.57/5.97
% 29.57/5.97 % (3652)Memory used [KB]: 7675
% 29.57/5.97 % (3652)Time elapsed: 0.240 s
% 29.57/5.97 % (3652)Instructions burned: 595 (million)
% 29.57/5.97 % (3652)------------------------------
% 29.57/5.97 % (3652)------------------------------
% 29.57/5.98 % (3651)Instruction limit reached!
% 29.57/5.98 % (3651)------------------------------
% 29.57/5.98 % (3651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.57/5.98 % (3651)Termination reason: Unknown
% 29.57/5.98 % (3651)Termination phase: Saturation
% 29.57/5.98
% 29.57/5.98 % (3651)Memory used [KB]: 10618
% 29.57/5.98 % (3651)Time elapsed: 0.412 s
% 29.57/5.98 % (3651)Instructions burned: 866 (million)
% 29.57/5.98 % (3651)------------------------------
% 29.57/5.98 % (3651)------------------------------
% 29.57/5.98 % (3655)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3370 for (2959ds/327Mi)
% 29.57/5.99 % (3656)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3370 for (2959ds/5411Mi)
% 29.57/5.99 % (3657)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3370 for (2959ds/1762Mi)
% 29.57/5.99 % (3658)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3370 for (2959ds/96Mi)
% 31.98/6.04 % (3658)Instruction limit reached!
% 31.98/6.04 % (3658)------------------------------
% 31.98/6.04 % (3658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.98/6.04 % (3658)Termination reason: Unknown
% 31.98/6.04 % (3658)Termination phase: Property scanning
% 31.98/6.04
% 31.98/6.04 % (3658)Memory used [KB]: 2686
% 31.98/6.04 % (3658)Time elapsed: 0.045 s
% 31.98/6.04 % (3658)Instructions burned: 96 (million)
% 31.98/6.04 % (3658)------------------------------
% 31.98/6.04 % (3658)------------------------------
% 31.98/6.06 % (3659)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3370 for (2958ds/503Mi)
% 32.63/6.14 % (3655)Instruction limit reached!
% 32.63/6.14 % (3655)------------------------------
% 32.63/6.14 % (3655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/6.14 % (3655)Termination reason: Unknown
% 32.63/6.14 % (3655)Termination phase: Saturation
% 32.63/6.14
% 32.63/6.14 % (3655)Memory used [KB]: 11257
% 32.63/6.14 % (3655)Time elapsed: 0.163 s
% 32.63/6.14 % (3655)Instructions burned: 328 (million)
% 32.63/6.14 % (3655)------------------------------
% 32.63/6.14 % (3655)------------------------------
% 32.63/6.16 % (3660)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3370 for (2957ds/90Mi)
% 32.63/6.19 % (3654)Instruction limit reached!
% 32.63/6.19 % (3654)------------------------------
% 32.63/6.19 % (3654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/6.19 % (3654)Termination reason: Unknown
% 32.63/6.19 % (3654)Termination phase: Saturation
% 32.63/6.19
% 32.63/6.19 % (3654)Memory used [KB]: 9850
% 32.63/6.19 % (3654)Time elapsed: 0.278 s
% 32.63/6.19 % (3654)Instructions burned: 595 (million)
% 32.63/6.19 % (3654)------------------------------
% 32.63/6.19 % (3654)------------------------------
% 33.04/6.20 % (3660)Instruction limit reached!
% 33.04/6.20 % (3660)------------------------------
% 33.04/6.20 % (3660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.04/6.20 % (3660)Termination reason: Unknown
% 33.04/6.20 % (3660)Termination phase: Preprocessing 3
% 33.04/6.20
% 33.04/6.20 % (3660)Memory used [KB]: 2686
% 33.04/6.20 % (3660)Time elapsed: 0.042 s
% 33.04/6.20 % (3660)Instructions burned: 90 (million)
% 33.04/6.20 % (3660)------------------------------
% 33.04/6.20 % (3660)------------------------------
% 33.04/6.21 % (3661)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3370 for (2957ds/593Mi)
% 33.04/6.22 % (3662)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3370 for (2957ds/1512Mi)
% 33.04/6.29 % (3659)Instruction limit reached!
% 33.04/6.29 % (3659)------------------------------
% 33.04/6.29 % (3659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.04/6.29 % (3659)Termination reason: Unknown
% 33.04/6.29 % (3659)Termination phase: Saturation
% 33.04/6.29
% 33.04/6.29 % (3659)Memory used [KB]: 9850
% 33.04/6.29 % (3659)Time elapsed: 0.233 s
% 33.04/6.29 % (3659)Instructions burned: 504 (million)
% 33.04/6.29 % (3659)------------------------------
% 33.04/6.29 % (3659)------------------------------
% 33.75/6.31 % (3663)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3370 for (2956ds/569Mi)
% 34.16/6.40 % (3643)Instruction limit reached!
% 34.16/6.40 % (3643)------------------------------
% 34.16/6.40 % (3643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.16/6.40 % (3643)Termination reason: Unknown
% 34.16/6.40 % (3643)Termination phase: Saturation
% 34.16/6.40
% 34.16/6.40 % (3643)Memory used [KB]: 7675
% 34.16/6.40 % (3643)Time elapsed: 1.746 s
% 34.16/6.40 % (3643)Instructions burned: 4714 (million)
% 34.16/6.40 % (3643)------------------------------
% 34.16/6.40 % (3643)------------------------------
% 34.16/6.42 % (3664)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3370 for (2955ds/501Mi)
% 34.16/6.49 % (3661)Instruction limit reached!
% 34.16/6.49 % (3661)------------------------------
% 34.16/6.49 % (3661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.16/6.49 % (3661)Termination reason: Unknown
% 34.16/6.49 % (3661)Termination phase: Saturation
% 34.16/6.49
% 34.16/6.49 % (3661)Memory used [KB]: 10106
% 34.16/6.49 % (3661)Time elapsed: 0.279 s
% 34.16/6.49 % (3661)Instructions burned: 594 (million)
% 34.16/6.49 % (3661)------------------------------
% 34.16/6.49 % (3661)------------------------------
% 34.75/6.51 % (3665)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3370 for (2954ds/562Mi)
% 34.75/6.52 % (3663)Instruction limit reached!
% 34.75/6.52 % (3663)------------------------------
% 34.75/6.52 % (3663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.75/6.52 % (3663)Termination reason: Unknown
% 34.75/6.52 % (3663)Termination phase: Saturation
% 34.75/6.52
% 34.75/6.52 % (3663)Memory used [KB]: 7675
% 34.75/6.52 % (3663)Time elapsed: 0.215 s
% 34.75/6.52 % (3663)Instructions burned: 569 (million)
% 34.75/6.52 % (3663)------------------------------
% 34.75/6.52 % (3663)------------------------------
% 34.75/6.53 % (3666)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3370 for (2954ds/406Mi)
% 35.27/6.64 % (3657)Instruction limit reached!
% 35.27/6.64 % (3657)------------------------------
% 35.27/6.64 % (3657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.27/6.64 % (3657)Termination reason: Unknown
% 35.27/6.64 % (3657)Termination phase: Saturation
% 35.27/6.64
% 35.27/6.64 % (3657)Memory used [KB]: 22899
% 35.27/6.64 % (3657)Time elapsed: 0.655 s
% 35.27/6.64 % (3657)Instructions burned: 1764 (million)
% 35.27/6.64 % (3657)------------------------------
% 35.27/6.64 % (3657)------------------------------
% 35.27/6.66 % (3667)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3370 for (2952ds/582Mi)
% 35.27/6.66 % (3664)Instruction limit reached!
% 35.27/6.66 % (3664)------------------------------
% 35.27/6.66 % (3664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.27/6.66 % (3664)Termination reason: Unknown
% 35.27/6.66 % (3664)Termination phase: Saturation
% 35.27/6.66
% 35.27/6.66 % (3664)Memory used [KB]: 10618
% 35.27/6.66 % (3664)Time elapsed: 0.245 s
% 35.27/6.66 % (3664)Instructions burned: 502 (million)
% 35.27/6.66 % (3664)------------------------------
% 35.27/6.66 % (3664)------------------------------
% 35.27/6.68 % (3665)Instruction limit reached!
