%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU802^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:37:19 AM UTC 2026
% Result : Theorem 40.97s 7.39s
% Output : Refutation 40.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 4995 (1336 equ; 0 cnn)
% Maximal formula atoms : 320 ( 156 avg)
% Number of connectives : 2513 ( 28 ~; 17 |; 967 &; 218 @)
% ( 2 <=>;1281 =>; 0 <=; 0 <~>)
% Maximal formula depth : 327 ( 74 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 557 ( 554 usr; 325 con; 0-6 aty)
% Number of variables : 93 ( 30 ^; 45 !; 18 ?; 93 :)
% 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_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_364,type,
injective: $i > $i > $i > $o ).
thf(func_def_365,type,
injFuncSet: $i > $i > $i ).
thf(func_def_369,type,
surjective: $i > $i > $i > $o ).
thf(func_def_370,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_388,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_389,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_390,type,
sP2: $i > $i > $i > $i > $o ).
thf(func_def_393,type,
sP5: $i > $i > $o ).
thf(func_def_394,type,
sP6: $i > $o ).
thf(func_def_395,type,
sP7: $i > $i > $o ).
thf(func_def_396,type,
sP8: $i > $i > $o ).
thf(func_def_399,type,
sP11: $i > $i > $i > $o ).
thf(func_def_404,type,
sP16: $o > $i > $i > $i > $o ).
thf(func_def_406,type,
sP18: $i > $i > $i > $o ).
thf(func_def_413,type,
sK25: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_414,type,
sK26: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_418,type,
sK30: $i > $o ).
thf(func_def_433,type,
sK45: $i > $i > $o ).
thf(func_def_444,type,
sK56: $i > $o ).
thf(func_def_446,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_447,type,
sK59: $i > ( $i > $o ) > $i ).
thf(func_def_448,type,
sK60: $i > $o ).
thf(func_def_460,type,
sK72: $i > $o ).
thf(func_def_462,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_465,type,
sK77: $i > $o ).
thf(func_def_466,type,
sK78: ( $i > $o ) > $i ).
thf(func_def_471,type,
sK83: $i > $i > $i ).
thf(func_def_500,type,
sK112: $i > $i > $i > $i > $i ).
thf(func_def_501,type,
sK113: $i > $i > $i > $i > $i ).
thf(func_def_502,type,
sK114: $i > $i > $i > $i > $i ).
thf(func_def_503,type,
sK115: $i > $i > $i > $i > $i ).
thf(func_def_514,type,
sK126: $i > $i ).
thf(func_def_515,type,
sK127: ( $i > $i ) > $i > $i > $i ).
thf(func_def_522,type,
sK134: $i > $o ).
thf(func_def_524,type,
sK136: $i > $i > $i > $i ).
thf(func_def_525,type,
sK137: $i > $i > $i > $i ).
thf(func_def_555,type,
sK167: $i > $i > $o ).
thf(func_def_574,type,
sK186: $i > $o ).
thf(func_def_580,type,
sK192: $i > $i > $i > $i ).
thf(func_def_626,type,
sK238: $i > $i ).
thf(func_def_627,type,
sK239: $i > $i ).
thf(func_def_631,type,
sK243: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_632,type,
sK244: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_636,type,
sK248: $i > $o ).
thf(func_def_644,type,
sK256: $i > $i > $o ).
thf(func_def_658,type,
sK270: $i > $o ).
thf(func_def_660,type,
sK272: ( $i > $o ) > $i > $i > $i ).
thf(func_def_661,type,
sK273: ( $i > $o ) > $i > $i > $i ).
thf(func_def_683,type,
sK295: $i > $i ).
thf(func_def_690,type,
sK302: $i > $i > $o ).
thf(func_def_702,type,
sK314: $i > ( $i > $o ) > $i ).
thf(func_def_703,type,
sK315: $i > $o ).
thf(func_def_707,type,
sK319: $i > $o ).
thf(func_def_717,type,
sK329: $i > $i > $i ).
thf(func_def_720,type,
sK332: ( $i > $i ) > $i > $i ).
thf(func_def_721,type,
sK333: $i > ( $i > $i ) > $i > $i ).
thf(func_def_723,type,
sK335: $i > $i ).
thf(func_def_724,type,
sK336: $i > $i ).
thf(func_def_725,type,
sK337: $i > $i ).
thf(func_def_729,type,
sK341: $i > $i > $i > $i > $i ).
thf(func_def_734,type,
sK346: $i > $i > $i ).
thf(func_def_735,type,
sK347: $i > $i > $i ).
thf(func_def_736,type,
sK348: $i > $i > $i ).
thf(func_def_737,type,
sK349: $i > $i > $i ).
thf(func_def_738,type,
sK350: $i > $i > $i ).
thf(func_def_739,type,
sK351: $i > $i > $i > $i ).
thf(func_def_740,type,
sK352: $i > $i ).
thf(func_def_741,type,
sK353: $i > $i ).
thf(func_def_742,type,
sK354: $i > $i ).
thf(func_def_743,type,
sK355: $i > $i ).
thf(func_def_744,type,
sK356: $i > $i > $i > $i ).
thf(func_def_745,type,
sK357: $i > $i > $i > $i ).
thf(func_def_746,type,
sK358: $i > $i > $i ).
thf(func_def_747,type,
sK359: $i > $i > $i ).
thf(func_def_748,type,
sK360: $i > $i > $i ).
thf(func_def_750,type,
sK362: $i > $i ).
thf(func_def_751,type,
sK363: $i > $i ).
thf(func_def_752,type,
sK364: $i > $i ).
thf(func_def_769,type,
sK381: $i > $i > $i ).
thf(func_def_779,type,
sK391: $i > $i ).
thf(func_def_793,type,
sK405: $i > $o ).
thf(func_def_798,type,
sK410: $i > $o ).
thf(func_def_823,type,
sK435: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_824,type,
sK436: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_825,type,
sK437: $i > $o ).
thf(func_def_826,type,
sK438: $i > $o ).
thf(func_def_831,type,
sK443: $i > $o ).
thf(func_def_837,type,
sK449: $i > $i ).
thf(func_def_850,type,
sK462: $i > $i > $o ).
thf(func_def_852,type,
sK464: $i > $i ).
thf(func_def_853,type,
sK465: $i > $i ).
thf(func_def_854,type,
sK466: $i > ( $i > $i > $o ) > $i ).
thf(func_def_855,type,
sK467: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_856,type,
sK468: $i > ( $i > $i > $o ) > $i ).
thf(func_def_871,type,
sK483: $i > $o ).
thf(func_def_872,type,
sK484: $i > $o ).
thf(func_def_873,type,
sK485: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_874,type,
sK486: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_881,type,
sK493: $i > $i > $i > $i > $i ).
thf(func_def_882,type,
sK494: $i > $o ).
thf(func_def_885,type,
sK497: $i > ( $i > $o ) > $i ).
thf(func_def_901,type,
sK513: $i > $i > $i > $i ).
thf(func_def_902,type,
sK514: $i > $i > $i > $i ).
thf(func_def_903,type,
sK515: $i > $i > $i > $i ).
thf(func_def_904,type,
sK516: $i > $i > $i > $i ).
thf(func_def_905,type,
sK517: $i > $i > ( $i > $i ) > $i ).
thf(func_def_906,type,
sK518: $i > $i ).
thf(func_def_923,type,
sK535: $i > $o ).
thf(func_def_931,type,
sK543: $i > $i ).
thf(func_def_939,type,
sK551: $i > $o ).
thf(func_def_954,type,
sK566: $i > $o ).
thf(func_def_956,type,
sK568: ( $i > $o ) > $i > $i ).
thf(func_def_957,type,
sK569: ( $i > $o ) > $i > $i ).
thf(func_def_968,type,
sK580: ( $i > $o ) > $i ).
thf(func_def_969,type,
sK581: $i > $o ).
thf(func_def_970,type,
sK582: $i > $i ).
thf(func_def_971,type,
sK583: $i > $o ).
thf(func_def_974,type,
sK586: $i > $i > ( $i > $o ) > $i ).
thf(func_def_986,type,
sK598: $i > $i > $i ).
thf(func_def_1012,type,
sK624: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_1013,type,
sK625: $i > ( $i > $o ) > $i ).
thf(func_def_1014,type,
sK626: $i > $o ).
thf(func_def_1024,type,
sK636: $i > $o ).
thf(func_def_1027,type,
sK639: $i > $i > $i > $i ).
thf(func_def_1044,type,
sK656: $i > $i > $i > $i > $i > $i ).
thf(func_def_1056,type,
sK668: $i > $i ).
thf(func_def_1059,type,
sK671: $i > $i ).
thf(func_def_1061,type,
sK673: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1065,type,
sK677: $i > $i > $i ).
thf(func_def_1078,type,
sK690: $i > $i ).
thf(func_def_1082,type,
sK694: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1087,type,
sK699: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1090,type,
sK702: $i > $i ).
thf(func_def_1097,type,
sK709: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1098,type,
sK710: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1101,type,
sK713: $i > $o ).
thf(func_def_1112,type,
sK724: $i > $o ).
thf(func_def_1114,type,
sK726: ( $i > $o ) > $i > $i ).
thf(func_def_1115,type,
sK727: ( $i > $o ) > $i > $i ).
thf(func_def_1132,type,
sK744: $i > $o ).
thf(func_def_1133,type,
sK745: $i > $i ).
thf(func_def_1134,type,
sK746: ( $i > $o ) > $i ).
thf(func_def_1139,type,
sK751: $i > $i > $i ).
thf(func_def_1148,type,
sK760: $i > $i > $i > $i ).
thf(func_def_1149,type,
sK761: $i > $i > $i > $i ).
thf(func_def_1172,type,
sK784: $i > $o ).
thf(func_def_1175,type,
sK787: $i > ( $i > $o ) > $i ).
thf(func_def_1185,type,
sK797: $i > $o ).
thf(func_def_1188,type,
sK800: $o > $i > $i > $i ).
thf(func_def_1209,type,
sK821: $i > $i ).
thf(func_def_1210,type,
sK822: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1220,type,
sK832: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1223,type,
sK835: $i > $i ).
thf(func_def_1252,type,
sK864: $i > $o ).
thf(func_def_1255,type,
sK867: $i > ( $i > $o ) > $i ).
thf(func_def_1259,type,
sK871: $i > $i ).
thf(func_def_1262,type,
sK874: $i > $o ).
thf(func_def_1264,type,
sK876: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1265,type,
sK877: $i > $i ).
thf(func_def_1277,type,
sK889: $i > $i > $o ).
thf(func_def_1287,type,
sK899: $i > $i > $i > $i > $i ).
thf(func_def_1288,type,
sK900: $i > $i > $i > $i > $i ).
thf(func_def_1293,type,
sK905: $i > $i > $i > $i > $i ).
thf(func_def_1296,type,
sK908: $i > $i > $i > $i ).
thf(func_def_1300,type,
sK912: $i > $i > $i > $i ).
thf(func_def_1303,type,
sK915: $i > $i > $i ).
thf(func_def_1304,type,
sK916: $i > $i > $i ).
thf(func_def_1312,type,
sK924: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1313,type,
sK925: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1314,type,
sK926: $i > $o ).
thf(func_def_1315,type,
sK927: $i > $o ).
thf(func_def_1332,type,
sK944: $i > $i > $o ).
thf(func_def_1339,type,
sK951: $i > $i > $o ).
thf(func_def_1353,type,
sK965: $i > $o ).
thf(func_def_1355,type,
sK967: $i > ( $i > $o ) > $i ).
thf(func_def_1386,type,
sK998: $i > $o ).
thf(func_def_1400,type,
sK1012: $i > $o ).
thf(func_def_1403,type,
sK1015: ( $i > $o ) > $i ).
thf(func_def_1404,type,
sK1016: ( $i > $o ) > $i ).
thf(func_def_1405,type,
sK1017: $i > $o ).
thf(func_def_1409,type,
sK1021: $i > $i > $i ).
thf(func_def_1436,type,
sK1048: $i > $i > $o ).
thf(func_def_1449,type,
sK1061: $i > $i > $i ).
thf(func_def_1457,type,
ph1069:
!>[X0: $tType] : X0 ).
thf(f8211,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f8186,f3423]) ).
thf(f3423,plain,
( $true
!= ( surjective @ sK212 @ sK214 @ sK213 ) ),
inference(cnf_transformation,[status(thm)],[f1753]) ).
thf(f1753,plain,
( ( binintersectSubset3 = $true )
& ( ubforcartprodlem2 = $true )
& ( inCongP = $true )
& ( demorgan1a = $true )
& ( subsetemptysetimpeq = $true )
& ( breln1compEex = $true )
& ( exuE3u = $true )
& ( subsetTrans = $true )
& ( funcext = $true )
& ( cartprodmempair = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectEL = $true )
& ( ex1E1 = $true )
& ( ubforcartprodlem1 = $true )
& ( nonemptyImpWitness = $true )
& ( theprop = $true )
& ( inPowerset = $true )
& ( notdexE = $true )
& ( symdiffIneg1 = $true )
& ( emptyE1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( breln1compI = $true )
& ( emptyset__Cong = $true )
& ( demorgan1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetI1 = $true )
& ( eqinunit = $true )
& ( demorgan2b2 = $true )
& ( cartprodfstpairEq = $true )
& ( setunionE = $true )
& ( doubleComplementSub2 = $true )
& ( breln1unionprop = $true )
& ( nonemptyE1 = $true )
& ( injFuncSetFuncIn = $true )
& ( setminusER = $true )
& ( emptyinunitempty = $true )
& ( powersetT_lem = $true )
& ( binintersectER = $true )
& ( breln1unionE = $true )
& ( breln1compprop = $true )
& ( ksndsingleton = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( symdiffI2 = $true )
& ( demorgan2a2 = $true )
& ( ap2apEq2 = $true )
& ( image1Ex1 = $true )
& ( complementTI1 = $true )
& ( doubleComplementSub1 = $true )
& ( subPowSU = $true )
& ( kpairiskpair = $true )
& ( lamProp = $true )
& ( doubleComplementI1 = $true )
& ( exu__Cong = $true )
& ( subbreln1 = $true )
& ( setunion__Cong = $true )
& ( iffalseProp1 = $true )
& ( descr__Cong = $true )
& ( iftrueProp1 = $true )
& ( dsetconstrI = $true )
& ( breln1unionEcases = $true )
& ( secondinupair = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( binintersectI = $true )
& ( woz13rule1 = $true )
& ( binintersectRsub = $true )
& ( setukpairinjL = $true )
& ( dsetconstrEL = $true )
& ( beta2 = $true )
& ( inIntersectImpInUnion = $true )
& ( setbeta = $true )
& ( iftrueProp2 = $true )
& ( app = $true )
& ( doubleComplementEq = $true )
& ( binunionRsub = $true )
& ( breln1all1 = $true )
& ( subset2powerset = $true )
& ( eqimpsubset2 = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( nonemptyI1 = $true )
& ( dpsetconstrEL2 = $true )
& ( funcinfuncset = $true )
& ( eqimpsubset1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjR11 = $true )
& ( subsetI1 = $true )
& ( setukpairinjR12 = $true )
& ( upairsubunion = $true )
& ( funcGraphProp3 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetimpfalse = $true )
& ( lam2lamEq = $true )
& ( notsubsetI = $true )
& ( replAx = $true )
& ( binintersectLsub = $true )
& ( iftrueorfalse = $true )
& ( notequalI1 = $true )
& ( ex1I = $true )
& ( lamp = $true )
& ( singletonprop = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( woz1_1 = $true )
& ( prop2set2propI = $true )
& ( setminusERneg = $true )
& ( contrasubsetT2 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( breln1invE = $true )
& ( ifSingleton = $true )
& ( setukpairIL = $true )
& ( kfstpairEq = $true )
& ( notinemptyset = $true )
& ( complementTnotintersectT = $true )
& ( image1I = $true )
& ( injFuncSetFuncInj = $true )
& ( foundationAx = $true )
& ( singletoninpowunion = $true )
& ( woz13rule4 = $true )
& ( surjFuncSetFuncIn = $true )
& ( dpsetconstrERa = $true )
& ( woz2B = $true )
& ( dpsetconstrEL1 = $true )
& ( emptysetE = $true )
& ( exuI1 = $true )
& ( setadjoinOr = $true )
& ( image1E = $true )
& ( woz13rule2 = $true )
& ( bs114d = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR = $true )
& ( subsetE2 = $true )
& ( woz2W = $true )
& ( eqbreln = $true )
& ( binintersectTELcontra = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( iffalse = $true )
& ( complementImpComplementIntersect = $true )
& ( iftrue = $true )
& ( beta1 = $true )
& ( setadjoinIL = $true )
& ( image1Ex = $true )
& ( binintersectT_lem = $true )
& ( setminusT_lem = $true )
& ( woz2Ex = $true )
& ( binunionT_lem = $true )
& ( image1Equiv = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( ap2p = $true )
& ( binunionTILcontra = $true )
& ( setminusSubset1 = $true )
& ( powersetTI1 = $true )
& ( dsetconstr__Cong = $true )
& ( omega0Ax = $true )
& ( kpairsurjEq = $true )
& ( breln1unionCommutes = $true )
& ( setminusI = $true )
& ( woz13rule0 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( breln1invI = $true )
& ( setunionsingleton1 = $true )
& ( exuE1 = $true )
& ( prop2setI = $true )
& ( upairset2IR = $true )
& ( cartprodsndin = $true )
& ( wellorderingAx = $true )
& ( binunionIR = $true )
& ( woz1_4 = $true )
& ( complementT_lem = $true )
& ( setextT = $true )
& ( setunionsingleton = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( vacuousDall = $true )
& ( dsetconstrER = $true )
& ( exuE3e = $true )
& ( woz13rule3 = $true )
& ( symdiffE = $true )
& ( binunionEcases = $true )
& ( cartprodpairsurjEq = $true )
& ( exuEu = $true )
& ( setukpairinjR1 = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( cartprodsndpairEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( breln1SetBreln1 = $true )
& ( notinsingleton = $true )
& ( cartprodfstin = $true )
& ( eta1 = $true )
& ( powersetTE1 = $true )
& ( cartprodmempair1 = $true )
& ( subbreln = $true )
& ( funcGraphProp1 = $true )
& ( subsetE = $true )
& ( brelnall1 = $true )
& ( setukpairIR = $true )
& ( in__Cong = $true )
& ( ksndpairEq = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( $true
!= ( surjective @ sK212 @ sK214 @ sK213 ) )
& ( $true
= ( in @ sK213 @ ( surjFuncSet @ sK212 @ sK214 ) ) )
& ( singletonsuniq = $true )
& ( woz1_2 = $true )
& ( quantDeMorgan1 = $true )
& ( demorgan2a1 = $true )
& ( demorgan1b = $true )
& ( breln1unionI = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( binunionLsub = $true )
& ( powersetAx = $true )
& ( binintersectSubset4 = $true )
& ( injFuncInInjFuncSet = $true )
& ( apProp = $true )
& ( demorgan2a = $true )
& ( setminusIRneg = $true )
& ( breln1unionIL = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrI = $true )
& ( funcGraphProp4 = $true )
& ( cartprodmempaircEq = $true )
& ( ifp = $true )
& ( sepInPowerset = $true )
& ( singletonsswitch = $true )
& ( binunionTEcontra = $true )
& ( setminusELneg = $true )
& ( quantDeMorgan4 = $true )
& ( demorgan2b = $true )
& ( omegaSAx = $true )
& ( iffalseProp2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL1 = $true )
& ( binunionIL = $true )
& ( complementTcontraSubset = $true )
& ( brelnall2 = $true )
& ( infuncsetfunc = $true )
& ( setextsub = $true )
& ( setadjoin__Cong = $true )
& ( contrasubsetT3 = $true )
& ( choice2fnsingleton = $true )
& ( breln1compE = $true )
& ( disjointsetsI1 = $true )
& ( demorgan2 = $true )
& ( complementTE1 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( upairinpowunion = $true )
& ( prop2setE = $true )
& ( ex1E2 = $true )
& ( binunionTIRcontra = $true )
& ( setunionAx = $true )
& ( cartprodpairin = $true )
& ( woz1_3 = $true )
& ( woz2A = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( emptyinPowerset = $true )
& ( woz1_5 = $true )
& ( setadjoinSub = $true )
& ( binunionE = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( breln1all2 = $true )
& ( omega__Cong = $true )
& ( cartprodpairmemER = $true )
& ( setminusILneg = $true )
& ( breln1unionIR = $true )
& ( powersetE1 = $true )
& ( ex1I2 = $true )
& ( lam2p = $true )
& ( setminusSubset2 = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( contrasubsetT = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetRefl = $true )
& ( breln1invprop = $true )
& ( eta2 = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset1 = $true )
& ( sepSubset = $true )
& ( powerset__Cong = $true )
& ( notdallE = $true )
& ( dpsetconstrER = $true )
& ( subsetI2 = $true )
& ( contrasubsetT1 = $true )
& ( symdiffI1 = $true )
& ( descrp = $true )
& ( setunionE2 = $true )
& ( upairsetIL = $true )
& ( exuI3 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( funcGraphProp2 = $true )
& ( upairequniteq = $true )
& ( funcImageSingleton = $true )
& ( kpairp = $true )
& ( upairset2E = $true )
& ( binintersectTERcontra = $true )
& ( funcextLem = $true )
& ( eqbreln1 = $true )
& ( setunionsingleton2 = $true )
& ( theeq = $true )
& ( powersetI = $true )
& ( funcext2 = $true )
& ( doubleComplementE1 = $true )
& ( contraSubsetComplement = $true )
& ( symdiffIneg2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK212,sK213,sK214])],[f1281,f1752]) ).
thf(f1752,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( surjective @ X0 @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) ) ) )
=> ( ( $true
!= ( surjective @ sK212 @ sK214 @ sK213 ) )
& ( $true
= ( in @ sK213 @ ( surjFuncSet @ sK212 @ sK214 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1281,plain,
( ( binintersectSubset3 = $true )
& ( ubforcartprodlem2 = $true )
& ( inCongP = $true )
& ( demorgan1a = $true )
& ( subsetemptysetimpeq = $true )
& ( breln1compEex = $true )
& ( exuE3u = $true )
& ( subsetTrans = $true )
& ( funcext = $true )
& ( cartprodmempair = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectEL = $true )
& ( ex1E1 = $true )
& ( ubforcartprodlem1 = $true )
& ( nonemptyImpWitness = $true )
& ( theprop = $true )
& ( inPowerset = $true )
& ( notdexE = $true )
& ( symdiffIneg1 = $true )
& ( emptyE1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( breln1compI = $true )
& ( emptyset__Cong = $true )
& ( demorgan1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetI1 = $true )
& ( eqinunit = $true )
& ( demorgan2b2 = $true )
& ( cartprodfstpairEq = $true )
& ( setunionE = $true )
& ( doubleComplementSub2 = $true )
& ( breln1unionprop = $true )
& ( nonemptyE1 = $true )
& ( injFuncSetFuncIn = $true )
& ( setminusER = $true )
& ( emptyinunitempty = $true )
& ( powersetT_lem = $true )
& ( binintersectER = $true )
& ( breln1unionE = $true )
& ( breln1compprop = $true )
& ( ksndsingleton = $true )
& ( setminusEL = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( symdiffI2 = $true )
& ( demorgan2a2 = $true )
& ( ap2apEq2 = $true )
& ( image1Ex1 = $true )
& ( complementTI1 = $true )
& ( doubleComplementSub1 = $true )
& ( subPowSU = $true )
& ( kpairiskpair = $true )
& ( lamProp = $true )
& ( doubleComplementI1 = $true )
& ( exu__Cong = $true )
& ( subbreln1 = $true )
& ( setunion__Cong = $true )
& ( iffalseProp1 = $true )
& ( descr__Cong = $true )
& ( iftrueProp1 = $true )
& ( dsetconstrI = $true )
& ( breln1unionEcases = $true )
& ( secondinupair = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( binintersectI = $true )
& ( woz13rule1 = $true )
& ( binintersectRsub = $true )
& ( setukpairinjL = $true )
& ( dsetconstrEL = $true )
& ( beta2 = $true )
& ( inIntersectImpInUnion = $true )
& ( setbeta = $true )
& ( iftrueProp2 = $true )
& ( app = $true )
& ( doubleComplementEq = $true )
& ( binunionRsub = $true )
& ( breln1all1 = $true )
& ( subset2powerset = $true )
& ( eqimpsubset2 = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( nonemptyI1 = $true )
& ( dpsetconstrEL2 = $true )
& ( funcinfuncset = $true )
& ( eqimpsubset1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjR11 = $true )
& ( subsetI1 = $true )
& ( setukpairinjR12 = $true )
& ( upairsubunion = $true )
& ( funcGraphProp3 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetimpfalse = $true )
& ( lam2lamEq = $true )
& ( notsubsetI = $true )
& ( replAx = $true )
& ( binintersectLsub = $true )
& ( iftrueorfalse = $true )
& ( notequalI1 = $true )
& ( ex1I = $true )
& ( lamp = $true )
& ( singletonprop = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setextAx = $true )
& ( woz1_1 = $true )
& ( prop2set2propI = $true )
& ( setminusERneg = $true )
& ( contrasubsetT2 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( breln1invE = $true )
& ( ifSingleton = $true )
& ( setukpairIL = $true )
& ( kfstpairEq = $true )
& ( notinemptyset = $true )
& ( complementTnotintersectT = $true )
& ( image1I = $true )
& ( injFuncSetFuncInj = $true )
& ( foundationAx = $true )
& ( singletoninpowunion = $true )
& ( woz13rule4 = $true )
& ( surjFuncSetFuncIn = $true )
& ( dpsetconstrERa = $true )
& ( woz2B = $true )
& ( dpsetconstrEL1 = $true )
& ( emptysetE = $true )
& ( exuI1 = $true )
& ( setadjoinOr = $true )
& ( image1E = $true )
& ( woz13rule2 = $true )
& ( bs114d = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR = $true )
& ( subsetE2 = $true )
& ( woz2W = $true )
& ( eqbreln = $true )
& ( binintersectTELcontra = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( iffalse = $true )
& ( complementImpComplementIntersect = $true )
& ( iftrue = $true )
& ( beta1 = $true )
& ( setadjoinIL = $true )
& ( image1Ex = $true )
& ( binintersectT_lem = $true )
& ( setminusT_lem = $true )
& ( woz2Ex = $true )
& ( binunionT_lem = $true )
& ( image1Equiv = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( ap2p = $true )
& ( binunionTILcontra = $true )
& ( setminusSubset1 = $true )
& ( powersetTI1 = $true )
& ( dsetconstr__Cong = $true )
& ( omega0Ax = $true )
& ( kpairsurjEq = $true )
& ( breln1unionCommutes = $true )
& ( setminusI = $true )
& ( woz13rule0 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( breln1invI = $true )
& ( setunionsingleton1 = $true )
& ( exuE1 = $true )
& ( prop2setI = $true )
& ( upairset2IR = $true )
& ( cartprodsndin = $true )
& ( wellorderingAx = $true )
& ( binunionIR = $true )
& ( woz1_4 = $true )
& ( complementT_lem = $true )
& ( setextT = $true )
& ( setunionsingleton = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( vacuousDall = $true )
& ( dsetconstrER = $true )
& ( exuE3e = $true )
& ( woz13rule3 = $true )
& ( symdiffE = $true )
& ( binunionEcases = $true )
& ( cartprodpairsurjEq = $true )
& ( exuEu = $true )
& ( setukpairinjR1 = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( cartprodsndpairEq = $true )
& ( emptyInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( breln1SetBreln1 = $true )
& ( notinsingleton = $true )
& ( cartprodfstin = $true )
& ( eta1 = $true )
& ( powersetTE1 = $true )
& ( cartprodmempair1 = $true )
& ( subbreln = $true )
& ( funcGraphProp1 = $true )
& ( subsetE = $true )
& ( brelnall1 = $true )
& ( setukpairIR = $true )
& ( in__Cong = $true )
& ( ksndpairEq = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( surjective @ X0 @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) ) ) )
& ( singletonsuniq = $true )
& ( woz1_2 = $true )
& ( quantDeMorgan1 = $true )
& ( demorgan2a1 = $true )
& ( demorgan1b = $true )
& ( breln1unionI = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( binunionLsub = $true )
& ( powersetAx = $true )
& ( binintersectSubset4 = $true )
& ( injFuncInInjFuncSet = $true )
& ( apProp = $true )
& ( demorgan2a = $true )
& ( setminusIRneg = $true )
& ( breln1unionIL = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrI = $true )
& ( funcGraphProp4 = $true )
& ( cartprodmempaircEq = $true )
& ( ifp = $true )
& ( sepInPowerset = $true )
& ( singletonsswitch = $true )
& ( binunionTEcontra = $true )
& ( setminusELneg = $true )
& ( quantDeMorgan4 = $true )
& ( demorgan2b = $true )
& ( omegaSAx = $true )
& ( iffalseProp2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL1 = $true )
& ( binunionIL = $true )
& ( complementTcontraSubset = $true )
& ( brelnall2 = $true )
& ( infuncsetfunc = $true )
& ( setextsub = $true )
& ( setadjoin__Cong = $true )
& ( contrasubsetT3 = $true )
& ( choice2fnsingleton = $true )
& ( breln1compE = $true )
& ( disjointsetsI1 = $true )
& ( demorgan2 = $true )
& ( complementTE1 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL2 = $true )
& ( upairinpowunion = $true )
& ( prop2setE = $true )
& ( ex1E2 = $true )
& ( binunionTIRcontra = $true )
& ( setunionAx = $true )
& ( cartprodpairin = $true )
& ( woz1_3 = $true )
& ( woz2A = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( emptyinPowerset = $true )
& ( woz1_5 = $true )
& ( setadjoinSub = $true )
& ( binunionE = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( setoftrueEq = $true )
& ( breln1all2 = $true )
& ( omega__Cong = $true )
& ( cartprodpairmemER = $true )
& ( setminusILneg = $true )
& ( breln1unionIR = $true )
& ( powersetE1 = $true )
& ( ex1I2 = $true )
& ( lam2p = $true )
& ( setminusSubset2 = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( contrasubsetT = $true )
& ( setukpairinjR2 = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetRefl = $true )
& ( breln1invprop = $true )
& ( eta2 = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset1 = $true )
& ( sepSubset = $true )
& ( powerset__Cong = $true )
& ( notdallE = $true )
& ( dpsetconstrER = $true )
& ( subsetI2 = $true )
& ( contrasubsetT1 = $true )
& ( symdiffI1 = $true )
& ( descrp = $true )
& ( setunionE2 = $true )
& ( upairsetIL = $true )
& ( exuI3 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( funcGraphProp2 = $true )
& ( upairequniteq = $true )
& ( funcImageSingleton = $true )
& ( kpairp = $true )
& ( upairset2E = $true )
& ( binintersectTERcontra = $true )
& ( funcextLem = $true )
& ( eqbreln1 = $true )
& ( setunionsingleton2 = $true )
& ( theeq = $true )
& ( powersetI = $true )
& ( funcext2 = $true )
& ( doubleComplementE1 = $true )
& ( contraSubsetComplement = $true )
& ( symdiffIneg2 = $true ) ),
inference(flattening,[status(thm)],[f1280]) ).
thf(f1280,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( surjective @ X0 @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) ) ) )
& ( surjFuncSetFuncIn = $true )
& ( injFuncSetFuncInj = $true )
& ( injFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( 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)],[f427]) ).
thf(f427,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 )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) ) )
=> ( $true
= ( surjective @ X0 @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f426]) ).
thf(f426,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
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( surjFuncSet @ X0 @ X2 ) )
=> ( surjective @ X0 @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f324]) ).
thf(f324,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
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ! [X1: $i,X12: $i,X2: $i] :
( ( in @ X12 @ ( surjFuncSet @ X1 @ X2 ) )
=> ( surjective @ X1 @ X2 @ X12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f323]) ).
thf(f323,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
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ! [X1: $i,X12: $i,X2: $i] :
( ( in @ X12 @ ( surjFuncSet @ X1 @ X2 ) )
=> ( surjective @ X1 @ X2 @ X12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',surjFuncSetFuncSurj) ).
thf(f8186,plain,
( $true
= ( surjective @ sK212 @ sK214 @ sK213 ) ),
inference(trivial_inequality_removal,[status(thm)],[f8144]) ).
thf(f8144,plain,
( ( $true
= ( surjective @ sK212 @ sK214 @ sK213 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f6252,f6209]) ).
thf(f6209,plain,
( ( in @ sK213 @ ( dsetconstr @ ( funcSet @ sK212 @ sK214 ) @ ( surjective @ sK212 @ sK214 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f5060]) ).
thf(f5060,plain,
( $true
= ( in @ sK213
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) )
@ sK212
@ sK214 ) ) ),
inference(definition_unfolding,[status(thm)],[f3422,f4322]) ).
thf(f4322,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f409]) ).
thf(f409,plain,
( surjFuncSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( funcSet @ Y0 @ Y1 )
@ ^ [Y2: $i] : ( surjective @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f408]) ).
thf(f408,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( funcSet @ X0 @ X1 )
@ ^ [X2: $i] : ( surjective @ X0 @ X1 @ X2 ) ) )
= surjFuncSet ),
inference(rectify,[status(thm)],[f321]) ).
thf(f321,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( funcSet @ X3 @ X4 )
@ ^ [X12: $i] : ( surjective @ X3 @ X4 @ X12 ) ) )
= surjFuncSet ),
file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',surjFuncSet) ).
thf(f3422,plain,
( $true
= ( in @ sK213 @ ( surjFuncSet @ sK212 @ sK214 ) ) ),
inference(cnf_transformation,[status(thm)],[f1753]) ).
thf(f6252,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X2 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f6251]) ).
thf(f6251,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5562]) ).
thf(f5562,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4229,f3451]) ).
thf(f3451,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f1753]) ).
thf(f4229,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f2400]) ).
thf(f2400,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( sK636 @ sK637 )
!= $true )
& ( $true
= ( in @ sK637
@ ( dsetconstr @ sK638
@ ^ [Y0: $i] : ( sK636 @ Y0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK636,sK637,sK638])],[f2398,f2399]) ).
thf(f2399,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X4 ) )
& ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) )
=> ( ( ( sK636 @ sK637 )
!= $true )
& ( $true
= ( in @ sK637
@ ( dsetconstr @ sK638
@ ^ [Y0: $i] : ( sK636 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2398,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X3 @ X4 ) )
& ( $true
= ( in @ X4
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2397]) ).
thf(f2397,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1336]) ).
thf(f1336,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( ( X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f626]) ).
thf(f626,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X0: $i > $o,X1: $i,X3: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',dsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU802^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n012.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:34:15 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : SEU802^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.41 % Domain : Set Theory
% 0.17/0.41 % Problem : More about Functions - Surjective Functions
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English : (! x:i.! y:i.! f:i.in f (surjFuncSet x y) -> surjective x y f)
% 0.17/0.41
% 0.17/0.41 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.41 % Source : [Bro08]
% 0.17/0.41 % Names : ZFC304g [Bro08]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.70 v8.2.0, 0.69 v8.1.0, 0.73 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.71 v6.1.0, 1.00 v6.0.0, 0.86 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.17/0.41 % Syntax : Number of formulae : 694 ( 322 unt; 371 typ; 322 def)
% 0.17/0.41 % Number of atoms : 1981 ( 463 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 320 ( 6 avg)
% 0.17/0.41 % Number of connectives : 4355 ( 73 ~; 14 |; 54 &;3174 @)
% 0.17/0.41 % ( 17 <=>;1023 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 326 ( 2 avg)
% 0.17/0.41 % Number of types : 2 ( 0 usr)
% 0.17/0.41 % Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 374 ( 371 usr; 322 con; 0-4 aty)
% 0.17/0.41 % Number of variables : 1141 ( 81 ^;1016 !; 44 ?;1141 :)
% 0.17/0.41 % SPC : TH0_THM_EQU_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : http://mathgate.info/detsetitem.php?id=485
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf(in_type,type,
% 0.17/0.41 in: $i > $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(exu_type,type,
% 0.17/0.41 exu: ( $i > $o ) > $o ).
% 0.17/0.41
% 0.17/0.41 thf(exu,definition,
% 0.17/0.41 ( exu
% 0.17/0.41 = ( ^ [Xphi: $i > $o] :
% 0.17/0.41 ? [Xx: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 & ! [Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setextAx_type,type,
% 0.17/0.41 setextAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setextAx,definition,
% 0.17/0.41 ( setextAx
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 <=> ( in @ Xx @ B ) )
% 0.17/0.41 => ( A = B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyset_type,type,
% 0.17/0.41 emptyset: $i ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetAx_type,type,
% 0.17/0.41 emptysetAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetAx,definition,
% 0.17/0.41 ( emptysetAx
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoin_type,type,
% 0.17/0.41 setadjoin: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinAx_type,type,
% 0.17/0.41 setadjoinAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinAx,definition,
% 0.17/0.41 ( setadjoinAx
% 0.17/0.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.41 <=> ( ( Xy = Xx )
% 0.17/0.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powerset_type,type,
% 0.17/0.41 powerset: $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(powersetAx_type,type,
% 0.17/0.41 powersetAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetAx,definition,
% 0.17/0.41 ( powersetAx
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.41 <=> ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunion_type,type,
% 0.17/0.41 setunion: $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(setunionAx_type,type,
% 0.17/0.41 setunionAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionAx,definition,
% 0.17/0.41 ( setunionAx
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.41 <=> ? [B: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 & ( in @ B @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(omega_type,type,
% 0.17/0.41 omega: $i ).
% 0.17/0.41
% 0.17/0.41 thf(omega0Ax_type,type,
% 0.17/0.41 omega0Ax: $o ).
% 0.17/0.41
% 0.17/0.41 thf(omega0Ax,definition,
% 0.17/0.41 ( omega0Ax
% 0.17/0.41 = ( in @ emptyset @ omega ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(omegaSAx_type,type,
% 0.17/0.41 omegaSAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(omegaSAx,definition,
% 0.17/0.41 ( omegaSAx
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ omega )
% 0.17/0.41 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(omegaIndAx_type,type,
% 0.17/0.41 omegaIndAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(omegaIndAx,definition,
% 0.17/0.41 ( omegaIndAx
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ( ( in @ emptyset @ A )
% 0.17/0.41 & ! [Xx: $i] :
% 0.17/0.41 ( ( ( in @ Xx @ omega )
% 0.17/0.41 & ( in @ Xx @ A ) )
% 0.17/0.41 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.17/0.41 => ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ omega )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(replAx_type,type,
% 0.17/0.41 replAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(replAx,definition,
% 0.17/0.41 ( replAx
% 0.17/0.41 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( exu
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.41 => ? [B: $i] :
% 0.17/0.41 ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 <=> ? [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ A )
% 0.17/0.41 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(foundationAx_type,type,
% 0.17/0.41 foundationAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(foundationAx,definition,
% 0.17/0.41 ( foundationAx
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.41 => ? [B: $i] :
% 0.17/0.41 ( ( in @ B @ A )
% 0.17/0.41 & ~ ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(wellorderingAx_type,type,
% 0.17/0.41 wellorderingAx: $o ).