% 35.27/6.68 % (3665)------------------------------
% 35.27/6.68 % (3665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.27/6.69 % (3665)Termination reason: Unknown
% 35.27/6.69 % (3665)Termination phase: Saturation
% 35.27/6.69
% 35.27/6.69 % (3665)Memory used [KB]: 9338
% 35.27/6.69 % (3665)Time elapsed: 0.175 s
% 35.27/6.69 % (3665)Instructions burned: 562 (million)
% 35.27/6.69 % (3665)------------------------------
% 35.27/6.69 % (3665)------------------------------
% 35.27/6.69 % (3668)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3370 for (2952ds/456Mi)
% 35.98/6.70 % (3669)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3370 for (2952ds/393Mi)
% 35.98/6.71 % (3666)Instruction limit reached!
% 35.98/6.71 % (3666)------------------------------
% 35.98/6.71 % (3666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.98/6.71 % (3666)Termination reason: Unknown
% 35.98/6.71 % (3666)Termination phase: Saturation
% 35.98/6.71
% 35.98/6.71 % (3666)Memory used [KB]: 7803
% 35.98/6.71 % (3666)Time elapsed: 0.182 s
% 35.98/6.71 % (3666)Instructions burned: 407 (million)
% 35.98/6.71 % (3666)------------------------------
% 35.98/6.71 % (3666)------------------------------
% 35.98/6.73 % (3670)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3370 for (2952ds/1335Mi)
% 36.38/6.83 % (3662)First to succeed.
% 36.38/6.84 % (3662)Refutation found. Thanks to Tanya!
% 36.38/6.84 % SZS status Theorem for DTF2THF_3370
% 36.38/6.84 % SZS output start Proof for DTF2THF_3370
% 36.38/6.84 thf(func_def_0, type, in: $i > $i > $o).
% 36.38/6.84 thf(func_def_1, type, exu: ($i > $o) > $o).
% 36.38/6.84 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 36.38/6.84 thf(func_def_8, type, powerset: $i > $i).
% 36.38/6.84 thf(func_def_10, type, setunion: $i > $i).
% 36.38/6.84 thf(func_def_19, type, descr: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_26, type, prop2set: $o > $i).
% 36.38/6.84 thf(func_def_36, type, nonempty: $i > $o).
% 36.38/6.84 thf(func_def_69, type, set2prop: $i > $o).
% 36.38/6.84 thf(func_def_88, type, subset: $i > $i > $o).
% 36.38/6.84 thf(func_def_89, type, disjoint: $i > $i > $o).
% 36.38/6.84 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 36.38/6.84 thf(func_def_114, type, binunion: $i > $i > $i).
% 36.38/6.84 thf(func_def_122, type, binintersect: $i > $i > $i).
% 36.38/6.84 thf(func_def_135, type, regular: $i > $o).
% 36.38/6.84 thf(func_def_136, type, setminus: $i > $i > $i).
% 36.38/6.84 thf(func_def_147, type, symdiff: $i > $i > $i).
% 36.38/6.84 thf(func_def_153, type, iskpair: $i > $o).
% 36.38/6.84 thf(func_def_158, type, kpair: $i > $i > $i).
% 36.38/6.84 thf(func_def_160, type, cartprod: $i > $i > $i).
% 36.38/6.84 thf(func_def_177, type, singleton: $i > $o).
% 36.38/6.84 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 36.38/6.84 thf(func_def_184, type, atmost1p: $i > $o).
% 36.38/6.84 thf(func_def_185, type, atleast2p: $i > $o).
% 36.38/6.84 thf(func_def_186, type, atmost2p: $i > $o).
% 36.38/6.84 thf(func_def_187, type, upairsetp: $i > $o).
% 36.38/6.84 thf(func_def_191, type, kfst: $i > $i).
% 36.38/6.84 thf(func_def_203, type, ksnd: $i > $i).
% 36.38/6.84 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 36.38/6.84 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 36.38/6.84 thf(func_def_222, type, func: $i > $i > $i > $o).
% 36.38/6.84 thf(func_def_223, type, funcSet: $i > $i > $i).
% 36.38/6.84 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 36.38/6.84 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 36.38/6.84 thf(func_def_323, type, breln1: $i > $i > $o).
% 36.38/6.84 thf(func_def_325, type, breln1Set: $i > $i).
% 36.38/6.84 thf(func_def_327, type, transitive: $i > $i > $o).
% 36.38/6.84 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 36.38/6.84 thf(func_def_329, type, reflexive: $i > $i > $o).
% 36.38/6.84 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 36.38/6.84 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 36.38/6.84 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 36.38/6.84 thf(func_def_348, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 36.38/6.84 thf(func_def_349, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 36.38/6.84 thf(func_def_352, type, sP4: $i > $i > $i > $i > $o).
% 36.38/6.84 thf(func_def_355, type, sP7: $i > $i > $o).
% 36.38/6.84 thf(func_def_356, type, sP8: $i > $o).
% 36.38/6.84 thf(func_def_357, type, sP9: $i > $i > $o).
% 36.38/6.84 thf(func_def_358, type, sP10: $i > $i > $o).
% 36.38/6.84 thf(func_def_359, type, sP11: $i > $o > $i > $i > $o).
% 36.38/6.84 thf(func_def_362, type, sP14: $i > $i > $i > $o).
% 36.38/6.84 thf(func_def_370, type, sK22: $i > $o).
% 36.38/6.84 thf(func_def_393, type, sK45: $i > $i > $o).
% 36.38/6.84 thf(func_def_410, type, sK62: ($i > $o) > ($i > $o) > $i > $i > $i).
% 36.38/6.84 thf(func_def_411, type, sK63: ($i > $o) > ($i > $o) > $i > $i > $i).
% 36.38/6.84 thf(func_def_414, type, sK66: $i > $o).
% 36.38/6.84 thf(func_def_415, type, sK67: $i > $o).
% 36.38/6.84 thf(func_def_425, type, sK77: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_428, type, sK80: $i > $o).
% 36.38/6.84 thf(func_def_434, type, sK86: $i > $i > $o).
% 36.38/6.84 thf(func_def_444, type, sK96: $i > $o).
% 36.38/6.84 thf(func_def_445, type, sK97: $i > $o).
% 36.38/6.84 thf(func_def_446, type, sK98: ($i > $o) > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_447, type, sK99: ($i > $o) > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_449, type, sK101: $i > $i).
% 36.38/6.84 thf(func_def_463, type, sK115: ($i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_465, type, sK117: $i > $o).
% 36.38/6.84 thf(func_def_507, type, sK159: $i > $o).
% 36.38/6.84 thf(func_def_510, type, sK162: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_511, type, sK163: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_532, type, sK184: $i > $i > $o).
% 36.38/6.84 thf(func_def_536, type, sK188: $i > $i > $i).
% 36.38/6.84 thf(func_def_587, type, sK239: $i > $o).
% 36.38/6.84 thf(func_def_590, type, sK242: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_614, type, sK266: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_626, type, sK278: $i > ($i > $i) > $i > $i).
% 36.38/6.84 thf(func_def_628, type, sK280: $i > $i).
% 36.38/6.84 thf(func_def_633, type, sK285: $o > $i > $i > $i).
% 36.38/6.84 thf(func_def_641, type, sK293: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_642, type, sK294: $i > $o).
% 36.38/6.84 thf(func_def_649, type, sK301: $i > $i).
% 36.38/6.84 thf(func_def_651, type, sK303: $i > ($i > $i) > $i > $i).
% 36.38/6.84 thf(func_def_656, type, sK308: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_657, type, sK309: $i > $o).
% 36.38/6.84 thf(func_def_658, type, sK310: $i > $i).
% 36.38/6.84 thf(func_def_665, type, sK317: $i > ($i > $i) > $i > $i).
% 36.38/6.84 thf(func_def_667, type, sK319: $i > $i).
% 36.38/6.84 thf(func_def_669, type, sK321: ($i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_671, type, sK323: $i > $o).
% 36.38/6.84 thf(func_def_675, type, sK327: $i > $i > $i).
% 36.38/6.84 thf(func_def_679, type, sK331: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_680, type, sK332: $i > $o).
% 36.38/6.84 thf(func_def_715, type, sK367: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_716, type, sK368: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_724, type, sK376: $i > $i > $i).
% 36.38/6.84 thf(func_def_725, type, sK377: $i > $i > $i).
% 36.38/6.84 thf(func_def_737, type, sK389: $i > $o).
% 36.38/6.84 thf(func_def_739, type, sK391: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_741, type, sK393: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_742, type, sK394: $i > $o).
% 36.38/6.84 thf(func_def_747, type, sK399: ($i > $o) > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_748, type, sK400: ($i > $o) > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_749, type, sK401: $i > $o).
% 36.38/6.84 thf(func_def_750, type, sK402: $i > $o).
% 36.38/6.84 thf(func_def_758, type, sK410: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_759, type, sK411: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_760, type, sK412: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_761, type, sK413: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_777, type, sK429: $i > $i > $o).
% 36.38/6.84 thf(func_def_789, type, sK441: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_800, type, sK452: $i > $i > $o).
% 36.38/6.84 thf(func_def_804, type, sK456: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_807, type, sK459: $i > $o).
% 36.38/6.84 thf(func_def_826, type, sK478: $i > $i > $o).
% 36.38/6.84 thf(func_def_827, type, sK479: $i > $i).
% 36.38/6.84 thf(func_def_828, type, sK480: $i > $i).
% 36.38/6.84 thf(func_def_829, type, sK481: ($i > $i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_830, type, sK482: $i > ($i > $i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_831, type, sK483: ($i > $i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_842, type, sK494: $i > $i).
% 36.38/6.84 thf(func_def_855, type, sK507: $i > $i > $i).
% 36.38/6.84 thf(func_def_856, type, sK508: $i > $i > $i).
% 36.38/6.84 thf(func_def_857, type, sK509: $i > $i > $i).
% 36.38/6.84 thf(func_def_858, type, sK510: $i > $i > $i).
% 36.38/6.84 thf(func_def_859, type, sK511: $i > $i > $i).
% 36.38/6.84 thf(func_def_860, type, sK512: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_861, type, sK513: $i > $i).
% 36.38/6.84 thf(func_def_862, type, sK514: $i > $i).
% 36.38/6.84 thf(func_def_863, type, sK515: $i > $i).
% 36.38/6.84 thf(func_def_864, type, sK516: $i > $i).
% 36.38/6.84 thf(func_def_865, type, sK517: $i > $i > $i).
% 36.38/6.84 thf(func_def_866, type, sK518: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_867, type, sK519: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_868, type, sK520: $i > $i > $i).
% 36.38/6.84 thf(func_def_869, type, sK521: $i > $i > $i).
% 36.38/6.84 thf(func_def_871, type, sK523: $i > $i).
% 36.38/6.84 thf(func_def_872, type, sK524: $i > $i).
% 36.38/6.84 thf(func_def_873, type, sK525: $i > $i).
% 36.38/6.84 thf(func_def_877, type, sK529: $i > $i > $i).
% 36.38/6.84 thf(func_def_887, type, sK539: $i > $i > $o).
% 36.38/6.84 thf(func_def_891, type, sK543: $i > $i > $i).
% 36.38/6.84 thf(func_def_895, type, sK547: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_896, type, sK548: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_913, type, sK565: $i > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_916, type, sK568: $i > $i > $i).
% 36.38/6.84 thf(func_def_924, type, sK576: $i > $o).
% 36.38/6.84 thf(func_def_932, type, sK584: $i > $o).
% 36.38/6.84 thf(func_def_934, type, sK586: ($i > $o) > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_935, type, sK587: ($i > $o) > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_947, type, sK599: $i > $o).
% 36.38/6.84 thf(func_def_950, type, sK602: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_951, type, sK603: $i > $o).
% 36.38/6.84 thf(func_def_952, type, sK604: $i > $i).
% 36.38/6.84 thf(func_def_968, type, sK620: $i > $o).
% 36.38/6.84 thf(func_def_971, type, sK623: $i > $o).
% 36.38/6.84 thf(func_def_974, type, sK626: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_980, type, sK632: $i > $o).
% 36.38/6.84 thf(func_def_989, type, sK641: $i > $o).
% 36.38/6.84 thf(func_def_994, type, sK646: $i > $o).
% 36.38/6.84 thf(func_def_1015, type, sK667: $i > $o).
% 36.38/6.84 thf(func_def_1026, type, sK678: $i > $o).
% 36.38/6.84 thf(func_def_1029, type, sK681: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_1030, type, sK682: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_1043, type, sK695: $i > $i > ($i > $i) > $i).
% 36.38/6.84 thf(func_def_1044, type, sK696: $i > $i).
% 36.38/6.84 thf(func_def_1048, type, sK700: ($i > $i) > $i > $i > $i).
% 36.38/6.84 thf(func_def_1051, type, sK703: $i > $i).
% 36.38/6.84 thf(func_def_1053, type, sK705: $i > $o).
% 36.38/6.84 thf(func_def_1054, type, sK706: $i > ($i > $i) > $i > $i).
% 36.38/6.84 thf(func_def_1056, type, sK708: $i > $i).
% 36.38/6.84 thf(func_def_1059, type, sK711: $i > $o).
% 36.38/6.84 thf(func_def_1087, type, sK739: $i > $i > $i).
% 36.38/6.84 thf(func_def_1105, type, sK757: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_1106, type, sK758: ($i > $o) > $i).
% 36.38/6.84 thf(func_def_1107, type, sK759: $i > $o).
% 36.38/6.84 thf(func_def_1111, type, sK763: $i > $o).
% 36.38/6.84 thf(func_def_1112, type, sK764: ($i > $o) > $i > $i > $i).
% 36.38/6.84 thf(func_def_1118, type, sK770: ($i > $o) > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_1119, type, sK771: ($i > $o) > $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_1123, type, sK775: $i > $o).
% 36.38/6.84 thf(func_def_1128, type, sK780: $i > $i).
% 36.38/6.84 thf(func_def_1131, type, sK783: $i > $i).
% 36.38/6.84 thf(func_def_1139, type, sK791: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_1143, type, sK795: $i > $i > $i > $i).
% 36.38/6.84 thf(func_def_1154, type, sK806: $i > $o).
% 36.38/6.84 thf(func_def_1156, type, sK808: ($i > $o) > $i > $i).
% 36.38/6.84 thf(func_def_1157, type, sK809: $i > $i).
% 36.38/6.84 thf(func_def_1170, type, sK822: $i > $o).
% 36.38/6.84 thf(func_def_1178, type, sK830: $i > $i > ($i > $i > $o) > $i).
% 36.38/6.84 thf(func_def_1179, type, sK831: $i > $i > $o).
% 36.38/6.84 thf(func_def_1182, type, sK834: $i > $i).
% 36.38/6.84 thf(func_def_1199, type, sK851: $i > $i > $o).
% 36.38/6.84 thf(func_def_1221, type, sK873: $i > $i).
% 36.38/6.84 thf(func_def_1225, type, sK877: $i > $o).
% 36.38/6.84 thf(func_def_1227, type, sK879: ($i > $o) > $i > $i > $i).
% 36.38/6.84 thf(func_def_1228, type, sK880: ($i > $o) > $i > $i > $i).
% 36.38/6.84 thf(func_def_1260, type, sK912: $i > $o).
% 36.38/6.84 thf(func_def_1262, type, sK914: $i > ($i > $o) > $i).
% 36.38/6.84 thf(func_def_1270, type, sK922: $i > $i > $i).
% 36.38/6.84 thf(func_def_1273, type, sK925: $i > $i > $o).
% 36.38/6.84 thf(func_def_1284, type, sK936: $i > $o).
% 36.38/6.84 thf(func_def_1287, type, sK939: $i > $i > $i).
% 36.38/6.84 thf(func_def_1288, type, sK940: $i > $i).
% 36.38/6.84 thf(func_def_1295, type, ph947: !>[X0: $tType]:(X0)).
% 36.38/6.84 thf(f6113,plain,(
% 36.38/6.84 $false),
% 36.38/6.84 inference(avatar_sat_refutation,[status(thm)],[f5717,f5930,f6077,f6110])).
% 36.38/6.84 thf(f6110,plain,(
% 36.38/6.84 spl946_52 | spl946_69),
% 36.38/6.84 inference(avatar_split_clause,[status(thm)],[f6109,f6074,f5712])).