% 0.17/0.41
% 0.17/0.41 thf(wellorderingAx,definition,
% 0.17/0.41 ( wellorderingAx
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ? [B: $i] :
% 0.17/0.41 ( ! [C: $i] :
% 0.17/0.41 ( ( in @ C @ B )
% 0.17/0.41 => ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ C )
% 0.17/0.41 => ( in @ Xx @ A ) ) )
% 0.17/0.41 & ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( ( in @ Xx @ A )
% 0.17/0.41 & ( in @ Xy @ A ) )
% 0.17/0.41 => ( ! [C: $i] :
% 0.17/0.41 ( ( in @ C @ B )
% 0.17/0.41 => ( ( in @ Xx @ C )
% 0.17/0.41 <=> ( in @ Xy @ C ) ) )
% 0.17/0.41 => ( Xx = Xy ) ) )
% 0.17/0.41 & ! [C: $i,D: $i] :
% 0.17/0.41 ( ( ( in @ C @ B )
% 0.17/0.41 & ( in @ D @ B ) )
% 0.17/0.41 => ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ C )
% 0.17/0.41 => ( in @ Xx @ D ) )
% 0.17/0.41 | ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ D )
% 0.17/0.41 => ( in @ Xx @ C ) ) ) )
% 0.17/0.41 & ! [C: $i] :
% 0.17/0.41 ( ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ C )
% 0.17/0.41 => ( in @ Xx @ A ) )
% 0.17/0.41 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.17/0.41 => ? [D: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ D @ B )
% 0.17/0.41 & ( in @ Xx @ C )
% 0.17/0.41 & ~ ? [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ D )
% 0.17/0.41 & ( in @ Xy @ C ) )
% 0.17/0.41 & ! [E: $i] :
% 0.17/0.41 ( ( in @ E @ B )
% 0.17/0.41 => ( ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ E )
% 0.17/0.41 => ( in @ Xy @ D ) )
% 0.17/0.41 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(descr_type,type,
% 0.17/0.41 descr: ( $i > $o ) > $i ).
% 0.17/0.41
% 0.17/0.41 thf(descrp_type,type,
% 0.17/0.41 descrp: $o ).
% 0.17/0.41
% 0.17/0.41 thf(descrp,definition,
% 0.17/0.41 ( descrp
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ( Xphi
% 0.17/0.41 @ ( descr
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstr_type,type,
% 0.17/0.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrI_type,type,
% 0.17/0.41 dsetconstrI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrI,definition,
% 0.17/0.41 ( dsetconstrI
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 => ( in @ Xx
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrEL_type,type,
% 0.17/0.41 dsetconstrEL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrEL,definition,
% 0.17/0.41 ( dsetconstrEL
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrER_type,type,
% 0.17/0.41 dsetconstrER: $o ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstrER,definition,
% 0.17/0.41 ( dsetconstrER
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.41 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuE1_type,type,
% 0.17/0.41 exuE1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuE1,definition,
% 0.17/0.41 ( exuE1
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 & ! [Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(prop2set_type,type,
% 0.17/0.41 prop2set: $o > $i ).
% 0.17/0.41
% 0.17/0.41 thf(prop2setE_type,type,
% 0.17/0.41 prop2setE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(prop2setE,definition,
% 0.17/0.41 ( prop2setE
% 0.17/0.41 = ( ! [Xphi: $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.17/0.41 => Xphi ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetE_type,type,
% 0.17/0.41 emptysetE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetE,definition,
% 0.17/0.41 ( emptysetE
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ emptyset )
% 0.17/0.41 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetimpfalse_type,type,
% 0.17/0.41 emptysetimpfalse: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetimpfalse,definition,
% 0.17/0.41 ( emptysetimpfalse
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ emptyset )
% 0.17/0.41 => $false ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notinemptyset_type,type,
% 0.17/0.41 notinemptyset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notinemptyset,definition,
% 0.17/0.41 ( notinemptyset
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuE3e_type,type,
% 0.17/0.41 exuE3e: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuE3e,definition,
% 0.17/0.41 ( exuE3e
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setext_type,type,
% 0.17/0.41 setext: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setext,definition,
% 0.17/0.41 ( setext
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ B ) )
% 0.17/0.41 => ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ A ) )
% 0.17/0.41 => ( A = B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyI_type,type,
% 0.17/0.41 emptyI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyI,definition,
% 0.17/0.41 ( emptyI
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ~ ( in @ Xx @ A )
% 0.17/0.41 => ( A = emptyset ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(noeltsimpempty_type,type,
% 0.17/0.41 noeltsimpempty: $o ).
% 0.17/0.41
% 0.17/0.41 thf(noeltsimpempty,definition,
% 0.17/0.41 ( noeltsimpempty
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ~ ( in @ Xx @ A )
% 0.17/0.41 => ( A = emptyset ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setbeta_type,type,
% 0.17/0.41 setbeta: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setbeta,definition,
% 0.17/0.41 ( setbeta
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( in @ Xx
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.41 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(nonempty_type,type,
% 0.17/0.41 nonempty: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(nonempty,definition,
% 0.17/0.41 ( nonempty
% 0.17/0.41 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyE1_type,type,
% 0.17/0.41 nonemptyE1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyE1,definition,
% 0.17/0.41 ( nonemptyE1
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ( nonempty @ A )
% 0.17/0.41 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyI_type,type,
% 0.17/0.41 nonemptyI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyI,definition,
% 0.17/0.41 ( nonemptyI
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 => ( nonempty
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyI1_type,type,
% 0.17/0.41 nonemptyI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyI1,definition,
% 0.17/0.41 ( nonemptyI1
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.41 => ( nonempty @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinIL_type,type,
% 0.17/0.41 setadjoinIL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinIL,definition,
% 0.17/0.41 ( setadjoinIL
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyinunitempty_type,type,
% 0.17/0.41 emptyinunitempty: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyinunitempty,definition,
% 0.17/0.41 ( emptyinunitempty
% 0.17/0.41 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinIR_type,type,
% 0.17/0.41 setadjoinIR: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinIR,definition,
% 0.17/0.41 ( setadjoinIR
% 0.17/0.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ A )
% 0.17/0.41 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinE_type,type,
% 0.17/0.41 setadjoinE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinE,definition,
% 0.17/0.41 ( setadjoinE
% 0.17/0.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.41 => ! [Xphi: $o] :
% 0.17/0.41 ( ( ( Xy = Xx )
% 0.17/0.41 => Xphi )
% 0.17/0.41 => ( ( ( in @ Xy @ A )
% 0.17/0.41 => Xphi )
% 0.17/0.41 => Xphi ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinOr_type,type,
% 0.17/0.41 setadjoinOr: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinOr,definition,
% 0.17/0.41 ( setadjoinOr
% 0.17/0.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.41 => ( ( Xy = Xx )
% 0.17/0.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setoftrueEq_type,type,
% 0.17/0.41 setoftrueEq: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setoftrueEq,definition,
% 0.17/0.41 ( setoftrueEq
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : $true )
% 0.17/0.41 = A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powersetI_type,type,
% 0.17/0.41 powersetI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetI,definition,
% 0.17/0.41 ( powersetI
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ A ) )
% 0.17/0.41 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyinPowerset_type,type,
% 0.17/0.41 emptyinPowerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyinPowerset,definition,
% 0.17/0.41 ( emptyinPowerset
% 0.17/0.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyInPowerset_type,type,
% 0.17/0.41 emptyInPowerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyInPowerset,definition,
% 0.17/0.41 ( emptyInPowerset
% 0.17/0.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powersetE_type,type,
% 0.17/0.41 powersetE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetE,definition,
% 0.17/0.41 ( powersetE
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.41 => ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionI_type,type,
% 0.17/0.41 setunionI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionI,definition,
% 0.17/0.41 ( setunionI
% 0.17/0.41 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( ( in @ B @ A )
% 0.17/0.41 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionE_type,type,
% 0.17/0.41 setunionE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionE,definition,
% 0.17/0.41 ( setunionE
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.41 => ! [Xphi: $o] :
% 0.17/0.41 ( ! [B: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( ( in @ B @ A )
% 0.17/0.41 => Xphi ) )
% 0.17/0.41 => Xphi ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subPowSU_type,type,
% 0.17/0.41 subPowSU: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subPowSU,definition,
% 0.17/0.41 ( subPowSU
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuE2_type,type,
% 0.17/0.41 exuE2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuE2,definition,
% 0.17/0.41 ( exuE2
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ! [Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xy )
% 0.17/0.41 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyImpWitness_type,type,
% 0.17/0.41 nonemptyImpWitness: $o ).
% 0.17/0.41
% 0.17/0.41 thf(nonemptyImpWitness,definition,
% 0.17/0.41 ( nonemptyImpWitness
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ( nonempty @ A )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & $true ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(uniqinunit_type,type,
% 0.17/0.41 uniqinunit: $o ).
% 0.17/0.41
% 0.17/0.41 thf(uniqinunit,definition,
% 0.17/0.41 ( uniqinunit
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notinsingleton_type,type,
% 0.17/0.41 notinsingleton: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notinsingleton,definition,
% 0.17/0.41 ( notinsingleton
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx != Xy )
% 0.17/0.41 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(eqinunit_type,type,
% 0.17/0.41 eqinunit: $o ).
% 0.17/0.41
% 0.17/0.41 thf(eqinunit,definition,
% 0.17/0.41 ( eqinunit
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsswitch_type,type,
% 0.17/0.41 singletonsswitch: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsswitch,definition,
% 0.17/0.41 ( singletonsswitch
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.41 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetE_type,type,
% 0.17/0.41 upairsetE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetE,definition,
% 0.17/0.41 ( upairsetE
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.41 => ( ( Xz = Xx )
% 0.17/0.41 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetIL_type,type,
% 0.17/0.41 upairsetIL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetIL,definition,
% 0.17/0.41 ( upairsetIL
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetIR_type,type,
% 0.17/0.41 upairsetIR: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetIR,definition,
% 0.17/0.41 ( upairsetIR
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyE1_type,type,
% 0.17/0.41 emptyE1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyE1,definition,
% 0.17/0.41 ( emptyE1
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) )
% 0.17/0.41 => ( ( ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 = emptyset )
% 0.17/0.41 => $false ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(vacuousDall_type,type,
% 0.17/0.41 vacuousDall: $o ).
% 0.17/0.41
% 0.17/0.41 thf(vacuousDall,definition,
% 0.17/0.41 ( vacuousDall
% 0.17/0.41 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ emptyset )
% 0.17/0.41 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan1_type,type,
% 0.17/0.41 quantDeMorgan1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan1,definition,
% 0.17/0.41 ( quantDeMorgan1
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ~ ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan2_type,type,
% 0.17/0.41 quantDeMorgan2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan2,definition,
% 0.17/0.41 ( quantDeMorgan2
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ~ ( Xphi @ Xx ) )
% 0.17/0.41 => ~ ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan3_type,type,
% 0.17/0.41 quantDeMorgan3: $o ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan3,definition,
% 0.17/0.41 ( quantDeMorgan3
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ~ ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) )
% 0.17/0.41 => ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan4_type,type,
% 0.17/0.41 quantDeMorgan4: $o ).
% 0.17/0.41
% 0.17/0.41 thf(quantDeMorgan4,definition,
% 0.17/0.41 ( quantDeMorgan4
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ~ ( Xphi @ Xx ) )
% 0.17/0.41 => ~ ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(prop2setI_type,type,
% 0.17/0.41 prop2setI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(prop2setI,definition,
% 0.17/0.41 ( prop2setI
% 0.17/0.41 = ( ! [Xphi: $o] :
% 0.17/0.41 ( Xphi
% 0.17/0.41 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(set2prop_type,type,
% 0.17/0.41 set2prop: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(prop2set2propI_type,type,
% 0.17/0.41 prop2set2propI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(prop2set2propI,definition,
% 0.17/0.41 ( prop2set2propI
% 0.17/0.41 = ( ! [Xphi: $o] :
% 0.17/0.41 ( Xphi
% 0.17/0.41 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notdexE_type,type,
% 0.17/0.41 notdexE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notdexE,definition,
% 0.17/0.41 ( notdexE
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ~ ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) )
% 0.17/0.41 => ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notdallE_type,type,
% 0.17/0.41 notdallE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notdallE,definition,
% 0.17/0.41 ( notdallE
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ~ ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuI1_type,type,
% 0.17/0.41 exuI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuI1,definition,
% 0.17/0.41 ( exuI1
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ? [Xx: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 & ! [Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) )
% 0.17/0.41 => ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuI3_type,type,
% 0.17/0.41 exuI3: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuI3,definition,
% 0.17/0.41 ( exuI3
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.17/0.41 => ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) )
% 0.17/0.41 => ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuI2_type,type,
% 0.17/0.41 exuI2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuI2,definition,
% 0.17/0.41 ( exuI2
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ? [Xx: $i] :
% 0.17/0.41 ! [Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xy )
% 0.17/0.41 <=> ( Xy = Xx ) )
% 0.17/0.41 => ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(inCongP_type,type,
% 0.17/0.41 inCongP: $o ).
% 0.17/0.41
% 0.17/0.41 thf(inCongP,definition,
% 0.17/0.41 ( inCongP
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(in__Cong_type,type,
% 0.17/0.41 in__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(in__Cong,definition,
% 0.17/0.41 ( in__Cong
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( ( in @ Xx @ A )
% 0.17/0.41 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuE3u_type,type,
% 0.17/0.41 exuE3u: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuE3u,definition,
% 0.17/0.41 ( exuE3u
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exu__Cong_type,type,
% 0.17/0.41 exu__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exu__Cong,definition,
% 0.17/0.41 ( exu__Cong
% 0.17/0.41 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.41 => ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 <=> ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptyset__Cong_type,type,
% 0.17/0.41 emptyset__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptyset__Cong,definition,
% 0.17/0.41 ( emptyset__Cong
% 0.17/0.41 = ( emptyset = emptyset ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoin__Cong_type,type,
% 0.17/0.41 setadjoin__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoin__Cong,definition,
% 0.17/0.41 ( setadjoin__Cong
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ! [Xz: $i,Xu: $i] :
% 0.17/0.41 ( ( Xz = Xu )
% 0.17/0.41 => ( ( setadjoin @ Xx @ Xz )
% 0.17/0.41 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powerset__Cong_type,type,
% 0.17/0.41 powerset__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powerset__Cong,definition,
% 0.17/0.41 ( powerset__Cong
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ( ( powerset @ A )
% 0.17/0.41 = ( powerset @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunion__Cong_type,type,
% 0.17/0.41 setunion__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunion__Cong,definition,
% 0.17/0.41 ( setunion__Cong
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ( ( setunion @ A )
% 0.17/0.41 = ( setunion @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(omega__Cong_type,type,
% 0.17/0.41 omega__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(omega__Cong,definition,
% 0.17/0.41 ( omega__Cong
% 0.17/0.41 = ( omega = omega ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(exuEu_type,type,
% 0.17/0.41 exuEu: $o ).
% 0.17/0.41
% 0.17/0.41 thf(exuEu,definition,
% 0.17/0.41 ( exuEu
% 0.17/0.41 = ( ! [Xphi: $i > $o] :
% 0.17/0.41 ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xphi @ Xx )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(descr__Cong_type,type,
% 0.17/0.41 descr__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(descr__Cong,definition,
% 0.17/0.41 ( descr__Cong
% 0.17/0.41 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.41 => ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ( ( exu
% 0.17/0.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.17/0.41 => ( ( descr
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 = ( descr
% 0.17/0.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstr__Cong_type,type,
% 0.17/0.41 dsetconstr__Cong: $o ).
% 0.17/0.41
% 0.17/0.41 thf(dsetconstr__Cong,definition,
% 0.17/0.41 ( dsetconstr__Cong
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( ( Xx = Xy )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.17/0.41 => ( ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 = ( dsetconstr @ B
% 0.17/0.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subset_type,type,
% 0.17/0.41 subset: $i > $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(disjoint_type,type,
% 0.17/0.41 disjoint: $i > $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(setsmeet_type,type,
% 0.17/0.41 setsmeet: $i > $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetI1_type,type,
% 0.17/0.41 subsetI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetI1,definition,
% 0.17/0.41 ( subsetI1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ B ) )
% 0.17/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(eqimpsubset2_type,type,
% 0.17/0.41 eqimpsubset2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(eqimpsubset2,definition,
% 0.17/0.41 ( eqimpsubset2
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(eqimpsubset1_type,type,
% 0.17/0.41 eqimpsubset1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(eqimpsubset1,definition,
% 0.17/0.41 ( eqimpsubset1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( A = B )
% 0.17/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetI2_type,type,
% 0.17/0.41 subsetI2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetI2,definition,
% 0.17/0.41 ( subsetI2
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ B ) )
% 0.17/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetsubset_type,type,
% 0.17/0.41 emptysetsubset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(emptysetsubset,definition,
% 0.17/0.41 ( emptysetsubset
% 0.17/0.41 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetE_type,type,
% 0.17/0.41 subsetE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetE,definition,
% 0.17/0.41 ( subsetE
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetE2_type,type,
% 0.17/0.41 subsetE2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetE2,definition,
% 0.17/0.41 ( subsetE2
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notsubsetI_type,type,
% 0.17/0.41 notsubsetI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notsubsetI,definition,
% 0.17/0.41 ( notsubsetI
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notequalI1_type,type,
% 0.17/0.41 notequalI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notequalI1,definition,
% 0.17/0.41 ( notequalI1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ~ ( subset @ A @ B )
% 0.17/0.41 => ( A != B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(notequalI2_type,type,
% 0.17/0.41 notequalI2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(notequalI2,definition,
% 0.17/0.41 ( notequalI2
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ( A != B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetRefl_type,type,
% 0.17/0.41 subsetRefl: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetRefl,definition,
% 0.17/0.41 ( subsetRefl
% 0.17/0.41 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetTrans_type,type,
% 0.17/0.41 subsetTrans: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetTrans,definition,
% 0.17/0.41 ( subsetTrans
% 0.17/0.41 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ( subset @ B @ C )
% 0.17/0.41 => ( subset @ A @ C ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinSub_type,type,
% 0.17/0.41 setadjoinSub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinSub,definition,
% 0.17/0.41 ( setadjoinSub
% 0.17/0.41 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinSub2_type,type,
% 0.17/0.41 setadjoinSub2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setadjoinSub2,definition,
% 0.17/0.41 ( setadjoinSub2
% 0.17/0.41 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subset2powerset_type,type,
% 0.17/0.41 subset2powerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subset2powerset,definition,
% 0.17/0.41 ( subset2powerset
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setextsub_type,type,
% 0.17/0.41 setextsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setextsub,definition,
% 0.17/0.41 ( setextsub
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ( subset @ B @ A )
% 0.17/0.41 => ( A = B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(subsetemptysetimpeq_type,type,
% 0.17/0.41 subsetemptysetimpeq: $o ).
% 0.17/0.41
% 0.17/0.41 thf(subsetemptysetimpeq,definition,
% 0.17/0.41 ( subsetemptysetimpeq
% 0.17/0.41 = ( ! [A: $i] :
% 0.17/0.41 ( ( subset @ A @ emptyset )
% 0.17/0.41 => ( A = emptyset ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powersetI1_type,type,
% 0.17/0.41 powersetI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetI1,definition,
% 0.17/0.41 ( powersetI1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ B @ A )
% 0.17/0.41 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powersetE1_type,type,
% 0.17/0.41 powersetE1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetE1,definition,
% 0.17/0.41 ( powersetE1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.41 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(inPowerset_type,type,
% 0.17/0.41 inPowerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(inPowerset,definition,
% 0.17/0.41 ( inPowerset
% 0.17/0.41 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(powersetsubset_type,type,
% 0.17/0.41 powersetsubset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(powersetsubset,definition,
% 0.17/0.41 ( powersetsubset
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sepInPowerset_type,type,
% 0.17/0.41 sepInPowerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(sepInPowerset,definition,
% 0.17/0.41 ( sepInPowerset
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( in
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 @ ( powerset @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(sepSubset_type,type,
% 0.17/0.41 sepSubset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(sepSubset,definition,
% 0.17/0.41 ( sepSubset
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( subset
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunion_type,type,
% 0.17/0.41 binunion: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(binunionIL_type,type,
% 0.17/0.41 binunionIL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionIL,definition,
% 0.17/0.41 ( binunionIL
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairset2IR_type,type,
% 0.17/0.41 upairset2IR: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairset2IR,definition,
% 0.17/0.41 ( upairset2IR
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunionIR_type,type,
% 0.17/0.41 binunionIR: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionIR,definition,
% 0.17/0.41 ( binunionIR
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunionEcases_type,type,
% 0.17/0.41 binunionEcases: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionEcases,definition,
% 0.17/0.41 ( binunionEcases
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.17/0.41 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.41 => ( ( ( in @ Xx @ A )
% 0.17/0.41 => Xphi )
% 0.17/0.41 => ( ( ( in @ Xx @ B )
% 0.17/0.41 => Xphi )
% 0.17/0.41 => Xphi ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunionE_type,type,
% 0.17/0.41 binunionE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionE,definition,
% 0.17/0.41 ( binunionE
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.41 => ( ( in @ Xx @ A )
% 0.17/0.41 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunionLsub_type,type,
% 0.17/0.41 binunionLsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionLsub,definition,
% 0.17/0.41 ( binunionLsub
% 0.17/0.41 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binunionRsub_type,type,
% 0.17/0.41 binunionRsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binunionRsub,definition,
% 0.17/0.41 ( binunionRsub
% 0.17/0.41 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersect_type,type,
% 0.17/0.41 binintersect: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectI_type,type,
% 0.17/0.41 binintersectI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectI,definition,
% 0.17/0.41 ( binintersectI
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset5_type,type,
% 0.17/0.41 binintersectSubset5: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset5,definition,
% 0.17/0.41 ( binintersectSubset5
% 0.17/0.41 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.41 ( ( subset @ C @ A )
% 0.17/0.41 => ( ( subset @ C @ B )
% 0.17/0.41 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectEL_type,type,
% 0.17/0.41 binintersectEL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectEL,definition,
% 0.17/0.41 ( binintersectEL
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectLsub_type,type,
% 0.17/0.41 binintersectLsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectLsub,definition,
% 0.17/0.41 ( binintersectLsub
% 0.17/0.41 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset2_type,type,
% 0.17/0.41 binintersectSubset2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset2,definition,
% 0.17/0.41 ( binintersectSubset2
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ( binintersect @ A @ B )
% 0.17/0.41 = A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset3_type,type,
% 0.17/0.41 binintersectSubset3: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset3,definition,
% 0.17/0.41 ( binintersectSubset3
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( ( binintersect @ A @ B )
% 0.17/0.41 = B )
% 0.17/0.41 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectER_type,type,
% 0.17/0.41 binintersectER: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectER,definition,
% 0.17/0.41 ( binintersectER
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.41 => ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(disjointsetsI1_type,type,
% 0.17/0.41 disjointsetsI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(disjointsetsI1,definition,
% 0.17/0.41 ( disjointsetsI1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ~ ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( in @ Xx @ B ) )
% 0.17/0.41 => ( ( binintersect @ A @ B )
% 0.17/0.41 = emptyset ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectRsub_type,type,
% 0.17/0.41 binintersectRsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectRsub,definition,
% 0.17/0.41 ( binintersectRsub
% 0.17/0.41 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset4_type,type,
% 0.17/0.41 binintersectSubset4: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset4,definition,
% 0.17/0.41 ( binintersectSubset4
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ B @ A )
% 0.17/0.41 => ( ( binintersect @ A @ B )
% 0.17/0.41 = B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset1_type,type,
% 0.17/0.41 binintersectSubset1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(binintersectSubset1,definition,
% 0.17/0.41 ( binintersectSubset1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( ( binintersect @ A @ B )
% 0.17/0.41 = A )
% 0.17/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(bs114d_type,type,
% 0.17/0.41 bs114d: $o ).
% 0.17/0.41
% 0.17/0.41 thf(bs114d,definition,
% 0.17/0.41 ( bs114d
% 0.17/0.41 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.41 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.17/0.41 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(regular_type,type,
% 0.17/0.41 regular: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminus_type,type,
% 0.17/0.41 setminus: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(setminusI_type,type,
% 0.17/0.41 setminusI: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusI,definition,
% 0.17/0.41 ( setminusI
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusEL_type,type,
% 0.17/0.41 setminusEL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusEL,definition,
% 0.17/0.41 ( setminusEL
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.41 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusER_type,type,
% 0.17/0.41 setminusER: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusER,definition,
% 0.17/0.41 ( setminusER
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.41 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusSubset2_type,type,
% 0.17/0.41 setminusSubset2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusSubset2,definition,
% 0.17/0.41 ( setminusSubset2
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( subset @ A @ B )
% 0.17/0.41 => ( ( setminus @ A @ B )
% 0.17/0.41 = emptyset ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusERneg_type,type,
% 0.17/0.41 setminusERneg: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusERneg,definition,
% 0.17/0.41 ( setminusERneg
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.41 => ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusELneg_type,type,
% 0.17/0.41 setminusELneg: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusELneg,definition,
% 0.17/0.41 ( setminusELneg
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusILneg_type,type,
% 0.17/0.41 setminusILneg: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusILneg,definition,
% 0.17/0.41 ( setminusILneg
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ~ ( in @ Xx @ A )
% 0.17/0.41 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusIRneg_type,type,
% 0.17/0.41 setminusIRneg: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusIRneg,definition,
% 0.17/0.41 ( setminusIRneg
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ B )
% 0.17/0.41 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusLsub_type,type,
% 0.17/0.41 setminusLsub: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusLsub,definition,
% 0.17/0.41 ( setminusLsub
% 0.17/0.41 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setminusSubset1_type,type,
% 0.17/0.41 setminusSubset1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setminusSubset1,definition,
% 0.17/0.41 ( setminusSubset1
% 0.17/0.41 = ( ! [A: $i,B: $i] :
% 0.17/0.41 ( ( ( setminus @ A @ B )
% 0.17/0.41 = emptyset )
% 0.17/0.41 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(symdiff_type,type,
% 0.17/0.41 symdiff: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffE_type,type,
% 0.17/0.41 symdiffE: $o ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffE,definition,
% 0.17/0.41 ( symdiffE
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.17/0.41 => ! [Xphi: $o] :
% 0.17/0.41 ( ( ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => Xphi ) )
% 0.17/0.41 => ( ( ~ ( in @ Xx @ A )
% 0.17/0.41 => ( ( in @ Xx @ B )
% 0.17/0.41 => Xphi ) )
% 0.17/0.41 => Xphi ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffI1_type,type,
% 0.17/0.41 symdiffI1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffI1,definition,
% 0.17/0.41 ( symdiffI1
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffI2_type,type,
% 0.17/0.41 symdiffI2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffI2,definition,
% 0.17/0.41 ( symdiffI2
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ~ ( in @ Xx @ A )
% 0.17/0.41 => ( ( in @ Xx @ B )
% 0.17/0.41 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffIneg1_type,type,
% 0.17/0.41 symdiffIneg1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffIneg1,definition,
% 0.17/0.41 ( symdiffIneg1
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( in @ Xx @ B )
% 0.17/0.41 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffIneg2_type,type,
% 0.17/0.41 symdiffIneg2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(symdiffIneg2,definition,
% 0.17/0.41 ( symdiffIneg2
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ~ ( in @ Xx @ A )
% 0.17/0.41 => ( ~ ( in @ Xx @ B )
% 0.17/0.41 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(iskpair_type,type,
% 0.17/0.41 iskpair: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(secondinupair_type,type,
% 0.17/0.41 secondinupair: $o ).
% 0.17/0.41
% 0.17/0.41 thf(secondinupair,definition,
% 0.17/0.41 ( secondinupair
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairIL_type,type,
% 0.17/0.41 setukpairIL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairIL,definition,
% 0.17/0.41 ( setukpairIL
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairIR_type,type,
% 0.17/0.41 setukpairIR: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairIR,definition,
% 0.17/0.41 ( setukpairIR
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(kpairiskpair_type,type,
% 0.17/0.41 kpairiskpair: $o ).
% 0.17/0.41
% 0.17/0.41 thf(kpairiskpair,definition,
% 0.17/0.41 ( kpairiskpair
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(kpair_type,type,
% 0.17/0.41 kpair: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(kpairp_type,type,
% 0.17/0.41 kpairp: $o ).
% 0.17/0.41
% 0.17/0.41 thf(kpairp,definition,
% 0.17/0.41 ( kpairp
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(cartprod_type,type,
% 0.17/0.41 cartprod: $i > $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsubset_type,type,
% 0.17/0.41 singletonsubset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsubset,definition,
% 0.17/0.41 ( singletonsubset
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(singletoninpowerset_type,type,
% 0.17/0.41 singletoninpowerset: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletoninpowerset,definition,
% 0.17/0.41 ( singletoninpowerset
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(singletoninpowunion_type,type,
% 0.17/0.41 singletoninpowunion: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletoninpowunion,definition,
% 0.17/0.41 ( singletoninpowunion
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairset2E_type,type,
% 0.17/0.41 upairset2E: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairset2E,definition,
% 0.17/0.41 ( upairset2E
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.41 => ( ( Xz = Xx )
% 0.17/0.41 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairsubunion_type,type,
% 0.17/0.41 upairsubunion: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairsubunion,definition,
% 0.17/0.41 ( upairsubunion
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(upairinpowunion_type,type,
% 0.17/0.41 upairinpowunion: $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairinpowunion,definition,
% 0.17/0.41 ( upairinpowunion
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem1_type,type,
% 0.17/0.41 ubforcartprodlem1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem1,definition,
% 0.17/0.41 ( ubforcartprodlem1
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem2_type,type,
% 0.17/0.41 ubforcartprodlem2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem2,definition,
% 0.17/0.41 ( ubforcartprodlem2
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem3_type,type,
% 0.17/0.41 ubforcartprodlem3: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ubforcartprodlem3,definition,
% 0.17/0.41 ( ubforcartprodlem3
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodpairin_type,type,
% 0.17/0.41 cartprodpairin: $o ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodpairin,definition,
% 0.17/0.41 ( cartprodpairin
% 0.17/0.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodmempair1_type,type,
% 0.17/0.41 cartprodmempair1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodmempair1,definition,
% 0.17/0.41 ( cartprodmempair1
% 0.17/0.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ? [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ B )
% 0.17/0.41 & ( Xu
% 0.17/0.41 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodmempair_type,type,
% 0.17/0.41 cartprodmempair: $o ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodmempair,definition,
% 0.17/0.41 ( cartprodmempair
% 0.17/0.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.41 => ( iskpair @ Xu ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionE2_type,type,
% 0.17/0.41 setunionE2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionE2,definition,
% 0.17/0.41 ( setunionE2
% 0.17/0.41 = ( ! [A: $i,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.41 => ? [X: $i] :
% 0.17/0.41 ( ( in @ X @ A )
% 0.17/0.41 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton1_type,type,
% 0.17/0.41 setunionsingleton1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton1,definition,
% 0.17/0.41 ( setunionsingleton1
% 0.17/0.41 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton2_type,type,
% 0.17/0.41 setunionsingleton2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton2,definition,
% 0.17/0.41 ( setunionsingleton2
% 0.17/0.41 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton_type,type,
% 0.17/0.41 setunionsingleton: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setunionsingleton,definition,
% 0.17/0.41 ( setunionsingleton
% 0.17/0.41 = ( ! [Xx: $i] :
% 0.17/0.41 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.17/0.41 = Xx ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(singleton_type,type,
% 0.17/0.41 singleton: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletonprop_type,type,
% 0.17/0.41 singletonprop: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletonprop,definition,
% 0.17/0.41 ( singletonprop
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ A )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) )
% 0.17/0.41 => ( ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) )
% 0.17/0.41 => ( singleton
% 0.17/0.41 @ ( dsetconstr @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ex1_type,type,
% 0.17/0.41 ex1: $i > ( $i > $o ) > $o ).
% 0.17/0.41
% 0.17/0.41 thf(ex1E1_type,type,
% 0.17/0.41 ex1E1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ex1E1,definition,
% 0.17/0.41 ( ex1E1
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ( ex1 @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.41 => ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ex1I_type,type,
% 0.17/0.41 ex1I: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ex1I,definition,
% 0.17/0.41 ( ex1I
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 => ( ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ A )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xy = Xx ) ) )
% 0.17/0.41 => ( ex1 @ A
% 0.17/0.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(ex1I2_type,type,
% 0.17/0.41 ex1I2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(ex1I2,definition,
% 0.17/0.41 ( ex1I2
% 0.17/0.41 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.41 ( ! [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 => ! [Xy: $i] :
% 0.17/0.41 ( ( in @ Xy @ A )
% 0.17/0.41 => ( ( Xphi @ Xx )
% 0.17/0.41 => ( ( Xphi @ Xy )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) )
% 0.17/0.41 => ( ? [Xx: $i] :
% 0.17/0.41 ( ( in @ Xx @ A )
% 0.17/0.41 & ( Xphi @ Xx ) )
% 0.17/0.41 => ( ex1 @ A
% 0.17/0.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsuniq_type,type,
% 0.17/0.41 singletonsuniq: $o ).
% 0.17/0.41
% 0.17/0.41 thf(singletonsuniq,definition,
% 0.17/0.41 ( singletonsuniq
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( ( setadjoin @ Xx @ emptyset )
% 0.17/0.41 = ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.41 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(atmost1p_type,type,
% 0.17/0.41 atmost1p: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(atleast2p_type,type,
% 0.17/0.41 atleast2p: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(atmost2p_type,type,
% 0.17/0.41 atmost2p: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(upairsetp_type,type,
% 0.17/0.41 upairsetp: $i > $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL1_type,type,
% 0.17/0.41 setukpairinjL1: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL1,definition,
% 0.17/0.41 ( setukpairinjL1
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.41 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.41 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(kfstsingleton_type,type,
% 0.17/0.41 kfstsingleton: $o ).
% 0.17/0.41
% 0.17/0.41 thf(kfstsingleton,definition,
% 0.17/0.41 ( kfstsingleton
% 0.17/0.41 = ( ! [Xu: $i] :
% 0.17/0.41 ( ( iskpair @ Xu )
% 0.17/0.41 => ( singleton
% 0.17/0.41 @ ( dsetconstr @ ( setunion @ Xu )
% 0.17/0.41 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(theprop_type,type,
% 0.17/0.41 theprop: $o ).
% 0.17/0.41
% 0.17/0.41 thf(theprop,definition,
% 0.17/0.41 ( theprop
% 0.17/0.41 = ( ! [X: $i] :
% 0.17/0.41 ( ( singleton @ X )
% 0.17/0.41 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(kfst_type,type,
% 0.17/0.41 kfst: $i > $i ).
% 0.17/0.41
% 0.17/0.41 thf(kfstpairEq_type,type,
% 0.17/0.41 kfstpairEq: $o ).
% 0.17/0.41
% 0.17/0.41 thf(kfstpairEq,definition,
% 0.17/0.41 ( kfstpairEq
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.17/0.41 = Xx ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodfstin_type,type,
% 0.17/0.41 cartprodfstin: $o ).
% 0.17/0.41
% 0.17/0.41 thf(cartprodfstin,definition,
% 0.17/0.41 ( cartprodfstin
% 0.17/0.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.41 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL2_type,type,
% 0.17/0.41 setukpairinjL2: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL2,definition,
% 0.17/0.41 ( setukpairinjL2
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.41 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.41 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.41 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL_type,type,
% 0.17/0.41 setukpairinjL: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjL,definition,
% 0.17/0.41 ( setukpairinjL
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.41 ( ( ( kpair @ Xx @ Xy )
% 0.17/0.41 = ( kpair @ Xz @ Xu ) )
% 0.17/0.41 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjR11_type,type,
% 0.17/0.41 setukpairinjR11: $o ).
% 0.17/0.41
% 0.17/0.41 thf(setukpairinjR11,definition,
% 0.17/0.41 ( setukpairinjR11
% 0.17/0.41 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.41 ( ( Xx = Xy )
% 0.17/0.41 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.41 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR12_type,type,
% 0.17/0.42 setukpairinjR12: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR12,definition,
% 0.17/0.42 ( setukpairinjR12
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR1_type,type,
% 0.17/0.42 setukpairinjR1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR1,definition,
% 0.17/0.42 ( setukpairinjR1
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( ( Xz = Xu )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairequniteq_type,type,
% 0.17/0.42 upairequniteq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairequniteq,definition,
% 0.17/0.42 ( upairequniteq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.42 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ Xz @ emptyset ) )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR2_type,type,
% 0.17/0.42 setukpairinjR2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR2,definition,
% 0.17/0.42 ( setukpairinjR2
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR_type,type,
% 0.17/0.42 setukpairinjR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR,definition,
% 0.17/0.42 ( setukpairinjR
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( kpair @ Xx @ Xy )
% 0.17/0.42 = ( kpair @ Xz @ Xu ) )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ksndsingleton_type,type,
% 0.17/0.42 ksndsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ksndsingleton,definition,
% 0.17/0.42 ( ksndsingleton
% 0.17/0.42 = ( ! [Xu: $i] :
% 0.17/0.42 ( ( iskpair @ Xu )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ ( setunion @ Xu )
% 0.17/0.42 @ ^ [Xx: $i] :
% 0.17/0.42 ( Xu
% 0.17/0.42 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ksnd_type,type,
% 0.17/0.42 ksnd: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(ksndpairEq_type,type,
% 0.17/0.42 ksndpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ksndpairEq,definition,
% 0.17/0.42 ( ksndpairEq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xy ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kpairsurjEq_type,type,
% 0.17/0.42 kpairsurjEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kpairsurjEq,definition,
% 0.17/0.42 ( kpairsurjEq
% 0.17/0.42 = ( ! [Xu: $i] :
% 0.17/0.42 ( ( iskpair @ Xu )
% 0.17/0.42 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.17/0.42 = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndin_type,type,
% 0.17/0.42 cartprodsndin: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndin,definition,
% 0.17/0.42 ( cartprodsndin
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemEL_type,type,
% 0.17/0.42 cartprodpairmemEL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemEL,definition,
% 0.17/0.42 ( cartprodpairmemEL
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemER_type,type,
% 0.17/0.42 cartprodpairmemER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemER,definition,
% 0.17/0.42 ( cartprodpairmemER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ Xy @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempaircEq_type,type,
% 0.17/0.42 cartprodmempaircEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempaircEq,definition,
% 0.17/0.42 ( cartprodmempaircEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( kpair @ Xx @ Xy )
% 0.17/0.42 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstpairEq_type,type,
% 0.17/0.42 cartprodfstpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstpairEq,definition,
% 0.17/0.42 ( cartprodfstpairEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndpairEq_type,type,
% 0.17/0.42 cartprodsndpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndpairEq,definition,
% 0.17/0.42 ( cartprodsndpairEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairsurjEq_type,type,
% 0.17/0.42 cartprodpairsurjEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairsurjEq,definition,
% 0.17/0.42 ( cartprodpairsurjEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.17/0.42 = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln_type,type,
% 0.17/0.42 breln: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstr_type,type,
% 0.17/0.42 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrI_type,type,
% 0.17/0.42 dpsetconstrI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrI,definition,
% 0.17/0.42 ( dpsetconstrI
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( Xphi @ Xx @ Xy )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrSub_type,type,
% 0.17/0.42 dpsetconstrSub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrSub,definition,
% 0.17/0.42 ( dpsetconstrSub
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( subset
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.17/0.42 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln_type,type,
% 0.17/0.42 setOfPairsIsBReln: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln,definition,
% 0.17/0.42 ( setOfPairsIsBReln
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( breln @ A @ B
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrERa_type,type,
% 0.17/0.42 dpsetconstrERa: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrERa,definition,
% 0.17/0.42 ( dpsetconstrERa
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL1_type,type,
% 0.17/0.42 dpsetconstrEL1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL1,definition,
% 0.17/0.42 ( dpsetconstrEL1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL2_type,type,
% 0.17/0.42 dpsetconstrEL2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL2,definition,
% 0.17/0.42 ( dpsetconstrEL2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( in @ Xy @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrER_type,type,
% 0.17/0.42 dpsetconstrER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrER,definition,
% 0.17/0.42 ( dpsetconstrER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(func_type,type,
% 0.17/0.42 func: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcSet_type,type,
% 0.17/0.42 funcSet: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(funcImageSingleton_type,type,
% 0.17/0.42 funcImageSingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcImageSingleton,definition,
% 0.17/0.42 ( funcImageSingleton
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(apProp_type,type,
% 0.17/0.42 apProp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(apProp,definition,
% 0.17/0.42 ( apProp
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in
% 0.17/0.42 @ ( setunion
% 0.17/0.42 @ ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.17/0.42 @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ap_type,type,
% 0.17/0.42 ap: $i > $i > $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(app_type,type,
% 0.17/0.42 app: $o ).