% 36.38/6.84 thf(f5712,definition,(
% 36.38/6.84 spl946_52 <=> ! [X2 : $i] : (($true = (sK459 @ X2)) | ((in @ X2 @ sK457) != $true))),
% 36.38/6.84 introduced(definition,[new_symbols(naming,[spl946_52])],[avatar_definition])).
% 36.38/6.84 thf(f6074,definition,(
% 36.38/6.84 spl946_69 <=> ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) = $true)),
% 36.38/6.84 introduced(definition,[new_symbols(naming,[spl946_69])],[avatar_definition])).
% 36.38/6.84 thf(f6109,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((sK459 @ X0) = $true) | ((in @ X0 @ sK457) != $true)) ) | spl946_69),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f6108,f3480])).
% 36.38/6.84 thf(f3480,plain,(
% 36.38/6.84 ((breln1 @ sK458 @ sK457) = $true)),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f1984])).
% 36.38/6.84 thf(f1984,plain,(
% 36.38/6.84 (binintersectTELcontra = $true) & (woz1_4 = $true) & (setukpairinjR12 = $true) & (ksndpairEq = $true) & (setunionAx = $true) & (setOfPairsIsBReln = $true) & (ap2apEq1 = $true) & (omega0Ax = $true) & (setadjoinOr = $true) & (setOfPairsIsBReln1 = $true) & (kfstpairEq = $true) & (binintersectER = $true) & (subbreln = $true) & (setoftrueEq = $true) & (exuE3e = $true) & (powersetTE1 = $true) & (funcGraphProp1 = $true) & (singletonsuniq = $true) & (complementTE1 = $true) & (contrasubsetT3 = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (binintersectSubset1 = $true) & (doubleComplementI1 = $true) & (setext = $true) & (lam2lamEq = $true) & (singletoninpowerset = $true) & (cartprodpairmemEL = $true) & (emptysetimpfalse = $true) & (emptyinunitempty = $true) & (woz13rule1 = $true) & (binintersectSubset3 = $true) & (setadjoinIL = $true) & (ex1E1 = $true) & (iftrueProp2 = $true) & (funcImageSingleton = $true) & (singletonsubset = $true) & (notdallE = $true) & (setminusI = $true) & (descr__Cong = $true) & (emptysetE = $true) & (setminusILneg = $true) & (iffalseProp2 = $true) & (inComplementUnionImpInComplement1 = $true) & (cartprodfstin = $true) & (cartprodmempair = $true) & (cartprodpairin = $true) & (setminusT_lem = $true) & (setunionE2 = $true) & (contrasubsetT1 = $true) & (demorgan2b2 = $true) & (upairequniteq = $true) & (cartprodpairsurjEq = $true) & (cartprodsndin = $true) & (prop2setI = $true) & (contrasubsetT2 = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (omegaSAx = $true) & (omegaIndAx = $true) & (demorgan2a1 = $true) & (iftrue = $true) & (funcGraphProp2 = $true) & (complementTI1 = $true) & (subsetTI = $true) & (woz1_5 = $true) & (prop2set2propI = $true) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (ksndsingleton = $true) & (binintersectSubset4 = $true) & (nonemptyI1 = $true) & (setextsub = $true) & (exuI2 = $true) & (binunionTE = $true) & (setminusLsub = $true) & (setminusEL = $true) & (wellorderingAx = $true) & (ubforcartprodlem3 = $true) & (setukpairinjL1 = $true) & (dsetconstr__Cong = $true) & (setukpairinjL2 = $true) & (woz1_3 = $true) & (inCongP = $true) & (lamp = $true) & (singletonprop = $true) & (omega__Cong = $true) & (setextT = $true) & (binunionEcases = $true) & (powersetAx = $true) & (sepInPowerset = $true) & (funcinfuncset = $true) & (nonemptyImpWitness = $true) & (funcext = $true) & (ap2p = $true) & (iftrueProp1 = $true) & (brelnall1 = $true) & (binintersectT_lem = $true) & (binunionTILcontra = $true) & (exuI3 = $true) & (woz13rule4 = $true) & (descrp = $true) & (emptyset__Cong = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (demorgan1a = $true) & (symdiffE = $true) & (inIntersectImpInUnion2 = $true) & (woz13rule2 = $true) & (powersetI1 = $true) & (woz13rule3 = $true) & (woz1_1 = $true) & (setukpairinjR = $true) & (setunionsingleton1 = $true) & (setadjoinSub2 = $true) & (symdiffIneg2 = $true) & (emptyI = $true) & (emptysetsubset = $true) & (dpsetconstrERa = $true) & (setunionI = $true) & (symdiffI2 = $true) & (setminusSubset1 = $true) & (setadjoin__Cong = $true) & (intersectInPowersetIntersectUnions = $true) & (subsetE2 = $true) & (kpairiskpair = $true) & (lamProp = $true) & (setbeta = $true) & (binintersectI = $true) & (upairsetIL = $true) & (demorgan1 = $true) & (binintersectSubset2 = $true) & (inIntersectImpInIntersectUnions = $true) & (cartprodmempaircEq = $true) & (binunionTIRcontra = $true) & (infuncsetfunc = $true) & (setminusER = $true) & (sepSubset = $true) & (setunionE = $true) & (cartprodsndpairEq = $true) & (binintersectSubset5 = $true) & (demorgan2a = $true) & (doubleComplementEq = $true) & (kpairp = $true) & (dsetconstrI = $true) & (breln1all2 = $true) & (cartprodfstpairEq = $true) & (bs114d = $true) & (setadjoinSub = $true) & (uniqinunit = $true) & (iftrueorfalse = $true) & (eta1 = $true) & (iffalseProp1 = $true) & (demorgan2b = $true) & ((! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK458)) | ((in @ (kpair @ X3 @ X4) @ sK457) != $true) | ($true = (sK459 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ sK458) != $true)) & (((sK459 @ sK460) != $true) & ($true = (in @ sK460 @ sK457)))) & ((breln1 @ sK458 @ sK457) = $true)) & (setadjoinAx = $true) & (cartprodmempair1 = $true) & (ifp = $true) & (exu__Cong = $true) & (subsetI2 = $true) & (complementTnotintersectT = $true) & (app = $true) & (ubforcartprodlem1 = $true) & (complementSubsetComplementIntersect = $true) & (binunionT_lem = $true) & (powersetT_lem = $true) & (setminusELneg = $true) & (symdiffIneg1 = $true) & (exuE3u = $true) & (setunionsingleton2 = $true) & (powersetTI1 = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectLsub = $true) & (dpsetconstrEL2 = $true) & (beta1 = $true) & (binunionE = $true) & (complementUnionInPowersetComplement = $true) & (quantDeMorgan1 = $true) & (subsetI1 = $true) & (in__Cong = $true) & (setukpairinjL = $true) & (inIntersectImpInUnion = $true) & (binintersectRsub = $true) & (exuE1 = $true) & (vacuousDall = $true) & (quantDeMorgan4 = $true) & (binintersectTERcontra = $true) & (setukpairinjR11 = $true) & (choice2fnsingleton = $true) & (setunionsingleton = $true) & (binintersectEL = $true) & (upairset2E = $true) & (binunionLsub = $true) & (demorgan1b = $true) & (apProp = $true) & (dpsetconstrSub = $true) & (doubleComplementE1 = $true) & (binunionRsub = $true) & (woz1_2 = $true) & (inPowerset = $true) & (setextAx = $true) & (doubleComplementSub2 = $true) & (beta2 = $true) & (complementImpComplementIntersect = $true) & (eqbreln = $true) & (contraSubsetComplement = $true) & (notsubsetI = $true) & (exuEu = $true) & (setminusIRneg = $true) & (powersetE = $true) & (theeq = $true) & (cartprodpairmemER = $true) & (setminusSubset2 = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (dpsetconstrEL1 = $true) & (powerset__Cong = $true) & (ex1I2 = $true) & (kpairsurjEq = $true) & (quantDeMorgan2 = $true) & (emptyE1 = $true) & (demorgan2a2 = $true) & (funcGraphProp4 = $true) & (lam2p = $true) & (binunionTEcontra = $true) & (notequalI1 = $true) & (setukpairIR = $true) & (emptyinPowerset = $true) & (subsetemptysetimpeq = $true) & (exuE2 = $true) & (binunionIL = $true) & (foundationAx = $true) & (dpsetconstrI = $true) & (subset2powerset = $true) & (subsetRefl = $true) & (breln1SetBreln1 = $true) & (disjointsetsI1 = $true) & (eqimpsubset2 = $true) & (upairsetE = $true) & (upairsubunion = $true) & (singletoninpowunion = $true) & (woz13rule0 = $true) & (notinemptyset = $true) & (kfstsingleton = $true) & (ap2apEq2 = $true) & (notdexE = $true) & (doubleComplementSub1 = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (funcGraphProp3 = $true) & (funcextLem = $true) & (inComplementUnionImpNotIn1 = $true) & (nonemptyE1 = $true) & (setminusERneg = $true) & (dsetconstrEL = $true) & (exuI1 = $true) & (powersetE1 = $true) & (notequalI2 = $true) & (demorgan2 = $true) & (complementTcontraSubset = $true) & (setunion__Cong = $true) & (setukpairinjR1 = $true) & (subPowSU = $true) & (ubforcartprodlem2 = $true) & (upairset2IR = $true) & (theprop = $true) & (emptysetAx = $true) & (eqinunit = $true) & (subsetE = $true) & (emptyInPowerset = $true) & (iffalse = $true) & (setukpairIL = $true) & (complementT_lem = $true) & (setadjoinE = $true) & (ex1E2 = $true) & (powersetsubset = $true) & (contrasubsetT = $true) & (funcext2 = $true) & (ex1I = $true) & (upairinpowunion = $true) & (setukpairinjR2 = $true) & (notinsingleton = $true) & (symdiffI1 = $true) & (brelnall2 = $true) & (eta2 = $true) & (powersetI = $true) & (ifSingleton = $true) & (secondinupair = $true) & (subsetTrans = $true)),
% 36.38/6.84 inference(skolemisation,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460])],[f1135,f1983,f1982,f1981])).