% 0.17/0.42
% 0.17/0.42 thf(app,definition,
% 0.17/0.42 ( app
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(infuncsetfunc_type,type,
% 0.17/0.42 infuncsetfunc: $o ).
% 0.17/0.42
% 0.17/0.42 thf(infuncsetfunc,definition,
% 0.17/0.42 ( infuncsetfunc
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ap2p_type,type,
% 0.17/0.42 ap2p: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ap2p,definition,
% 0.17/0.42 ( ap2p
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcinfuncset_type,type,
% 0.17/0.42 funcinfuncset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcinfuncset,definition,
% 0.17/0.42 ( funcinfuncset
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(lamProp_type,type,
% 0.17/0.42 lamProp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(lamProp,definition,
% 0.17/0.42 ( lamProp
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ( func @ A @ B
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xf @ Xx )
% 0.17/0.42 = Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(lam_type,type,
% 0.17/0.42 lam: $i > $i > ( $i > $i ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(lamp_type,type,
% 0.17/0.42 lamp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(lamp,definition,
% 0.17/0.42 ( lamp
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ( func @ A @ B
% 0.17/0.42 @ ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(lam2p_type,type,
% 0.17/0.42 lam2p: $o ).
% 0.17/0.42
% 0.17/0.42 thf(lam2p,definition,
% 0.17/0.42 ( lam2p
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ( in
% 0.17/0.42 @ ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.17/0.42 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(brelnall1_type,type,
% 0.17/0.42 brelnall1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(brelnall1,definition,
% 0.17/0.42 ( brelnall1
% 0.17/0.42 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ R )
% 0.17/0.42 => ! [Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ R )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(brelnall2_type,type,
% 0.17/0.42 brelnall2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(brelnall2,definition,
% 0.17/0.42 ( brelnall2
% 0.17/0.42 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ R )
% 0.17/0.42 => ! [Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ R )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ex1E2_type,type,
% 0.17/0.42 ex1E2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ex1E2,definition,
% 0.17/0.42 ( ex1E2
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ( ex1 @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp1_type,type,
% 0.17/0.42 funcGraphProp1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp1,definition,
% 0.17/0.42 ( funcGraphProp1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp3_type,type,
% 0.17/0.42 funcGraphProp3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp3,definition,
% 0.17/0.42 ( funcGraphProp3
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp2_type,type,
% 0.17/0.42 funcGraphProp2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp2,definition,
% 0.17/0.42 ( funcGraphProp2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcextLem_type,type,
% 0.17/0.42 funcextLem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcextLem,definition,
% 0.17/0.42 ( funcextLem
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xg: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xg )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp4_type,type,
% 0.17/0.42 funcGraphProp4: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcGraphProp4,definition,
% 0.17/0.42 ( funcGraphProp4
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subbreln_type,type,
% 0.17/0.42 subbreln: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subbreln,definition,
% 0.17/0.42 ( subbreln
% 0.17/0.42 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ S )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.42 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eqbreln_type,type,
% 0.17/0.42 eqbreln: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eqbreln,definition,
% 0.17/0.42 ( eqbreln
% 0.17/0.42 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln @ A @ B @ S )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.17/0.42 => ( R = S ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcext_type,type,
% 0.17/0.42 funcext: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcext,definition,
% 0.17/0.42 ( funcext
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xg: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xg )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.42 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(funcext2_type,type,
% 0.17/0.42 funcext2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcext2,definition,
% 0.17/0.42 ( funcext2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ! [Xg: $i] :
% 0.17/0.42 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.42 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ap2apEq1_type,type,
% 0.17/0.42 ap2apEq1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ap2apEq1,definition,
% 0.17/0.42 ( ap2apEq1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ap2apEq2_type,type,
% 0.17/0.42 ap2apEq2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ap2apEq2,definition,
% 0.17/0.42 ( ap2apEq2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.42 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(beta1_type,type,
% 0.17/0.42 beta1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(beta1,definition,
% 0.17/0.42 ( beta1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B
% 0.17/0.42 @ ( lam @ A @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.17/0.42 @ Xx )
% 0.17/0.42 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eta1_type,type,
% 0.17/0.42 eta1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eta1,definition,
% 0.17/0.42 ( eta1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ( ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.17/0.42 = Xf ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(lam2lamEq_type,type,
% 0.17/0.42 lam2lamEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(lam2lamEq,definition,
% 0.17/0.42 ( lam2lamEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ( ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.17/0.42 = ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(beta2_type,type,
% 0.17/0.42 beta2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(beta2,definition,
% 0.17/0.42 ( beta2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( ap @ A @ B
% 0.17/0.42 @ ( lam @ A @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.17/0.42 @ Xx )
% 0.17/0.42 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eta2_type,type,
% 0.17/0.42 eta2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eta2,definition,
% 0.17/0.42 ( eta2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ( ( lam @ A @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.17/0.42 = Xf ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iffalseProp1_type,type,
% 0.17/0.42 iffalseProp1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iffalseProp1,definition,
% 0.17/0.42 ( iffalseProp1
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ~ Xphi
% 0.17/0.42 => ( in @ Xy
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xz: $i] :
% 0.17/0.42 ( ( Xphi
% 0.17/0.42 & ( Xz = Xx ) )
% 0.17/0.42 | ( ~ Xphi
% 0.17/0.42 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iffalseProp2_type,type,
% 0.17/0.42 iffalseProp2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iffalseProp2,definition,
% 0.17/0.42 ( iffalseProp2
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ~ Xphi
% 0.17/0.42 => ( ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xz: $i] :
% 0.17/0.42 ( ( Xphi
% 0.17/0.42 & ( Xz = Xx ) )
% 0.17/0.42 | ( ~ Xphi
% 0.17/0.42 & ( Xz = Xy ) ) ) )
% 0.17/0.42 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueProp1_type,type,
% 0.17/0.42 iftrueProp1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueProp1,definition,
% 0.17/0.42 ( iftrueProp1
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( Xphi
% 0.17/0.42 => ( in @ Xx
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xz: $i] :
% 0.17/0.42 ( ( Xphi
% 0.17/0.42 & ( Xz = Xx ) )
% 0.17/0.42 | ( ~ Xphi
% 0.17/0.42 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueProp2_type,type,
% 0.17/0.42 iftrueProp2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueProp2,definition,
% 0.17/0.42 ( iftrueProp2
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( Xphi
% 0.17/0.42 => ( ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xz: $i] :
% 0.17/0.42 ( ( Xphi
% 0.17/0.42 & ( Xz = Xx ) )
% 0.17/0.42 | ( ~ Xphi
% 0.17/0.42 & ( Xz = Xy ) ) ) )
% 0.17/0.42 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ifSingleton_type,type,
% 0.17/0.42 ifSingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ifSingleton,definition,
% 0.17/0.42 ( ifSingleton
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xz: $i] :
% 0.17/0.42 ( ( Xphi
% 0.17/0.42 & ( Xz = Xx ) )
% 0.17/0.42 | ( ~ Xphi
% 0.17/0.42 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(if_type,type,
% 0.17/0.42 if: $i > $o > $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(ifp_type,type,
% 0.17/0.42 ifp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ifp,definition,
% 0.17/0.42 ( ifp
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(theeq_type,type,
% 0.17/0.42 theeq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(theeq,definition,
% 0.17/0.42 ( theeq
% 0.17/0.42 = ( ! [X: $i] :
% 0.17/0.42 ( ( singleton @ X )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ X )
% 0.17/0.42 => ( ( setunion @ X )
% 0.17/0.42 = Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iftrue_type,type,
% 0.17/0.42 iftrue: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iftrue,definition,
% 0.17/0.42 ( iftrue
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( Xphi
% 0.17/0.42 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.17/0.42 = Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iffalse_type,type,
% 0.17/0.42 iffalse: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iffalse,definition,
% 0.17/0.42 ( iffalse
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ~ Xphi
% 0.17/0.42 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.17/0.42 = Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueorfalse_type,type,
% 0.17/0.42 iftrueorfalse: $o ).
% 0.17/0.42
% 0.17/0.42 thf(iftrueorfalse,definition,
% 0.17/0.42 ( iftrueorfalse
% 0.17/0.42 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectT_lem_type,type,
% 0.17/0.42 binintersectT_lem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectT_lem,definition,
% 0.17/0.42 ( binintersectT_lem
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionT_lem_type,type,
% 0.17/0.42 binunionT_lem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionT_lem,definition,
% 0.17/0.42 ( binunionT_lem
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetT_lem_type,type,
% 0.17/0.42 powersetT_lem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetT_lem,definition,
% 0.17/0.42 ( powersetT_lem
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusT_lem_type,type,
% 0.17/0.42 setminusT_lem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusT_lem,definition,
% 0.17/0.42 ( setminusT_lem
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementT_lem_type,type,
% 0.17/0.42 complementT_lem: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementT_lem,definition,
% 0.17/0.42 ( complementT_lem
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setextT_type,type,
% 0.17/0.42 setextT: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setextT,definition,
% 0.17/0.42 ( setextT
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ( in @ Xx @ Y ) ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ Y )
% 0.17/0.42 => ( in @ Xx @ X ) ) )
% 0.17/0.42 => ( X = Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetTI_type,type,
% 0.17/0.42 subsetTI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetTI,definition,
% 0.17/0.42 ( subsetTI
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ( in @ Xx @ Y ) ) )
% 0.17/0.42 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetTI1_type,type,
% 0.17/0.42 powersetTI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetTI1,definition,
% 0.17/0.42 ( powersetTI1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ( in @ Xx @ Y ) ) )
% 0.17/0.42 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetTE1_type,type,
% 0.17/0.42 powersetTE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetTE1,definition,
% 0.17/0.42 ( powersetTE1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ X @ ( powerset @ Y ) )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementTI1_type,type,
% 0.17/0.42 complementTI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementTI1,definition,
% 0.17/0.42 ( complementTI1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementTE1_type,type,
% 0.17/0.42 complementTE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementTE1,definition,
% 0.17/0.42 ( complementTE1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.42 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectTELcontra_type,type,
% 0.17/0.42 binintersectTELcontra: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectTELcontra,definition,
% 0.17/0.42 ( binintersectTELcontra
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ X )
% 0.17/0.42 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectTERcontra_type,type,
% 0.17/0.42 binintersectTERcontra: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectTERcontra,definition,
% 0.17/0.42 ( binintersectTERcontra
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ Y )
% 0.17/0.42 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT_type,type,
% 0.17/0.42 contrasubsetT: $o ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT,definition,
% 0.17/0.42 ( contrasubsetT
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.42 => ( ( in @ Xx @ Y )
% 0.17/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT1_type,type,
% 0.17/0.42 contrasubsetT1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT1,definition,
% 0.17/0.42 ( contrasubsetT1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( subset @ X @ Y )
% 0.17/0.42 => ( ~ ( in @ Xx @ Y )
% 0.17/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT2_type,type,
% 0.17/0.42 contrasubsetT2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT2,definition,
% 0.17/0.42 ( contrasubsetT2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ Y )
% 0.17/0.42 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT3_type,type,
% 0.17/0.42 contrasubsetT3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(contrasubsetT3,definition,
% 0.17/0.42 ( contrasubsetT3
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.17/0.42 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementI1_type,type,
% 0.17/0.42 doubleComplementI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementI1,definition,
% 0.17/0.42 ( doubleComplementI1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ X )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementE1_type,type,
% 0.17/0.42 doubleComplementE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementE1,definition,
% 0.17/0.42 ( doubleComplementE1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.17/0.42 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementSub1_type,type,
% 0.17/0.42 doubleComplementSub1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementSub1,definition,
% 0.17/0.42 ( doubleComplementSub1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementSub2_type,type,
% 0.17/0.42 doubleComplementSub2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementSub2,definition,
% 0.17/0.42 ( doubleComplementSub2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementEq_type,type,
% 0.17/0.42 doubleComplementEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(doubleComplementEq,definition,
% 0.17/0.42 ( doubleComplementEq
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ( X
% 0.17/0.42 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementTnotintersectT_type,type,
% 0.17/0.42 complementTnotintersectT: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementTnotintersectT,definition,
% 0.17/0.42 ( complementTnotintersectT
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.42 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementImpComplementIntersect_type,type,
% 0.17/0.42 complementImpComplementIntersect: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementImpComplementIntersect,definition,
% 0.17/0.42 ( complementImpComplementIntersect
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementSubsetComplementIntersect_type,type,
% 0.17/0.42 complementSubsetComplementIntersect: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementSubsetComplementIntersect,definition,
% 0.17/0.42 ( complementSubsetComplementIntersect
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementInPowersetComplementIntersect_type,type,
% 0.17/0.42 complementInPowersetComplementIntersect: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementInPowersetComplementIntersect,definition,
% 0.17/0.42 ( complementInPowersetComplementIntersect
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(contraSubsetComplement_type,type,
% 0.17/0.42 contraSubsetComplement: $o ).
% 0.17/0.42
% 0.17/0.42 thf(contraSubsetComplement,definition,
% 0.17/0.42 ( contraSubsetComplement
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ Y )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementTcontraSubset_type,type,
% 0.17/0.42 complementTcontraSubset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementTcontraSubset,definition,
% 0.17/0.42 ( complementTcontraSubset
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.42 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTILcontra_type,type,
% 0.17/0.42 binunionTILcontra: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTILcontra,definition,
% 0.17/0.42 ( binunionTILcontra
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTIRcontra_type,type,
% 0.17/0.42 binunionTIRcontra: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTIRcontra,definition,
% 0.17/0.42 ( binunionTIRcontra
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.42 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInUnion_type,type,
% 0.17/0.42 inIntersectImpInUnion: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInUnion,definition,
% 0.17/0.42 ( inIntersectImpInUnion
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.42 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInUnion2_type,type,
% 0.17/0.42 inIntersectImpInUnion2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInUnion2,definition,
% 0.17/0.42 ( inIntersectImpInUnion2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.42 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInIntersectUnions_type,type,
% 0.17/0.42 inIntersectImpInIntersectUnions: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inIntersectImpInIntersectUnions,definition,
% 0.17/0.42 ( inIntersectImpInIntersectUnions
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.42 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(intersectInPowersetIntersectUnions_type,type,
% 0.17/0.42 intersectInPowersetIntersectUnions: $o ).
% 0.17/0.42
% 0.17/0.42 thf(intersectInPowersetIntersectUnions,definition,
% 0.17/0.42 ( intersectInPowersetIntersectUnions
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inComplementUnionImpNotIn1_type,type,
% 0.17/0.42 inComplementUnionImpNotIn1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inComplementUnionImpNotIn1,definition,
% 0.17/0.42 ( inComplementUnionImpNotIn1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.42 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inComplementUnionImpInComplement1_type,type,
% 0.17/0.42 inComplementUnionImpInComplement1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inComplementUnionImpInComplement1,definition,
% 0.17/0.42 ( inComplementUnionImpInComplement1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTE_type,type,
% 0.17/0.42 binunionTE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTE,definition,
% 0.17/0.42 ( binunionTE
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.42 => ( ( ( in @ Xx @ X )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => ( ( ( in @ Xx @ Y )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => Xphi ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTEcontra_type,type,
% 0.17/0.42 binunionTEcontra: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionTEcontra,definition,
% 0.17/0.42 ( binunionTEcontra
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ X )
% 0.17/0.42 => ( ~ ( in @ Xx @ Y )
% 0.17/0.42 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a1_type,type,
% 0.17/0.42 demorgan2a1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a1,definition,
% 0.17/0.42 ( demorgan2a1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(complementUnionInPowersetComplement_type,type,
% 0.17/0.42 complementUnionInPowersetComplement: $o ).
% 0.17/0.42
% 0.17/0.42 thf(complementUnionInPowersetComplement,definition,
% 0.17/0.42 ( complementUnionInPowersetComplement
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a2_type,type,
% 0.17/0.42 demorgan2a2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a2,definition,
% 0.17/0.42 ( demorgan2a2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1a_type,type,
% 0.17/0.42 demorgan1a: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1a,definition,
% 0.17/0.42 ( demorgan1a
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1b_type,type,
% 0.17/0.42 demorgan1b: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1b,definition,
% 0.17/0.42 ( demorgan1b
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1_type,type,
% 0.17/0.42 demorgan1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan1,definition,
% 0.17/0.42 ( demorgan1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.17/0.42 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a_type,type,
% 0.17/0.42 demorgan2a: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2a,definition,
% 0.17/0.42 ( demorgan2a
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2b2_type,type,
% 0.17/0.42 demorgan2b2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2b2,definition,
% 0.17/0.42 ( demorgan2b2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.42 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2b_type,type,
% 0.17/0.42 demorgan2b: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2b,definition,
% 0.17/0.42 ( demorgan2b
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2_type,type,
% 0.17/0.42 demorgan2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(demorgan2,definition,
% 0.17/0.42 ( demorgan2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.17/0.42 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule0_type,type,
% 0.17/0.42 woz13rule0: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule0,definition,
% 0.17/0.42 ( woz13rule0
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule1_type,type,
% 0.17/0.42 woz13rule1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule1,definition,
% 0.17/0.42 ( woz13rule1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ Z )
% 0.17/0.42 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule2_type,type,
% 0.17/0.42 woz13rule2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule2,definition,
% 0.17/0.42 ( woz13rule2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ Y @ Z )
% 0.17/0.42 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule3_type,type,
% 0.17/0.42 woz13rule3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule3,definition,
% 0.17/0.42 ( woz13rule3
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ Y )
% 0.17/0.42 => ( ( subset @ X @ Z )
% 0.17/0.42 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule4_type,type,
% 0.17/0.42 woz13rule4: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz13rule4,definition,
% 0.17/0.42 ( woz13rule4
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ! [W: $i] :
% 0.17/0.42 ( ( in @ W @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ Z )
% 0.17/0.42 => ( ( subset @ Y @ W )
% 0.17/0.42 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_1_type,type,
% 0.17/0.42 woz1_1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_1,definition,
% 0.17/0.42 ( woz1_1
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_2_type,type,
% 0.17/0.42 woz1_2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_2,definition,
% 0.17/0.42 ( woz1_2
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ! [W: $i] :
% 0.17/0.42 ( ( in @ W @ ( powerset @ A ) )
% 0.17/0.42 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.17/0.42 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_3_type,type,
% 0.17/0.42 woz1_3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_3,definition,
% 0.17/0.42 ( woz1_3
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ! [Z: $i] :
% 0.17/0.42 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_4_type,type,
% 0.17/0.42 woz1_4: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_4,definition,
% 0.17/0.42 ( woz1_4
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.42 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_5_type,type,
% 0.17/0.42 woz1_5: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz1_5,definition,
% 0.17/0.42 ( woz1_5
% 0.17/0.42 = ( ! [A: $i,X: $i] :
% 0.17/0.42 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.42 => ! [Y: $i] :
% 0.17/0.42 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.42 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1_type,type,
% 0.17/0.42 breln1: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1all2_type,type,
% 0.17/0.42 breln1all2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1all2,definition,
% 0.17/0.42 ( breln1all2
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ R )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1Set_type,type,
% 0.17/0.42 breln1Set: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(breln1SetBreln1_type,type,
% 0.17/0.42 breln1SetBreln1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1SetBreln1,definition,
% 0.17/0.42 ( breln1SetBreln1
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( in @ R @ ( breln1Set @ A ) )
% 0.17/0.42 => ( breln1 @ A @ R ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(transitive_type,type,
% 0.17/0.42 transitive: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(antisymmetric_type,type,
% 0.17/0.42 antisymmetric: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(reflexive_type,type,
% 0.17/0.42 reflexive: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(refltransitive_type,type,
% 0.17/0.42 refltransitive: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(refllinearorder_type,type,
% 0.17/0.42 refllinearorder: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(reflwellordering_type,type,
% 0.17/0.42 reflwellordering: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(choice2fnsingleton_type,type,
% 0.17/0.42 choice2fnsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(choice2fnsingleton,definition,
% 0.17/0.42 ( choice2fnsingleton
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 & ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.42 => ! [R: $i] :
% 0.17/0.42 ( ( in @ R @ ( breln1Set @ B ) )
% 0.17/0.42 => ( ( reflwellordering @ B @ R )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xx @ Xy )
% 0.17/0.42 & ! [Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ B )
% 0.17/0.42 => ( ( Xphi @ Xx @ Xz )
% 0.17/0.42 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln1_type,type,
% 0.17/0.42 setOfPairsIsBReln1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln1,definition,
% 0.17/0.42 ( setOfPairsIsBReln1
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( breln1 @ A
% 0.17/0.42 @ ( dpsetconstr @ A @ A
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1all1_type,type,
% 0.17/0.42 breln1all1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1all1,definition,
% 0.17/0.42 ( breln1all1
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ R )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subbreln1_type,type,
% 0.17/0.42 subbreln1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subbreln1,definition,
% 0.17/0.42 ( subbreln1
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.42 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eqbreln1_type,type,
% 0.17/0.42 eqbreln1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eqbreln1,definition,
% 0.17/0.42 ( eqbreln1
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.17/0.42 => ( R = S ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invset_type,type,
% 0.17/0.42 breln1invset: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invprop_type,type,
% 0.17/0.42 breln1invprop: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invprop,definition,
% 0.17/0.42 ( breln1invprop
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invI_type,type,
% 0.17/0.42 breln1invI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invI,definition,
% 0.17/0.42 ( breln1invI
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invE_type,type,
% 0.17/0.42 breln1invE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1invE,definition,
% 0.17/0.42 ( breln1invE
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compset_type,type,
% 0.17/0.42 breln1compset: $i > $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compprop_type,type,
% 0.17/0.42 breln1compprop: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compprop,definition,
% 0.17/0.42 ( breln1compprop
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compI_type,type,
% 0.17/0.42 breln1compI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compI,definition,
% 0.17/0.42 ( breln1compI
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ! [Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.42 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compE_type,type,
% 0.17/0.42 breln1compE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compE,definition,
% 0.17/0.42 ( breln1compE
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.42 => ? [Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ A )
% 0.17/0.42 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.42 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compEex_type,type,
% 0.17/0.42 breln1compEex: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1compEex,definition,
% 0.17/0.42 ( breln1compEex
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.42 => ! [Xphi: $o] :
% 0.17/0.42 ( ! [Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.42 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.17/0.42 => Xphi ) ) )
% 0.17/0.42 => Xphi ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionprop_type,type,
% 0.17/0.42 breln1unionprop: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionprop,definition,
% 0.17/0.42 ( breln1unionprop
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionIL_type,type,
% 0.17/0.42 breln1unionIL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionIL,definition,
% 0.17/0.42 ( breln1unionIL
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionIR_type,type,
% 0.17/0.42 breln1unionIR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionIR,definition,
% 0.17/0.42 ( breln1unionIR
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionI_type,type,
% 0.17/0.42 breln1unionI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionI,definition,
% 0.17/0.42 ( breln1unionI
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionE_type,type,
% 0.17/0.42 breln1unionE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionE,definition,
% 0.17/0.42 ( breln1unionE
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionEcases_type,type,
% 0.17/0.42 breln1unionEcases: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionEcases,definition,
% 0.17/0.42 ( breln1unionEcases
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.17/0.42 => ! [Xphi: $o] :
% 0.17/0.42 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionCommutes_type,type,
% 0.17/0.42 breln1unionCommutes: $o ).
% 0.17/0.42
% 0.17/0.42 thf(breln1unionCommutes,definition,
% 0.17/0.42 ( breln1unionCommutes
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( ( binunion @ R @ S )
% 0.17/0.42 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz2Ex_type,type,
% 0.17/0.42 woz2Ex: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz2Ex,definition,
% 0.17/0.42 ( woz2Ex
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ( R
% 0.17/0.42 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz2W_type,type,
% 0.17/0.42 woz2W: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz2W,definition,
% 0.17/0.42 ( woz2W
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.42 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz2A_type,type,
% 0.17/0.42 woz2A: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz2A,definition,
% 0.17/0.42 ( woz2A
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [T: $i] :
% 0.17/0.42 ( ( breln1 @ A @ T )
% 0.17/0.42 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.17/0.42 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(woz2B_type,type,
% 0.17/0.42 woz2B: $o ).
% 0.17/0.42
% 0.17/0.42 thf(woz2B,definition,
% 0.17/0.42 ( woz2B
% 0.17/0.42 = ( ! [A: $i,R: $i] :
% 0.17/0.42 ( ( breln1 @ A @ R )
% 0.17/0.42 => ! [S: $i] :
% 0.17/0.42 ( ( breln1 @ A @ S )
% 0.17/0.42 => ! [T: $i] :
% 0.17/0.42 ( ( breln1 @ A @ T )
% 0.17/0.42 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.17/0.42 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(image1Ex_type,type,
% 0.17/0.42 image1Ex: $o ).
% 0.17/0.42
% 0.17/0.42 thf(image1Ex,definition,
% 0.17/0.42 ( image1Ex
% 0.17/0.42 = ( ! [A: $i,Xf: $i > $i] :
% 0.17/0.42 ? [B: $i] :
% 0.17/0.42 ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 <=> ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xx
% 0.17/0.42 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(image1Ex1_type,type,
% 0.17/0.42 image1Ex1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(image1Ex1,definition,
% 0.17/0.42 ( image1Ex1
% 0.17/0.42 = ( ! [A: $i,Xf: $i > $i] :
% 0.17/0.42 ( exu
% 0.17/0.42 @ ^ [B: $i] :
% 0.17/0.42 ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 <=> ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xx
% 0.17/0.42 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(image1_type,type,
% 0.17/0.42 image1: $i > ( $i > $i ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(image1Equiv_type,type,
% 0.17/0.42 image1Equiv: $o ).
% 0.17/0.42
% 0.17/0.42 thf(image1Equiv,definition,
% 0.17/0.42 ( image1Equiv
% 0.17/0.42 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx
% 0.17/0.42 @ ( image1 @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.42 <=> ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xx
% 0.17/0.42 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(image1E_type,type,
% 0.17/0.42 image1E: $o ).
% 0.17/0.42
% 0.17/0.42 thf(image1E,definition,
% 0.17/0.42 ( image1E
% 0.17/0.42 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx
% 0.17/0.42 @ ( image1 @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.42 => ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xx
% 0.17/0.42 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(image1I_type,type,
% 0.17/0.42 image1I: $o ).
% 0.17/0.42
% 0.17/0.42 thf(image1I,definition,
% 0.17/0.42 ( image1I
% 0.17/0.42 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.42 ( ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xx
% 0.17/0.42 = ( Xf @ Xy ) ) )
% 0.17/0.42 => ( in @ Xx
% 0.17/0.42 @ ( image1 @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(injective_type,type,
% 0.17/0.42 injective: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncSet_type,type,
% 0.17/0.42 injFuncSet: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncInInjFuncSet_type,type,
% 0.17/0.42 injFuncInInjFuncSet: $o ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncInInjFuncSet,definition,
% 0.17/0.42 ( injFuncInInjFuncSet
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.42 => ( ( injective @ A @ B @ Xf )
% 0.17/0.42 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncSetFuncIn_type,type,
% 0.17/0.42 injFuncSetFuncIn: $o ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncSetFuncIn,definition,
% 0.17/0.42 ( injFuncSetFuncIn
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.17/0.42 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncSetFuncInj_type,type,
% 0.17/0.42 injFuncSetFuncInj: $o ).
% 0.17/0.42
% 0.17/0.42 thf(injFuncSetFuncInj,definition,
% 0.17/0.42 ( injFuncSetFuncInj
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.17/0.42 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(surjective_type,type,
% 0.17/0.42 surjective: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(surjective,definition,
% 0.17/0.42 ( surjective
% 0.17/0.42 = ( ^ [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( ( ap @ A @ B @ Xf @ Xy )
% 0.17/0.42 = Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(surjFuncSet_type,type,
% 0.17/0.42 surjFuncSet: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(surjFuncSet,definition,
% 0.17/0.42 ( surjFuncSet
% 0.17/0.42 = ( ^ [A: $i,B: $i] :
% 0.17/0.42 ( dsetconstr @ ( funcSet @ A @ B )
% 0.17/0.42 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(surjFuncSetFuncIn_type,type,
% 0.17/0.42 surjFuncSetFuncIn: $o ).
% 0.17/0.42
% 0.17/0.42 thf(surjFuncSetFuncIn,definition,
% 0.17/0.42 ( surjFuncSetFuncIn
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.17/0.42 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(surjFuncSetFuncSurj,conjecture,
% 0.17/0.42 ( setextAx
% 0.17/0.42 => ( emptysetAx
% 0.17/0.42 => ( setadjoinAx
% 0.17/0.42 => ( powersetAx
% 0.17/0.42 => ( setunionAx
% 0.17/0.42 => ( omega0Ax
% 0.17/0.42 => ( omegaSAx
% 0.17/0.42 => ( omegaIndAx
% 0.17/0.42 => ( replAx
% 0.17/0.42 => ( foundationAx
% 0.17/0.42 => ( wellorderingAx
% 0.17/0.42 => ( descrp
% 0.17/0.42 => ( dsetconstrI
% 0.17/0.42 => ( dsetconstrEL
% 0.17/0.42 => ( dsetconstrER
% 0.17/0.42 => ( exuE1
% 0.17/0.42 => ( prop2setE
% 0.17/0.42 => ( emptysetE
% 0.17/0.42 => ( emptysetimpfalse
% 0.17/0.42 => ( notinemptyset
% 0.17/0.42 => ( exuE3e
% 0.17/0.42 => ( setext
% 0.17/0.42 => ( emptyI
% 0.17/0.42 => ( noeltsimpempty
% 0.17/0.42 => ( setbeta
% 0.17/0.42 => ( nonemptyE1
% 0.17/0.42 => ( nonemptyI
% 0.17/0.42 => ( nonemptyI1
% 0.17/0.42 => ( setadjoinIL
% 0.17/0.42 => ( emptyinunitempty
% 0.17/0.42 => ( setadjoinIR
% 0.17/0.42 => ( setadjoinE
% 0.17/0.42 => ( setadjoinOr
% 0.17/0.42 => ( setoftrueEq
% 0.17/0.42 => ( powersetI
% 0.17/0.42 => ( emptyinPowerset
% 0.17/0.42 => ( emptyInPowerset
% 0.17/0.42 => ( powersetE
% 0.17/0.42 => ( setunionI
% 0.17/0.42 => ( setunionE
% 0.17/0.42 => ( subPowSU
% 0.17/0.42 => ( exuE2
% 0.17/0.42 => ( nonemptyImpWitness
% 0.17/0.42 => ( uniqinunit
% 0.17/0.42 => ( notinsingleton
% 0.17/0.42 => ( eqinunit
% 0.17/0.42 => ( singletonsswitch
% 0.17/0.42 => ( upairsetE
% 0.17/0.42 => ( upairsetIL
% 0.17/0.42 => ( upairsetIR
% 0.17/0.42 => ( emptyE1
% 0.17/0.42 => ( vacuousDall
% 0.17/0.42 => ( quantDeMorgan1
% 0.17/0.42 => ( quantDeMorgan2
% 0.17/0.42 => ( quantDeMorgan3
% 0.17/0.42 => ( quantDeMorgan4
% 0.17/0.42 => ( prop2setI
% 0.17/0.42 => ( prop2set2propI
% 0.17/0.42 => ( notdexE
% 0.17/0.42 => ( notdallE
% 0.17/0.42 => ( exuI1
% 0.17/0.42 => ( exuI3
% 0.17/0.42 => ( exuI2
% 0.17/0.42 => ( inCongP
% 0.17/0.42 => ( in__Cong
% 0.17/0.42 => ( exuE3u
% 0.17/0.42 => ( exu__Cong
% 0.17/0.42 => ( emptyset__Cong
% 0.17/0.42 => ( setadjoin__Cong
% 0.17/0.42 => ( powerset__Cong
% 0.17/0.42 => ( setunion__Cong
% 0.17/0.42 => ( omega__Cong
% 0.17/0.42 => ( exuEu
% 0.17/0.42 => ( descr__Cong
% 0.17/0.42 => ( dsetconstr__Cong
% 0.17/0.42 => ( subsetI1
% 0.17/0.42 => ( eqimpsubset2
% 0.17/0.42 => ( eqimpsubset1
% 0.17/0.42 => ( subsetI2
% 0.17/0.42 => ( emptysetsubset
% 0.17/0.42 => ( subsetE
% 0.17/0.42 => ( subsetE2
% 0.17/0.42 => ( notsubsetI
% 0.17/0.42 => ( notequalI1
% 0.17/0.42 => ( notequalI2
% 0.17/0.42 => ( subsetRefl
% 0.17/0.42 => ( subsetTrans
% 0.17/0.42 => ( setadjoinSub
% 0.17/0.42 => ( setadjoinSub2
% 0.17/0.42 => ( subset2powerset
% 0.17/0.42 => ( setextsub
% 0.17/0.42 => ( subsetemptysetimpeq
% 0.17/0.42 => ( powersetI1
% 0.17/0.42 => ( powersetE1
% 0.17/0.42 => ( inPowerset
% 0.17/0.42 => ( powersetsubset
% 0.17/0.42 => ( sepInPowerset
% 0.17/0.42 => ( sepSubset
% 0.17/0.42 => ( binunionIL
% 0.17/0.42 => ( upairset2IR
% 0.17/0.42 => ( binunionIR
% 0.17/0.42 => ( binunionEcases
% 0.17/0.42 => ( binunionE
% 0.17/0.42 => ( binunionLsub
% 0.17/0.42 => ( binunionRsub
% 0.17/0.42 => ( binintersectI
% 0.17/0.42 => ( binintersectSubset5
% 0.17/0.42 => ( binintersectEL
% 0.17/0.42 => ( binintersectLsub
% 0.17/0.42 => ( binintersectSubset2
% 0.17/0.42 => ( binintersectSubset3
% 0.17/0.42 => ( binintersectER
% 0.17/0.42 => ( disjointsetsI1
% 0.17/0.42 => ( binintersectRsub
% 0.17/0.42 => ( binintersectSubset4
% 0.17/0.42 => ( binintersectSubset1
% 0.17/0.42 => ( bs114d
% 0.17/0.42 => ( setminusI
% 0.17/0.42 => ( setminusEL
% 0.17/0.42 => ( setminusER
% 0.17/0.42 => ( setminusSubset2
% 0.17/0.42 => ( setminusERneg
% 0.17/0.42 => ( setminusELneg
% 0.17/0.42 => ( setminusILneg
% 0.17/0.42 => ( setminusIRneg
% 0.17/0.42 => ( setminusLsub
% 0.17/0.42 => ( setminusSubset1
% 0.17/0.42 => ( symdiffE
% 0.17/0.42 => ( symdiffI1
% 0.17/0.42 => ( symdiffI2
% 0.17/0.42 => ( symdiffIneg1
% 0.17/0.42 => ( symdiffIneg2
% 0.17/0.42 => ( secondinupair
% 0.17/0.42 => ( setukpairIL
% 0.17/0.42 => ( setukpairIR
% 0.17/0.42 => ( kpairiskpair
% 0.17/0.42 => ( kpairp
% 0.17/0.42 => ( singletonsubset
% 0.17/0.42 => ( singletoninpowerset
% 0.17/0.42 => ( singletoninpowunion
% 0.17/0.42 => ( upairset2E
% 0.17/0.42 => ( upairsubunion
% 0.17/0.42 => ( upairinpowunion
% 0.17/0.42 => ( ubforcartprodlem1
% 0.17/0.42 => ( ubforcartprodlem2
% 0.17/0.42 => ( ubforcartprodlem3
% 0.17/0.42 => ( cartprodpairin
% 0.17/0.42 => ( cartprodmempair1
% 0.17/0.42 => ( cartprodmempair
% 0.17/0.42 => ( setunionE2
% 0.17/0.42 => ( setunionsingleton1
% 0.17/0.42 => ( setunionsingleton2
% 0.17/0.42 => ( setunionsingleton
% 0.17/0.42 => ( singletonprop
% 0.17/0.42 => ( ex1E1
% 0.17/0.42 => ( ex1I
% 0.17/0.42 => ( ex1I2
% 0.17/0.42 => ( singletonsuniq
% 0.17/0.42 => ( setukpairinjL1
% 0.17/0.42 => ( kfstsingleton
% 0.17/0.42 => ( theprop
% 0.17/0.42 => ( kfstpairEq
% 0.17/0.42 => ( cartprodfstin
% 0.17/0.42 => ( setukpairinjL2
% 0.17/0.42 => ( setukpairinjL
% 0.17/0.42 => ( setukpairinjR11
% 0.17/0.42 => ( setukpairinjR12
% 0.17/0.42 => ( setukpairinjR1
% 0.17/0.42 => ( upairequniteq
% 0.17/0.42 => ( setukpairinjR2
% 0.17/0.42 => ( setukpairinjR
% 0.17/0.42 => ( ksndsingleton
% 0.17/0.42 => ( ksndpairEq
% 0.17/0.42 => ( kpairsurjEq
% 0.17/0.42 => ( cartprodsndin
% 0.17/0.42 => ( cartprodpairmemEL
% 0.17/0.42 => ( cartprodpairmemER
% 0.17/0.42 => ( cartprodmempaircEq
% 0.17/0.42 => ( cartprodfstpairEq
% 0.17/0.42 => ( cartprodsndpairEq
% 0.17/0.42 => ( cartprodpairsurjEq
% 0.17/0.42 => ( dpsetconstrI
% 0.17/0.42 => ( dpsetconstrSub
% 0.17/0.42 => ( setOfPairsIsBReln
% 0.17/0.42 => ( dpsetconstrERa
% 0.17/0.42 => ( dpsetconstrEL1
% 0.17/0.42 => ( dpsetconstrEL2
% 0.17/0.42 => ( dpsetconstrER
% 0.17/0.42 => ( funcImageSingleton
% 0.17/0.42 => ( apProp
% 0.17/0.42 => ( app
% 0.17/0.42 => ( infuncsetfunc
% 0.17/0.42 => ( ap2p
% 0.17/0.42 => ( funcinfuncset
% 0.17/0.42 => ( lamProp
% 0.17/0.42 => ( lamp
% 0.17/0.42 => ( lam2p
% 0.17/0.42 => ( brelnall1
% 0.17/0.42 => ( brelnall2
% 0.17/0.42 => ( ex1E2
% 0.17/0.42 => ( funcGraphProp1
% 0.17/0.42 => ( funcGraphProp3
% 0.17/0.42 => ( funcGraphProp2
% 0.17/0.42 => ( funcextLem
% 0.17/0.42 => ( funcGraphProp4
% 0.17/0.42 => ( subbreln
% 0.17/0.42 => ( eqbreln
% 0.17/0.42 => ( funcext
% 0.17/0.42 => ( funcext2
% 0.17/0.42 => ( ap2apEq1
% 0.17/0.42 => ( ap2apEq2
% 0.17/0.42 => ( beta1
% 0.17/0.42 => ( eta1
% 0.17/0.42 => ( lam2lamEq
% 0.17/0.42 => ( beta2
% 0.17/0.42 => ( eta2
% 0.17/0.42 => ( iffalseProp1
% 0.17/0.42 => ( iffalseProp2
% 0.17/0.42 => ( iftrueProp1
% 0.17/0.42 => ( iftrueProp2
% 0.17/0.42 => ( ifSingleton
% 0.17/0.42 => ( ifp
% 0.17/0.42 => ( theeq
% 0.17/0.42 => ( iftrue
% 0.17/0.42 => ( iffalse
% 0.17/0.42 => ( iftrueorfalse
% 0.17/0.42 => ( binintersectT_lem
% 0.17/0.42 => ( binunionT_lem
% 0.17/0.42 => ( powersetT_lem
% 0.17/0.42 => ( setminusT_lem
% 0.17/0.42 => ( complementT_lem
% 0.17/0.42 => ( setextT
% 0.17/0.42 => ( subsetTI
% 0.17/0.42 => ( powersetTI1
% 0.17/0.42 => ( powersetTE1
% 0.17/0.42 => ( complementTI1
% 0.17/0.42 => ( complementTE1
% 0.17/0.42 => ( binintersectTELcontra
% 0.17/0.42 => ( binintersectTERcontra
% 0.17/0.42 => ( contrasubsetT
% 0.17/0.42 => ( contrasubsetT1
% 0.17/0.42 => ( contrasubsetT2
% 0.17/0.42 => ( contrasubsetT3
% 0.17/0.42 => ( doubleComplementI1
% 0.17/0.42 => ( doubleComplementE1
% 0.17/0.42 => ( doubleComplementSub1
% 0.17/0.42 => ( doubleComplementSub2
% 0.17/0.42 => ( doubleComplementEq
% 0.17/0.42 => ( complementTnotintersectT
% 0.17/0.42 => ( complementImpComplementIntersect
% 0.17/0.42 => ( complementSubsetComplementIntersect
% 0.17/0.42 => ( complementInPowersetComplementIntersect
% 0.17/0.42 => ( contraSubsetComplement
% 0.17/0.42 => ( complementTcontraSubset
% 0.17/0.42 => ( binunionTILcontra
% 0.17/0.42 => ( binunionTIRcontra
% 0.17/0.42 => ( inIntersectImpInUnion
% 0.17/0.42 => ( inIntersectImpInUnion2
% 0.17/0.42 => ( inIntersectImpInIntersectUnions
% 0.17/0.42 => ( intersectInPowersetIntersectUnions
% 0.17/0.42 => ( inComplementUnionImpNotIn1
% 0.17/0.42 => ( inComplementUnionImpInComplement1
% 0.17/0.42 => ( binunionTE
% 0.17/0.42 => ( binunionTEcontra
% 0.17/0.42 => ( demorgan2a1
% 0.17/0.42 => ( complementUnionInPowersetComplement
% 0.17/0.42 => ( demorgan2a2
% 0.17/0.42 => ( demorgan1a
% 0.17/0.42 => ( demorgan1b
% 0.17/0.42 => ( demorgan1
% 0.17/0.42 => ( demorgan2a
% 0.17/0.42 => ( demorgan2b2
% 0.17/0.42 => ( demorgan2b
% 0.17/0.42 => ( demorgan2
% 0.17/0.42 => ( woz13rule0
% 0.17/0.42 => ( woz13rule1
% 0.17/0.42 => ( woz13rule2
% 0.17/0.42 => ( woz13rule3
% 0.17/0.42 => ( woz13rule4
% 0.17/0.42 => ( woz1_1
% 0.17/0.42 => ( woz1_2
% 0.17/0.42 => ( woz1_3
% 0.17/0.42 => ( woz1_4
% 0.17/0.42 => ( woz1_5
% 0.17/0.42 => ( breln1all2
% 0.17/0.42 => ( breln1SetBreln1
% 0.17/0.42 => ( choice2fnsingleton
% 0.17/0.42 => ( setOfPairsIsBReln1
% 0.17/0.42 => ( breln1all1
% 0.17/0.42 => ( subbreln1
% 0.17/0.42 => ( eqbreln1
% 0.17/0.42 => ( breln1invprop
% 0.17/0.42 => ( breln1invI
% 0.17/0.42 => ( breln1invE
% 0.17/0.42 => ( breln1compprop
% 0.17/0.42 => ( breln1compI
% 0.17/0.42 => ( breln1compE
% 0.17/0.42 => ( breln1compEex
% 0.17/0.42 => ( breln1unionprop
% 0.17/0.42 => ( breln1unionIL
% 0.17/0.42 => ( breln1unionIR
% 0.17/0.42 => ( breln1unionI
% 0.17/0.42 => ( breln1unionE
% 0.17/0.42 => ( breln1unionEcases
% 0.17/0.42 => ( breln1unionCommutes
% 0.17/0.42 => ( woz2Ex
% 0.17/0.42 => ( woz2W
% 0.17/0.42 => ( woz2A
% 0.17/0.42 => ( woz2B
% 0.17/0.42 => ( image1Ex
% 0.17/0.42 => ( image1Ex1
% 0.17/0.42 => ( image1Equiv
% 0.17/0.42 => ( image1E
% 0.17/0.42 => ( image1I
% 0.17/0.42 => ( injFuncInInjFuncSet
% 0.17/0.42 => ( injFuncSetFuncIn
% 0.17/0.42 => ( injFuncSetFuncInj
% 0.17/0.42 => ( surjFuncSetFuncIn
% 0.17/0.42 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.17/0.42 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.17/0.42 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 ------------------------
% 3.37/1.77 ---- Embedded in THF ---
% 3.37/1.77 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.37/1.77 %%% Generated on Tue Feb 24 12:34:17 EST 2026
% 3.37/1.77 %%% using '$$dhol' embedding, version 1.3.0.
% 3.37/1.77 %%% Logic specification used:
% 3.37/1.77 %%% thf(spec, logic, $$dhol).
% 3.37/1.77
% 3.37/1.77 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2DTF22692.p
% See solution above
% 3.37/1.77 ------------------------
% 3.58/1.85 ---- Cleaned THF ---
% 3.58/1.85 thf(in_type,type,
% 3.58/1.85 in: $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(exu_type,type,
% 3.58/1.85 exu: ( $i > $o ) > $o ).
% 3.58/1.85
% 3.58/1.85 thf(exu,definition,
% 3.58/1.85 ( exu
% 3.58/1.85 = ( ^ [Xphi: $i > $o] :
% 3.58/1.85 ? [Xx: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 & ! [Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setextAx_type,type,
% 3.58/1.85 setextAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setextAx,definition,
% 3.58/1.85 ( setextAx
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 <=> ( in @ Xx @ B ) )
% 3.58/1.85 => ( A = B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyset_type,type,
% 3.58/1.85 emptyset: $i ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetAx_type,type,
% 3.58/1.85 emptysetAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetAx,definition,
% 3.58/1.85 ( emptysetAx
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoin_type,type,
% 3.58/1.85 setadjoin: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinAx_type,type,
% 3.58/1.85 setadjoinAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinAx,definition,
% 3.58/1.85 ( setadjoinAx
% 3.58/1.85 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.58/1.85 <=> ( ( Xy = Xx )
% 3.58/1.85 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powerset_type,type,
% 3.58/1.85 powerset: $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(powersetAx_type,type,
% 3.58/1.85 powersetAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetAx,definition,
% 3.58/1.85 ( powersetAx
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( in @ B @ ( powerset @ A ) )
% 3.58/1.85 <=> ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunion_type,type,
% 3.58/1.85 setunion: $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(setunionAx_type,type,
% 3.58/1.85 setunionAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionAx,definition,
% 3.58/1.85 ( setunionAx
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setunion @ A ) )
% 3.58/1.85 <=> ? [B: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 & ( in @ B @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(omega_type,type,
% 3.58/1.85 omega: $i ).
% 3.58/1.85
% 3.58/1.85 thf(omega0Ax_type,type,
% 3.58/1.85 omega0Ax: $o ).
% 3.58/1.85
% 3.58/1.85 thf(omega0Ax,definition,
% 3.58/1.85 ( omega0Ax
% 3.58/1.85 = ( in @ emptyset @ omega ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(omegaSAx_type,type,
% 3.58/1.85 omegaSAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(omegaSAx,definition,
% 3.58/1.85 ( omegaSAx
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ omega )
% 3.58/1.85 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(omegaIndAx_type,type,
% 3.58/1.85 omegaIndAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(omegaIndAx,definition,
% 3.58/1.85 ( omegaIndAx
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ( ( in @ emptyset @ A )
% 3.58/1.85 & ! [Xx: $i] :
% 3.58/1.85 ( ( ( in @ Xx @ omega )
% 3.58/1.85 & ( in @ Xx @ A ) )
% 3.58/1.85 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ omega )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(replAx_type,type,
% 3.58/1.85 replAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(replAx,definition,
% 3.58/1.85 ( replAx
% 3.58/1.85 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( exu
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.58/1.85 => ? [B: $i] :
% 3.58/1.85 ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 <=> ? [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(foundationAx_type,type,
% 3.58/1.85 foundationAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(foundationAx,definition,
% 3.58/1.85 ( foundationAx
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.58/1.85 => ? [B: $i] :
% 3.58/1.85 ( ( in @ B @ A )
% 3.58/1.85 & ~ ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(wellorderingAx_type,type,
% 3.58/1.85 wellorderingAx: $o ).
% 3.58/1.85
% 3.58/1.85 thf(wellorderingAx,definition,
% 3.58/1.85 ( wellorderingAx
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ? [B: $i] :
% 3.58/1.85 ( ! [C: $i] :
% 3.58/1.85 ( ( in @ C @ B )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ C )
% 3.58/1.85 => ( in @ Xx @ A ) ) )
% 3.58/1.85 & ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( ( in @ Xx @ A )
% 3.58/1.85 & ( in @ Xy @ A ) )
% 3.58/1.85 => ( ! [C: $i] :
% 3.58/1.85 ( ( in @ C @ B )
% 3.58/1.85 => ( ( in @ Xx @ C )
% 3.58/1.85 <=> ( in @ Xy @ C ) ) )
% 3.58/1.85 => ( Xx = Xy ) ) )
% 3.58/1.85 & ! [C: $i,D: $i] :
% 3.58/1.85 ( ( ( in @ C @ B )
% 3.58/1.85 & ( in @ D @ B ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ C )
% 3.58/1.85 => ( in @ Xx @ D ) )
% 3.58/1.85 | ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ D )
% 3.58/1.85 => ( in @ Xx @ C ) ) ) )
% 3.58/1.85 & ! [C: $i] :
% 3.58/1.85 ( ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ C )
% 3.58/1.85 => ( in @ Xx @ A ) )
% 3.58/1.85 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.58/1.85 => ? [D: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ D @ B )
% 3.58/1.85 & ( in @ Xx @ C )
% 3.58/1.85 & ~ ? [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ D )
% 3.58/1.85 & ( in @ Xy @ C ) )
% 3.58/1.85 & ! [E: $i] :
% 3.58/1.85 ( ( in @ E @ B )
% 3.58/1.85 => ( ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ E )
% 3.58/1.85 => ( in @ Xy @ D ) )
% 3.58/1.85 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(descr_type,type,
% 3.58/1.85 descr: ( $i > $o ) > $i ).
% 3.58/1.85
% 3.58/1.85 thf(descrp_type,type,
% 3.58/1.85 descrp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(descrp,definition,
% 3.58/1.85 ( descrp
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ( Xphi
% 3.58/1.85 @ ( descr
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstr_type,type,
% 3.58/1.85 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrI_type,type,
% 3.58/1.85 dsetconstrI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrI,definition,
% 3.58/1.85 ( dsetconstrI
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( in @ Xx
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrEL_type,type,
% 3.58/1.85 dsetconstrEL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrEL,definition,
% 3.58/1.85 ( dsetconstrEL
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrER_type,type,
% 3.58/1.85 dsetconstrER: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstrER,definition,
% 3.58/1.85 ( dsetconstrER
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.58/1.85 => ( Xphi @ Xx ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuE1_type,type,
% 3.58/1.85 exuE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuE1,definition,
% 3.58/1.85 ( exuE1
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 & ! [Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(prop2set_type,type,
% 3.58/1.85 prop2set: $o > $i ).
% 3.58/1.85
% 3.58/1.85 thf(prop2setE_type,type,
% 3.58/1.85 prop2setE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(prop2setE,definition,
% 3.58/1.85 ( prop2setE
% 3.58/1.85 = ( ! [Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.58/1.85 => Xphi ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetE_type,type,
% 3.58/1.85 emptysetE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetE,definition,
% 3.58/1.85 ( emptysetE
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ emptyset )
% 3.58/1.85 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetimpfalse_type,type,
% 3.58/1.85 emptysetimpfalse: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetimpfalse,definition,
% 3.58/1.85 ( emptysetimpfalse
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ emptyset )
% 3.58/1.85 => $false ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notinemptyset_type,type,
% 3.58/1.85 notinemptyset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notinemptyset,definition,
% 3.58/1.85 ( notinemptyset
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuE3e_type,type,
% 3.58/1.85 exuE3e: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuE3e,definition,
% 3.58/1.85 ( exuE3e
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setext_type,type,
% 3.58/1.85 setext: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setext,definition,
% 3.58/1.85 ( setext
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ B ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ A ) )
% 3.58/1.85 => ( A = B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyI_type,type,
% 3.58/1.85 emptyI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyI,definition,
% 3.58/1.85 ( emptyI
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ~ ( in @ Xx @ A )
% 3.58/1.85 => ( A = emptyset ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(noeltsimpempty_type,type,
% 3.58/1.85 noeltsimpempty: $o ).
% 3.58/1.85
% 3.58/1.85 thf(noeltsimpempty,definition,
% 3.58/1.85 ( noeltsimpempty
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ~ ( in @ Xx @ A )
% 3.58/1.85 => ( A = emptyset ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setbeta_type,type,
% 3.58/1.85 setbeta: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setbeta,definition,
% 3.58/1.85 ( setbeta
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.58/1.85 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(nonempty_type,type,
% 3.58/1.85 nonempty: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(nonempty,definition,
% 3.58/1.85 ( nonempty
% 3.58/1.85 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyE1_type,type,
% 3.58/1.85 nonemptyE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyE1,definition,
% 3.58/1.85 ( nonemptyE1
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ( nonempty @ A )
% 3.58/1.85 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyI_type,type,
% 3.58/1.85 nonemptyI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyI,definition,
% 3.58/1.85 ( nonemptyI
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( nonempty
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyI1_type,type,
% 3.58/1.85 nonemptyI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyI1,definition,
% 3.58/1.85 ( nonemptyI1
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.58/1.85 => ( nonempty @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinIL_type,type,
% 3.58/1.85 setadjoinIL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinIL,definition,
% 3.58/1.85 ( setadjoinIL
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyinunitempty_type,type,
% 3.58/1.85 emptyinunitempty: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyinunitempty,definition,
% 3.58/1.85 ( emptyinunitempty
% 3.58/1.85 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinIR_type,type,
% 3.58/1.85 setadjoinIR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinIR,definition,
% 3.58/1.85 ( setadjoinIR
% 3.58/1.85 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinE_type,type,
% 3.58/1.85 setadjoinE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinE,definition,
% 3.58/1.85 ( setadjoinE
% 3.58/1.85 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.58/1.85 => ! [Xphi: $o] :
% 3.58/1.85 ( ( ( Xy = Xx )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => ( ( ( in @ Xy @ A )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => Xphi ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinOr_type,type,
% 3.58/1.85 setadjoinOr: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinOr,definition,
% 3.58/1.85 ( setadjoinOr
% 3.58/1.85 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.58/1.85 => ( ( Xy = Xx )
% 3.58/1.85 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setoftrueEq_type,type,
% 3.58/1.85 setoftrueEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setoftrueEq,definition,
% 3.58/1.85 ( setoftrueEq
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : $true )
% 3.58/1.85 = A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetI_type,type,
% 3.58/1.85 powersetI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetI,definition,
% 3.58/1.85 ( powersetI
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ A ) )
% 3.58/1.85 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyinPowerset_type,type,
% 3.58/1.85 emptyinPowerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyinPowerset,definition,
% 3.58/1.85 ( emptyinPowerset
% 3.58/1.85 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyInPowerset_type,type,
% 3.58/1.85 emptyInPowerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyInPowerset,definition,
% 3.58/1.85 ( emptyInPowerset
% 3.58/1.85 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetE_type,type,
% 3.58/1.85 powersetE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetE,definition,
% 3.58/1.85 ( powersetE
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ B @ ( powerset @ A ) )
% 3.58/1.85 => ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionI_type,type,
% 3.58/1.85 setunionI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionI,definition,
% 3.58/1.85 ( setunionI
% 3.58/1.85 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( ( in @ B @ A )
% 3.58/1.85 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionE_type,type,
% 3.58/1.85 setunionE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionE,definition,
% 3.58/1.85 ( setunionE
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setunion @ A ) )
% 3.58/1.85 => ! [Xphi: $o] :
% 3.58/1.85 ( ! [B: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( ( in @ B @ A )
% 3.58/1.85 => Xphi ) )
% 3.58/1.85 => Xphi ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subPowSU_type,type,
% 3.58/1.85 subPowSU: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subPowSU,definition,
% 3.58/1.85 ( subPowSU
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuE2_type,type,
% 3.58/1.85 exuE2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuE2,definition,
% 3.58/1.85 ( exuE2
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ! [Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xy )
% 3.58/1.85 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyImpWitness_type,type,
% 3.58/1.85 nonemptyImpWitness: $o ).
% 3.58/1.85
% 3.58/1.85 thf(nonemptyImpWitness,definition,
% 3.58/1.85 ( nonemptyImpWitness
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ( nonempty @ A )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & $true ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(uniqinunit_type,type,
% 3.58/1.85 uniqinunit: $o ).
% 3.58/1.85
% 3.58/1.85 thf(uniqinunit,definition,
% 3.58/1.85 ( uniqinunit
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notinsingleton_type,type,
% 3.58/1.85 notinsingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notinsingleton,definition,
% 3.58/1.85 ( notinsingleton
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx != Xy )
% 3.58/1.85 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eqinunit_type,type,
% 3.58/1.85 eqinunit: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eqinunit,definition,
% 3.58/1.85 ( eqinunit
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsswitch_type,type,
% 3.58/1.85 singletonsswitch: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsswitch,definition,
% 3.58/1.85 ( singletonsswitch
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.58/1.85 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetE_type,type,
% 3.58/1.85 upairsetE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetE,definition,
% 3.58/1.85 ( upairsetE
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.58/1.85 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.58/1.85 => ( ( Xz = Xx )
% 3.58/1.85 | ( Xz = Xy ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetIL_type,type,
% 3.58/1.85 upairsetIL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetIL,definition,
% 3.58/1.85 ( upairsetIL
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetIR_type,type,
% 3.58/1.85 upairsetIR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetIR,definition,
% 3.58/1.85 ( upairsetIR
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyE1_type,type,
% 3.58/1.85 emptyE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyE1,definition,
% 3.58/1.85 ( emptyE1
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) )
% 3.58/1.85 => ( ( ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 = emptyset )
% 3.58/1.85 => $false ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(vacuousDall_type,type,
% 3.58/1.85 vacuousDall: $o ).
% 3.58/1.85
% 3.58/1.85 thf(vacuousDall,definition,
% 3.58/1.85 ( vacuousDall
% 3.58/1.85 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ emptyset )
% 3.58/1.85 => ( Xphi @ Xx ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan1_type,type,
% 3.58/1.85 quantDeMorgan1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan1,definition,
% 3.58/1.85 ( quantDeMorgan1
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ~ ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan2_type,type,
% 3.58/1.85 quantDeMorgan2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan2,definition,
% 3.58/1.85 ( quantDeMorgan2
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ~ ( Xphi @ Xx ) )
% 3.58/1.85 => ~ ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan3_type,type,
% 3.58/1.85 quantDeMorgan3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan3,definition,
% 3.58/1.85 ( quantDeMorgan3
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ~ ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan4_type,type,
% 3.58/1.85 quantDeMorgan4: $o ).
% 3.58/1.85
% 3.58/1.85 thf(quantDeMorgan4,definition,
% 3.58/1.85 ( quantDeMorgan4
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ~ ( Xphi @ Xx ) )
% 3.58/1.85 => ~ ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(prop2setI_type,type,
% 3.58/1.85 prop2setI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(prop2setI,definition,
% 3.58/1.85 ( prop2setI
% 3.58/1.85 = ( ! [Xphi: $o] :
% 3.58/1.85 ( Xphi
% 3.58/1.85 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(set2prop_type,type,
% 3.58/1.85 set2prop: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(prop2set2propI_type,type,
% 3.58/1.85 prop2set2propI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(prop2set2propI,definition,
% 3.58/1.85 ( prop2set2propI
% 3.58/1.85 = ( ! [Xphi: $o] :
% 3.58/1.85 ( Xphi
% 3.58/1.85 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notdexE_type,type,
% 3.58/1.85 notdexE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notdexE,definition,
% 3.58/1.85 ( notdexE
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ~ ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notdallE_type,type,
% 3.58/1.85 notdallE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notdallE,definition,
% 3.58/1.85 ( notdallE
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ~ ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuI1_type,type,
% 3.58/1.85 exuI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuI1,definition,
% 3.58/1.85 ( exuI1
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ? [Xx: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 & ! [Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) )
% 3.58/1.85 => ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuI3_type,type,
% 3.58/1.85 exuI3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuI3,definition,
% 3.58/1.85 ( exuI3
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.58/1.85 => ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) )
% 3.58/1.85 => ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuI2_type,type,
% 3.58/1.85 exuI2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuI2,definition,
% 3.58/1.85 ( exuI2
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ? [Xx: $i] :
% 3.58/1.85 ! [Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xy )
% 3.58/1.85 <=> ( Xy = Xx ) )
% 3.58/1.85 => ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inCongP_type,type,
% 3.58/1.85 inCongP: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inCongP,definition,
% 3.58/1.85 ( inCongP
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(in__Cong_type,type,
% 3.58/1.85 in__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(in__Cong,definition,
% 3.58/1.85 ( in__Cong
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( in @ Xx @ A )
% 3.58/1.85 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuE3u_type,type,
% 3.58/1.85 exuE3u: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuE3u,definition,
% 3.58/1.85 ( exuE3u
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exu__Cong_type,type,
% 3.58/1.85 exu__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exu__Cong,definition,
% 3.58/1.85 ( exu__Cong
% 3.58/1.85 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 <=> ( Xpsi @ Xy ) ) )
% 3.58/1.85 => ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 <=> ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptyset__Cong_type,type,
% 3.58/1.85 emptyset__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptyset__Cong,definition,
% 3.58/1.85 ( emptyset__Cong
% 3.58/1.85 = ( emptyset = emptyset ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoin__Cong_type,type,
% 3.58/1.85 setadjoin__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoin__Cong,definition,
% 3.58/1.85 ( setadjoin__Cong
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ! [Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( Xz = Xu )
% 3.58/1.85 => ( ( setadjoin @ Xx @ Xz )
% 3.58/1.85 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powerset__Cong_type,type,
% 3.58/1.85 powerset__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powerset__Cong,definition,
% 3.58/1.85 ( powerset__Cong
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ( ( powerset @ A )
% 3.58/1.85 = ( powerset @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunion__Cong_type,type,
% 3.58/1.85 setunion__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunion__Cong,definition,
% 3.58/1.85 ( setunion__Cong
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ( ( setunion @ A )
% 3.58/1.85 = ( setunion @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(omega__Cong_type,type,
% 3.58/1.85 omega__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(omega__Cong,definition,
% 3.58/1.85 ( omega__Cong
% 3.58/1.85 = ( omega = omega ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(exuEu_type,type,
% 3.58/1.85 exuEu: $o ).
% 3.58/1.85
% 3.58/1.85 thf(exuEu,definition,
% 3.58/1.85 ( exuEu
% 3.58/1.85 = ( ! [Xphi: $i > $o] :
% 3.58/1.85 ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(descr__Cong_type,type,
% 3.58/1.85 descr__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(descr__Cong,definition,
% 3.58/1.85 ( descr__Cong
% 3.58/1.85 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 <=> ( Xpsi @ Xy ) ) )
% 3.58/1.85 => ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ( ( exu
% 3.58/1.85 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.58/1.85 => ( ( descr
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 = ( descr
% 3.58/1.85 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstr__Cong_type,type,
% 3.58/1.85 dsetconstr__Cong: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dsetconstr__Cong,definition,
% 3.58/1.85 ( dsetconstr__Cong
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( Xx = Xy )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.58/1.85 => ( ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 = ( dsetconstr @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subset_type,type,
% 3.58/1.85 subset: $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(disjoint_type,type,
% 3.58/1.85 disjoint: $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(setsmeet_type,type,
% 3.58/1.85 setsmeet: $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetI1_type,type,
% 3.58/1.85 subsetI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetI1,definition,
% 3.58/1.85 ( subsetI1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ B ) )
% 3.58/1.85 => ( subset @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eqimpsubset2_type,type,
% 3.58/1.85 eqimpsubset2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eqimpsubset2,definition,
% 3.58/1.85 ( eqimpsubset2
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ( subset @ B @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eqimpsubset1_type,type,
% 3.58/1.85 eqimpsubset1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eqimpsubset1,definition,
% 3.58/1.85 ( eqimpsubset1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( A = B )
% 3.58/1.85 => ( subset @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetI2_type,type,
% 3.58/1.85 subsetI2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetI2,definition,
% 3.58/1.85 ( subsetI2
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ B ) )
% 3.58/1.85 => ( subset @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetsubset_type,type,
% 3.58/1.85 emptysetsubset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(emptysetsubset,definition,
% 3.58/1.85 ( emptysetsubset
% 3.58/1.85 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetE_type,type,
% 3.58/1.85 subsetE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetE,definition,
% 3.58/1.85 ( subsetE
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetE2_type,type,
% 3.58/1.85 subsetE2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetE2,definition,
% 3.58/1.85 ( subsetE2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notsubsetI_type,type,
% 3.58/1.85 notsubsetI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notsubsetI,definition,
% 3.58/1.85 ( notsubsetI
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notequalI1_type,type,
% 3.58/1.85 notequalI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notequalI1,definition,
% 3.58/1.85 ( notequalI1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ~ ( subset @ A @ B )
% 3.58/1.85 => ( A != B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(notequalI2_type,type,
% 3.58/1.85 notequalI2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(notequalI2,definition,
% 3.58/1.85 ( notequalI2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ( A != B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetRefl_type,type,
% 3.58/1.85 subsetRefl: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetRefl,definition,
% 3.58/1.85 ( subsetRefl
% 3.58/1.85 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetTrans_type,type,
% 3.58/1.85 subsetTrans: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetTrans,definition,
% 3.58/1.85 ( subsetTrans
% 3.58/1.85 = ( ! [A: $i,B: $i,C: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ( subset @ B @ C )
% 3.58/1.85 => ( subset @ A @ C ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinSub_type,type,
% 3.58/1.85 setadjoinSub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinSub,definition,
% 3.58/1.85 ( setadjoinSub
% 3.58/1.85 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinSub2_type,type,
% 3.58/1.85 setadjoinSub2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setadjoinSub2,definition,
% 3.58/1.85 ( setadjoinSub2
% 3.58/1.85 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subset2powerset_type,type,
% 3.58/1.85 subset2powerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subset2powerset,definition,
% 3.58/1.85 ( subset2powerset
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setextsub_type,type,
% 3.58/1.85 setextsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setextsub,definition,
% 3.58/1.85 ( setextsub
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ( subset @ B @ A )
% 3.58/1.85 => ( A = B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetemptysetimpeq_type,type,
% 3.58/1.85 subsetemptysetimpeq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetemptysetimpeq,definition,
% 3.58/1.85 ( subsetemptysetimpeq
% 3.58/1.85 = ( ! [A: $i] :
% 3.58/1.85 ( ( subset @ A @ emptyset )
% 3.58/1.85 => ( A = emptyset ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetI1_type,type,
% 3.58/1.85 powersetI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetI1,definition,
% 3.58/1.85 ( powersetI1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ B @ A )
% 3.58/1.85 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetE1_type,type,
% 3.58/1.85 powersetE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetE1,definition,
% 3.58/1.85 ( powersetE1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( in @ B @ ( powerset @ A ) )
% 3.58/1.85 => ( subset @ B @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inPowerset_type,type,
% 3.58/1.85 inPowerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inPowerset,definition,
% 3.58/1.85 ( inPowerset
% 3.58/1.85 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetsubset_type,type,
% 3.58/1.85 powersetsubset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetsubset,definition,
% 3.58/1.85 ( powersetsubset
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(sepInPowerset_type,type,
% 3.58/1.85 sepInPowerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(sepInPowerset,definition,
% 3.58/1.85 ( sepInPowerset
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( in
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 @ ( powerset @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(sepSubset_type,type,
% 3.58/1.85 sepSubset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(sepSubset,definition,
% 3.58/1.85 ( sepSubset
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( subset
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunion_type,type,
% 3.58/1.85 binunion: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(binunionIL_type,type,
% 3.58/1.85 binunionIL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionIL,definition,
% 3.58/1.85 ( binunionIL
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairset2IR_type,type,
% 3.58/1.85 upairset2IR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairset2IR,definition,
% 3.58/1.85 ( upairset2IR
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionIR_type,type,
% 3.58/1.85 binunionIR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionIR,definition,
% 3.58/1.85 ( binunionIR
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionEcases_type,type,
% 3.58/1.85 binunionEcases: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionEcases,definition,
% 3.58/1.85 ( binunionEcases
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.58/1.85 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.58/1.85 => ( ( ( in @ Xx @ A )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => ( ( ( in @ Xx @ B )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => Xphi ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionE_type,type,
% 3.58/1.85 binunionE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionE,definition,
% 3.58/1.85 ( binunionE
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.58/1.85 => ( ( in @ Xx @ A )
% 3.58/1.85 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionLsub_type,type,
% 3.58/1.85 binunionLsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionLsub,definition,
% 3.58/1.85 ( binunionLsub
% 3.58/1.85 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionRsub_type,type,
% 3.58/1.85 binunionRsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionRsub,definition,
% 3.58/1.85 ( binunionRsub
% 3.58/1.85 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersect_type,type,
% 3.58/1.85 binintersect: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectI_type,type,
% 3.58/1.85 binintersectI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectI,definition,
% 3.58/1.85 ( binintersectI
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset5_type,type,
% 3.58/1.85 binintersectSubset5: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset5,definition,
% 3.58/1.85 ( binintersectSubset5
% 3.58/1.85 = ( ! [A: $i,B: $i,C: $i] :
% 3.58/1.85 ( ( subset @ C @ A )
% 3.58/1.85 => ( ( subset @ C @ B )
% 3.58/1.85 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectEL_type,type,
% 3.58/1.85 binintersectEL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectEL,definition,
% 3.58/1.85 ( binintersectEL
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectLsub_type,type,
% 3.58/1.85 binintersectLsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectLsub,definition,
% 3.58/1.85 ( binintersectLsub
% 3.58/1.85 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset2_type,type,
% 3.58/1.85 binintersectSubset2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset2,definition,
% 3.58/1.85 ( binintersectSubset2
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ( binintersect @ A @ B )
% 3.58/1.85 = A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset3_type,type,
% 3.58/1.85 binintersectSubset3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset3,definition,
% 3.58/1.85 ( binintersectSubset3
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( ( binintersect @ A @ B )
% 3.58/1.85 = B )
% 3.58/1.85 => ( subset @ B @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectER_type,type,
% 3.58/1.85 binintersectER: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectER,definition,
% 3.58/1.85 ( binintersectER
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.58/1.85 => ( in @ Xx @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(disjointsetsI1_type,type,
% 3.58/1.85 disjointsetsI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(disjointsetsI1,definition,
% 3.58/1.85 ( disjointsetsI1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ~ ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( in @ Xx @ B ) )
% 3.58/1.85 => ( ( binintersect @ A @ B )
% 3.58/1.85 = emptyset ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectRsub_type,type,
% 3.58/1.85 binintersectRsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectRsub,definition,
% 3.58/1.85 ( binintersectRsub
% 3.58/1.85 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset4_type,type,
% 3.58/1.85 binintersectSubset4: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset4,definition,
% 3.58/1.85 ( binintersectSubset4
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ B @ A )
% 3.58/1.85 => ( ( binintersect @ A @ B )
% 3.58/1.85 = B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset1_type,type,
% 3.58/1.85 binintersectSubset1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectSubset1,definition,
% 3.58/1.85 ( binintersectSubset1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( ( binintersect @ A @ B )
% 3.58/1.85 = A )
% 3.58/1.85 => ( subset @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(bs114d_type,type,
% 3.58/1.85 bs114d: $o ).
% 3.58/1.85
% 3.58/1.85 thf(bs114d,definition,
% 3.58/1.85 ( bs114d
% 3.58/1.85 = ( ! [A: $i,B: $i,C: $i] :
% 3.58/1.85 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.58/1.85 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(regular_type,type,
% 3.58/1.85 regular: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminus_type,type,
% 3.58/1.85 setminus: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(setminusI_type,type,
% 3.58/1.85 setminusI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusI,definition,
% 3.58/1.85 ( setminusI
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusEL_type,type,
% 3.58/1.85 setminusEL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusEL,definition,
% 3.58/1.85 ( setminusEL
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusER_type,type,
% 3.58/1.85 setminusER: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusER,definition,
% 3.58/1.85 ( setminusER
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.58/1.85 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusSubset2_type,type,
% 3.58/1.85 setminusSubset2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusSubset2,definition,
% 3.58/1.85 ( setminusSubset2
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( subset @ A @ B )
% 3.58/1.85 => ( ( setminus @ A @ B )
% 3.58/1.85 = emptyset ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusERneg_type,type,
% 3.58/1.85 setminusERneg: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusERneg,definition,
% 3.58/1.85 ( setminusERneg
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.58/1.85 => ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusELneg_type,type,
% 3.58/1.85 setminusELneg: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusELneg,definition,
% 3.58/1.85 ( setminusELneg
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusILneg_type,type,
% 3.58/1.85 setminusILneg: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusILneg,definition,
% 3.58/1.85 ( setminusILneg
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ~ ( in @ Xx @ A )
% 3.58/1.85 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusIRneg_type,type,
% 3.58/1.85 setminusIRneg: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusIRneg,definition,
% 3.58/1.85 ( setminusIRneg
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ B )
% 3.58/1.85 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusLsub_type,type,
% 3.58/1.85 setminusLsub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusLsub,definition,
% 3.58/1.85 ( setminusLsub
% 3.58/1.85 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusSubset1_type,type,
% 3.58/1.85 setminusSubset1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusSubset1,definition,
% 3.58/1.85 ( setminusSubset1
% 3.58/1.85 = ( ! [A: $i,B: $i] :
% 3.58/1.85 ( ( ( setminus @ A @ B )
% 3.58/1.85 = emptyset )
% 3.58/1.85 => ( subset @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(symdiff_type,type,
% 3.58/1.85 symdiff: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffE_type,type,
% 3.58/1.85 symdiffE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffE,definition,
% 3.58/1.85 ( symdiffE
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.58/1.85 => ! [Xphi: $o] :
% 3.58/1.85 ( ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => Xphi ) )
% 3.58/1.85 => ( ( ~ ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ B )
% 3.58/1.85 => Xphi ) )
% 3.58/1.85 => Xphi ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffI1_type,type,
% 3.58/1.85 symdiffI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffI1,definition,
% 3.58/1.85 ( symdiffI1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffI2_type,type,
% 3.58/1.85 symdiffI2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffI2,definition,
% 3.58/1.85 ( symdiffI2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ~ ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ B )
% 3.58/1.85 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffIneg1_type,type,
% 3.58/1.85 symdiffIneg1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffIneg1,definition,
% 3.58/1.85 ( symdiffIneg1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ B )
% 3.58/1.85 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffIneg2_type,type,
% 3.58/1.85 symdiffIneg2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(symdiffIneg2,definition,
% 3.58/1.85 ( symdiffIneg2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ~ ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ B )
% 3.58/1.85 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iskpair_type,type,
% 3.58/1.85 iskpair: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(secondinupair_type,type,
% 3.58/1.85 secondinupair: $o ).
% 3.58/1.85
% 3.58/1.85 thf(secondinupair,definition,
% 3.58/1.85 ( secondinupair
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairIL_type,type,
% 3.58/1.85 setukpairIL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairIL,definition,
% 3.58/1.85 ( setukpairIL
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairIR_type,type,
% 3.58/1.85 setukpairIR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairIR,definition,
% 3.58/1.85 ( setukpairIR
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(kpairiskpair_type,type,
% 3.58/1.85 kpairiskpair: $o ).