% 36.38/6.84 thf(f1981,plain,(
% 36.38/6.84 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true = (X2 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ X1) != $true)) & ? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X0) = $true))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i > $o] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK458)) | ((in @ (kpair @ X3 @ X4) @ sK457) != $true) | ($true = (X2 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ sK458) != $true)) & ? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ sK457) = $true))) & ((breln1 @ sK458 @ sK457) = $true))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f1982,plain,(
% 36.38/6.84 ? [X2 : $i > $o] : (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK458)) | ((in @ (kpair @ X3 @ X4) @ sK457) != $true) | ($true = (X2 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ sK458) != $true)) & ? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ sK457) = $true))) => (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK458)) | ((in @ (kpair @ X3 @ X4) @ sK457) != $true) | ($true = (sK459 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ sK458) != $true)) & ? [X5 : $i] : (((sK459 @ X5) != $true) & ((in @ X5 @ sK457) = $true)))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f1983,plain,(
% 36.38/6.84 ? [X5 : $i] : (((sK459 @ X5) != $true) & ((in @ X5 @ sK457) = $true)) => (((sK459 @ sK460) != $true) & ($true = (in @ sK460 @ sK457)))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f1135,plain,(
% 36.38/6.84 (binintersectTELcontra = $true) & (woz1_4 = $true) & (setukpairinjR12 = $true) & (ksndpairEq = $true) & (setunionAx = $true) & (setOfPairsIsBReln = $true) & (ap2apEq1 = $true) & (omega0Ax = $true) & (setadjoinOr = $true) & (setOfPairsIsBReln1 = $true) & (kfstpairEq = $true) & (binintersectER = $true) & (subbreln = $true) & (setoftrueEq = $true) & (exuE3e = $true) & (powersetTE1 = $true) & (funcGraphProp1 = $true) & (singletonsuniq = $true) & (complementTE1 = $true) & (contrasubsetT3 = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (binintersectSubset1 = $true) & (doubleComplementI1 = $true) & (setext = $true) & (lam2lamEq = $true) & (singletoninpowerset = $true) & (cartprodpairmemEL = $true) & (emptysetimpfalse = $true) & (emptyinunitempty = $true) & (woz13rule1 = $true) & (binintersectSubset3 = $true) & (setadjoinIL = $true) & (ex1E1 = $true) & (iftrueProp2 = $true) & (funcImageSingleton = $true) & (singletonsubset = $true) & (notdallE = $true) & (setminusI = $true) & (descr__Cong = $true) & (emptysetE = $true) & (setminusILneg = $true) & (iffalseProp2 = $true) & (inComplementUnionImpInComplement1 = $true) & (cartprodfstin = $true) & (cartprodmempair = $true) & (cartprodpairin = $true) & (setminusT_lem = $true) & (setunionE2 = $true) & (contrasubsetT1 = $true) & (demorgan2b2 = $true) & (upairequniteq = $true) & (cartprodpairsurjEq = $true) & (cartprodsndin = $true) & (prop2setI = $true) & (contrasubsetT2 = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (omegaSAx = $true) & (omegaIndAx = $true) & (demorgan2a1 = $true) & (iftrue = $true) & (funcGraphProp2 = $true) & (complementTI1 = $true) & (subsetTI = $true) & (woz1_5 = $true) & (prop2set2propI = $true) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (ksndsingleton = $true) & (binintersectSubset4 = $true) & (nonemptyI1 = $true) & (setextsub = $true) & (exuI2 = $true) & (binunionTE = $true) & (setminusLsub = $true) & (setminusEL = $true) & (wellorderingAx = $true) & (ubforcartprodlem3 = $true) & (setukpairinjL1 = $true) & (dsetconstr__Cong = $true) & (setukpairinjL2 = $true) & (woz1_3 = $true) & (inCongP = $true) & (lamp = $true) & (singletonprop = $true) & (omega__Cong = $true) & (setextT = $true) & (binunionEcases = $true) & (powersetAx = $true) & (sepInPowerset = $true) & (funcinfuncset = $true) & (nonemptyImpWitness = $true) & (funcext = $true) & (ap2p = $true) & (iftrueProp1 = $true) & (brelnall1 = $true) & (binintersectT_lem = $true) & (binunionTILcontra = $true) & (exuI3 = $true) & (woz13rule4 = $true) & (descrp = $true) & (emptyset__Cong = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (demorgan1a = $true) & (symdiffE = $true) & (inIntersectImpInUnion2 = $true) & (woz13rule2 = $true) & (powersetI1 = $true) & (woz13rule3 = $true) & (woz1_1 = $true) & (setukpairinjR = $true) & (setunionsingleton1 = $true) & (setadjoinSub2 = $true) & (symdiffIneg2 = $true) & (emptyI = $true) & (emptysetsubset = $true) & (dpsetconstrERa = $true) & (setunionI = $true) & (symdiffI2 = $true) & (setminusSubset1 = $true) & (setadjoin__Cong = $true) & (intersectInPowersetIntersectUnions = $true) & (subsetE2 = $true) & (kpairiskpair = $true) & (lamProp = $true) & (setbeta = $true) & (binintersectI = $true) & (upairsetIL = $true) & (demorgan1 = $true) & (binintersectSubset2 = $true) & (inIntersectImpInIntersectUnions = $true) & (cartprodmempaircEq = $true) & (binunionTIRcontra = $true) & (infuncsetfunc = $true) & (setminusER = $true) & (sepSubset = $true) & (setunionE = $true) & (cartprodsndpairEq = $true) & (binintersectSubset5 = $true) & (demorgan2a = $true) & (doubleComplementEq = $true) & (kpairp = $true) & (dsetconstrI = $true) & (breln1all2 = $true) & (cartprodfstpairEq = $true) & (bs114d = $true) & (setadjoinSub = $true) & (uniqinunit = $true) & (iftrueorfalse = $true) & (eta1 = $true) & (iffalseProp1 = $true) & (demorgan2b = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X0) != $true) | ($true = (X2 @ (kpair @ X3 @ X4)))) | ((in @ X3 @ X1) != $true)) & ? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X0) = $true))) & ($true = (breln1 @ X1 @ X0))) & (setadjoinAx = $true) & (cartprodmempair1 = $true) & (ifp = $true) & (exu__Cong = $true) & (subsetI2 = $true) & (complementTnotintersectT = $true) & (app = $true) & (ubforcartprodlem1 = $true) & (complementSubsetComplementIntersect = $true) & (binunionT_lem = $true) & (powersetT_lem = $true) & (setminusELneg = $true) & (symdiffIneg1 = $true) & (exuE3u = $true) & (setunionsingleton2 = $true) & (powersetTI1 = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectLsub = $true) & (dpsetconstrEL2 = $true) & (beta1 = $true) & (binunionE = $true) & (complementUnionInPowersetComplement = $true) & (quantDeMorgan1 = $true) & (subsetI1 = $true) & (in__Cong = $true) & (setukpairinjL = $true) & (inIntersectImpInUnion = $true) & (binintersectRsub = $true) & (exuE1 = $true) & (vacuousDall = $true) & (quantDeMorgan4 = $true) & (binintersectTERcontra = $true) & (setukpairinjR11 = $true) & (choice2fnsingleton = $true) & (setunionsingleton = $true) & (binintersectEL = $true) & (upairset2E = $true) & (binunionLsub = $true) & (demorgan1b = $true) & (apProp = $true) & (dpsetconstrSub = $true) & (doubleComplementE1 = $true) & (binunionRsub = $true) & (woz1_2 = $true) & (inPowerset = $true) & (setextAx = $true) & (doubleComplementSub2 = $true) & (beta2 = $true) & (complementImpComplementIntersect = $true) & (eqbreln = $true) & (contraSubsetComplement = $true) & (notsubsetI = $true) & (exuEu = $true) & (setminusIRneg = $true) & (powersetE = $true) & (theeq = $true) & (cartprodpairmemER = $true) & (setminusSubset2 = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (dpsetconstrEL1 = $true) & (powerset__Cong = $true) & (ex1I2 = $true) & (kpairsurjEq = $true) & (quantDeMorgan2 = $true) & (emptyE1 = $true) & (demorgan2a2 = $true) & (funcGraphProp4 = $true) & (lam2p = $true) & (binunionTEcontra = $true) & (notequalI1 = $true) & (setukpairIR = $true) & (emptyinPowerset = $true) & (subsetemptysetimpeq = $true) & (exuE2 = $true) & (binunionIL = $true) & (foundationAx = $true) & (dpsetconstrI = $true) & (subset2powerset = $true) & (subsetRefl = $true) & (breln1SetBreln1 = $true) & (disjointsetsI1 = $true) & (eqimpsubset2 = $true) & (upairsetE = $true) & (upairsubunion = $true) & (singletoninpowunion = $true) & (woz13rule0 = $true) & (notinemptyset = $true) & (kfstsingleton = $true) & (ap2apEq2 = $true) & (notdexE = $true) & (doubleComplementSub1 = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (funcGraphProp3 = $true) & (funcextLem = $true) & (inComplementUnionImpNotIn1 = $true) & (nonemptyE1 = $true) & (setminusERneg = $true) & (dsetconstrEL = $true) & (exuI1 = $true) & (powersetE1 = $true) & (notequalI2 = $true) & (demorgan2 = $true) & (complementTcontraSubset = $true) & (setunion__Cong = $true) & (setukpairinjR1 = $true) & (subPowSU = $true) & (ubforcartprodlem2 = $true) & (upairset2IR = $true) & (theprop = $true) & (emptysetAx = $true) & (eqinunit = $true) & (subsetE = $true) & (emptyInPowerset = $true) & (iffalse = $true) & (setukpairIL = $true) & (complementT_lem = $true) & (setadjoinE = $true) & (ex1E2 = $true) & (powersetsubset = $true) & (contrasubsetT = $true) & (funcext2 = $true) & (ex1I = $true) & (upairinpowunion = $true) & (setukpairinjR2 = $true) & (notinsingleton = $true) & (symdiffI1 = $true) & (brelnall2 = $true) & (eta2 = $true) & (powersetI = $true) & (ifSingleton = $true) & (secondinupair = $true) & (subsetTrans = $true)),
% 36.38/6.84 inference(flattening,[status(thm)],[f1134])).
% 36.38/6.84 thf(f1134,plain,(
% 36.38/6.84 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X0) = $true)) & ! [X3 : $i] : (! [X4 : $i] : ((($true = (X2 @ (kpair @ X3 @ X4))) | ((in @ (kpair @ X3 @ X4) @ X0) != $true)) | ((in @ X4 @ X1) != $true)) | ((in @ X3 @ X1) != $true))) & ($true = (breln1 @ X1 @ X0))) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 36.38/6.84 inference(ennf_transformation,[status(thm)],[f833])).
% 36.38/6.84 thf(f833,plain,(
% 36.38/6.84 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i > $o] : (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ X0) = $true) => ($true = (X2 @ (kpair @ X3 @ X4)))))) => ! [X5 : $i] : (((in @ X5 @ X0) = $true) => ($true = (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.38/6.84 inference(fool_elimination,[status(thm)],[f832])).
% 36.38/6.84 thf(f832,plain,(
% 36.38/6.84 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i > $o] : (! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X0) => (X2 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.38/6.84 inference(rectify,[status(thm)],[f294])).
% 36.38/6.84 thf(f294,negated_conjecture,(
% 36.38/6.84 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X13) => (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.38/6.84 inference(negated_conjecture,[status(cth)],[f293])).
% 36.38/6.84 thf(f293,conjecture,(
% 36.38/6.84 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X13) => (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.38/6.84 file('/export/starexec/sandbox/tmp/tmp.1jLE4W7LvF/DTF2THF_3370.p',breln1all1)).
% 36.38/6.84 thf(f6108,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((breln1 @ sK458 @ sK457) != $true) | ((sK459 @ X0) = $true) | ((in @ X0 @ sK457) != $true)) ) | spl946_69),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f6104,f3492])).
% 36.38/6.84 thf(f3492,plain,(
% 36.38/6.84 (breln1all2 = $true)),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f1984])).
% 36.38/6.84 thf(f6104,plain,(
% 36.38/6.84 ( ! [X0 : $i] : ((breln1all2 != $true) | ((sK459 @ X0) = $true) | ((breln1 @ sK458 @ sK457) != $true) | ((in @ X0 @ sK457) != $true)) ) | spl946_69),
% 36.38/6.84 inference(trivial_inequality_removal,[status(thm)],[f6101])).
% 36.38/6.84 thf(f6101,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((in @ X0 @ sK457) != $true) | ($true != $true) | ((breln1 @ sK458 @ sK457) != $true) | ((sK459 @ X0) = $true) | (breln1all2 != $true)) ) | spl946_69),
% 36.38/6.84 inference(superposition,[status(thm)],[f6076,f4220])).
% 36.38/6.84 thf(f4220,plain,(
% 36.38/6.84 ( ! [X8 : $i > $o,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (sK879 @ X8 @ X7 @ X6) @ X6)) | ($true != (breln1 @ X6 @ X7)) | ((in @ X9 @ X7) != $true) | (breln1all2 != $true) | ($true = (X8 @ X9))) )),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f2653])).
% 36.38/6.84 thf(f2653,plain,(
% 36.38/6.84 ((breln1all2 = $true) | (((($true != (sK877 @ sK878)) & ((in @ sK878 @ sK876) = $true)) & ! [X4 : $i] : (((in @ X4 @ sK875) != $true) | ! [X5 : $i] : (((in @ X5 @ sK875) != $true) | ((sK877 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK876))))) & ((breln1 @ sK875 @ sK876) = $true))) & (! [X6 : $i,X7 : $i] : (! [X8 : $i > $o] : (! [X9 : $i] : (($true = (X8 @ X9)) | ((in @ X9 @ X7) != $true)) | (($true = (in @ (sK879 @ X8 @ X7 @ X6) @ X6)) & (((in @ (sK880 @ X8 @ X7 @ X6) @ X6) = $true) & ($true != (X8 @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)))) & ((in @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)) @ X7) = $true)))) | ($true != (breln1 @ X6 @ X7))) | (breln1all2 != $true))),
% 36.38/6.84 inference(skolemisation,[status(esa),new_symbols(skolem,[sK875,sK876,sK877,sK878,sK879,sK880])],[f2647,f2652,f2651,f2650,f2649,f2648])).