% 3.58/1.85
% 3.58/1.85 thf(kpairiskpair,definition,
% 3.58/1.85 ( kpairiskpair
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(kpair_type,type,
% 3.58/1.85 kpair: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(kpairp_type,type,
% 3.58/1.85 kpairp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(kpairp,definition,
% 3.58/1.85 ( kpairp
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprod_type,type,
% 3.58/1.85 cartprod: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsubset_type,type,
% 3.58/1.85 singletonsubset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsubset,definition,
% 3.58/1.85 ( singletonsubset
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(singletoninpowerset_type,type,
% 3.58/1.85 singletoninpowerset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletoninpowerset,definition,
% 3.58/1.85 ( singletoninpowerset
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(singletoninpowunion_type,type,
% 3.58/1.85 singletoninpowunion: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletoninpowunion,definition,
% 3.58/1.85 ( singletoninpowunion
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairset2E_type,type,
% 3.58/1.85 upairset2E: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairset2E,definition,
% 3.58/1.85 ( upairset2E
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.58/1.85 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.58/1.85 => ( ( Xz = Xx )
% 3.58/1.85 | ( Xz = Xy ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairsubunion_type,type,
% 3.58/1.85 upairsubunion: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairsubunion,definition,
% 3.58/1.85 ( upairsubunion
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairinpowunion_type,type,
% 3.58/1.85 upairinpowunion: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairinpowunion,definition,
% 3.58/1.85 ( upairinpowunion
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem1_type,type,
% 3.58/1.85 ubforcartprodlem1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem1,definition,
% 3.58/1.85 ( ubforcartprodlem1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem2_type,type,
% 3.58/1.85 ubforcartprodlem2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem2,definition,
% 3.58/1.85 ( ubforcartprodlem2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem3_type,type,
% 3.58/1.85 ubforcartprodlem3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ubforcartprodlem3,definition,
% 3.58/1.85 ( ubforcartprodlem3
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairin_type,type,
% 3.58/1.85 cartprodpairin: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairin,definition,
% 3.58/1.85 ( cartprodpairin
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempair1_type,type,
% 3.58/1.85 cartprodmempair1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempair1,definition,
% 3.58/1.85 ( cartprodmempair1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.58/1.85 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ? [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 & ( Xu
% 3.58/1.85 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempair_type,type,
% 3.58/1.85 cartprodmempair: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempair,definition,
% 3.58/1.85 ( cartprodmempair
% 3.58/1.85 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.58/1.85 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( iskpair @ Xu ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionE2_type,type,
% 3.58/1.85 setunionE2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionE2,definition,
% 3.58/1.85 ( setunionE2
% 3.58/1.85 = ( ! [A: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( setunion @ A ) )
% 3.58/1.85 => ? [X: $i] :
% 3.58/1.85 ( ( in @ X @ A )
% 3.58/1.85 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton1_type,type,
% 3.58/1.85 setunionsingleton1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton1,definition,
% 3.58/1.85 ( setunionsingleton1
% 3.58/1.85 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton2_type,type,
% 3.58/1.85 setunionsingleton2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton2,definition,
% 3.58/1.85 ( setunionsingleton2
% 3.58/1.85 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton_type,type,
% 3.58/1.85 setunionsingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setunionsingleton,definition,
% 3.58/1.85 ( setunionsingleton
% 3.58/1.85 = ( ! [Xx: $i] :
% 3.58/1.85 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.58/1.85 = Xx ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(singleton_type,type,
% 3.58/1.85 singleton: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletonprop_type,type,
% 3.58/1.85 singletonprop: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletonprop,definition,
% 3.58/1.85 ( singletonprop
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) )
% 3.58/1.85 => ( ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) )
% 3.58/1.85 => ( singleton
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ex1_type,type,
% 3.58/1.85 ex1: $i > ( $i > $o ) > $o ).
% 3.58/1.85
% 3.58/1.85 thf(ex1E1_type,type,
% 3.58/1.85 ex1E1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ex1E1,definition,
% 3.58/1.85 ( ex1E1
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ( ex1 @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ex1I_type,type,
% 3.58/1.85 ex1I: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ex1I,definition,
% 3.58/1.85 ( ex1I
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xy = Xx ) ) )
% 3.58/1.85 => ( ex1 @ A
% 3.58/1.85 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ex1I2_type,type,
% 3.58/1.85 ex1I2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ex1I2,definition,
% 3.58/1.85 ( ex1I2
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) )
% 3.58/1.85 => ( ? [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 & ( Xphi @ Xx ) )
% 3.58/1.85 => ( ex1 @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsuniq_type,type,
% 3.58/1.85 singletonsuniq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(singletonsuniq,definition,
% 3.58/1.85 ( singletonsuniq
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( ( setadjoin @ Xx @ emptyset )
% 3.58/1.85 = ( setadjoin @ Xy @ emptyset ) )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(atmost1p_type,type,
% 3.58/1.85 atmost1p: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(atleast2p_type,type,
% 3.58/1.85 atleast2p: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(atmost2p_type,type,
% 3.58/1.85 atmost2p: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairsetp_type,type,
% 3.58/1.85 upairsetp: $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL1_type,type,
% 3.58/1.85 setukpairinjL1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL1,definition,
% 3.58/1.85 ( setukpairinjL1
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.58/1.85 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.58/1.85 => ( Xx = Xz ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(kfstsingleton_type,type,
% 3.58/1.85 kfstsingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(kfstsingleton,definition,
% 3.58/1.85 ( kfstsingleton
% 3.58/1.85 = ( ! [Xu: $i] :
% 3.58/1.85 ( ( iskpair @ Xu )
% 3.58/1.85 => ( singleton
% 3.58/1.85 @ ( dsetconstr @ ( setunion @ Xu )
% 3.58/1.85 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(theprop_type,type,
% 3.58/1.85 theprop: $o ).
% 3.58/1.85
% 3.58/1.85 thf(theprop,definition,
% 3.58/1.85 ( theprop
% 3.58/1.85 = ( ! [X: $i] :
% 3.58/1.85 ( ( singleton @ X )
% 3.58/1.85 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(kfst_type,type,
% 3.58/1.85 kfst: $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(kfstpairEq_type,type,
% 3.58/1.85 kfstpairEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(kfstpairEq,definition,
% 3.58/1.85 ( kfstpairEq
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.58/1.85 = Xx ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodfstin_type,type,
% 3.58/1.85 cartprodfstin: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodfstin,definition,
% 3.58/1.85 ( cartprodfstin
% 3.58/1.85 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.58/1.85 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL2_type,type,
% 3.58/1.85 setukpairinjL2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL2,definition,
% 3.58/1.85 ( setukpairinjL2
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.58/1.85 => ( Xx = Xz ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL_type,type,
% 3.58/1.85 setukpairinjL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjL,definition,
% 3.58/1.85 ( setukpairinjL
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( ( kpair @ Xx @ Xy )
% 3.58/1.85 = ( kpair @ Xz @ Xu ) )
% 3.58/1.85 => ( Xx = Xz ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR11_type,type,
% 3.58/1.85 setukpairinjR11: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR11,definition,
% 3.58/1.85 ( setukpairinjR11
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR12_type,type,
% 3.58/1.85 setukpairinjR12: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR12,definition,
% 3.58/1.85 ( setukpairinjR12
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xx = Xy )
% 3.58/1.85 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR1_type,type,
% 3.58/1.85 setukpairinjR1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR1,definition,
% 3.58/1.85 ( setukpairinjR1
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.58/1.85 => ( ( Xz = Xu )
% 3.58/1.85 => ( Xy = Xu ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(upairequniteq_type,type,
% 3.58/1.85 upairequniteq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(upairequniteq,definition,
% 3.58/1.85 ( upairequniteq
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.58/1.85 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ Xz @ emptyset ) )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR2_type,type,
% 3.58/1.85 setukpairinjR2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR2,definition,
% 3.58/1.85 ( setukpairinjR2
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.58/1.85 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.58/1.85 => ( Xy = Xu ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR_type,type,
% 3.58/1.85 setukpairinjR: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setukpairinjR,definition,
% 3.58/1.85 ( setukpairinjR
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.58/1.85 ( ( ( kpair @ Xx @ Xy )
% 3.58/1.85 = ( kpair @ Xz @ Xu ) )
% 3.58/1.85 => ( Xy = Xu ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ksndsingleton_type,type,
% 3.58/1.85 ksndsingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ksndsingleton,definition,
% 3.58/1.85 ( ksndsingleton
% 3.58/1.85 = ( ! [Xu: $i] :
% 3.58/1.85 ( ( iskpair @ Xu )
% 3.58/1.85 => ( singleton
% 3.58/1.85 @ ( dsetconstr @ ( setunion @ Xu )
% 3.58/1.85 @ ^ [Xx: $i] :
% 3.58/1.85 ( Xu
% 3.58/1.85 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ksnd_type,type,
% 3.58/1.85 ksnd: $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(ksndpairEq_type,type,
% 3.58/1.85 ksndpairEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ksndpairEq,definition,
% 3.58/1.85 ( ksndpairEq
% 3.58/1.85 = ( ! [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.58/1.85 = Xy ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(kpairsurjEq_type,type,
% 3.58/1.85 kpairsurjEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(kpairsurjEq,definition,
% 3.58/1.85 ( kpairsurjEq
% 3.58/1.85 = ( ! [Xu: $i] :
% 3.58/1.85 ( ( iskpair @ Xu )
% 3.58/1.85 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.58/1.85 = Xu ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodsndin_type,type,
% 3.58/1.85 cartprodsndin: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodsndin,definition,
% 3.58/1.85 ( cartprodsndin
% 3.58/1.85 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.58/1.85 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairmemEL_type,type,
% 3.58/1.85 cartprodpairmemEL: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairmemEL,definition,
% 3.58/1.85 ( cartprodpairmemEL
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairmemER_type,type,
% 3.58/1.85 cartprodpairmemER: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairmemER,definition,
% 3.58/1.85 ( cartprodpairmemER
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( in @ Xy @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempaircEq_type,type,
% 3.58/1.85 cartprodmempaircEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodmempaircEq,definition,
% 3.58/1.85 ( cartprodmempaircEq
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( kpair @ Xx @ Xy )
% 3.58/1.85 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodfstpairEq_type,type,
% 3.58/1.85 cartprodfstpairEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodfstpairEq,definition,
% 3.58/1.85 ( cartprodfstpairEq
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.58/1.85 = Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodsndpairEq_type,type,
% 3.58/1.85 cartprodsndpairEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodsndpairEq,definition,
% 3.58/1.85 ( cartprodsndpairEq
% 3.58/1.85 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.58/1.85 = Xy ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairsurjEq_type,type,
% 3.58/1.85 cartprodpairsurjEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(cartprodpairsurjEq,definition,
% 3.58/1.85 ( cartprodpairsurjEq
% 3.58/1.85 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.58/1.85 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.58/1.85 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.58/1.85 = Xu ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(breln_type,type,
% 3.58/1.85 breln: $i > $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstr_type,type,
% 3.58/1.85 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrI_type,type,
% 3.58/1.85 dpsetconstrI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrI,definition,
% 3.58/1.85 ( dpsetconstrI
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( Xphi @ Xx @ Xy )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy )
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrSub_type,type,
% 3.58/1.85 dpsetconstrSub: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrSub,definition,
% 3.58/1.85 ( dpsetconstrSub
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.58/1.85 ( subset
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.58/1.85 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setOfPairsIsBReln_type,type,
% 3.58/1.85 setOfPairsIsBReln: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setOfPairsIsBReln,definition,
% 3.58/1.85 ( setOfPairsIsBReln
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.58/1.85 ( breln @ A @ B
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrERa_type,type,
% 3.58/1.85 dpsetconstrERa: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrERa,definition,
% 3.58/1.85 ( dpsetconstrERa
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.58/1.85 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrEL1_type,type,
% 3.58/1.85 dpsetconstrEL1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrEL1,definition,
% 3.58/1.85 ( dpsetconstrEL1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ ( kpair @ Xx @ Xy )
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrEL2_type,type,
% 3.58/1.85 dpsetconstrEL2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrEL2,definition,
% 3.58/1.85 ( dpsetconstrEL2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ ( kpair @ Xx @ Xy )
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.58/1.85 => ( in @ Xy @ B ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrER_type,type,
% 3.58/1.85 dpsetconstrER: $o ).
% 3.58/1.85
% 3.58/1.85 thf(dpsetconstrER,definition,
% 3.58/1.85 ( dpsetconstrER
% 3.58/1.85 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( in @ ( kpair @ Xx @ Xy )
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.58/1.85 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(func_type,type,
% 3.58/1.85 func: $i > $i > $i > $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcSet_type,type,
% 3.58/1.85 funcSet: $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(funcImageSingleton_type,type,
% 3.58/1.85 funcImageSingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcImageSingleton,definition,
% 3.58/1.85 ( funcImageSingleton
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( singleton
% 3.58/1.85 @ ( dsetconstr @ B
% 3.58/1.85 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(apProp_type,type,
% 3.58/1.85 apProp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(apProp,definition,
% 3.58/1.85 ( apProp
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in
% 3.58/1.85 @ ( setunion
% 3.58/1.85 @ ( dsetconstr @ B
% 3.58/1.85 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.58/1.85 @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ap_type,type,
% 3.58/1.85 ap: $i > $i > $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(app_type,type,
% 3.58/1.85 app: $o ).
% 3.58/1.85
% 3.58/1.85 thf(app,definition,
% 3.58/1.85 ( app
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(infuncsetfunc_type,type,
% 3.58/1.85 infuncsetfunc: $o ).
% 3.58/1.85
% 3.58/1.85 thf(infuncsetfunc,definition,
% 3.58/1.85 ( infuncsetfunc
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ap2p_type,type,
% 3.58/1.85 ap2p: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ap2p,definition,
% 3.58/1.85 ( ap2p
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcinfuncset_type,type,
% 3.58/1.85 funcinfuncset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcinfuncset,definition,
% 3.58/1.85 ( funcinfuncset
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(lamProp_type,type,
% 3.58/1.85 lamProp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(lamProp,definition,
% 3.58/1.85 ( lamProp
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ( func @ A @ B
% 3.58/1.85 @ ( dpsetconstr @ A @ B
% 3.58/1.85 @ ^ [Xx: $i,Xy: $i] :
% 3.58/1.85 ( ( Xf @ Xx )
% 3.58/1.85 = Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(lam_type,type,
% 3.58/1.85 lam: $i > $i > ( $i > $i ) > $i ).
% 3.58/1.85
% 3.58/1.85 thf(lamp_type,type,
% 3.58/1.85 lamp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(lamp,definition,
% 3.58/1.85 ( lamp
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ( func @ A @ B
% 3.58/1.85 @ ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(lam2p_type,type,
% 3.58/1.85 lam2p: $o ).
% 3.58/1.85
% 3.58/1.85 thf(lam2p,definition,
% 3.58/1.85 ( lam2p
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ( in
% 3.58/1.85 @ ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.58/1.85 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(brelnall1_type,type,
% 3.58/1.85 brelnall1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(brelnall1,definition,
% 3.58/1.85 ( brelnall1
% 3.58/1.85 = ( ! [A: $i,B: $i,R: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ R )
% 3.58/1.85 => ! [Xphi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.85 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ R )
% 3.58/1.85 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(brelnall2_type,type,
% 3.58/1.85 brelnall2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(brelnall2,definition,
% 3.58/1.85 ( brelnall2
% 3.58/1.85 = ( ! [A: $i,B: $i,R: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ R )
% 3.58/1.85 => ! [Xphi: $i > $o] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.85 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ R )
% 3.58/1.85 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ex1E2_type,type,
% 3.58/1.85 ex1E2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ex1E2,definition,
% 3.58/1.85 ( ex1E2
% 3.58/1.85 = ( ! [A: $i,Xphi: $i > $o] :
% 3.58/1.85 ( ( ex1 @ A
% 3.58/1.85 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ( Xphi @ Xx )
% 3.58/1.85 => ( ( Xphi @ Xy )
% 3.58/1.85 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp1_type,type,
% 3.58/1.85 funcGraphProp1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp1,definition,
% 3.58/1.85 ( funcGraphProp1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp3_type,type,
% 3.58/1.85 funcGraphProp3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp3,definition,
% 3.58/1.85 ( funcGraphProp3
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp2_type,type,
% 3.58/1.85 funcGraphProp2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp2,definition,
% 3.58/1.85 ( funcGraphProp2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcextLem_type,type,
% 3.58/1.85 funcextLem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcextLem,definition,
% 3.58/1.85 ( funcextLem
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xg: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xg )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp4_type,type,
% 3.58/1.85 funcGraphProp4: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcGraphProp4,definition,
% 3.58/1.85 ( funcGraphProp4
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = Xy ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subbreln_type,type,
% 3.58/1.85 subbreln: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subbreln,definition,
% 3.58/1.85 ( subbreln
% 3.58/1.85 = ( ! [A: $i,B: $i,R: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ R )
% 3.58/1.85 => ! [S: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ S )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.58/1.85 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eqbreln_type,type,
% 3.58/1.85 eqbreln: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eqbreln,definition,
% 3.58/1.85 ( eqbreln
% 3.58/1.85 = ( ! [A: $i,B: $i,R: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ R )
% 3.58/1.85 => ! [S: $i] :
% 3.58/1.85 ( ( breln @ A @ B @ S )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ B )
% 3.58/1.85 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.58/1.85 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.58/1.85 => ( R = S ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcext_type,type,
% 3.58/1.85 funcext: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcext,definition,
% 3.58/1.85 ( funcext
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xg: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xg )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.58/1.85 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(funcext2_type,type,
% 3.58/1.85 funcext2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(funcext2,definition,
% 3.58/1.85 ( funcext2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ! [Xg: $i] :
% 3.58/1.85 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.58/1.85 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ap2apEq1_type,type,
% 3.58/1.85 ap2apEq1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ap2apEq1,definition,
% 3.58/1.85 ( ap2apEq1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ap2apEq2_type,type,
% 3.58/1.85 ap2apEq2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ap2apEq2,definition,
% 3.58/1.85 ( ap2apEq2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.58/1.85 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(beta1_type,type,
% 3.58/1.85 beta1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(beta1,definition,
% 3.58/1.85 ( beta1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B
% 3.58/1.85 @ ( lam @ A @ B
% 3.58/1.85 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.58/1.85 @ Xx )
% 3.58/1.85 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eta1_type,type,
% 3.58/1.85 eta1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eta1,definition,
% 3.58/1.85 ( eta1
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( func @ A @ B @ Xf )
% 3.58/1.85 => ( ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.58/1.85 = Xf ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(lam2lamEq_type,type,
% 3.58/1.85 lam2lamEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(lam2lamEq,definition,
% 3.58/1.85 ( lam2lamEq
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ( ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.58/1.85 = ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(beta2_type,type,
% 3.58/1.85 beta2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(beta2,definition,
% 3.58/1.85 ( beta2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.58/1.85 ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( ap @ A @ B
% 3.58/1.85 @ ( lam @ A @ B
% 3.58/1.85 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.58/1.85 @ Xx )
% 3.58/1.85 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(eta2_type,type,
% 3.58/1.85 eta2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(eta2,definition,
% 3.58/1.85 ( eta2
% 3.58/1.85 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.85 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.85 => ( ( lam @ A @ B
% 3.58/1.85 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.58/1.85 = Xf ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iffalseProp1_type,type,
% 3.58/1.85 iffalseProp1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iffalseProp1,definition,
% 3.58/1.85 ( iffalseProp1
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ~ Xphi
% 3.58/1.85 => ( in @ Xy
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xz: $i] :
% 3.58/1.85 ( ( Xphi
% 3.58/1.85 & ( Xz = Xx ) )
% 3.58/1.85 | ( ~ Xphi
% 3.58/1.85 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iffalseProp2_type,type,
% 3.58/1.85 iffalseProp2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iffalseProp2,definition,
% 3.58/1.85 ( iffalseProp2
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ~ Xphi
% 3.58/1.85 => ( ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xz: $i] :
% 3.58/1.85 ( ( Xphi
% 3.58/1.85 & ( Xz = Xx ) )
% 3.58/1.85 | ( ~ Xphi
% 3.58/1.85 & ( Xz = Xy ) ) ) )
% 3.58/1.85 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueProp1_type,type,
% 3.58/1.85 iftrueProp1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueProp1,definition,
% 3.58/1.85 ( iftrueProp1
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( Xphi
% 3.58/1.85 => ( in @ Xx
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xz: $i] :
% 3.58/1.85 ( ( Xphi
% 3.58/1.85 & ( Xz = Xx ) )
% 3.58/1.85 | ( ~ Xphi
% 3.58/1.85 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueProp2_type,type,
% 3.58/1.85 iftrueProp2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueProp2,definition,
% 3.58/1.85 ( iftrueProp2
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( Xphi
% 3.58/1.85 => ( ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xz: $i] :
% 3.58/1.85 ( ( Xphi
% 3.58/1.85 & ( Xz = Xx ) )
% 3.58/1.85 | ( ~ Xphi
% 3.58/1.85 & ( Xz = Xy ) ) ) )
% 3.58/1.85 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(ifSingleton_type,type,
% 3.58/1.85 ifSingleton: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ifSingleton,definition,
% 3.58/1.85 ( ifSingleton
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( singleton
% 3.58/1.85 @ ( dsetconstr @ A
% 3.58/1.85 @ ^ [Xz: $i] :
% 3.58/1.85 ( ( Xphi
% 3.58/1.85 & ( Xz = Xx ) )
% 3.58/1.85 | ( ~ Xphi
% 3.58/1.85 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(if_type,type,
% 3.58/1.85 if: $i > $o > $i > $i > $i ).
% 3.58/1.85
% 3.58/1.85 thf(ifp_type,type,
% 3.58/1.85 ifp: $o ).
% 3.58/1.85
% 3.58/1.85 thf(ifp,definition,
% 3.58/1.85 ( ifp
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(theeq_type,type,
% 3.58/1.85 theeq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(theeq,definition,
% 3.58/1.85 ( theeq
% 3.58/1.85 = ( ! [X: $i] :
% 3.58/1.85 ( ( singleton @ X )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ X )
% 3.58/1.85 => ( ( setunion @ X )
% 3.58/1.85 = Xx ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iftrue_type,type,
% 3.58/1.85 iftrue: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iftrue,definition,
% 3.58/1.85 ( iftrue
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( Xphi
% 3.58/1.85 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.58/1.85 = Xx ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iffalse_type,type,
% 3.58/1.85 iffalse: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iffalse,definition,
% 3.58/1.85 ( iffalse
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( ~ Xphi
% 3.58/1.85 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.58/1.85 = Xy ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueorfalse_type,type,
% 3.58/1.85 iftrueorfalse: $o ).
% 3.58/1.85
% 3.58/1.85 thf(iftrueorfalse,definition,
% 3.58/1.85 ( iftrueorfalse
% 3.58/1.85 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ! [Xy: $i] :
% 3.58/1.85 ( ( in @ Xy @ A )
% 3.58/1.85 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectT_lem_type,type,
% 3.58/1.85 binintersectT_lem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectT_lem,definition,
% 3.58/1.85 ( binintersectT_lem
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionT_lem_type,type,
% 3.58/1.85 binunionT_lem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionT_lem,definition,
% 3.58/1.85 ( binunionT_lem
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetT_lem_type,type,
% 3.58/1.85 powersetT_lem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetT_lem,definition,
% 3.58/1.85 ( powersetT_lem
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setminusT_lem_type,type,
% 3.58/1.85 setminusT_lem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setminusT_lem,definition,
% 3.58/1.85 ( setminusT_lem
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementT_lem_type,type,
% 3.58/1.85 complementT_lem: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementT_lem,definition,
% 3.58/1.85 ( complementT_lem
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(setextT_type,type,
% 3.58/1.85 setextT: $o ).
% 3.58/1.85
% 3.58/1.85 thf(setextT,definition,
% 3.58/1.85 ( setextT
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ( in @ Xx @ Y ) ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ Y )
% 3.58/1.85 => ( in @ Xx @ X ) ) )
% 3.58/1.85 => ( X = Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(subsetTI_type,type,
% 3.58/1.85 subsetTI: $o ).
% 3.58/1.85
% 3.58/1.85 thf(subsetTI,definition,
% 3.58/1.85 ( subsetTI
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ( in @ Xx @ Y ) ) )
% 3.58/1.85 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetTI1_type,type,
% 3.58/1.85 powersetTI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetTI1,definition,
% 3.58/1.85 ( powersetTI1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ( in @ Xx @ Y ) ) )
% 3.58/1.85 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(powersetTE1_type,type,
% 3.58/1.85 powersetTE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(powersetTE1,definition,
% 3.58/1.85 ( powersetTE1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ X @ ( powerset @ Y ) )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementTI1_type,type,
% 3.58/1.85 complementTI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementTI1,definition,
% 3.58/1.85 ( complementTI1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementTE1_type,type,
% 3.58/1.85 complementTE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementTE1,definition,
% 3.58/1.85 ( complementTE1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.58/1.85 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectTELcontra_type,type,
% 3.58/1.85 binintersectTELcontra: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectTELcontra,definition,
% 3.58/1.85 ( binintersectTELcontra
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ X )
% 3.58/1.85 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectTERcontra_type,type,
% 3.58/1.85 binintersectTERcontra: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binintersectTERcontra,definition,
% 3.58/1.85 ( binintersectTERcontra
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ Y )
% 3.58/1.85 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT_type,type,
% 3.58/1.85 contrasubsetT: $o ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT,definition,
% 3.58/1.85 ( contrasubsetT
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.58/1.85 => ( ( in @ Xx @ Y )
% 3.58/1.85 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT1_type,type,
% 3.58/1.85 contrasubsetT1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT1,definition,
% 3.58/1.85 ( contrasubsetT1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( subset @ X @ Y )
% 3.58/1.85 => ( ~ ( in @ Xx @ Y )
% 3.58/1.85 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT2_type,type,
% 3.58/1.85 contrasubsetT2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT2,definition,
% 3.58/1.85 ( contrasubsetT2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ Y )
% 3.58/1.85 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT3_type,type,
% 3.58/1.85 contrasubsetT3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(contrasubsetT3,definition,
% 3.58/1.85 ( contrasubsetT3
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.58/1.85 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementI1_type,type,
% 3.58/1.85 doubleComplementI1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementI1,definition,
% 3.58/1.85 ( doubleComplementI1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ X )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementE1_type,type,
% 3.58/1.85 doubleComplementE1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementE1,definition,
% 3.58/1.85 ( doubleComplementE1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.58/1.85 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementSub1_type,type,
% 3.58/1.85 doubleComplementSub1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementSub1,definition,
% 3.58/1.85 ( doubleComplementSub1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementSub2_type,type,
% 3.58/1.85 doubleComplementSub2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementSub2,definition,
% 3.58/1.85 ( doubleComplementSub2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementEq_type,type,
% 3.58/1.85 doubleComplementEq: $o ).
% 3.58/1.85
% 3.58/1.85 thf(doubleComplementEq,definition,
% 3.58/1.85 ( doubleComplementEq
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ( X
% 3.58/1.85 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementTnotintersectT_type,type,
% 3.58/1.85 complementTnotintersectT: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementTnotintersectT,definition,
% 3.58/1.85 ( complementTnotintersectT
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.58/1.85 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementImpComplementIntersect_type,type,
% 3.58/1.85 complementImpComplementIntersect: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementImpComplementIntersect,definition,
% 3.58/1.85 ( complementImpComplementIntersect
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementSubsetComplementIntersect_type,type,
% 3.58/1.85 complementSubsetComplementIntersect: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementSubsetComplementIntersect,definition,
% 3.58/1.85 ( complementSubsetComplementIntersect
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementInPowersetComplementIntersect_type,type,
% 3.58/1.85 complementInPowersetComplementIntersect: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementInPowersetComplementIntersect,definition,
% 3.58/1.85 ( complementInPowersetComplementIntersect
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(contraSubsetComplement_type,type,
% 3.58/1.85 contraSubsetComplement: $o ).
% 3.58/1.85
% 3.58/1.85 thf(contraSubsetComplement,definition,
% 3.58/1.85 ( contraSubsetComplement
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ Y )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementTcontraSubset_type,type,
% 3.58/1.85 complementTcontraSubset: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementTcontraSubset,definition,
% 3.58/1.85 ( complementTcontraSubset
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.58/1.85 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTILcontra_type,type,
% 3.58/1.85 binunionTILcontra: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTILcontra,definition,
% 3.58/1.85 ( binunionTILcontra
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.58/1.85 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTIRcontra_type,type,
% 3.58/1.85 binunionTIRcontra: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTIRcontra,definition,
% 3.58/1.85 ( binunionTIRcontra
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.58/1.85 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInUnion_type,type,
% 3.58/1.85 inIntersectImpInUnion: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInUnion,definition,
% 3.58/1.85 ( inIntersectImpInUnion
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.58/1.85 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInUnion2_type,type,
% 3.58/1.85 inIntersectImpInUnion2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInUnion2,definition,
% 3.58/1.85 ( inIntersectImpInUnion2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.58/1.85 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInIntersectUnions_type,type,
% 3.58/1.85 inIntersectImpInIntersectUnions: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inIntersectImpInIntersectUnions,definition,
% 3.58/1.85 ( inIntersectImpInIntersectUnions
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.58/1.85 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(intersectInPowersetIntersectUnions_type,type,
% 3.58/1.85 intersectInPowersetIntersectUnions: $o ).
% 3.58/1.85
% 3.58/1.85 thf(intersectInPowersetIntersectUnions,definition,
% 3.58/1.85 ( intersectInPowersetIntersectUnions
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inComplementUnionImpNotIn1_type,type,
% 3.58/1.85 inComplementUnionImpNotIn1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inComplementUnionImpNotIn1,definition,
% 3.58/1.85 ( inComplementUnionImpNotIn1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.58/1.85 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(inComplementUnionImpInComplement1_type,type,
% 3.58/1.85 inComplementUnionImpInComplement1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(inComplementUnionImpInComplement1,definition,
% 3.58/1.85 ( inComplementUnionImpInComplement1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTE_type,type,
% 3.58/1.85 binunionTE: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTE,definition,
% 3.58/1.85 ( binunionTE
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xphi: $o,Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.58/1.85 => ( ( ( in @ Xx @ X )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => ( ( ( in @ Xx @ Y )
% 3.58/1.85 => Xphi )
% 3.58/1.85 => Xphi ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTEcontra_type,type,
% 3.58/1.85 binunionTEcontra: $o ).
% 3.58/1.85
% 3.58/1.85 thf(binunionTEcontra,definition,
% 3.58/1.85 ( binunionTEcontra
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ~ ( in @ Xx @ X )
% 3.58/1.85 => ( ~ ( in @ Xx @ Y )
% 3.58/1.85 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a1_type,type,
% 3.58/1.85 demorgan2a1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a1,definition,
% 3.58/1.85 ( demorgan2a1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(complementUnionInPowersetComplement_type,type,
% 3.58/1.85 complementUnionInPowersetComplement: $o ).
% 3.58/1.85
% 3.58/1.85 thf(complementUnionInPowersetComplement,definition,
% 3.58/1.85 ( complementUnionInPowersetComplement
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a2_type,type,
% 3.58/1.85 demorgan2a2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a2,definition,
% 3.58/1.85 ( demorgan2a2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1a_type,type,
% 3.58/1.85 demorgan1a: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1a,definition,
% 3.58/1.85 ( demorgan1a
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1b_type,type,
% 3.58/1.85 demorgan1b: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1b,definition,
% 3.58/1.85 ( demorgan1b
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1_type,type,
% 3.58/1.85 demorgan1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan1,definition,
% 3.58/1.85 ( demorgan1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.58/1.85 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a_type,type,
% 3.58/1.85 demorgan2a: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2a,definition,
% 3.58/1.85 ( demorgan2a
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2b2_type,type,
% 3.58/1.85 demorgan2b2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2b2,definition,
% 3.58/1.85 ( demorgan2b2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.58/1.85 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2b_type,type,
% 3.58/1.85 demorgan2b: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2b,definition,
% 3.58/1.85 ( demorgan2b
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ A )
% 3.58/1.85 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.58/1.85 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2_type,type,
% 3.58/1.85 demorgan2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(demorgan2,definition,
% 3.58/1.85 ( demorgan2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.58/1.85 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule0_type,type,
% 3.58/1.85 woz13rule0: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule0,definition,
% 3.58/1.85 ( woz13rule0
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Xx: $i] :
% 3.58/1.85 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.58/1.85 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule1_type,type,
% 3.58/1.85 woz13rule1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule1,definition,
% 3.58/1.85 ( woz13rule1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ Z )
% 3.58/1.85 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule2_type,type,
% 3.58/1.85 woz13rule2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule2,definition,
% 3.58/1.85 ( woz13rule2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ Y @ Z )
% 3.58/1.85 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule3_type,type,
% 3.58/1.85 woz13rule3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule3,definition,
% 3.58/1.85 ( woz13rule3
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ Y )
% 3.58/1.85 => ( ( subset @ X @ Z )
% 3.58/1.85 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule4_type,type,
% 3.58/1.85 woz13rule4: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz13rule4,definition,
% 3.58/1.85 ( woz13rule4
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ! [W: $i] :
% 3.58/1.85 ( ( in @ W @ ( powerset @ A ) )
% 3.58/1.85 => ( ( subset @ X @ Z )
% 3.58/1.85 => ( ( subset @ Y @ W )
% 3.58/1.85 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_1_type,type,
% 3.58/1.85 woz1_1: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_1,definition,
% 3.58/1.85 ( woz1_1
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_2_type,type,
% 3.58/1.85 woz1_2: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_2,definition,
% 3.58/1.85 ( woz1_2
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ! [W: $i] :
% 3.58/1.85 ( ( in @ W @ ( powerset @ A ) )
% 3.58/1.85 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.58/1.85 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_3_type,type,
% 3.58/1.85 woz1_3: $o ).
% 3.58/1.85
% 3.58/1.85 thf(woz1_3,definition,
% 3.58/1.85 ( woz1_3
% 3.58/1.85 = ( ! [A: $i,X: $i] :
% 3.58/1.85 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.85 => ! [Y: $i] :
% 3.58/1.85 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.85 => ! [Z: $i] :
% 3.58/1.85 ( ( in @ Z @ ( powerset @ A ) )
% 3.58/1.85 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz1_4_type,type,
% 3.58/1.86 woz1_4: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz1_4,definition,
% 3.58/1.86 ( woz1_4
% 3.58/1.86 = ( ! [A: $i,X: $i] :
% 3.58/1.86 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.86 => ! [Y: $i] :
% 3.58/1.86 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.86 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.58/1.86 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz1_5_type,type,
% 3.58/1.86 woz1_5: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz1_5,definition,
% 3.58/1.86 ( woz1_5
% 3.58/1.86 = ( ! [A: $i,X: $i] :
% 3.58/1.86 ( ( in @ X @ ( powerset @ A ) )
% 3.58/1.86 => ! [Y: $i] :
% 3.58/1.86 ( ( in @ Y @ ( powerset @ A ) )
% 3.58/1.86 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1_type,type,
% 3.58/1.86 breln1: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1all2_type,type,
% 3.58/1.86 breln1all2: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1all2,definition,
% 3.58/1.86 ( breln1all2
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [Xphi: $i > $o] :
% 3.58/1.86 ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ R )
% 3.58/1.86 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1Set_type,type,
% 3.58/1.86 breln1Set: $i > $i ).
% 3.58/1.86
% 3.58/1.86 thf(breln1SetBreln1_type,type,
% 3.58/1.86 breln1SetBreln1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1SetBreln1,definition,
% 3.58/1.86 ( breln1SetBreln1
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( in @ R @ ( breln1Set @ A ) )
% 3.58/1.86 => ( breln1 @ A @ R ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(transitive_type,type,
% 3.58/1.86 transitive: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(antisymmetric_type,type,
% 3.58/1.86 antisymmetric: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(reflexive_type,type,
% 3.58/1.86 reflexive: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(refltransitive_type,type,
% 3.58/1.86 refltransitive: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(refllinearorder_type,type,
% 3.58/1.86 refllinearorder: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(reflwellordering_type,type,
% 3.58/1.86 reflwellordering: $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(choice2fnsingleton_type,type,
% 3.58/1.86 choice2fnsingleton: $o ).
% 3.58/1.86
% 3.58/1.86 thf(choice2fnsingleton,definition,
% 3.58/1.86 ( choice2fnsingleton
% 3.58/1.86 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.58/1.86 ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ B )
% 3.58/1.86 & ( Xphi @ Xx @ Xy ) ) )
% 3.58/1.86 => ! [R: $i] :
% 3.58/1.86 ( ( in @ R @ ( breln1Set @ B ) )
% 3.58/1.86 => ( ( reflwellordering @ B @ R )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ( singleton
% 3.58/1.86 @ ( dsetconstr @ B
% 3.58/1.86 @ ^ [Xy: $i] :
% 3.58/1.86 ( ( Xphi @ Xx @ Xy )
% 3.58/1.86 & ! [Xz: $i] :
% 3.58/1.86 ( ( in @ Xz @ B )
% 3.58/1.86 => ( ( Xphi @ Xx @ Xz )
% 3.58/1.86 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(setOfPairsIsBReln1_type,type,
% 3.58/1.86 setOfPairsIsBReln1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(setOfPairsIsBReln1,definition,
% 3.58/1.86 ( setOfPairsIsBReln1
% 3.58/1.86 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.58/1.86 ( breln1 @ A
% 3.58/1.86 @ ( dpsetconstr @ A @ A
% 3.58/1.86 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1all1_type,type,
% 3.58/1.86 breln1all1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1all1,definition,
% 3.58/1.86 ( breln1all1
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [Xphi: $i > $o] :
% 3.58/1.86 ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ R )
% 3.58/1.86 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(subbreln1_type,type,
% 3.58/1.86 subbreln1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(subbreln1,definition,
% 3.58/1.86 ( subbreln1
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.58/1.86 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(eqbreln1_type,type,
% 3.58/1.86 eqbreln1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(eqbreln1,definition,
% 3.58/1.86 ( eqbreln1
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.58/1.86 => ( ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.58/1.86 => ( R = S ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invset_type,type,
% 3.58/1.86 breln1invset: $i > $i > $i ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invprop_type,type,
% 3.58/1.86 breln1invprop: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invprop,definition,
% 3.58/1.86 ( breln1invprop
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invI_type,type,
% 3.58/1.86 breln1invI: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invI,definition,
% 3.58/1.86 ( breln1invI
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invE_type,type,
% 3.58/1.86 breln1invE: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1invE,definition,
% 3.58/1.86 ( breln1invE
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compset_type,type,
% 3.58/1.86 breln1compset: $i > $i > $i > $i ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compprop_type,type,
% 3.58/1.86 breln1compprop: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compprop,definition,
% 3.58/1.86 ( breln1compprop
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compI_type,type,
% 3.58/1.86 breln1compI: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compI,definition,
% 3.58/1.86 ( breln1compI
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ! [Xz: $i] :
% 3.58/1.86 ( ( in @ Xz @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.58/1.86 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compE_type,type,
% 3.58/1.86 breln1compE: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compE,definition,
% 3.58/1.86 ( breln1compE
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.58/1.86 => ? [Xz: $i] :
% 3.58/1.86 ( ( in @ Xz @ A )
% 3.58/1.86 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.58/1.86 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compEex_type,type,
% 3.58/1.86 breln1compEex: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1compEex,definition,
% 3.58/1.86 ( breln1compEex
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.58/1.86 => ! [Xphi: $o] :
% 3.58/1.86 ( ! [Xz: $i] :
% 3.58/1.86 ( ( in @ Xz @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.58/1.86 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.58/1.86 => Xphi ) ) )
% 3.58/1.86 => Xphi ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionprop_type,type,
% 3.58/1.86 breln1unionprop: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionprop,definition,
% 3.58/1.86 ( breln1unionprop
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionIL_type,type,
% 3.58/1.86 breln1unionIL: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionIL,definition,
% 3.58/1.86 ( breln1unionIL
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionIR_type,type,
% 3.58/1.86 breln1unionIR: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionIR,definition,
% 3.58/1.86 ( breln1unionIR
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionI_type,type,
% 3.58/1.86 breln1unionI: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionI,definition,
% 3.58/1.86 ( breln1unionI
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.58/1.86 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionE_type,type,
% 3.58/1.86 breln1unionE: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionE,definition,
% 3.58/1.86 ( breln1unionE
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionEcases_type,type,
% 3.58/1.86 breln1unionEcases: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionEcases,definition,
% 3.58/1.86 ( breln1unionEcases
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ A )
% 3.58/1.86 => ! [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.58/1.86 => ! [Xphi: $o] :
% 3.58/1.86 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.58/1.86 => Xphi )
% 3.58/1.86 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.58/1.86 => Xphi )
% 3.58/1.86 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionCommutes_type,type,
% 3.58/1.86 breln1unionCommutes: $o ).
% 3.58/1.86
% 3.58/1.86 thf(breln1unionCommutes,definition,
% 3.58/1.86 ( breln1unionCommutes
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( ( binunion @ R @ S )
% 3.58/1.86 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz2Ex_type,type,
% 3.58/1.86 woz2Ex: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz2Ex,definition,
% 3.58/1.86 ( woz2Ex
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ( R
% 3.58/1.86 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz2W_type,type,
% 3.58/1.86 woz2W: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz2W,definition,
% 3.58/1.86 ( woz2W
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.58/1.86 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz2A_type,type,
% 3.58/1.86 woz2A: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz2A,definition,
% 3.58/1.86 ( woz2A
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [T: $i] :
% 3.58/1.86 ( ( breln1 @ A @ T )
% 3.58/1.86 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.58/1.86 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(woz2B_type,type,
% 3.58/1.86 woz2B: $o ).
% 3.58/1.86
% 3.58/1.86 thf(woz2B,definition,
% 3.58/1.86 ( woz2B
% 3.58/1.86 = ( ! [A: $i,R: $i] :
% 3.58/1.86 ( ( breln1 @ A @ R )
% 3.58/1.86 => ! [S: $i] :
% 3.58/1.86 ( ( breln1 @ A @ S )
% 3.58/1.86 => ! [T: $i] :
% 3.58/1.86 ( ( breln1 @ A @ T )
% 3.58/1.86 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.58/1.86 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(image1Ex_type,type,
% 3.58/1.86 image1Ex: $o ).
% 3.58/1.86
% 3.58/1.86 thf(image1Ex,definition,
% 3.58/1.86 ( image1Ex
% 3.58/1.86 = ( ! [A: $i,Xf: $i > $i] :
% 3.58/1.86 ? [B: $i] :
% 3.58/1.86 ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ B )
% 3.58/1.86 <=> ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( Xx
% 3.58/1.86 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(image1Ex1_type,type,
% 3.58/1.86 image1Ex1: $o ).
% 3.58/1.86
% 3.58/1.86 thf(image1Ex1,definition,
% 3.58/1.86 ( image1Ex1
% 3.58/1.86 = ( ! [A: $i,Xf: $i > $i] :
% 3.58/1.86 ( exu
% 3.58/1.86 @ ^ [B: $i] :
% 3.58/1.86 ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ B )
% 3.58/1.86 <=> ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( Xx
% 3.58/1.86 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(image1_type,type,
% 3.58/1.86 image1: $i > ( $i > $i ) > $i ).
% 3.58/1.86
% 3.58/1.86 thf(image1Equiv_type,type,
% 3.58/1.86 image1Equiv: $o ).
% 3.58/1.86
% 3.58/1.86 thf(image1Equiv,definition,
% 3.58/1.86 ( image1Equiv
% 3.58/1.86 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.58/1.86 ( ( in @ Xx
% 3.58/1.86 @ ( image1 @ A
% 3.58/1.86 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.58/1.86 <=> ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( Xx
% 3.58/1.86 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(image1E_type,type,
% 3.58/1.86 image1E: $o ).
% 3.58/1.86
% 3.58/1.86 thf(image1E,definition,
% 3.58/1.86 ( image1E
% 3.58/1.86 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.58/1.86 ( ( in @ Xx
% 3.58/1.86 @ ( image1 @ A
% 3.58/1.86 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.58/1.86 => ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( Xx
% 3.58/1.86 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(image1I_type,type,
% 3.58/1.86 image1I: $o ).
% 3.58/1.86
% 3.58/1.86 thf(image1I,definition,
% 3.58/1.86 ( image1I
% 3.58/1.86 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.58/1.86 ( ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( Xx
% 3.58/1.86 = ( Xf @ Xy ) ) )
% 3.58/1.86 => ( in @ Xx
% 3.58/1.86 @ ( image1 @ A
% 3.58/1.86 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(injective_type,type,
% 3.58/1.86 injective: $i > $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncSet_type,type,
% 3.58/1.86 injFuncSet: $i > $i > $i ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncInInjFuncSet_type,type,
% 3.58/1.86 injFuncInInjFuncSet: $o ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncInInjFuncSet,definition,
% 3.58/1.86 ( injFuncInInjFuncSet
% 3.58/1.86 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.86 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.58/1.86 => ( ( injective @ A @ B @ Xf )
% 3.58/1.86 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncSetFuncIn_type,type,
% 3.58/1.86 injFuncSetFuncIn: $o ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncSetFuncIn,definition,
% 3.58/1.86 ( injFuncSetFuncIn
% 3.58/1.86 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.86 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.58/1.86 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncSetFuncInj_type,type,
% 3.58/1.86 injFuncSetFuncInj: $o ).
% 3.58/1.86
% 3.58/1.86 thf(injFuncSetFuncInj,definition,
% 3.58/1.86 ( injFuncSetFuncInj
% 3.58/1.86 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.58/1.86 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.58/1.86 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(surjective_type,type,
% 3.58/1.86 surjective: $i > $i > $i > $o ).
% 3.58/1.86
% 3.58/1.86 thf(surjective,definition,
% 3.58/1.86 ( surjective
% 3.58/1.86 = ( ^ [A: $i,B: $i,Xf: $i] :
% 3.58/1.86 ! [Xx: $i] :
% 3.58/1.86 ( ( in @ Xx @ B )
% 3.58/1.86 => ? [Xy: $i] :
% 3.58/1.86 ( ( in @ Xy @ A )
% 3.58/1.86 & ( ( ap @ A @ B @ Xf @ Xy )
% 3.58/1.86 = Xx ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(surjFuncSet_type,type,
% 3.58/1.86 surjFuncSet: $i > $i > $i ).
% 3.58/1.86
% 3.58/1.86 thf(surjFuncSet,definition,
% 3.58/1.86 ( surjFuncSet
% 3.58/1.86 = ( ^ [A: $i,B: $i] :
% 3.58/1.86 ( dsetconstr @ ( funcSet @ A @ B )
% 3.58/1.86 @ ^ [Xf: $i] : ( surjective @ A @ B @ Xf ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(surjFuncSetFuncIn_type,type,
% 3.58/1.86 surjFuncSetFuncIn: $o ).
% 3.58/1.86
% 3.58/1.86 thf(surjFuncSetFuncIn,definition,
% 3.58/1.86 ( surjFuncSetFuncIn
% 3.58/1.86 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.58/1.86 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.58/1.86 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.58/1.86
% 3.58/1.86 thf(surjFuncSetFuncSurj,conjecture,
% 3.58/1.86 ( setextAx
% 3.58/1.86 => ( emptysetAx
% 3.58/1.86 => ( setadjoinAx
% 3.58/1.86 => ( powersetAx
% 3.58/1.86 => ( setunionAx
% 3.58/1.86 => ( omega0Ax
% 3.58/1.86 => ( omegaSAx
% 3.58/1.86 => ( omegaIndAx
% 3.58/1.86 => ( replAx
% 3.58/1.86 => ( foundationAx
% 3.58/1.86 => ( wellorderingAx
% 3.58/1.86 => ( descrp
% 3.58/1.86 => ( dsetconstrI
% 3.58/1.86 => ( dsetconstrEL
% 3.58/1.86 => ( dsetconstrER
% 3.58/1.86 => ( exuE1
% 3.58/1.86 => ( prop2setE
% 3.58/1.86 => ( emptysetE
% 3.58/1.86 => ( emptysetimpfalse
% 3.58/1.86 => ( notinemptyset
% 3.58/1.86 => ( exuE3e
% 3.58/1.86 => ( setext
% 3.58/1.86 => ( emptyI
% 3.58/1.86 => ( noeltsimpempty
% 3.58/1.86 => ( setbeta
% 3.58/1.86 => ( nonemptyE1
% 3.58/1.86 => ( nonemptyI
% 3.58/1.86 => ( nonemptyI1
% 3.58/1.86 => ( setadjoinIL
% 3.58/1.86 => ( emptyinunitempty
% 3.58/1.86 => ( setadjoinIR
% 3.58/1.86 => ( setadjoinE
% 3.58/1.86 => ( setadjoinOr
% 3.58/1.86 => ( setoftrueEq
% 3.58/1.86 => ( powersetI
% 3.58/1.86 => ( emptyinPowerset
% 3.58/1.86 => ( emptyInPowerset
% 3.58/1.86 => ( powersetE
% 3.58/1.86 => ( setunionI
% 3.58/1.86 => ( setunionE
% 3.58/1.86 => ( subPowSU
% 3.58/1.86 => ( exuE2
% 3.58/1.86 => ( nonemptyImpWitness
% 3.58/1.86 => ( uniqinunit
% 3.58/1.86 => ( notinsingleton
% 3.58/1.86 => ( eqinunit
% 3.58/1.86 => ( singletonsswitch
% 3.58/1.86 => ( upairsetE
% 3.58/1.86 => ( upairsetIL
% 3.58/1.86 => ( upairsetIR
% 3.58/1.86 => ( emptyE1
% 3.58/1.86 => ( vacuousDall
% 3.58/1.86 => ( quantDeMorgan1
% 3.58/1.86 => ( quantDeMorgan2
% 3.58/1.86 => ( quantDeMorgan3
% 3.58/1.86 => ( quantDeMorgan4
% 3.58/1.86 => ( prop2setI
% 3.58/1.86 => ( prop2set2propI
% 3.58/1.86 => ( notdexE
% 3.58/1.86 => ( notdallE
% 3.58/1.86 => ( exuI1
% 3.58/1.86 => ( exuI3
% 3.58/1.86 => ( exuI2
% 3.58/1.86 => ( inCongP
% 3.58/1.86 => ( in__Cong
% 3.58/1.86 => ( exuE3u
% 3.58/1.86 => ( exu__Cong
% 3.58/1.86 => ( emptyset__Cong
% 3.58/1.86 => ( setadjoin__Cong
% 3.58/1.86 => ( powerset__Cong
% 3.58/1.86 => ( setunion__Cong
% 3.58/1.86 => ( omega__Cong
% 3.58/1.86 => ( exuEu
% 3.58/1.86 => ( descr__Cong
% 3.58/1.86 => ( dsetconstr__Cong
% 3.58/1.86 => ( subsetI1
% 3.58/1.86 => ( eqimpsubset2
% 3.58/1.86 => ( eqimpsubset1
% 3.58/1.86 => ( subsetI2
% 3.58/1.86 => ( emptysetsubset
% 3.58/1.86 => ( subsetE
% 3.58/1.86 => ( subsetE2
% 3.58/1.86 => ( notsubsetI
% 3.58/1.86 => ( notequalI1
% 3.58/1.86 => ( notequalI2
% 3.58/1.86 => ( subsetRefl
% 3.58/1.86 => ( subsetTrans
% 3.58/1.86 => ( setadjoinSub
% 3.58/1.86 => ( setadjoinSub2
% 3.58/1.86 => ( subset2powerset
% 3.58/1.86 => ( setextsub
% 3.58/1.86 => ( subsetemptysetimpeq
% 3.58/1.86 => ( powersetI1
% 3.58/1.86 => ( powersetE1
% 3.58/1.86 => ( inPowerset
% 3.58/1.86 => ( powersetsubset
% 3.58/1.86 => ( sepInPowerset
% 3.58/1.86 => ( sepSubset
% 3.58/1.86 => ( binunionIL
% 3.58/1.86 => ( upairset2IR
% 3.58/1.86 => ( binunionIR
% 3.58/1.86 => ( binunionEcases
% 3.58/1.86 => ( binunionE
% 3.58/1.86 => ( binunionLsub
% 3.58/1.86 => ( binunionRsub
% 3.58/1.86 => ( binintersectI
% 3.58/1.86 => ( binintersectSubset5
% 3.58/1.86 => ( binintersectEL
% 3.58/1.86 => ( binintersectLsub
% 3.58/1.86 => ( binintersectSubset2
% 3.58/1.86 => ( binintersectSubset3
% 3.58/1.86 => ( binintersectER
% 3.58/1.86 => ( disjointsetsI1
% 3.58/1.86 => ( binintersectRsub
% 3.58/1.86 => ( binintersectSubset4
% 3.58/1.86 => ( binintersectSubset1
% 3.58/1.86 => ( bs114d
% 3.58/1.86 => ( setminusI
% 3.58/1.86 => ( setminusEL
% 3.58/1.86 => ( setminusER
% 3.58/1.86 => ( setminusSubset2
% 3.58/1.86 => ( setminusERneg
% 3.58/1.86 => ( setminusELneg
% 3.58/1.86 => ( setminusILneg
% 3.58/1.86 => ( setminusIRneg
% 3.58/1.86 => ( setminusLsub
% 3.58/1.86 => ( setminusSubset1
% 3.58/1.86 => ( symdiffE
% 3.58/1.86 => ( symdiffI1
% 3.58/1.86 => ( symdiffI2
% 3.58/1.86 => ( symdiffIneg1
% 3.58/1.86 => ( symdiffIneg2
% 3.58/1.86 => ( secondinupair
% 3.58/1.86 => ( setukpairIL
% 3.58/1.86 => ( setukpairIR
% 3.58/1.86 => ( kpairiskpair
% 3.58/1.86 => ( kpairp
% 3.58/1.86 => ( singletonsubset
% 3.58/1.86 => ( singletoninpowerset
% 3.58/1.86 => ( singletoninpowunion
% 3.58/1.86 => ( upairset2E
% 3.58/1.86 => ( upairsubunion
% 3.58/1.86 => ( upairinpowunion
% 3.58/1.86 => ( ubforcartprodlem1
% 3.58/1.86 => ( ubforcartprodlem2
% 3.58/1.86 => ( ubforcartprodlem3
% 3.58/1.86 => ( cartprodpairin
% 3.58/1.86 => ( cartprodmempair1
% 3.58/1.86 => ( cartprodmempair
% 3.58/1.86 => ( setunionE2
% 3.58/1.86 => ( setunionsingleton1
% 3.58/1.86 => ( setunionsingleton2
% 3.58/1.86 => ( setunionsingleton
% 3.58/1.86 => ( singletonprop
% 3.58/1.86 => ( ex1E1
% 3.58/1.86 => ( ex1I
% 3.58/1.86 => ( ex1I2
% 3.58/1.86 => ( singletonsuniq
% 3.58/1.86 => ( setukpairinjL1
% 3.58/1.86 => ( kfstsingleton
% 3.58/1.86 => ( theprop
% 3.58/1.86 => ( kfstpairEq
% 3.58/1.86 => ( cartprodfstin
% 3.58/1.86 => ( setukpairinjL2
% 3.58/1.86 => ( setukpairinjL
% 3.58/1.86 => ( setukpairinjR11
% 3.58/1.86 => ( setukpairinjR12
% 3.58/1.86 => ( setukpairinjR1
% 3.58/1.86 => ( upairequniteq
% 3.58/1.86 => ( setukpairinjR2
% 3.58/1.86 => ( setukpairinjR
% 3.58/1.86 => ( ksndsingleton
% 3.58/1.86 => ( ksndpairEq
% 3.58/1.86 => ( kpairsurjEq
% 3.58/1.86 => ( cartprodsndin
% 3.58/1.86 => ( cartprodpairmemEL
% 3.58/1.86 => ( cartprodpairmemER
% 3.58/1.86 => ( cartprodmempaircEq
% 3.58/1.86 => ( cartprodfstpairEq
% 3.58/1.86 => ( cartprodsndpairEq
% 3.58/1.86 => ( cartprodpairsurjEq
% 3.58/1.86 => ( dpsetconstrI
% 3.58/1.86 => ( dpsetconstrSub
% 3.58/1.86 => ( setOfPairsIsBReln
% 3.58/1.86 => ( dpsetconstrERa
% 3.58/1.86 => ( dpsetconstrEL1
% 3.58/1.86 => ( dpsetconstrEL2
% 3.58/1.86 => ( dpsetconstrER
% 3.58/1.86 => ( funcImageSingleton
% 3.58/1.86 => ( apProp
% 3.58/1.86 => ( app
% 3.58/1.86 => ( infuncsetfunc
% 3.58/1.86 => ( ap2p
% 3.58/1.86 => ( funcinfuncset
% 3.58/1.86 => ( lamProp
% 3.58/1.86 => ( lamp
% 3.58/1.86 => ( lam2p
% 3.58/1.86 => ( brelnall1
% 3.58/1.86 => ( brelnall2
% 3.58/1.86 => ( ex1E2
% 3.58/1.86 => ( funcGraphProp1
% 3.58/1.86 => ( funcGraphProp3
% 3.58/1.86 => ( funcGraphProp2
% 3.58/1.86 => ( funcextLem
% 3.58/1.86 => ( funcGraphProp4
% 3.58/1.86 => ( subbreln
% 3.58/1.86 => ( eqbreln
% 3.58/1.86 => ( funcext
% 3.58/1.86 => ( funcext2
% 3.58/1.86 => ( ap2apEq1
% 3.58/1.86 => ( ap2apEq2
% 3.58/1.86 => ( beta1
% 3.58/1.86 => ( eta1
% 3.58/1.86 => ( lam2lamEq
% 3.58/1.86 => ( beta2
% 3.58/1.86 => ( eta2
% 3.58/1.86 => ( iffalseProp1
% 3.58/1.86 => ( iffalseProp2
% 3.58/1.86 => ( iftrueProp1
% 3.58/1.86 => ( iftrueProp2
% 3.58/1.86 => ( ifSingleton
% 3.58/1.86 => ( ifp
% 3.58/1.86 => ( theeq
% 3.58/1.86 => ( iftrue
% 3.58/1.86 => ( iffalse
% 3.58/1.86 => ( iftrueorfalse
% 3.58/1.86 => ( binintersectT_lem
% 3.58/1.86 => ( binunionT_lem
% 3.58/1.86 => ( powersetT_lem
% 3.58/1.86 => ( setminusT_lem
% 3.58/1.86 => ( complementT_lem
% 3.58/1.86 => ( setextT
% 3.58/1.86 => ( subsetTI
% 3.58/1.86 => ( powersetTI1
% 3.58/1.86 => ( powersetTE1
% 3.58/1.86 => ( complementTI1
% 3.58/1.86 => ( complementTE1
% 3.58/1.86 => ( binintersectTELcontra
% 3.58/1.86 => ( binintersectTERcontra
% 3.58/1.86 => ( contrasubsetT
% 3.58/1.86 => ( contrasubsetT1
% 3.58/1.86 => ( contrasubsetT2
% 3.58/1.86 => ( contrasubsetT3
% 3.58/1.86 => ( doubleComplementI1
% 3.58/1.86 => ( doubleComplementE1
% 3.58/1.86 => ( doubleComplementSub1
% 3.58/1.86 => ( doubleComplementSub2
% 3.58/1.86 => ( doubleComplementEq
% 3.58/1.86 => ( complementTnotintersectT
% 3.58/1.86 => ( complementImpComplementIntersect
% 3.58/1.86 => ( complementSubsetComplementIntersect
% 3.58/1.86 => ( complementInPowersetComplementIntersect
% 3.58/1.86 => ( contraSubsetComplement
% 3.58/1.86 => ( complementTcontraSubset
% 3.58/1.86 => ( binunionTILcontra
% 3.58/1.86 => ( binunionTIRcontra
% 3.58/1.86 => ( inIntersectImpInUnion
% 3.58/1.86 => ( inIntersectImpInUnion2
% 3.58/1.86 => ( inIntersectImpInIntersectUnions
% 3.58/1.86 => ( intersectInPowersetIntersectUnions
% 3.58/1.86 => ( inComplementUnionImpNotIn1
% 3.58/1.86 => ( inComplementUnionImpInComplement1
% 3.58/1.86 => ( binunionTE
% 3.58/1.86 => ( binunionTEcontra
% 3.58/1.86 => ( demorgan2a1
% 3.58/1.86 => ( complementUnionInPowersetComplement
% 3.58/1.86 => ( demorgan2a2
% 3.58/1.86 => ( demorgan1a
% 3.58/1.86 => ( demorgan1b
% 3.58/1.86 => ( demorgan1
% 3.58/1.86 => ( demorgan2a
% 3.58/1.86 => ( demorgan2b2
% 3.58/1.86 => ( demorgan2b
% 3.58/1.86 => ( demorgan2
% 3.58/1.86 => ( woz13rule0
% 3.58/1.86 => ( woz13rule1
% 3.58/1.86 => ( woz13rule2
% 3.58/1.86 => ( woz13rule3
% 3.58/1.86 => ( woz13rule4
% 3.58/1.86 => ( woz1_1
% 3.58/1.86 => ( woz1_2
% 3.58/1.86 => ( woz1_3
% 3.58/1.86 => ( woz1_4
% 3.58/1.86 => ( woz1_5
% 3.58/1.86 => ( breln1all2
% 3.58/1.86 => ( breln1SetBreln1
% 3.58/1.86 => ( choice2fnsingleton
% 3.58/1.86 => ( setOfPairsIsBReln1
% 3.58/1.86 => ( breln1all1
% 3.58/1.86 => ( subbreln1
% 3.58/1.86 => ( eqbreln1
% 3.58/1.86 => ( breln1invprop
% 3.58/1.86 => ( breln1invI
% 3.58/1.86 => ( breln1invE
% 3.58/1.86 => ( breln1compprop
% 3.58/1.86 => ( breln1compI
% 3.58/1.86 => ( breln1compE
% 3.58/1.86 => ( breln1compEex
% 3.58/1.86 => ( breln1unionprop
% 3.58/1.86 => ( breln1unionIL
% 3.58/1.86 => ( breln1unionIR
% 3.58/1.86 => ( breln1unionI
% 3.58/1.86 => ( breln1unionE
% 3.58/1.86 => ( breln1unionEcases
% 3.58/1.86 => ( breln1unionCommutes
% 3.58/1.86 => ( woz2Ex
% 3.58/1.86 => ( woz2W
% 3.58/1.86 => ( woz2A
% 3.58/1.86 => ( woz2B
% 3.58/1.86 => ( image1Ex
% 3.58/1.86 => ( image1Ex1
% 3.58/1.86 => ( image1Equiv
% 3.58/1.86 => ( image1E
% 3.58/1.86 => ( image1I
% 3.58/1.86 => ( injFuncInInjFuncSet
% 3.58/1.86 => ( injFuncSetFuncIn
% 3.58/1.86 => ( injFuncSetFuncInj
% 3.58/1.86 => ( surjFuncSetFuncIn
% 3.58/1.86 => ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.58/1.86 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.58/1.86 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.58/1.86 ------------------------
% 3.66/1.90 % (22795)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_22692 for (2999ds/4Mi)
% 3.66/1.90 % (22797)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/2Mi)
% 3.66/1.90 % (22798)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_22692 for (2999ds/2Mi)
% 3.66/1.90 % (22800)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/18Mi)
% 3.66/1.90 % (22799)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_22692 for (2999ds/275Mi)
% 3.66/1.91 % (22796)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_22692 for (2999ds/27Mi)
% 3.66/1.91 % (22797)Instruction limit reached!
% 3.66/1.91 % (22797)------------------------------
% 3.66/1.91 % (22797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.91 % (22797)Termination reason: Unknown
% 3.66/1.91 % (22797)Termination phase: shuffling
% 3.66/1.91
% 3.66/1.91 % (22797)Memory used [KB]: 1663
% 3.66/1.91 % (22797)Time elapsed: 0.004 s
% 3.66/1.91 % (22797)Instructions burned: 3 (million)
% 3.66/1.91 % (22797)------------------------------
% 3.66/1.91 % (22797)------------------------------
% 3.66/1.91 % (22798)Instruction limit reached!
% 3.66/1.91 % (22798)------------------------------
% 3.66/1.91 % (22798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.91 % (22798)Termination reason: Unknown
% 3.66/1.91 % (22798)Termination phase: shuffling
% 3.66/1.91
% 3.66/1.91 % (22798)Memory used [KB]: 1663
% 3.66/1.91 % (22798)Time elapsed: 0.004 s
% 3.66/1.91 % (22798)Instructions burned: 3 (million)
% 3.66/1.91 % (22798)------------------------------
% 3.66/1.91 % (22798)------------------------------
% 3.66/1.91 % (22794)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/183Mi)
% 3.66/1.91 % (22795)Instruction limit reached!
% 3.66/1.91 % (22795)------------------------------
% 3.66/1.91 % (22795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.91 % (22795)Termination reason: Unknown
% 3.66/1.91 % (22795)Termination phase: shuffling
% 3.66/1.91
% 3.66/1.91 % (22795)Memory used [KB]: 1663
% 3.66/1.91 % (22795)Time elapsed: 0.004 s
% 3.66/1.91 % (22795)Instructions burned: 5 (million)
% 3.66/1.91 % (22795)------------------------------
% 3.66/1.91 % (22795)------------------------------
% 3.66/1.91 % (22800)Instruction limit reached!
% 3.66/1.91 % (22800)------------------------------
% 3.66/1.91 % (22800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.91 % (22800)Termination reason: Unknown
% 3.66/1.91 % (22800)Termination phase: shuffling
% 3.66/1.91
% 3.66/1.91 % (22800)Memory used [KB]: 1918
% 3.66/1.91 % (22800)Time elapsed: 0.011 s
% 3.66/1.91 % (22800)Instructions burned: 18 (million)
% 3.66/1.91 % (22800)------------------------------
% 3.66/1.91 % (22800)------------------------------
% 3.66/1.92 % (22796)Instruction limit reached!
% 3.66/1.92 % (22796)------------------------------
% 3.66/1.92 % (22796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.92 % (22796)Termination reason: Unknown
% 3.66/1.92 % (22796)Termination phase: shuffling
% 3.66/1.92
% 3.66/1.92 % (22796)Memory used [KB]: 2174
% 3.66/1.92 % (22796)Time elapsed: 0.015 s
% 3.66/1.92 % (22796)Instructions burned: 28 (million)
% 3.66/1.92 % (22796)------------------------------
% 3.66/1.92 % (22796)------------------------------
% 3.66/1.92 % (22801)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/3Mi)
% 3.66/1.92 % (22803)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_22692 for (2999ds/15Mi)
% 3.66/1.92 % (22802)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_22692 for (2999ds/37Mi)
% 3.66/1.92 % (22801)Instruction limit reached!
% 3.66/1.92 % (22801)------------------------------
% 3.66/1.92 % (22801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.92 % (22801)Termination reason: Unknown
% 3.66/1.92 % (22801)Termination phase: shuffling
% 3.66/1.92
% 3.66/1.92 % (22801)Memory used [KB]: 1663
% 3.66/1.92 % (22801)Time elapsed: 0.004 s
% 3.66/1.92 % (22801)Instructions burned: 4 (million)
% 3.66/1.92 % (22801)------------------------------
% 3.66/1.92 % (22801)------------------------------
% 3.66/1.93 % (22803)Instruction limit reached!
% 3.66/1.93 % (22803)------------------------------
% 3.66/1.93 % (22803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.93 % (22803)Termination reason: Unknown
% 3.66/1.93 % (22803)Termination phase: shuffling
% 3.66/1.93
% 3.66/1.93 % (22803)Memory used [KB]: 1791
% 3.66/1.93 % (22803)Time elapsed: 0.009 s
% 3.66/1.93 % (22803)Instructions burned: 15 (million)
% 3.66/1.93 % (22803)------------------------------
% 3.66/1.93 % (22803)------------------------------
% 3.66/1.93 % (22804)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_22692 for (2999ds/3Mi)
% 3.66/1.93 % (22804)Instruction limit reached!
% 3.66/1.93 % (22804)------------------------------
% 3.66/1.93 % (22804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.93 % (22804)Termination reason: Unknown
% 3.66/1.93 % (22804)Termination phase: shuffling
% 3.66/1.93
% 3.66/1.93 % (22804)Memory used [KB]: 1663
% 3.66/1.93 % (22804)Time elapsed: 0.003 s
% 3.66/1.93 % (22804)Instructions burned: 3 (million)
% 3.66/1.93 % (22804)------------------------------
% 3.66/1.93 % (22804)------------------------------
% 3.66/1.94 % (22805)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_22692 for (2999ds/1041Mi)
% 3.66/1.94 % (22802)Instruction limit reached!
% 3.66/1.94 % (22802)------------------------------
% 3.66/1.94 % (22802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.94 % (22802)Termination reason: Unknown
% 3.66/1.94 % (22802)Termination phase: shuffling
% 3.66/1.94
% 3.66/1.94 % (22802)Memory used [KB]: 2302
% 3.66/1.94 % (22802)Time elapsed: 0.018 s
% 3.66/1.94 % (22802)Instructions burned: 37 (million)
% 3.66/1.94 % (22802)------------------------------
% 3.66/1.94 % (22802)------------------------------
% 3.66/1.94 % (22806)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/7Mi)
% 3.66/1.94 % (22806)Instruction limit reached!
% 3.66/1.94 % (22806)------------------------------
% 3.66/1.94 % (22806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.94 % (22806)Termination reason: Unknown
% 3.66/1.94 % (22806)Termination phase: shuffling
% 3.66/1.94
% 3.66/1.94 % (22806)Memory used [KB]: 1663
% 3.66/1.94 % (22806)Time elapsed: 0.006 s
% 3.66/1.94 % (22806)Instructions burned: 9 (million)
% 3.66/1.94 % (22806)------------------------------
% 3.66/1.94 % (22806)------------------------------
% 3.66/1.95 % (22807)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/16Mi)
% 3.66/1.95 % (22808)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_22692 for (2999ds/3Mi)
% 3.66/1.95 % (22808)Instruction limit reached!
% 3.66/1.95 % (22808)------------------------------
% 3.66/1.95 % (22808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.95 % (22808)Termination reason: Unknown
% 3.66/1.95 % (22808)Termination phase: shuffling
% 3.66/1.95
% 3.66/1.95 % (22808)Memory used [KB]: 1663
% 3.66/1.95 % (22808)Time elapsed: 0.004 s
% 3.66/1.95 % (22808)Instructions burned: 4 (million)
% 3.66/1.95 % (22808)------------------------------
% 3.66/1.95 % (22808)------------------------------
% 3.66/1.95 % (22807)Instruction limit reached!
% 3.66/1.95 % (22807)------------------------------
% 3.66/1.95 % (22807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.95 % (22807)Termination reason: Unknown
% 3.66/1.95 % (22807)Termination phase: shuffling
% 3.66/1.95
% 3.66/1.95 % (22807)Memory used [KB]: 1918
% 3.66/1.95 % (22807)Time elapsed: 0.009 s
% 3.66/1.95 % (22807)Instructions burned: 17 (million)
% 3.66/1.95 % (22807)------------------------------
% 3.66/1.95 % (22807)------------------------------
% 3.66/1.96 % (22809)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_22692 for (2999ds/3Mi)
% 3.66/1.96 % (22809)Instruction limit reached!
% 3.66/1.96 % (22809)------------------------------
% 3.66/1.96 % (22809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.96 % (22809)Termination reason: Unknown
% 3.66/1.96 % (22809)Termination phase: shuffling
% 3.66/1.96
% 3.66/1.96 % (22809)Memory used [KB]: 1663
% 3.66/1.96 % (22809)Time elapsed: 0.004 s
% 3.66/1.96 % (22809)Instructions burned: 5 (million)
% 3.66/1.96 % (22809)------------------------------
% 3.66/1.96 % (22809)------------------------------
% 3.66/1.96 % (22810)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/7Mi)
% 3.66/1.96 % (22810)Instruction limit reached!
% 3.66/1.96 % (22810)------------------------------
% 3.66/1.96 % (22810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.96 % (22810)Termination reason: Unknown
% 3.66/1.96 % (22810)Termination phase: shuffling
% 3.66/1.96
% 3.66/1.96 % (22810)Memory used [KB]: 1663
% 3.66/1.96 % (22810)Time elapsed: 0.005 s
% 3.66/1.96 % (22810)Instructions burned: 7 (million)
% 3.66/1.96 % (22810)------------------------------
% 3.66/1.96 % (22810)------------------------------
% 3.66/1.96 % (22811)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/3Mi)
% 3.66/1.97 % (22811)Instruction limit reached!
% 3.66/1.97 % (22811)------------------------------
% 3.66/1.97 % (22811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.97 % (22811)Termination reason: Unknown
% 3.66/1.97 % (22811)Termination phase: shuffling
% 3.66/1.97
% 3.66/1.97 % (22811)Memory used [KB]: 1663
% 3.66/1.97 % (22811)Time elapsed: 0.004 s
% 3.66/1.97 % (22811)Instructions burned: 4 (million)
% 3.66/1.97 % (22811)------------------------------
% 3.66/1.97 % (22811)------------------------------
% 3.66/1.97 % (22812)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/4Mi)
% 3.66/1.97 % (22812)Instruction limit reached!
% 3.66/1.97 % (22812)------------------------------
% 3.66/1.97 % (22812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.97 % (22812)Termination reason: Unknown
% 3.66/1.97 % (22812)Termination phase: shuffling
% 3.66/1.97
% 3.66/1.97 % (22812)Memory used [KB]: 1663
% 3.66/1.97 % (22812)Time elapsed: 0.004 s
% 3.66/1.97 % (22812)Instructions burned: 4 (million)
% 3.66/1.97 % (22812)------------------------------
% 3.66/1.97 % (22812)------------------------------
% 3.66/1.97 % (22813)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/18Mi)
% 3.66/1.98 % (22814)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/710Mi)
% 3.66/1.98 % (22815)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22692 for (2999ds/6Mi)
% 3.66/1.98 % (22813)Instruction limit reached!
% 3.66/1.98 % (22813)------------------------------
% 3.66/1.98 % (22813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.98 % (22813)Termination reason: Unknown
% 3.66/1.98 % (22813)Termination phase: shuffling
% 3.66/1.98
% 3.66/1.98 % (22813)Memory used [KB]: 2046
% 3.66/1.98 % (22813)Time elapsed: 0.011 s
% 3.66/1.98 % (22813)Instructions burned: 20 (million)
% 3.66/1.98 % (22813)------------------------------
% 3.66/1.98 % (22813)------------------------------
% 3.66/1.98 % (22815)Instruction limit reached!
% 3.66/1.98 % (22815)------------------------------
% 3.66/1.98 % (22815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.98 % (22815)Termination reason: Unknown
% 3.66/1.98 % (22815)Termination phase: shuffling
% 3.66/1.98
% 3.66/1.98 % (22815)Memory used [KB]: 1663
% 3.66/1.98 % (22815)Time elapsed: 0.005 s
% 3.66/1.98 % (22815)Instructions burned: 8 (million)
% 3.66/1.98 % (22815)------------------------------
% 3.66/1.98 % (22815)------------------------------
% 3.66/1.99 % (22816)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_22692 for (2998ds/902Mi)
% 3.66/1.99 % (22794)Instruction limit reached!
% 3.66/1.99 % (22794)------------------------------
% 3.66/1.99 % (22794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/1.99 % (22794)Termination reason: Unknown
% 3.66/1.99 % (22794)Termination phase: Property scanning
% 3.66/1.99
% 3.66/1.99 % (22794)Memory used [KB]: 3070
% 3.66/1.99 % (22794)Time elapsed: 0.087 s
% 3.66/1.99 % (22794)Instructions burned: 183 (million)
% 3.66/1.99 % (22794)------------------------------
% 3.66/1.99 % (22794)------------------------------
% 3.66/2.00 % (22817)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_22692 for (2998ds/21Mi)
% 3.66/2.00 % (22818)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22692 for (2998ds/5Mi)
% 3.66/2.00 % (22818)Instruction limit reached!
% 3.66/2.00 % (22818)------------------------------
% 3.66/2.00 % (22818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.00 % (22818)Termination reason: Unknown
% 3.66/2.00 % (22818)Termination phase: shuffling
% 3.66/2.00
% 3.66/2.00 % (22818)Memory used [KB]: 1663
% 3.66/2.00 % (22818)Time elapsed: 0.005 s
% 3.66/2.00 % (22818)Instructions burned: 7 (million)
% 3.66/2.00 % (22818)------------------------------
% 3.66/2.00 % (22818)------------------------------
% 3.66/2.01 % (22817)Instruction limit reached!
% 3.66/2.01 % (22817)------------------------------
% 3.66/2.01 % (22817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.01 % (22817)Termination reason: Unknown
% 3.66/2.01 % (22817)Termination phase: shuffling
% 3.66/2.01
% 3.66/2.01 % (22817)Memory used [KB]: 1918
% 3.66/2.01 % (22817)Time elapsed: 0.012 s
% 3.66/2.01 % (22817)Instructions burned: 22 (million)
% 3.66/2.01 % (22817)------------------------------
% 3.66/2.01 % (22817)------------------------------
% 3.66/2.01 % (22819)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_22692 for (2998ds/6Mi)
% 3.66/2.01 % (22819)Instruction limit reached!