% 36.38/6.84 thf(f2648,plain,(
% 36.38/6.84 ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ((in @ X3 @ X1) = $true)) & ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ! [X5 : $i] : (((in @ X5 @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)))) & ((breln1 @ X0 @ X1) = $true)) => (? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ sK876))) & ! [X4 : $i] : (((in @ X4 @ sK875) != $true) | ! [X5 : $i] : (((in @ X5 @ sK875) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK876))))) & ((breln1 @ sK875 @ sK876) = $true))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f2649,plain,(
% 36.38/6.84 ? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ($true = (in @ X3 @ sK876))) & ! [X4 : $i] : (((in @ X4 @ sK875) != $true) | ! [X5 : $i] : (((in @ X5 @ sK875) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ($true != (in @ (kpair @ X4 @ X5) @ sK876))))) => (? [X3 : $i] : (((sK877 @ X3) != $true) & ($true = (in @ X3 @ sK876))) & ! [X4 : $i] : (((in @ X4 @ sK875) != $true) | ! [X5 : $i] : (((in @ X5 @ sK875) != $true) | ((sK877 @ (kpair @ X4 @ X5)) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK876)))))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f2650,plain,(
% 36.38/6.84 ? [X3 : $i] : (((sK877 @ X3) != $true) & ($true = (in @ X3 @ sK876))) => (($true != (sK877 @ sK878)) & ((in @ sK878 @ sK876) = $true))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f2651,plain,(
% 36.38/6.84 ! [X6 : $i,X7 : $i,X8 : $i > $o] : (? [X10 : $i] : (($true = (in @ X10 @ X6)) & ? [X11 : $i] : (((in @ X11 @ X6) = $true) & ($true != (X8 @ (kpair @ X10 @ X11))) & ($true = (in @ (kpair @ X10 @ X11) @ X7)))) => (($true = (in @ (sK879 @ X8 @ X7 @ X6) @ X6)) & ? [X11 : $i] : (((in @ X11 @ X6) = $true) & ($true != (X8 @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ X11))) & ((in @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ X11) @ X7) = $true))))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f2652,plain,(
% 36.38/6.84 ! [X6 : $i,X7 : $i,X8 : $i > $o] : (? [X11 : $i] : (((in @ X11 @ X6) = $true) & ($true != (X8 @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ X11))) & ((in @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ X11) @ X7) = $true)) => (((in @ (sK880 @ X8 @ X7 @ X6) @ X6) = $true) & ($true != (X8 @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)))) & ((in @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)) @ X7) = $true)))),
% 36.38/6.84 introduced(definition,[],[choice_axiom])).
% 36.38/6.84 thf(f2647,plain,(
% 36.38/6.84 ((breln1all2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X3 : $i] : (($true != (X2 @ X3)) & ((in @ X3 @ X1) = $true)) & ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ! [X5 : $i] : (((in @ X5 @ X0) != $true) | ($true = (X2 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X1) != $true)))) & ((breln1 @ X0 @ X1) = $true))) & (! [X6 : $i,X7 : $i] : (! [X8 : $i > $o] : (! [X9 : $i] : (($true = (X8 @ X9)) | ((in @ X9 @ X7) != $true)) | ? [X10 : $i] : (($true = (in @ X10 @ X6)) & ? [X11 : $i] : (((in @ X11 @ X6) = $true) & ($true != (X8 @ (kpair @ X10 @ X11))) & ($true = (in @ (kpair @ X10 @ X11) @ X7))))) | ($true != (breln1 @ X6 @ X7))) | (breln1all2 != $true))),
% 36.38/6.84 inference(rectify,[status(thm)],[f2646])).
% 36.38/6.84 thf(f2646,plain,(
% 36.38/6.84 ((breln1all2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i > $o] : (? [X5 : $i] : (($true != (X2 @ X5)) & ((in @ X5 @ X1) = $true)) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ($true = (X2 @ (kpair @ X3 @ X4))) | ((in @ (kpair @ X3 @ X4) @ X1) != $true)))) & ((breln1 @ X0 @ X1) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i > $o] : (! [X5 : $i] : (($true = (X2 @ X5)) | ((in @ X5 @ X1) != $true)) | ? [X3 : $i] : (($true = (in @ X3 @ X0)) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ($true != (X2 @ (kpair @ X3 @ X4))) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)))) | ((breln1 @ X0 @ X1) != $true)) | (breln1all2 != $true))),
% 36.38/6.84 inference(nnf_transformation,[status(thm)],[f1226])).
% 36.38/6.84 thf(f1226,plain,(
% 36.38/6.84 (breln1all2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i > $o] : (! [X5 : $i] : (($true = (X2 @ X5)) | ((in @ X5 @ X1) != $true)) | ? [X3 : $i] : (($true = (in @ X3 @ X0)) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ($true != (X2 @ (kpair @ X3 @ X4))) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)))) | ((breln1 @ X0 @ X1) != $true))),
% 36.38/6.84 inference(flattening,[status(thm)],[f1225])).
% 36.38/6.84 thf(f1225,plain,(
% 36.38/6.84 (breln1all2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i > $o] : (! [X5 : $i] : (($true = (X2 @ X5)) | ((in @ X5 @ X1) != $true)) | ? [X3 : $i] : (? [X4 : $i] : ((($true != (X2 @ (kpair @ X3 @ X4))) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0)))) | ((breln1 @ X0 @ X1) != $true))),
% 36.38/6.84 inference(ennf_transformation,[status(thm)],[f652])).
% 36.38/6.84 thf(f652,plain,(
% 36.38/6.84 (breln1all2 = $true) <=> ! [X0 : $i,X1 : $i] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i > $o] : (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ! [X4 : $i] : (((in @ X4 @ X0) = $true) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ($true = (X2 @ (kpair @ X3 @ X4)))))) => ! [X5 : $i] : (((in @ X5 @ X1) = $true) => ($true = (X2 @ X5)))))),
% 36.38/6.84 inference(fool_elimination,[status(thm)],[f651])).
% 36.38/6.84 thf(f651,plain,(
% 36.38/6.84 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i > $o] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))) = breln1all2)),
% 36.38/6.84 inference(rectify,[status(thm)],[f289])).
% 36.38/6.84 thf(f289,axiom,(
% 36.38/6.84 (! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1 : $i] : ((in @ X1 @ X13) => (X0 @ X1)))) = breln1all2)),
% 36.38/6.84 file('/export/starexec/sandbox/tmp/tmp.1jLE4W7LvF/DTF2THF_3370.p',breln1all2)).
% 36.38/6.84 thf(f6076,plain,(
% 36.38/6.84 ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true) | spl946_69),
% 36.38/6.84 inference(avatar_component_clause,[status(thm)],[f6074])).
% 36.38/6.84 thf(f6077,plain,(
% 36.38/6.84 ~spl946_69 | spl946_52 | ~spl946_53),
% 36.38/6.84 inference(avatar_split_clause,[status(thm)],[f6072,f5715,f5712,f6074])).
% 36.38/6.84 thf(f5715,definition,(
% 36.38/6.84 spl946_53 <=> ! [X0 : $i] : (((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true))),
% 36.38/6.84 introduced(definition,[new_symbols(naming,[spl946_53])],[avatar_definition])).
% 36.38/6.84 thf(f6072,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((sK459 @ X0) = $true) | ((in @ X0 @ sK457) != $true) | ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f6071,f3480])).
% 36.38/6.84 thf(f6071,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((in @ X0 @ sK457) != $true) | ((breln1 @ sK458 @ sK457) != $true) | ((sK459 @ X0) = $true) | ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f6063,f3492])).
% 36.38/6.84 thf(f6063,plain,(
% 36.38/6.84 ( ! [X0 : $i] : ((breln1all2 != $true) | ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true) | ((sK459 @ X0) = $true) | ((in @ X0 @ sK457) != $true) | ((breln1 @ sK458 @ sK457) != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(trivial_inequality_removal,[status(thm)],[f6062])).
% 36.38/6.84 thf(f6062,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((breln1 @ sK458 @ sK457) != $true) | ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true) | ((in @ X0 @ sK457) != $true) | ((sK459 @ X0) = $true) | ($true != $true) | (breln1all2 != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(duplicate_literal_removal,[status(thm)],[f6061])).