% 3.66/2.01 % (22819)------------------------------
% 3.66/2.01 % (22819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.01 % (22819)Termination reason: Unknown
% 3.66/2.01 % (22819)Termination phase: shuffling
% 3.66/2.01
% 3.66/2.01 % (22819)Memory used [KB]: 1663
% 3.66/2.01 % (22819)Time elapsed: 0.006 s
% 3.66/2.01 % (22819)Instructions burned: 7 (million)
% 3.66/2.01 % (22819)------------------------------
% 3.66/2.01 % (22819)------------------------------
% 4.53/2.03 % (22820)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22692 for (2998ds/377Mi)
% 4.53/2.03 % (22821)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_22692 for (2998ds/779Mi)
% 4.53/2.03 % (22822)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_22692 for (2998ds/19Mi)
% 4.53/2.04 % (22799)Instruction limit reached!
% 4.53/2.04 % (22799)------------------------------
% 4.53/2.04 % (22799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.53/2.04 % (22799)Termination reason: Unknown
% 4.53/2.04 % (22799)Termination phase: Property scanning
% 4.53/2.04
% 4.53/2.04 % (22799)Memory used [KB]: 5884
% 4.53/2.04 % (22799)Time elapsed: 0.133 s
% 4.53/2.04 % (22799)Instructions burned: 276 (million)
% 4.53/2.04 % (22799)------------------------------
% 4.53/2.04 % (22799)------------------------------
% 4.53/2.04 % (22822)Instruction limit reached!
% 4.53/2.04 % (22822)------------------------------
% 4.53/2.04 % (22822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.53/2.04 % (22822)Termination reason: Unknown
% 4.53/2.04 % (22822)Termination phase: shuffling
% 4.53/2.04
% 4.53/2.04 % (22822)Memory used [KB]: 1918
% 4.53/2.04 % (22822)Time elapsed: 0.011 s
% 4.53/2.04 % (22822)Instructions burned: 19 (million)
% 4.53/2.04 % (22822)------------------------------
% 4.53/2.04 % (22822)------------------------------
% 4.53/2.05 % (22823)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22692 for (2998ds/879Mi)
% 4.53/2.06 % (22824)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22692 for (2998ds/17Mi)
% 4.53/2.07 % (22824)Instruction limit reached!
% 4.53/2.07 % (22824)------------------------------
% 4.53/2.07 % (22824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.53/2.07 % (22824)Termination reason: Unknown
% 4.53/2.07 % (22824)Termination phase: shuffling
% 4.53/2.07
% 4.53/2.07 % (22824)Memory used [KB]: 1918
% 4.53/2.07 % (22824)Time elapsed: 0.011 s
% 4.53/2.07 % (22824)Instructions burned: 18 (million)
% 4.53/2.07 % (22824)------------------------------
% 4.53/2.07 % (22824)------------------------------
% 4.53/2.09 % (22825)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22692 for (2997ds/3Mi)
% 4.53/2.09 % (22825)Instruction limit reached!
% 4.53/2.09 % (22825)------------------------------
% 4.53/2.09 % (22825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.53/2.09 % (22825)Termination reason: Unknown
% 4.53/2.09 % (22825)Termination phase: shuffling
% 4.53/2.09
% 4.53/2.09 % (22825)Memory used [KB]: 1663
% 4.53/2.09 % (22825)Time elapsed: 0.004 s
% 4.53/2.09 % (22825)Instructions burned: 3 (million)
% 4.53/2.09 % (22825)------------------------------
% 4.53/2.09 % (22825)------------------------------
% 4.53/2.10 % (22826)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22692 for (2997ds/30Mi)
% 4.53/2.12 % (22826)Instruction limit reached!
% 4.53/2.12 % (22826)------------------------------
% 4.53/2.12 % (22826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.53/2.12 % (22826)Termination reason: Unknown
% 4.53/2.12 % (22826)Termination phase: shuffling
% 4.53/2.12
% 4.53/2.12 % (22826)Memory used [KB]: 2174
% 4.53/2.12 % (22826)Time elapsed: 0.016 s
% 4.53/2.12 % (22826)Instructions burned: 30 (million)
% 4.53/2.12 % (22826)------------------------------
% 4.53/2.12 % (22826)------------------------------
% 4.95/2.14 % (22827)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22692 for (2997ds/127Mi)
% 4.95/2.19 % (22820)Instruction limit reached!
% 4.95/2.19 % (22820)------------------------------
% 4.95/2.19 % (22820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.95/2.19 % (22820)Termination reason: Unknown
% 4.95/2.19 % (22820)Termination phase: Saturation
% 4.95/2.19
% 4.95/2.19 % (22820)Memory used [KB]: 9466
% 4.95/2.19 % (22820)Time elapsed: 0.167 s
% 4.95/2.19 % (22820)Instructions burned: 378 (million)
% 4.95/2.19 % (22820)------------------------------
% 4.95/2.19 % (22820)------------------------------
% 4.95/2.19 % (22827)Instruction limit reached!
% 4.95/2.19 % (22827)------------------------------
% 4.95/2.19 % (22827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.95/2.19 % (22827)Termination reason: Unknown
% 4.95/2.19 % (22827)Termination phase: Property scanning
% 4.95/2.19
% 4.95/2.19 % (22827)Memory used [KB]: 2942
% 4.95/2.19 % (22827)Time elapsed: 0.058 s
% 4.95/2.19 % (22827)Instructions burned: 129 (million)
% 4.95/2.19 % (22827)------------------------------
% 4.95/2.19 % (22827)------------------------------
% 5.42/2.21 % (22829)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_22692 for (2996ds/3Mi)
% 5.42/2.21 % (22828)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22692 for (2996ds/100Mi)
% 5.42/2.21 % (22829)Instruction limit reached!
% 5.42/2.21 % (22829)------------------------------
% 5.42/2.21 % (22829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.21 % (22829)Termination reason: Unknown
% 5.42/2.21 % (22829)Termination phase: shuffling
% 5.42/2.21
% 5.42/2.21 % (22829)Memory used [KB]: 1663
% 5.42/2.21 % (22829)Time elapsed: 0.004 s
% 5.42/2.21 % (22829)Instructions burned: 4 (million)
% 5.42/2.21 % (22829)------------------------------
% 5.42/2.21 % (22829)------------------------------
% 5.42/2.22 % (22816)Refutation not found, incomplete strategy
% 5.42/2.22 % (22816)------------------------------
% 5.42/2.22 % (22816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.22 % (22816)Termination reason: Refutation not found, incomplete strategy
% 5.42/2.22
% 5.42/2.22
% 5.42/2.22 % (22816)Memory used [KB]: 11257
% 5.42/2.22 % (22816)Time elapsed: 0.232 s
% 5.42/2.22 % (22816)Instructions burned: 469 (million)
% 5.42/2.22 % (22816)------------------------------
% 5.42/2.22 % (22816)------------------------------
% 5.42/2.23 % (22830)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_22692 for (2996ds/20Mi)
% 5.42/2.24 % (22830)Instruction limit reached!
% 5.42/2.24 % (22830)------------------------------
% 5.42/2.24 % (22830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.24 % (22830)Termination reason: Unknown
% 5.42/2.24 % (22830)Termination phase: shuffling
% 5.42/2.24
% 5.42/2.24 % (22830)Memory used [KB]: 1918
% 5.42/2.24 % (22830)Time elapsed: 0.012 s
% 5.42/2.24 % (22830)Instructions burned: 20 (million)
% 5.42/2.24 % (22830)------------------------------
% 5.42/2.24 % (22830)------------------------------
% 5.42/2.24 % (22831)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_22692 for (2996ds/86Mi)
% 5.42/2.25 % (22828)Instruction limit reached!
% 5.42/2.25 % (22828)------------------------------
% 5.42/2.25 % (22828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.25 % (22828)Termination reason: Unknown
% 5.42/2.25 % (22828)Termination phase: Preprocessing 3
% 5.42/2.25
% 5.42/2.25 % (22828)Memory used [KB]: 2814
% 5.42/2.25 % (22828)Time elapsed: 0.045 s
% 5.42/2.25 % (22828)Instructions burned: 100 (million)
% 5.42/2.25 % (22828)------------------------------
% 5.42/2.25 % (22828)------------------------------
% 5.42/2.25 % (22832)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_22692 for (2996ds/107Mi)
% 5.42/2.27 % (22833)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_22692 for (2996ds/39Mi)
% 5.42/2.28 % (22831)Instruction limit reached!
% 5.42/2.28 % (22831)------------------------------
% 5.42/2.28 % (22831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.28 % (22831)Termination reason: Unknown
% 5.42/2.28 % (22831)Termination phase: Property scanning
% 5.42/2.28
% 5.42/2.28 % (22831)Memory used [KB]: 2814
% 5.42/2.28 % (22831)Time elapsed: 0.041 s
% 5.42/2.28 % (22831)Instructions burned: 86 (million)
% 5.42/2.28 % (22831)------------------------------
% 5.42/2.28 % (22831)------------------------------
% 5.42/2.28 % (22833)Instruction limit reached!
% 5.42/2.28 % (22833)------------------------------
% 5.42/2.28 % (22833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.28 % (22833)Termination reason: Unknown
% 5.42/2.28 % (22833)Termination phase: shuffling
% 5.42/2.28
% 5.42/2.28 % (22833)Memory used [KB]: 2302
% 5.42/2.28 % (22833)Time elapsed: 0.019 s
% 5.42/2.28 % (22833)Instructions burned: 39 (million)
% 5.42/2.28 % (22833)------------------------------
% 5.42/2.28 % (22833)------------------------------
% 5.42/2.29 % (22834)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_22692 for (2995ds/448Mi)
% 5.86/2.30 % (22832)Instruction limit reached!
% 5.86/2.30 % (22832)------------------------------
% 5.86/2.30 % (22832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.30 % (22832)Termination reason: Unknown
% 5.86/2.30 % (22832)Termination phase: SInE selection
% 5.86/2.30
% 5.86/2.30 % (22832)Memory used [KB]: 2814
% 5.86/2.30 % (22832)Time elapsed: 0.050 s
% 5.86/2.30 % (22832)Instructions burned: 108 (million)
% 5.86/2.30 % (22832)------------------------------
% 5.86/2.30 % (22832)------------------------------
% 5.86/2.30 % (22835)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_22692 for (2995ds/46Mi)
% 5.86/2.32 % (22836)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_22692 for (2995ds/98Mi)
% 5.86/2.32 % (22835)Instruction limit reached!
% 5.86/2.32 % (22835)------------------------------
% 5.86/2.32 % (22835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.32 % (22835)Termination reason: Unknown
% 5.86/2.32 % (22835)Termination phase: shuffling
% 5.86/2.32
% 5.86/2.32 % (22835)Memory used [KB]: 2430
% 5.86/2.32 % (22835)Time elapsed: 0.023 s
% 5.86/2.32 % (22835)Instructions burned: 48 (million)
% 5.86/2.32 % (22835)------------------------------
% 5.86/2.32 % (22835)------------------------------
% 5.86/2.33 % (22814)Instruction limit reached!
% 5.86/2.33 % (22814)------------------------------
% 5.86/2.33 % (22814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.33 % (22814)Termination reason: Unknown
% 5.86/2.33 % (22814)Termination phase: Saturation
% 5.86/2.33
% 5.86/2.33 % (22814)Memory used [KB]: 11769
% 5.86/2.33 % (22814)Time elapsed: 0.352 s
% 5.86/2.33 % (22814)Instructions burned: 710 (million)
% 5.86/2.33 % (22814)------------------------------
% 5.86/2.33 % (22814)------------------------------
% 5.86/2.34 % (22837)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_22692 for (2995ds/507Mi)
% 5.86/2.34 % (22821)Instruction limit reached!
% 5.86/2.34 % (22821)------------------------------
% 5.86/2.34 % (22821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.34 % (22821)Termination reason: Unknown
% 5.86/2.34 % (22821)Termination phase: Saturation
% 5.86/2.34
% 5.86/2.34 % (22821)Memory used [KB]: 7931
% 5.86/2.34 % (22821)Time elapsed: 0.317 s
% 5.86/2.34 % (22821)Instructions burned: 779 (million)
% 5.86/2.34 % (22821)------------------------------
% 5.86/2.34 % (22821)------------------------------
% 5.86/2.35 % (22838)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_22692 for (2995ds/149Mi)
% 5.86/2.36 % (22839)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22692 for (2995ds/39Mi)
% 5.86/2.36 % (22836)Instruction limit reached!
% 5.86/2.36 % (22836)------------------------------
% 5.86/2.36 % (22836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.36 % (22836)Termination reason: Unknown
% 5.86/2.36 % (22836)Termination phase: Property scanning
% 5.86/2.36
% 5.86/2.36 % (22836)Memory used [KB]: 2814
% 5.86/2.36 % (22836)Time elapsed: 0.044 s
% 5.86/2.36 % (22836)Instructions burned: 99 (million)
% 5.86/2.36 % (22836)------------------------------
% 5.86/2.36 % (22836)------------------------------
% 5.86/2.38 % (22839)Instruction limit reached!
% 5.86/2.38 % (22839)------------------------------
% 5.86/2.38 % (22839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.38 % (22839)Termination reason: Unknown
% 5.86/2.38 % (22839)Termination phase: shuffling
% 5.86/2.38
% 5.86/2.38 % (22839)Memory used [KB]: 2430
% 5.86/2.38 % (22839)Time elapsed: 0.021 s
% 5.86/2.38 % (22839)Instructions burned: 40 (million)
% 5.86/2.38 % (22839)------------------------------
% 5.86/2.38 % (22839)------------------------------
% 5.86/2.38 % (22840)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_22692 for (2994ds/6Mi)
% 5.86/2.38 % (22840)Instruction limit reached!
% 5.86/2.38 % (22840)------------------------------
% 5.86/2.38 % (22840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.38 % (22840)Termination reason: Unknown
% 5.86/2.38 % (22840)Termination phase: shuffling
% 5.86/2.38
% 5.86/2.38 % (22840)Memory used [KB]: 1663
% 5.86/2.38 % (22840)Time elapsed: 0.005 s
% 5.86/2.38 % (22840)Instructions burned: 6 (million)
% 5.86/2.38 % (22840)------------------------------
% 5.86/2.38 % (22840)------------------------------
% 5.86/2.39 % (22805)Instruction limit reached!
% 5.86/2.39 % (22805)------------------------------
% 5.86/2.39 % (22805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.39 % (22805)Termination reason: Unknown
% 5.86/2.39 % (22805)Termination phase: Saturation
% 5.86/2.39
% 5.86/2.39 % (22805)Memory used [KB]: 18293
% 5.86/2.39 % (22805)Time elapsed: 0.451 s
% 5.86/2.39 % (22805)Instructions burned: 1043 (million)
% 5.86/2.39 % (22805)------------------------------
% 5.86/2.39 % (22805)------------------------------
% 5.86/2.39 % (22841)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_22692 for (2994ds/1087Mi)
% 6.57/2.40 % (22842)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22692 for (2994ds/47Mi)
% 6.57/2.40 % (22843)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_22692 for (2994ds/44Mi)
% 6.57/2.41 % (22838)Instruction limit reached!
% 6.57/2.41 % (22838)------------------------------
% 6.57/2.41 % (22838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.41 % (22838)Termination reason: Unknown
% 6.57/2.41 % (22838)Termination phase: Function definition elimination
% 6.57/2.41
% 6.57/2.41 % (22838)Memory used [KB]: 2942
% 6.57/2.41 % (22838)Time elapsed: 0.066 s
% 6.57/2.41 % (22838)Instructions burned: 149 (million)
% 6.57/2.41 % (22838)------------------------------
% 6.57/2.41 % (22838)------------------------------
% 6.57/2.42 % (22842)Instruction limit reached!
% 6.57/2.42 % (22842)------------------------------
% 6.57/2.42 % (22842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.42 % (22842)Termination reason: Unknown
% 6.57/2.42 % (22842)Termination phase: shuffling
% 6.57/2.42
% 6.57/2.42 % (22842)Memory used [KB]: 2558
% 6.57/2.42 % (22842)Time elapsed: 0.024 s
% 6.57/2.42 % (22842)Instructions burned: 47 (million)
% 6.57/2.42 % (22842)------------------------------
% 6.57/2.42 % (22842)------------------------------
% 6.57/2.43 % (22843)Instruction limit reached!
% 6.57/2.43 % (22843)------------------------------
% 6.57/2.43 % (22843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.43 % (22843)Termination reason: Unknown
% 6.57/2.43 % (22843)Termination phase: shuffling
% 6.57/2.43
% 6.57/2.43 % (22843)Memory used [KB]: 2430
% 6.57/2.43 % (22843)Time elapsed: 0.024 s
% 6.57/2.43 % (22843)Instructions burned: 44 (million)
% 6.57/2.43 % (22843)------------------------------
% 6.57/2.43 % (22843)------------------------------
% 6.57/2.43 % (22844)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_22692 for (2994ds/432Mi)
% 6.57/2.44 % (22845)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22692 for (2994ds/62Mi)
% 6.57/2.44 % (22846)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_22692 for (2994ds/31Mi)
% 6.57/2.46 % (22846)Instruction limit reached!
% 6.57/2.46 % (22846)------------------------------
% 6.57/2.46 % (22846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.46 % (22846)Termination reason: Unknown
% 6.57/2.46 % (22846)Termination phase: shuffling
% 6.57/2.46
% 6.57/2.46 % (22846)Memory used [KB]: 2302
% 6.57/2.46 % (22846)Time elapsed: 0.017 s
% 6.57/2.46 % (22846)Instructions burned: 33 (million)
% 6.57/2.46 % (22846)------------------------------
% 6.57/2.46 % (22846)------------------------------
% 6.57/2.46 % (22845)Instruction limit reached!
% 6.57/2.46 % (22845)------------------------------
% 6.57/2.46 % (22845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.46 % (22845)Termination reason: Unknown
% 6.57/2.46 % (22845)Termination phase: shuffling
% 6.57/2.46
% 6.57/2.46 % (22845)Memory used [KB]: 2686
% 6.57/2.46 % (22845)Time elapsed: 0.030 s
% 6.57/2.46 % (22845)Instructions burned: 62 (million)
% 6.57/2.46 % (22845)------------------------------
% 6.57/2.46 % (22845)------------------------------
% 6.57/2.48 % (22847)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22692 for (2993ds/96Mi)
% 6.57/2.48 % (22834)Instruction limit reached!
% 6.57/2.48 % (22834)------------------------------
% 6.57/2.48 % (22834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.48 % (22834)Termination reason: Unknown
% 6.57/2.48 % (22834)Termination phase: Saturation
% 6.57/2.48
% 6.57/2.48 % (22834)Memory used [KB]: 7803
% 6.57/2.48 % (22834)Time elapsed: 0.187 s
% 6.57/2.48 % (22834)Instructions burned: 448 (million)
% 6.57/2.48 % (22834)------------------------------
% 6.57/2.48 % (22834)------------------------------
% 6.57/2.48 % (22848)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_22692 for (2993ds/453Mi)
% 6.57/2.50 % (22849)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_22692 for (2993ds/71Mi)
% 7.00/2.50 % (22823)Instruction limit reached!
% 7.00/2.50 % (22823)------------------------------
% 7.00/2.50 % (22823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.50 % (22823)Termination reason: Unknown
% 7.00/2.50 % (22823)Termination phase: Saturation
% 7.00/2.50
% 7.00/2.50 % (22823)Memory used [KB]: 10746
% 7.00/2.50 % (22823)Time elapsed: 0.448 s
% 7.00/2.50 % (22823)Instructions burned: 879 (million)
% 7.00/2.50 % (22823)------------------------------
% 7.00/2.50 % (22823)------------------------------
% 7.00/2.52 % (22850)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22692 for (2993ds/83Mi)
% 7.00/2.52 % (22847)Instruction limit reached!
% 7.00/2.52 % (22847)------------------------------
% 7.00/2.52 % (22847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.52 % (22847)Termination reason: Unknown
% 7.00/2.52 % (22847)Termination phase: Property scanning
% 7.00/2.52
% 7.00/2.52 % (22847)Memory used [KB]: 2814
% 7.00/2.52 % (22847)Time elapsed: 0.048 s
% 7.00/2.52 % (22847)Instructions burned: 97 (million)
% 7.00/2.52 % (22847)------------------------------
% 7.00/2.52 % (22847)------------------------------
% 7.00/2.53 % (22849)Instruction limit reached!
% 7.00/2.53 % (22849)------------------------------
% 7.00/2.53 % (22849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.53 % (22849)Termination reason: Unknown
% 7.00/2.53 % (22849)Termination phase: Property scanning
% 7.00/2.53
% 7.00/2.53 % (22849)Memory used [KB]: 2814
% 7.00/2.53 % (22849)Time elapsed: 0.033 s
% 7.00/2.53 % (22849)Instructions burned: 71 (million)
% 7.00/2.53 % (22849)------------------------------
% 7.00/2.53 % (22849)------------------------------
% 7.00/2.54 % (22851)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22692 for (2993ds/11Mi)
% 7.00/2.54 % (22852)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_22692 for (2993ds/41Mi)
% 7.00/2.55 % (22851)Instruction limit reached!
% 7.00/2.55 % (22851)------------------------------
% 7.00/2.55 % (22851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.55 % (22851)Termination reason: Unknown
% 7.00/2.55 % (22851)Termination phase: shuffling
% 7.00/2.55
% 7.00/2.55 % (22851)Memory used [KB]: 1791
% 7.00/2.55 % (22851)Time elapsed: 0.008 s
% 7.00/2.55 % (22851)Instructions burned: 12 (million)
% 7.00/2.55 % (22851)------------------------------
% 7.00/2.55 % (22851)------------------------------
% 7.00/2.56 % (22850)Instruction limit reached!
% 7.00/2.56 % (22850)------------------------------
% 7.00/2.56 % (22850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.56 % (22850)Termination reason: Unknown
% 7.00/2.56 % (22850)Termination phase: Property scanning
% 7.00/2.56
% 7.00/2.56 % (22850)Memory used [KB]: 2814
% 7.00/2.56 % (22850)Time elapsed: 0.042 s
% 7.00/2.56 % (22850)Instructions burned: 83 (million)
% 7.00/2.56 % (22850)------------------------------
% 7.00/2.56 % (22850)------------------------------
% 7.00/2.56 % (22852)Instruction limit reached!
% 7.00/2.56 % (22852)------------------------------
% 7.00/2.56 % (22852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.56 % (22852)Termination reason: Unknown
% 7.00/2.56 % (22852)Termination phase: shuffling
% 7.00/2.56
% 7.00/2.56 % (22852)Memory used [KB]: 2430
% 7.00/2.56 % (22852)Time elapsed: 0.020 s
% 7.00/2.56 % (22852)Instructions burned: 42 (million)
% 7.00/2.56 % (22852)------------------------------
% 7.00/2.56 % (22852)------------------------------
% 7.00/2.57 % (22853)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22692 for (2993ds/6Mi)
% 7.00/2.57 % (22853)Instruction limit reached!
% 7.00/2.57 % (22853)------------------------------
% 7.00/2.57 % (22853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.57 % (22853)Termination reason: Unknown
% 7.00/2.57 % (22853)Termination phase: shuffling
% 7.00/2.57
% 7.00/2.57 % (22853)Memory used [KB]: 1663
% 7.00/2.57 % (22853)Time elapsed: 0.005 s
% 7.00/2.57 % (22853)Instructions burned: 6 (million)
% 7.00/2.57 % (22853)------------------------------
% 7.00/2.57 % (22853)------------------------------
% 7.00/2.58 % (22837)Instruction limit reached!
% 7.00/2.58 % (22837)------------------------------
% 7.00/2.58 % (22837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.58 % (22837)Termination reason: Unknown
% 7.00/2.58 % (22837)Termination phase: Saturation
% 7.00/2.58
% 7.00/2.58 % (22837)Memory used [KB]: 8315
% 7.00/2.58 % (22837)Time elapsed: 0.261 s
% 7.00/2.58 % (22837)Instructions burned: 508 (million)
% 7.00/2.58 % (22837)------------------------------
% 7.00/2.58 % (22837)------------------------------
% 7.00/2.58 % (22854)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22692 for (2993ds/150Mi)
% 7.00/2.58 % (22855)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22692 for (2992ds/343Mi)
% 7.00/2.58 % (22856)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_22692 for (2992ds/109Mi)
% 7.00/2.59 % (22857)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_22692 for (2992ds/253Mi)
% 7.97/2.61 % (22844)Instruction limit reached!
% 7.97/2.61 % (22844)------------------------------
% 7.97/2.61 % (22844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.97/2.61 % (22844)Termination reason: Unknown
% 7.97/2.61 % (22844)Termination phase: Saturation
% 7.97/2.61
% 7.97/2.61 % (22844)Memory used [KB]: 3326
% 7.97/2.61 % (22844)Time elapsed: 0.186 s
% 7.97/2.61 % (22844)Instructions burned: 433 (million)
% 7.97/2.61 % (22844)------------------------------
% 7.97/2.61 % (22844)------------------------------
% 7.97/2.63 % (22858)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22692 for (2992ds/140Mi)
% 7.97/2.63 % (22856)Instruction limit reached!
% 7.97/2.63 % (22856)------------------------------
% 7.97/2.63 % (22856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.97/2.63 % (22856)Termination reason: Unknown
% 7.97/2.63 % (22856)Termination phase: SInE selection
% 7.97/2.63
% 7.97/2.63 % (22856)Memory used [KB]: 2814
% 7.97/2.63 % (22856)Time elapsed: 0.048 s
% 7.97/2.63 % (22856)Instructions burned: 109 (million)
% 7.97/2.63 % (22856)------------------------------
% 7.97/2.63 % (22856)------------------------------
% 7.97/2.65 % (22859)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_22692 for (2992ds/614Mi)
% 7.97/2.65 % (22854)Instruction limit reached!
% 7.97/2.65 % (22854)------------------------------
% 7.97/2.65 % (22854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.97/2.65 % (22854)Termination reason: Unknown
% 7.97/2.65 % (22854)Termination phase: Preprocessing 3
% 7.97/2.65
% 7.97/2.65 % (22854)Memory used [KB]: 5245
% 7.97/2.65 % (22854)Time elapsed: 0.079 s
% 7.97/2.65 % (22854)Instructions burned: 151 (million)
% 7.97/2.65 % (22854)------------------------------
% 7.97/2.65 % (22854)------------------------------
% 7.97/2.67 % (22848)Instruction limit reached!
% 7.97/2.67 % (22848)------------------------------
% 7.97/2.67 % (22848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.97/2.67 % (22848)Termination reason: Unknown
% 7.97/2.67 % (22848)Termination phase: Saturation
% 7.97/2.67
% 7.97/2.67 % (22848)Memory used [KB]: 7803
% 7.97/2.67 % (22848)Time elapsed: 0.190 s
% 7.97/2.67 % (22848)Instructions burned: 453 (million)
% 7.97/2.67 % (22848)------------------------------
% 7.97/2.67 % (22848)------------------------------
% 7.97/2.67 % (22860)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_22692 for (2992ds/202Mi)
% 7.97/2.69 % (22861)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_22692 for (2991ds/339Mi)
% 7.97/2.69 % (22858)Instruction limit reached!
% 7.97/2.69 % (22858)------------------------------
% 7.97/2.69 % (22858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.97/2.69 % (22858)Termination reason: Unknown
% 7.97/2.69 % (22858)Termination phase: Property scanning
% 7.97/2.69
% 7.97/2.69 % (22858)Memory used [KB]: 2942
% 7.97/2.69 % (22858)Time elapsed: 0.063 s
% 7.97/2.69 % (22858)Instructions burned: 141 (million)
% 7.97/2.69 % (22858)------------------------------
% 7.97/2.69 % (22858)------------------------------
% 8.61/2.71 % (22862)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_22692 for (2991ds/283Mi)
% 8.61/2.71 % (22857)Instruction limit reached!
% 8.61/2.71 % (22857)------------------------------
% 8.61/2.71 % (22857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.71 % (22857)Termination reason: Unknown
% 8.61/2.71 % (22857)Termination phase: Property scanning
% 8.61/2.71
% 8.61/2.71 % (22857)Memory used [KB]: 5884
% 8.61/2.71 % (22857)Time elapsed: 0.120 s
% 8.61/2.71 % (22857)Instructions burned: 254 (million)
% 8.61/2.71 % (22857)------------------------------
% 8.61/2.71 % (22857)------------------------------
% 8.61/2.73 % (22855)Instruction limit reached!
% 8.61/2.73 % (22855)------------------------------
% 8.61/2.73 % (22855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.73 % (22855)Termination reason: Unknown
% 8.61/2.73 % (22855)Termination phase: Saturation
% 8.61/2.73
% 8.61/2.73 % (22855)Memory used [KB]: 8443
% 8.61/2.73 % (22855)Time elapsed: 0.151 s
% 8.61/2.73 % (22855)Instructions burned: 343 (million)
% 8.61/2.73 % (22855)------------------------------
% 8.61/2.73 % (22855)------------------------------
% 8.61/2.73 % (22863)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22692 for (2991ds/134Mi)
% 8.61/2.74 % (22864)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22692 for (2991ds/298Mi)
% 8.61/2.77 % (22860)Instruction limit reached!
% 8.61/2.77 % (22860)------------------------------
% 8.61/2.77 % (22860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.77 % (22860)Termination reason: Unknown
% 8.61/2.77 % (22860)Termination phase: Property scanning
% 8.61/2.77
% 8.61/2.77 % (22860)Memory used [KB]: 5628
% 8.61/2.77 % (22860)Time elapsed: 0.103 s
% 8.61/2.77 % (22860)Instructions burned: 203 (million)
% 8.61/2.77 % (22860)------------------------------
% 8.61/2.77 % (22860)------------------------------
% 8.61/2.79 % (22863)Instruction limit reached!
% 8.61/2.79 % (22863)------------------------------
% 8.61/2.79 % (22863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.79 % (22863)Termination reason: Unknown
% 8.61/2.79 % (22863)Termination phase: Property scanning
% 8.61/2.79
% 8.61/2.79 % (22863)Memory used [KB]: 2942
% 8.61/2.79 % (22863)Time elapsed: 0.060 s
% 8.61/2.79 % (22863)Instructions burned: 134 (million)
% 8.61/2.79 % (22863)------------------------------
% 8.61/2.79 % (22863)------------------------------
% 8.61/2.79 % (22865)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22692 for (2990ds/192Mi)
% 9.11/2.81 % (22866)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_22692 for (2990ds/258Mi)
% 9.11/2.83 % (22862)Instruction limit reached!
% 9.11/2.83 % (22862)------------------------------
% 9.11/2.83 % (22862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.83 % (22862)Termination reason: Unknown
% 9.11/2.83 % (22862)Termination phase: Saturation
% 9.11/2.83
% 9.11/2.83 % (22862)Memory used [KB]: 7675
% 9.11/2.83 % (22862)Time elapsed: 0.121 s
% 9.11/2.83 % (22862)Instructions burned: 283 (million)
% 9.11/2.83 % (22862)------------------------------
% 9.11/2.83 % (22862)------------------------------
% 9.11/2.84 % (22861)Instruction limit reached!
% 9.11/2.84 % (22861)------------------------------
% 9.11/2.84 % (22861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.84 % (22861)Termination reason: Unknown
% 9.11/2.84 % (22861)Termination phase: Saturation
% 9.11/2.84
% 9.11/2.84 % (22861)Memory used [KB]: 8315
% 9.11/2.84 % (22861)Time elapsed: 0.155 s
% 9.11/2.84 % (22861)Instructions burned: 339 (million)
% 9.11/2.84 % (22861)------------------------------
% 9.11/2.84 % (22861)------------------------------
% 9.11/2.84 % (22867)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_22692 for (2990ds/90Mi)
% 9.11/2.86 % (22868)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_22692 for (2990ds/231Mi)
% 9.11/2.87 % (22864)Instruction limit reached!
% 9.11/2.87 % (22864)------------------------------
% 9.11/2.87 % (22864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.87 % (22864)Termination reason: Unknown
% 9.11/2.87 % (22864)Termination phase: Saturation
% 9.11/2.87
% 9.11/2.87 % (22864)Memory used [KB]: 7675
% 9.11/2.87 % (22864)Time elapsed: 0.127 s
% 9.11/2.87 % (22864)Instructions burned: 298 (million)
% 9.11/2.87 % (22864)------------------------------
% 9.11/2.87 % (22864)------------------------------
% 9.11/2.88 % (22865)Instruction limit reached!
% 9.11/2.88 % (22865)------------------------------
% 9.11/2.88 % (22865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.88 % (22865)Termination reason: Unknown
% 9.11/2.88 % (22865)Termination phase: Property scanning
% 9.11/2.88
% 9.11/2.88 % (22865)Memory used [KB]: 3070
% 9.11/2.88 % (22865)Time elapsed: 0.092 s
% 9.11/2.88 % (22865)Instructions burned: 192 (million)
% 9.11/2.88 % (22865)------------------------------
% 9.11/2.88 % (22865)------------------------------
% 9.11/2.88 % (22867)Instruction limit reached!
% 9.11/2.88 % (22867)------------------------------
% 9.11/2.88 % (22867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.88 % (22867)Termination reason: Unknown
% 9.11/2.88 % (22867)Termination phase: Property scanning
% 9.11/2.88
% 9.11/2.88 % (22867)Memory used [KB]: 2814
% 9.11/2.88 % (22867)Time elapsed: 0.041 s
% 9.11/2.88 % (22867)Instructions burned: 90 (million)
% 9.11/2.88 % (22867)------------------------------
% 9.11/2.88 % (22867)------------------------------
% 9.11/2.89 % (22869)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_22692 for (2990ds/458Mi)
% 9.72/2.90 % (22871)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_22692 for (2989ds/297Mi)
% 9.72/2.90 % (22870)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_22692 for (2989ds/31Mi)
% 9.72/2.92 % (22870)Instruction limit reached!
% 9.72/2.92 % (22870)------------------------------
% 9.72/2.92 % (22870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.92 % (22870)Termination reason: Unknown
% 9.72/2.92 % (22870)Termination phase: shuffling
% 9.72/2.92
% 9.72/2.92 % (22870)Memory used [KB]: 2302
% 9.72/2.92 % (22870)Time elapsed: 0.017 s
% 9.72/2.92 % (22870)Instructions burned: 31 (million)
% 9.72/2.92 % (22870)------------------------------
% 9.72/2.92 % (22870)------------------------------
% 9.72/2.92 % (22866)Instruction limit reached!
% 9.72/2.92 % (22866)------------------------------
% 9.72/2.92 % (22866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.92 % (22866)Termination reason: Unknown
% 9.72/2.92 % (22866)Termination phase: Saturation
% 9.72/2.92
% 9.72/2.92 % (22866)Memory used [KB]: 7931
% 9.72/2.92 % (22866)Time elapsed: 0.113 s
% 9.72/2.92 % (22866)Instructions burned: 259 (million)
% 9.72/2.92 % (22866)------------------------------
% 9.72/2.92 % (22866)------------------------------
% 9.72/2.93 % (22873)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_22692 for (2989ds/182Mi)
% 9.72/2.93 % (22872)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_22692 for (2989ds/987Mi)
% 9.72/2.95 % (22841)Instruction limit reached!
% 9.72/2.95 % (22841)------------------------------
% 9.72/2.95 % (22841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.95 % (22841)Termination reason: Unknown
% 9.72/2.95 % (22841)Termination phase: Saturation
% 9.72/2.95
% 9.72/2.95 % (22841)Memory used [KB]: 13176
% 9.72/2.95 % (22841)Time elapsed: 0.553 s
% 9.72/2.95 % (22841)Instructions burned: 1088 (million)
% 9.72/2.95 % (22841)------------------------------
% 9.72/2.95 % (22841)------------------------------
% 9.72/2.95 % (22859)Instruction limit reached!
% 9.72/2.95 % (22859)------------------------------
% 9.72/2.95 % (22859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.95 % (22859)Termination reason: Unknown
% 9.72/2.95 % (22859)Termination phase: Saturation
% 9.72/2.95
% 9.72/2.95 % (22859)Memory used [KB]: 10362
% 9.72/2.95 % (22859)Time elapsed: 0.300 s
% 9.72/2.95 % (22859)Instructions burned: 615 (million)
% 9.72/2.95 % (22859)------------------------------
% 9.72/2.95 % (22859)------------------------------
% 9.72/2.96 % (22868)Instruction limit reached!
% 9.72/2.96 % (22868)------------------------------
% 9.72/2.96 % (22868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.96 % (22868)Termination reason: Unknown
% 9.72/2.96 % (22868)Termination phase: Property scanning
% 9.72/2.96
% 9.72/2.96 % (22868)Memory used [KB]: 4349
% 9.72/2.96 % (22868)Time elapsed: 0.105 s
% 9.72/2.96 % (22868)Instructions burned: 231 (million)
% 9.72/2.96 % (22868)------------------------------
% 9.72/2.96 % (22868)------------------------------
% 9.72/2.96 % (22874)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_22692 for (2989ds/182Mi)
% 9.72/2.96 % (22875)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_22692 for (2989ds/154Mi)
% 9.72/2.98 % (22876)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_22692 for (2989ds/79Mi)
% 9.72/3.01 % (22876)Instruction limit reached!
% 9.72/3.01 % (22876)------------------------------
% 9.72/3.01 % (22876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/3.01 % (22876)Termination reason: Unknown
% 9.72/3.01 % (22876)Termination phase: Property scanning
% 9.72/3.01
% 9.72/3.01 % (22876)Memory used [KB]: 2814
% 9.72/3.01 % (22876)Time elapsed: 0.036 s
% 9.72/3.01 % (22876)Instructions burned: 80 (million)
% 9.72/3.01 % (22876)------------------------------
% 9.72/3.01 % (22876)------------------------------
% 9.72/3.01 % (22873)Instruction limit reached!
% 9.72/3.01 % (22873)------------------------------
% 9.72/3.01 % (22873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/3.01 % (22873)Termination reason: Unknown
% 9.72/3.01 % (22873)Termination phase: Property scanning
% 9.72/3.01
% 9.72/3.01 % (22873)Memory used [KB]: 3070
% 9.72/3.01 % (22873)Time elapsed: 0.082 s
% 9.72/3.01 % (22873)Instructions burned: 184 (million)
% 9.72/3.01 % (22873)------------------------------
% 9.72/3.01 % (22873)------------------------------
% 9.72/3.03 % (22877)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_22692 for (2988ds/216Mi)
% 9.72/3.03 % (22878)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22692 for (2988ds/114Mi)
% 9.72/3.03 % (22875)Instruction limit reached!