% 36.38/6.84 thf(f6061,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((breln1 @ sK458 @ sK457) != $true) | ((in @ X0 @ sK457) != $true) | ($true != $true) | ((in @ (sK879 @ sK459 @ sK457 @ sK458) @ sK458) != $true) | ((sK459 @ X0) = $true) | (breln1all2 != $true) | ((breln1 @ sK458 @ sK457) != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(superposition,[status(thm)],[f5716,f4219])).
% 36.38/6.84 thf(f4219,plain,(
% 36.38/6.84 ( ! [X8 : $i > $o,X6 : $i,X9 : $i,X7 : $i] : (((in @ (sK880 @ X8 @ X7 @ X6) @ X6) = $true) | ($true = (X8 @ X9)) | (breln1all2 != $true) | ((in @ X9 @ X7) != $true) | ($true != (breln1 @ X6 @ X7))) )),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f2653])).
% 36.38/6.84 thf(f5716,plain,(
% 36.38/6.84 ( ! [X0 : $i] : (((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true)) ) | ~spl946_53),
% 36.38/6.84 inference(avatar_component_clause,[status(thm)],[f5715])).
% 36.38/6.84 thf(f5930,plain,(
% 36.38/6.84 ~spl946_52),
% 36.38/6.84 inference(avatar_contradiction_clause,[status(thm)],[f5929])).
% 36.38/6.84 thf(f5929,plain,(
% 36.38/6.84 $false | ~spl946_52),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f5923,f3482])).
% 36.38/6.84 thf(f3482,plain,(
% 36.38/6.84 ((sK459 @ sK460) != $true)),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f1984])).
% 36.38/6.84 thf(f5923,plain,(
% 36.38/6.84 ((sK459 @ sK460) = $true) | ~spl946_52),
% 36.38/6.84 inference(trivial_inequality_removal,[status(thm)],[f5742])).
% 36.38/6.84 thf(f5742,plain,(
% 36.38/6.84 ($true != $true) | ((sK459 @ sK460) = $true) | ~spl946_52),
% 36.38/6.84 inference(superposition,[status(thm)],[f5713,f3481])).
% 36.38/6.84 thf(f3481,plain,(
% 36.38/6.84 ($true = (in @ sK460 @ sK457))),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f1984])).
% 36.38/6.84 thf(f5713,plain,(
% 36.38/6.84 ( ! [X2 : $i] : (((in @ X2 @ sK457) != $true) | ($true = (sK459 @ X2))) ) | ~spl946_52),
% 36.38/6.84 inference(avatar_component_clause,[status(thm)],[f5712])).
% 36.38/6.84 thf(f5717,plain,(
% 36.38/6.84 spl946_52 | spl946_53 | spl946_52),
% 36.38/6.84 inference(avatar_split_clause,[status(thm)],[f5710,f5712,f5715,f5712])).
% 36.38/6.84 thf(f5710,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sK459 @ X2)) | ($true != (in @ X1 @ sK457)) | ((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ($true = (sK459 @ X1)) | ((in @ X2 @ sK457) != $true)) )),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f5709,f3492])).
% 36.38/6.84 thf(f5709,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sK459 @ X1)) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ($true = (sK459 @ X2)) | ((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true) | ((in @ X2 @ sK457) != $true) | (breln1all2 != $true) | ($true != (in @ X1 @ sK457))) )),
% 36.38/6.84 inference(trivial_inequality_removal,[status(thm)],[f5708])).
% 36.38/6.84 thf(f5708,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ sK457) != $true) | ((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true) | ($true = (sK459 @ X1)) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ($true != (in @ X1 @ sK457)) | (breln1all2 != $true) | ($true != $true) | ($true = (sK459 @ X2))) )),
% 36.38/6.84 inference(duplicate_literal_removal,[status(thm)],[f5705])).
% 36.38/6.84 thf(f5705,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sK459 @ X1)) | (breln1all2 != $true) | ($true != $true) | ((in @ X2 @ sK457) != $true) | ((in @ (sK880 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true) | ($true = (sK459 @ X2)) | ((in @ (sK879 @ sK459 @ sK457 @ X0) @ sK458) != $true) | ((breln1 @ X0 @ sK457) != $true) | ($true != (in @ X1 @ sK457))) )),
% 36.38/6.84 inference(superposition,[status(thm)],[f4218,f4559])).
% 36.38/6.84 thf(f4559,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK459 @ (kpair @ (sK879 @ X0 @ sK457 @ X1) @ (sK880 @ X0 @ sK457 @ X1)))) | ($true != (breln1 @ X1 @ sK457)) | ((X0 @ X2) = $true) | ((in @ X2 @ sK457) != $true) | ($true != (in @ (sK880 @ X0 @ sK457 @ X1) @ sK458)) | ((in @ (sK879 @ X0 @ sK457 @ X1) @ sK458) != $true)) )),
% 36.38/6.84 inference(subsumption_resolution,[status(thm)],[f4529,f3492])).
% 36.38/6.84 thf(f4529,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ($true != (breln1 @ X1 @ sK457)) | ((in @ (sK879 @ X0 @ sK457 @ X1) @ sK458) != $true) | ((in @ X2 @ sK457) != $true) | ($true = (sK459 @ (kpair @ (sK879 @ X0 @ sK457 @ X1) @ (sK880 @ X0 @ sK457 @ X1)))) | ($true != (in @ (sK880 @ X0 @ sK457 @ X1) @ sK458)) | (breln1all2 != $true)) )),
% 36.38/6.84 inference(trivial_inequality_removal,[status(thm)],[f4519])).
% 36.38/6.84 thf(f4519,plain,(
% 36.38/6.84 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != $true) | (breln1all2 != $true) | ((in @ X2 @ sK457) != $true) | ((X0 @ X2) = $true) | ($true != (breln1 @ X1 @ sK457)) | ((in @ (sK879 @ X0 @ sK457 @ X1) @ sK458) != $true) | ($true = (sK459 @ (kpair @ (sK879 @ X0 @ sK457 @ X1) @ (sK880 @ X0 @ sK457 @ X1)))) | ($true != (in @ (sK880 @ X0 @ sK457 @ X1) @ sK458))) )),
% 36.38/6.84 inference(superposition,[status(thm)],[f3483,f4217])).
% 36.38/6.84 thf(f4217,plain,(
% 36.38/6.84 ( ! [X8 : $i > $o,X6 : $i,X9 : $i,X7 : $i] : (((in @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)) @ X7) = $true) | ((in @ X9 @ X7) != $true) | ($true != (breln1 @ X6 @ X7)) | (breln1all2 != $true) | ($true = (X8 @ X9))) )),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f2653])).
% 36.38/6.84 thf(f3483,plain,(
% 36.38/6.84 ( ! [X3 : $i,X4 : $i] : (((in @ (kpair @ X3 @ X4) @ sK457) != $true) | ((in @ X3 @ sK458) != $true) | ($true = (sK459 @ (kpair @ X3 @ X4))) | ($true != (in @ X4 @ sK458))) )),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f1984])).
% 36.38/6.84 thf(f4218,plain,(
% 36.38/6.84 ( ! [X8 : $i > $o,X6 : $i,X9 : $i,X7 : $i] : (($true != (X8 @ (kpair @ (sK879 @ X8 @ X7 @ X6) @ (sK880 @ X8 @ X7 @ X6)))) | (breln1all2 != $true) | ($true = (X8 @ X9)) | ((in @ X9 @ X7) != $true) | ($true != (breln1 @ X6 @ X7))) )),
% 36.38/6.84 inference(cnf_transformation,[status(thm)],[f2653])).
% 36.38/6.84 % SZS output end Proof for DTF2THF_3370
% 36.38/6.84 % (3662)------------------------------
% 36.38/6.84 % (3662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.38/6.84 % (3662)Termination reason: Refutation
% 36.38/6.84
% 36.38/6.84 % (3662)Memory used [KB]: 12920
% 36.38/6.84 % (3662)Time elapsed: 0.619 s
% 36.38/6.84 % (3662)Instructions burned: 1228 (million)
% 36.38/6.84 % (3662)------------------------------
% 36.38/6.84 % (3662)------------------------------
% 36.38/6.84 % (3522)Success in time 4.897 s
%------------------------------------------------------------------------------