% 9.72/3.03 % (22875)------------------------------
% 9.72/3.03 % (22875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/3.03 % (22875)Termination reason: Unknown
% 9.72/3.03 % (22875)Termination phase: Function definition elimination
% 9.72/3.03
% 9.72/3.03 % (22875)Memory used [KB]: 2942
% 9.72/3.03 % (22875)Time elapsed: 0.069 s
% 9.72/3.03 % (22875)Instructions burned: 156 (million)
% 9.72/3.03 % (22875)------------------------------
% 9.72/3.03 % (22875)------------------------------
% 11.60/3.05 % (22871)Instruction limit reached!
% 11.60/3.05 % (22871)------------------------------
% 11.60/3.05 % (22871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.05 % (22871)Termination reason: Unknown
% 11.60/3.05 % (22871)Termination phase: Saturation
% 11.60/3.05
% 11.60/3.05 % (22871)Memory used [KB]: 7675
% 11.60/3.05 % (22871)Time elapsed: 0.131 s
% 11.60/3.05 % (22871)Instructions burned: 298 (million)
% 11.60/3.05 % (22871)------------------------------
% 11.60/3.05 % (22871)------------------------------
% 11.60/3.05 % (22879)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_22692 for (2988ds/922Mi)
% 11.60/3.05 % (22874)Instruction limit reached!
% 11.60/3.05 % (22874)------------------------------
% 11.60/3.05 % (22874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.05 % (22874)Termination reason: Unknown
% 11.60/3.05 % (22874)Termination phase: Property scanning
% 11.60/3.05
% 11.60/3.05 % (22874)Memory used [KB]: 5628
% 11.60/3.05 % (22874)Time elapsed: 0.091 s
% 11.60/3.05 % (22874)Instructions burned: 183 (million)
% 11.60/3.05 % (22874)------------------------------
% 11.60/3.05 % (22874)------------------------------
% 11.60/3.06 % (22880)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_22692 for (2988ds/182Mi)
% 11.60/3.07 % (22881)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_22692 for (2987ds/164Mi)
% 11.60/3.08 % (22878)Instruction limit reached!
% 11.60/3.08 % (22878)------------------------------
% 11.60/3.08 % (22878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.08 % (22878)Termination reason: Unknown
% 11.60/3.08 % (22878)Termination phase: Property scanning
% 11.60/3.08
% 11.60/3.08 % (22878)Memory used [KB]: 2942
% 11.60/3.08 % (22878)Time elapsed: 0.053 s
% 11.60/3.08 % (22878)Instructions burned: 115 (million)
% 11.60/3.08 % (22878)------------------------------
% 11.60/3.08 % (22878)------------------------------
% 11.60/3.09 % (22869)Instruction limit reached!
% 11.60/3.09 % (22869)------------------------------
% 11.60/3.09 % (22869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.09 % (22869)Termination reason: Unknown
% 11.60/3.09 % (22869)Termination phase: Saturation
% 11.60/3.09
% 11.60/3.09 % (22869)Memory used [KB]: 9722
% 11.60/3.09 % (22869)Time elapsed: 0.201 s
% 11.60/3.09 % (22869)Instructions burned: 459 (million)
% 11.60/3.09 % (22869)------------------------------
% 11.60/3.09 % (22869)------------------------------
% 11.60/3.10 % (22882)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_22692 for (2987ds/50Mi)
% 11.60/3.10 % (22883)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22692 for (2987ds/368Mi)
% 11.60/3.12 % (22877)Instruction limit reached!
% 11.60/3.12 % (22877)------------------------------
% 11.60/3.12 % (22877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.12 % (22877)Termination reason: Unknown
% 11.60/3.12 % (22877)Termination phase: Property scanning
% 11.60/3.12
% 11.60/3.12 % (22877)Memory used [KB]: 3198
% 11.60/3.12 % (22877)Time elapsed: 0.091 s
% 11.60/3.12 % (22877)Instructions burned: 217 (million)
% 11.60/3.12 % (22877)------------------------------
% 11.60/3.12 % (22877)------------------------------
% 11.60/3.12 % (22882)Instruction limit reached!
% 11.60/3.12 % (22882)------------------------------
% 11.60/3.12 % (22882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.12 % (22882)Termination reason: Unknown
% 11.60/3.12 % (22882)Termination phase: shuffling
% 11.60/3.12
% 11.60/3.12 % (22882)Memory used [KB]: 2558
% 11.60/3.12 % (22882)Time elapsed: 0.025 s
% 11.60/3.12 % (22882)Instructions burned: 51 (million)
% 11.60/3.12 % (22882)------------------------------
% 11.60/3.12 % (22882)------------------------------
% 11.60/3.13 % (22884)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_22692 for (2987ds/1021Mi)
% 11.60/3.14 % (22885)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_22692 for (2987ds/267Mi)
% 11.60/3.14 % (22880)Instruction limit reached!
% 11.60/3.14 % (22880)------------------------------
% 11.60/3.14 % (22880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.60/3.14 % (22880)Termination reason: Unknown
% 11.60/3.14 % (22880)Termination phase: Property scanning
% 11.60/3.14
% 11.60/3.14 % (22880)Memory used [KB]: 3198
% 11.60/3.14 % (22880)Time elapsed: 0.080 s
% 11.60/3.14 % (22880)Instructions burned: 182 (million)
% 11.60/3.14 % (22880)------------------------------
% 11.60/3.14 % (22880)------------------------------
% 12.02/3.15 % (22881)Instruction limit reached!
% 12.02/3.15 % (22881)------------------------------
% 12.02/3.15 % (22881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.15 % (22881)Termination reason: Unknown
% 12.02/3.15 % (22881)Termination phase: Property scanning
% 12.02/3.15
% 12.02/3.15 % (22881)Memory used [KB]: 2942
% 12.02/3.15 % (22881)Time elapsed: 0.077 s
% 12.02/3.15 % (22881)Instructions burned: 164 (million)
% 12.02/3.15 % (22881)------------------------------
% 12.02/3.15 % (22881)------------------------------
% 12.02/3.16 % (22886)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_22692 for (2987ds/204Mi)
% 12.02/3.16 % (22887)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_22692 for (2987ds/26Mi)
% 12.02/3.18 % (22887)Instruction limit reached!
% 12.02/3.18 % (22887)------------------------------
% 12.02/3.18 % (22887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.18 % (22887)Termination reason: Unknown
% 12.02/3.18 % (22887)Termination phase: shuffling
% 12.02/3.18
% 12.02/3.18 % (22887)Memory used [KB]: 2046
% 12.02/3.18 % (22887)Time elapsed: 0.014 s
% 12.02/3.18 % (22887)Instructions burned: 27 (million)
% 12.02/3.18 % (22887)------------------------------
% 12.02/3.18 % (22887)------------------------------
% 12.02/3.19 % (22888)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_22692 for (2986ds/53Mi)
% 12.29/3.22 % (22888)Instruction limit reached!
% 12.29/3.22 % (22888)------------------------------
% 12.29/3.22 % (22888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.29/3.22 % (22888)Termination reason: Unknown
% 12.29/3.22 % (22888)Termination phase: shuffling
% 12.29/3.22
% 12.29/3.22 % (22888)Memory used [KB]: 2558
% 12.29/3.22 % (22888)Time elapsed: 0.026 s
% 12.29/3.22 % (22888)Instructions burned: 54 (million)
% 12.29/3.22 % (22888)------------------------------
% 12.29/3.22 % (22888)------------------------------
% 12.29/3.24 % (22889)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_22692 for (2986ds/4436Mi)
% 12.29/3.24 % (22886)Instruction limit reached!
% 12.29/3.24 % (22886)------------------------------
% 12.29/3.24 % (22886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.29/3.24 % (22886)Termination reason: Unknown
% 12.29/3.24 % (22886)Termination phase: Property scanning
% 12.29/3.24
% 12.29/3.24 % (22886)Memory used [KB]: 3070
% 12.29/3.24 % (22886)Time elapsed: 0.088 s
% 12.29/3.24 % (22886)Instructions burned: 205 (million)
% 12.29/3.24 % (22886)------------------------------
% 12.29/3.24 % (22886)------------------------------
% 12.29/3.25 % (22885)Instruction limit reached!
% 12.29/3.25 % (22885)------------------------------
% 12.29/3.25 % (22885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.29/3.25 % (22885)Termination reason: Unknown
% 12.29/3.25 % (22885)Termination phase: Saturation
% 12.29/3.25
% 12.29/3.25 % (22885)Memory used [KB]: 7675
% 12.29/3.25 % (22885)Time elapsed: 0.115 s
% 12.29/3.25 % (22885)Instructions burned: 268 (million)
% 12.29/3.25 % (22885)------------------------------
% 12.29/3.25 % (22885)------------------------------
% 12.29/3.26 % (22890)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_22692 for (2986ds/1539Mi)
% 12.29/3.26 % (22883)Instruction limit reached!
% 12.29/3.26 % (22883)------------------------------
% 12.29/3.26 % (22883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.29/3.26 % (22883)Termination reason: Unknown
% 12.29/3.26 % (22883)Termination phase: Saturation
% 12.29/3.26
% 12.29/3.26 % (22883)Memory used [KB]: 9466
% 12.29/3.26 % (22883)Time elapsed: 0.163 s
% 12.29/3.26 % (22883)Instructions burned: 368 (million)
% 12.29/3.26 % (22883)------------------------------
% 12.29/3.26 % (22883)------------------------------
% 12.29/3.27 % (22891)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_22692 for (2986ds/408Mi)
% 12.29/3.28 % (22892)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_22692 for (2985ds/5205Mi)
% 12.85/3.37 % (22872)Instruction limit reached!
% 12.85/3.37 % (22872)------------------------------
% 12.85/3.37 % (22872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/3.37 % (22872)Termination reason: Unknown
% 12.85/3.37 % (22872)Termination phase: Saturation
% 12.85/3.37
% 12.85/3.37 % (22872)Memory used [KB]: 14200
% 12.85/3.37 % (22872)Time elapsed: 0.441 s
% 12.85/3.37 % (22872)Instructions burned: 988 (million)
% 12.85/3.37 % (22872)------------------------------
% 12.85/3.37 % (22872)------------------------------
% 12.85/3.39 % (22893)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_22692 for (2984ds/1913Mi)
% 12.94/3.47 % (22891)Instruction limit reached!
% 12.94/3.47 % (22891)------------------------------
% 12.94/3.47 % (22891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.94/3.47 % (22891)Termination reason: Unknown
% 12.94/3.47 % (22891)Termination phase: Saturation
% 12.94/3.47
% 12.94/3.47 % (22891)Memory used [KB]: 11769
% 12.94/3.47 % (22891)Time elapsed: 0.202 s
% 12.94/3.47 % (22891)Instructions burned: 408 (million)
% 12.94/3.47 % (22891)------------------------------
% 12.94/3.47 % (22891)------------------------------
% 12.94/3.49 % (22894)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_22692 for (2983ds/4350Mi)
% 13.15/3.51 % (22879)Instruction limit reached!
% 13.15/3.51 % (22879)------------------------------
% 13.15/3.51 % (22879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.51 % (22879)Termination reason: Unknown
% 13.15/3.51 % (22879)Termination phase: Saturation
% 13.15/3.51
% 13.15/3.51 % (22879)Memory used [KB]: 12792
% 13.15/3.51 % (22879)Time elapsed: 0.461 s
% 13.15/3.51 % (22879)Instructions burned: 923 (million)
% 13.15/3.51 % (22879)------------------------------
% 13.15/3.51 % (22879)------------------------------
% 13.15/3.53 % (22895)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_22692 for (2983ds/68Mi)
% 13.15/3.56 % (22895)Instruction limit reached!
% 13.15/3.56 % (22895)------------------------------
% 13.15/3.56 % (22895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.56 % (22895)Termination reason: Unknown
% 13.15/3.56 % (22895)Termination phase: Property scanning
% 13.15/3.56
% 13.15/3.56 % (22895)Memory used [KB]: 2814
% 13.15/3.56 % (22895)Time elapsed: 0.033 s
% 13.15/3.56 % (22895)Instructions burned: 69 (million)
% 13.15/3.56 % (22895)------------------------------
% 13.15/3.56 % (22895)------------------------------
% 13.15/3.57 % (22896)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_22692 for (2983ds/358Mi)
% 13.68/3.64 % (22884)Instruction limit reached!
% 13.68/3.64 % (22884)------------------------------
% 13.68/3.64 % (22884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.64 % (22884)Termination reason: Unknown
% 13.68/3.64 % (22884)Termination phase: Saturation
% 13.68/3.64
% 13.68/3.64 % (22884)Memory used [KB]: 13176
% 13.68/3.64 % (22884)Time elapsed: 0.512 s
% 13.68/3.64 % (22884)Instructions burned: 1021 (million)
% 13.68/3.64 % (22884)------------------------------
% 13.68/3.64 % (22884)------------------------------
% 13.68/3.66 % (22897)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_22692 for (2982ds/31Mi)
% 13.68/3.68 % (22897)Instruction limit reached!
% 13.68/3.68 % (22897)------------------------------
% 13.68/3.68 % (22897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.68 % (22897)Termination reason: Unknown
% 13.68/3.68 % (22897)Termination phase: shuffling
% 13.68/3.68
% 13.68/3.68 % (22897)Memory used [KB]: 2302
% 13.68/3.68 % (22897)Time elapsed: 0.016 s
% 13.68/3.68 % (22897)Instructions burned: 31 (million)
% 13.68/3.68 % (22897)------------------------------
% 13.68/3.68 % (22897)------------------------------
% 13.68/3.70 % (22898)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22692 for (2981ds/279Mi)
% 14.25/3.73 % (22896)Instruction limit reached!
% 14.25/3.73 % (22896)------------------------------
% 14.25/3.73 % (22896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.25/3.73 % (22896)Termination reason: Unknown
% 14.25/3.73 % (22896)Termination phase: Saturation
% 14.25/3.73
% 14.25/3.73 % (22896)Memory used [KB]: 8443
% 14.25/3.73 % (22896)Time elapsed: 0.155 s
% 14.25/3.73 % (22896)Instructions burned: 358 (million)
% 14.25/3.73 % (22896)------------------------------
% 14.25/3.73 % (22896)------------------------------
% 14.25/3.75 % (22899)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22692 for (2981ds/258Mi)
% 14.41/3.81 % (22898)Instruction limit reached!
% 14.41/3.81 % (22898)------------------------------
% 14.41/3.81 % (22898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.41/3.81 % (22898)Termination reason: Unknown
% 14.41/3.81 % (22898)Termination phase: Saturation
% 14.41/3.81
% 14.41/3.81 % (22898)Memory used [KB]: 7675
% 14.41/3.81 % (22898)Time elapsed: 0.121 s
% 14.41/3.81 % (22898)Instructions burned: 280 (million)
% 14.41/3.81 % (22898)------------------------------
% 14.41/3.81 % (22898)------------------------------
% 14.41/3.83 % (22900)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_22692 for (2980ds/26Mi)
% 14.41/3.84 % (22900)Instruction limit reached!
% 14.41/3.84 % (22900)------------------------------
% 14.41/3.84 % (22900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.41/3.84 % (22900)Termination reason: Unknown
% 14.41/3.84 % (22900)Termination phase: shuffling
% 14.41/3.84
% 14.41/3.84 % (22900)Memory used [KB]: 2174
% 14.41/3.84 % (22900)Time elapsed: 0.014 s
% 14.41/3.84 % (22900)Instructions burned: 27 (million)
% 14.41/3.84 % (22900)------------------------------
% 14.41/3.84 % (22900)------------------------------
% 14.41/3.86 % (22899)Instruction limit reached!
% 14.41/3.86 % (22899)------------------------------
% 14.41/3.86 % (22899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.41/3.86 % (22899)Termination reason: Unknown
% 14.41/3.86 % (22899)Termination phase: Saturation
% 14.41/3.86
% 14.41/3.86 % (22899)Memory used [KB]: 8315
% 14.41/3.86 % (22899)Time elapsed: 0.115 s
% 14.41/3.86 % (22899)Instructions burned: 259 (million)
% 14.41/3.86 % (22899)------------------------------
% 14.41/3.86 % (22899)------------------------------
% 14.41/3.86 % (22901)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_22692 for (2980ds/995Mi)
% 14.41/3.88 % (22902)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_22692 for (2980ds/373Mi)
% 18.53/4.03 % (22890)Instruction limit reached!
% 18.53/4.03 % (22890)------------------------------
% 18.53/4.03 % (22890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/4.03 % (22890)Termination reason: Unknown
% 18.53/4.03 % (22890)Termination phase: Saturation
% 18.53/4.03
% 18.53/4.03 % (22890)Memory used [KB]: 11001
% 18.53/4.03 % (22890)Time elapsed: 0.774 s
% 18.53/4.03 % (22890)Instructions burned: 1540 (million)
% 18.53/4.03 % (22890)------------------------------
% 18.53/4.03 % (22890)------------------------------
% 18.53/4.04 % (22902)Instruction limit reached!
% 18.53/4.04 % (22902)------------------------------
% 18.53/4.04 % (22902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.53/4.04 % (22902)Termination reason: Unknown
% 18.53/4.04 % (22902)Termination phase: Saturation
% 18.53/4.04
% 18.53/4.04 % (22902)Memory used [KB]: 9466
% 18.53/4.04 % (22902)Time elapsed: 0.168 s
% 18.53/4.04 % (22902)Instructions burned: 374 (million)
% 18.53/4.04 % (22902)------------------------------
% 18.53/4.04 % (22902)------------------------------
% 18.53/4.05 % (22903)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_22692 for (2978ds/253Mi)
% 18.53/4.06 % (22904)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_22692 for (2978ds/832Mi)
% 19.08/4.16 % (22903)Instruction limit reached!
% 19.08/4.16 % (22903)------------------------------
% 19.08/4.16 % (22903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.08/4.16 % (22903)Termination reason: Unknown
% 19.08/4.16 % (22903)Termination phase: Saturation
% 19.08/4.16
% 19.08/4.16 % (22903)Memory used [KB]: 7675
% 19.08/4.16 % (22903)Time elapsed: 0.114 s
% 19.08/4.16 % (22903)Instructions burned: 253 (million)
% 19.08/4.16 % (22903)------------------------------
% 19.08/4.16 % (22903)------------------------------
% 19.08/4.18 % (22905)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_22692 for (2977ds/668Mi)
% 19.57/4.25 % (22901)Instruction limit reached!
% 19.57/4.25 % (22901)------------------------------
% 19.57/4.25 % (22901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.57/4.25 % (22901)Termination reason: Unknown
% 19.57/4.25 % (22901)Termination phase: Saturation
% 19.57/4.25
% 19.57/4.25 % (22901)Memory used [KB]: 17910
% 19.57/4.25 % (22901)Time elapsed: 0.395 s
% 19.57/4.25 % (22901)Instructions burned: 995 (million)
% 19.57/4.25 % (22901)------------------------------
% 19.57/4.25 % (22901)------------------------------
% 19.57/4.27 % (22893)Instruction limit reached!
% 19.57/4.27 % (22893)------------------------------
% 19.57/4.27 % (22893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.57/4.27 % (22893)Termination reason: Unknown
% 19.57/4.27 % (22893)Termination phase: Saturation
% 19.57/4.27
% 19.57/4.27 % (22893)Memory used [KB]: 6396
% 19.57/4.27 % (22893)Time elapsed: 0.877 s
% 19.57/4.27 % (22893)Instructions burned: 1913 (million)
% 19.57/4.27 % (22893)------------------------------
% 19.57/4.27 % (22893)------------------------------
% 19.57/4.27 % (22906)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_22692 for (2976ds/40Mi)
% 19.57/4.29 % (22907)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_22692 for (2976ds/294Mi)
% 19.57/4.29 % (22906)Instruction limit reached!
% 19.57/4.29 % (22906)------------------------------
% 19.57/4.29 % (22906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.57/4.29 % (22906)Termination reason: Unknown
% 19.57/4.29 % (22906)Termination phase: shuffling
% 19.57/4.29
% 19.57/4.29 % (22906)Memory used [KB]: 2430
% 19.57/4.29 % (22906)Time elapsed: 0.021 s
% 19.57/4.29 % (22906)Instructions burned: 41 (million)
% 19.57/4.29 % (22906)------------------------------
% 19.57/4.29 % (22906)------------------------------
% 20.07/4.31 % (22904)Refutation not found, incomplete strategy
% 20.07/4.31 % (22904)------------------------------
% 20.07/4.31 % (22904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.31 % (22904)Termination reason: Refutation not found, incomplete strategy
% 20.07/4.31
% 20.07/4.31
% 20.07/4.31 % (22904)Memory used [KB]: 11769
% 20.07/4.31 % (22904)Time elapsed: 0.251 s
% 20.07/4.31 % (22904)Instructions burned: 506 (million)
% 20.07/4.31 % (22904)------------------------------
% 20.07/4.31 % (22904)------------------------------
% 20.07/4.31 % (22908)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_22692 for (2975ds/187Mi)
% 20.07/4.33 % (22909)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_22692 for (2975ds/371Mi)
% 20.07/4.39 % (22908)Instruction limit reached!
% 20.07/4.39 % (22908)------------------------------
% 20.07/4.39 % (22908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.39 % (22908)Termination reason: Unknown
% 20.07/4.39 % (22908)Termination phase: Property scanning
% 20.07/4.39
% 20.07/4.39 % (22908)Memory used [KB]: 3070
% 20.07/4.39 % (22908)Time elapsed: 0.082 s
% 20.07/4.39 % (22908)Instructions burned: 187 (million)
% 20.07/4.39 % (22908)------------------------------
% 20.07/4.39 % (22908)------------------------------
% 20.71/4.41 % (22910)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_22692 for (2974ds/1827Mi)
% 20.71/4.41 % (22907)Instruction limit reached!
% 20.71/4.41 % (22907)------------------------------
% 20.71/4.41 % (22907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.41 % (22907)Termination reason: Unknown
% 20.71/4.41 % (22907)Termination phase: Saturation
% 20.71/4.41
% 20.71/4.41 % (22907)Memory used [KB]: 7675
% 20.71/4.41 % (22907)Time elapsed: 0.128 s
% 20.71/4.41 % (22907)Instructions burned: 294 (million)
% 20.71/4.41 % (22907)------------------------------
% 20.71/4.41 % (22907)------------------------------
% 20.71/4.43 % (22911)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_22692 for (2974ds/70Mi)
% 20.71/4.46 % (22911)Instruction limit reached!
% 20.71/4.46 % (22911)------------------------------
% 20.71/4.46 % (22911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.46 % (22911)Termination reason: Unknown
% 20.71/4.46 % (22911)Termination phase: Property scanning
% 20.71/4.46
% 20.71/4.46 % (22911)Memory used [KB]: 2686
% 20.71/4.46 % (22911)Time elapsed: 0.033 s
% 20.71/4.46 % (22911)Instructions burned: 71 (million)
% 20.71/4.46 % (22911)------------------------------
% 20.71/4.46 % (22911)------------------------------
% 20.71/4.47 % (22905)Instruction limit reached!
% 20.71/4.47 % (22905)------------------------------
% 20.71/4.47 % (22905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.47 % (22905)Termination reason: Unknown
% 20.71/4.47 % (22905)Termination phase: Saturation
% 20.71/4.47
% 20.71/4.47 % (22905)Memory used [KB]: 12409
% 20.71/4.47 % (22905)Time elapsed: 0.293 s
% 20.71/4.47 % (22905)Instructions burned: 669 (million)
% 20.71/4.47 % (22905)------------------------------
% 20.71/4.47 % (22905)------------------------------
% 20.71/4.48 % (22912)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_22692 for (2973ds/316Mi)
% 20.71/4.48 % (22913)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_22692 for (2973ds/932Mi)
% 20.71/4.49 % (22909)Instruction limit reached!
% 20.71/4.49 % (22909)------------------------------
% 20.71/4.49 % (22909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.71/4.49 % (22909)Termination reason: Unknown
% 20.71/4.49 % (22909)Termination phase: Saturation
% 20.71/4.49
% 20.71/4.49 % (22909)Memory used [KB]: 8827
% 20.71/4.49 % (22909)Time elapsed: 0.165 s
% 20.71/4.49 % (22909)Instructions burned: 371 (million)
% 20.71/4.49 % (22909)------------------------------
% 20.71/4.49 % (22909)------------------------------
% 21.71/4.51 % (22914)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_22692 for (2973ds/4714Mi)
% 22.01/4.61 % (22912)Instruction limit reached!
% 22.01/4.61 % (22912)------------------------------
% 22.01/4.61 % (22912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.61 % (22912)Termination reason: Unknown
% 22.01/4.61 % (22912)Termination phase: Saturation
% 22.01/4.61
% 22.01/4.61 % (22912)Memory used [KB]: 7803
% 22.01/4.61 % (22912)Time elapsed: 0.135 s
% 22.01/4.61 % (22912)Instructions burned: 317 (million)
% 22.01/4.61 % (22912)------------------------------
% 22.01/4.61 % (22912)------------------------------
% 22.01/4.63 % (22915)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_22692 for (2972ds/8250Mi)
% 23.06/4.90 % (22913)Instruction limit reached!
% 23.06/4.90 % (22913)------------------------------
% 23.06/4.90 % (22913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.06/4.90 % (22913)Termination reason: Unknown
% 23.06/4.90 % (22913)Termination phase: Saturation
% 23.06/4.90
% 23.06/4.90 % (22913)Memory used [KB]: 15479
% 23.06/4.90 % (22913)Time elapsed: 0.419 s
% 23.06/4.90 % (22913)Instructions burned: 933 (million)
% 23.06/4.90 % (22913)------------------------------
% 23.06/4.90 % (22913)------------------------------
% 23.06/4.92 % (22916)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_22692 for (2969ds/770Mi)
% 26.71/5.25 % (22910)Instruction limit reached!
% 26.71/5.25 % (22910)------------------------------
% 26.71/5.25 % (22910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.71/5.25 % (22910)Termination reason: Unknown
% 26.71/5.25 % (22910)Termination phase: Saturation
% 26.71/5.25
% 26.71/5.25 % (22910)Memory used [KB]: 22131
% 26.71/5.25 % (22910)Time elapsed: 0.841 s
% 26.71/5.25 % (22910)Instructions burned: 1828 (million)
% 26.71/5.25 % (22910)------------------------------
% 26.71/5.25 % (22910)------------------------------
% 26.71/5.27 % (22917)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_22692 for (2966ds/794Mi)
% 26.71/5.27 % (22892)Instruction limit reached!
% 26.71/5.27 % (22892)------------------------------
% 26.71/5.27 % (22892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.71/5.27 % (22892)Termination reason: Unknown
% 26.71/5.27 % (22892)Termination phase: Saturation
% 26.71/5.27
% 26.71/5.27 % (22892)Memory used [KB]: 19061
% 26.71/5.27 % (22892)Time elapsed: 1.989 s
% 26.71/5.27 % (22892)Instructions burned: 5207 (million)
% 26.71/5.27 % (22892)------------------------------
% 26.71/5.27 % (22892)------------------------------
% 26.71/5.29 % (22918)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_22692 for (2965ds/464Mi)
% 27.36/5.31 % (22916)Instruction limit reached!
% 27.36/5.31 % (22916)------------------------------
% 27.36/5.31 % (22916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.36/5.31 % (22916)Termination reason: Unknown
% 27.36/5.31 % (22916)Termination phase: Saturation
% 27.36/5.31
% 27.36/5.31 % (22916)Memory used [KB]: 8059
% 27.36/5.31 % (22916)Time elapsed: 0.386 s
% 27.36/5.31 % (22916)Instructions burned: 770 (million)
% 27.36/5.31 % (22916)------------------------------
% 27.36/5.31 % (22916)------------------------------
% 27.36/5.33 % (22919)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_22692 for (2965ds/1376Mi)
% 27.79/5.49 % (22918)Instruction limit reached!
% 27.79/5.49 % (22918)------------------------------
% 27.79/5.49 % (22918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.79/5.49 % (22918)Termination reason: Unknown
% 27.79/5.49 % (22918)Termination phase: Saturation
% 27.79/5.49
% 27.79/5.49 % (22918)Memory used [KB]: 9722
% 27.79/5.49 % (22918)Time elapsed: 0.209 s
% 27.79/5.49 % (22918)Instructions burned: 464 (million)
% 27.79/5.49 % (22918)------------------------------
% 27.79/5.49 % (22918)------------------------------
% 28.42/5.51 % (22920)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_22692 for (2963ds/906Mi)
% 28.82/5.65 % (22894)Instruction limit reached!
% 28.82/5.65 % (22894)------------------------------
% 28.82/5.65 % (22894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.82/5.65 % (22894)Termination reason: Unknown
% 28.82/5.65 % (22894)Termination phase: Saturation
% 28.82/5.65
% 28.82/5.65 % (22894)Memory used [KB]: 14583
% 28.82/5.65 % (22894)Time elapsed: 2.169 s
% 28.82/5.65 % (22894)Instructions burned: 4351 (million)
% 28.82/5.65 % (22894)------------------------------
% 28.82/5.65 % (22894)------------------------------
% 28.82/5.67 % (22921)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_22692 for (2962ds/434Mi)
% 28.82/5.67 % (22917)Instruction limit reached!
% 28.82/5.67 % (22917)------------------------------
% 28.82/5.67 % (22917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.82/5.67 % (22917)Termination reason: Unknown
% 28.82/5.67 % (22917)Termination phase: Saturation
% 28.82/5.67
% 28.82/5.67 % (22917)Memory used [KB]: 6396
% 28.82/5.67 % (22917)Time elapsed: 0.406 s
% 28.82/5.67 % (22917)Instructions burned: 794 (million)
% 28.82/5.67 % (22917)------------------------------
% 28.82/5.67 % (22917)------------------------------
% 28.82/5.69 % (22889)Instruction limit reached!
% 28.82/5.69 % (22889)------------------------------
% 28.82/5.69 % (22889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.82/5.69 % (22889)Termination reason: Unknown
% 28.82/5.69 % (22889)Termination phase: Saturation
% 28.82/5.69
% 28.82/5.69 % (22889)Memory used [KB]: 15479
% 28.82/5.69 % (22889)Time elapsed: 2.451 s
% 28.82/5.69 % (22889)Instructions burned: 4436 (million)
% 28.82/5.69 % (22889)------------------------------
% 28.82/5.69 % (22889)------------------------------
% 28.82/5.69 % (22922)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_22692 for (2961ds/865Mi)
% 29.60/5.71 % (22923)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_22692 for (2961ds/593Mi)
% 29.80/5.88 % (22921)Instruction limit reached!
% 29.80/5.88 % (22921)------------------------------
% 29.80/5.88 % (22921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.80/5.88 % (22921)Termination reason: Unknown
% 29.80/5.88 % (22921)Termination phase: Saturation
% 29.80/5.88
% 29.80/5.88 % (22921)Memory used [KB]: 11897
% 29.80/5.88 % (22921)Time elapsed: 0.210 s
% 29.80/5.88 % (22921)Instructions burned: 434 (million)
% 29.80/5.88 % (22921)------------------------------
% 29.80/5.88 % (22921)------------------------------
% 29.80/5.89 % (22919)Instruction limit reached!
% 29.80/5.89 % (22919)------------------------------
% 29.80/5.89 % (22919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.80/5.89 % (22919)Termination reason: Unknown
% 29.80/5.89 % (22919)Termination phase: Saturation
% 29.80/5.89
% 29.80/5.89 % (22919)Memory used [KB]: 10618
% 29.80/5.89 % (22919)Time elapsed: 0.570 s
% 29.80/5.89 % (22919)Instructions burned: 1376 (million)
% 29.80/5.89 % (22919)------------------------------
% 29.80/5.89 % (22919)------------------------------
% 30.81/5.90 % (22924)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_22692 for (2959ds/443Mi)
% 30.81/5.91 % (22925)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_22692 for (2959ds/594Mi)
% 30.81/5.94 % (22920)Instruction limit reached!
% 30.81/5.94 % (22920)------------------------------
% 30.81/5.94 % (22920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.81/5.94 % (22920)Termination reason: Unknown
% 30.81/5.94 % (22920)Termination phase: Saturation
% 30.81/5.94
% 30.81/5.94 % (22920)Memory used [KB]: 11641
% 30.81/5.94 % (22920)Time elapsed: 0.432 s
% 30.81/5.94 % (22920)Instructions burned: 907 (million)
% 30.81/5.94 % (22920)------------------------------
% 30.81/5.94 % (22920)------------------------------
% 30.81/5.96 % (22926)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_22692 for (2959ds/327Mi)
% 30.81/5.98 % (22923)Instruction limit reached!
% 30.81/5.98 % (22923)------------------------------
% 30.81/5.98 % (22923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.81/5.98 % (22923)Termination reason: Unknown
% 30.81/5.98 % (22923)Termination phase: Saturation
% 30.81/5.98
% 30.81/5.98 % (22923)Memory used [KB]: 7803
% 30.81/5.98 % (22923)Time elapsed: 0.273 s
% 30.81/5.98 % (22923)Instructions burned: 595 (million)
% 30.81/5.98 % (22923)------------------------------
% 30.81/5.98 % (22923)------------------------------
% 30.81/6.00 % (22927)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_22692 for (2958ds/5411Mi)
% 32.49/6.11 % (22922)Instruction limit reached!
% 32.49/6.11 % (22922)------------------------------
% 32.49/6.11 % (22922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/6.11 % (22922)Termination reason: Unknown
% 32.49/6.11 % (22922)Termination phase: Saturation
% 32.49/6.11
% 32.49/6.11 % (22922)Memory used [KB]: 10874
% 32.49/6.11 % (22922)Time elapsed: 0.423 s
% 32.49/6.11 % (22922)Instructions burned: 866 (million)
% 32.49/6.11 % (22922)------------------------------
% 32.49/6.11 % (22922)------------------------------
% 32.49/6.11 % (22926)Instruction limit reached!
% 32.49/6.11 % (22926)------------------------------
% 32.49/6.11 % (22926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/6.11 % (22926)Termination reason: Unknown
% 32.49/6.11 % (22926)Termination phase: Saturation
% 32.49/6.11
% 32.49/6.11 % (22926)Memory used [KB]: 11257
% 32.49/6.11 % (22926)Time elapsed: 0.157 s
% 32.49/6.11 % (22926)Instructions burned: 328 (million)
% 32.49/6.11 % (22926)------------------------------
% 32.49/6.11 % (22926)------------------------------
% 32.49/6.12 % (22924)Instruction limit reached!
% 32.49/6.12 % (22924)------------------------------
% 32.49/6.12 % (22924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/6.12 % (22924)Termination reason: Unknown
% 32.49/6.12 % (22924)Termination phase: Saturation
% 32.49/6.12
% 32.49/6.12 % (22924)Memory used [KB]: 9722
% 32.49/6.12 % (22924)Time elapsed: 0.208 s
% 32.49/6.12 % (22924)Instructions burned: 443 (million)
% 32.49/6.12 % (22924)------------------------------
% 32.49/6.12 % (22924)------------------------------
% 33.20/6.13 % (22929)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_22692 for (2957ds/96Mi)
% 33.20/6.13 % (22928)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_22692 for (2957ds/1762Mi)
% 33.20/6.14 % (22930)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_22692 for (2957ds/503Mi)
% 33.20/6.17 % (22929)Instruction limit reached!
% 33.20/6.17 % (22929)------------------------------
% 33.20/6.17 % (22929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.20/6.17 % (22929)Termination reason: Unknown
% 33.20/6.17 % (22929)Termination phase: Property scanning
% 33.20/6.17
% 33.20/6.17 % (22929)Memory used [KB]: 2814
% 33.20/6.17 % (22929)Time elapsed: 0.043 s
% 33.20/6.17 % (22929)Instructions burned: 98 (million)
% 33.20/6.17 % (22929)------------------------------
% 33.20/6.17 % (22929)------------------------------
% 33.20/6.19 % (22931)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_22692 for (2956ds/90Mi)
% 33.20/6.20 % (22925)Instruction limit reached!
% 33.20/6.20 % (22925)------------------------------
% 33.20/6.20 % (22925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.20/6.20 % (22925)Termination reason: Unknown
% 33.20/6.20 % (22925)Termination phase: Saturation
% 33.20/6.20
% 33.20/6.20 % (22925)Memory used [KB]: 10106
% 33.20/6.20 % (22925)Time elapsed: 0.283 s
% 33.20/6.20 % (22925)Instructions burned: 595 (million)
% 33.20/6.20 % (22925)------------------------------
% 33.20/6.20 % (22925)------------------------------
% 33.26/6.21 % (22932)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_22692 for (2956ds/593Mi)
% 33.26/6.23 % (22931)Instruction limit reached!
% 33.26/6.23 % (22931)------------------------------
% 33.26/6.23 % (22931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.26/6.23 % (22931)Termination reason: Unknown
% 33.26/6.23 % (22931)Termination phase: Property scanning
% 33.26/6.23
% 33.26/6.23 % (22931)Memory used [KB]: 2814
% 33.26/6.23 % (22931)Time elapsed: 0.041 s
% 33.26/6.23 % (22931)Instructions burned: 91 (million)
% 33.26/6.23 % (22931)------------------------------
% 33.26/6.23 % (22931)------------------------------
% 33.26/6.25 % (22933)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_22692 for (2956ds/1512Mi)
% 33.26/6.26 % (22914)Instruction limit reached!
% 33.26/6.26 % (22914)------------------------------
% 33.26/6.26 % (22914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.26/6.26 % (22914)Termination reason: Unknown
% 33.26/6.26 % (22914)Termination phase: Saturation
% 33.26/6.26
% 33.26/6.26 % (22914)Memory used [KB]: 7931
% 33.26/6.26 % (22914)Time elapsed: 1.758 s
% 33.26/6.26 % (22914)Instructions burned: 4715 (million)
% 33.26/6.26 % (22914)------------------------------
% 33.26/6.26 % (22914)------------------------------
% 33.26/6.28 % (22934)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_22692 for (2956ds/569Mi)
% 33.89/6.36 % (22930)Instruction limit reached!
% 33.89/6.36 % (22930)------------------------------
% 33.89/6.36 % (22930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.89/6.36 % (22930)Termination reason: Unknown
% 33.89/6.36 % (22930)Termination phase: Saturation
% 33.89/6.36
% 33.89/6.36 % (22930)Memory used [KB]: 10106
% 33.89/6.36 % (22930)Time elapsed: 0.223 s
% 33.89/6.36 % (22930)Instructions burned: 504 (million)
% 33.89/6.36 % (22930)------------------------------
% 33.89/6.36 % (22930)------------------------------
% 33.89/6.37 % (22935)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_22692 for (2955ds/501Mi)
% 34.33/6.42 % (22934)Instruction limit reached!
% 34.33/6.42 % (22934)------------------------------
% 34.33/6.42 % (22934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.33/6.42 % (22934)Termination reason: Unknown
% 34.33/6.42 % (22934)Termination phase: Saturation
% 34.33/6.42
% 34.33/6.42 % (22934)Memory used [KB]: 7803
% 34.33/6.42 % (22934)Time elapsed: 0.146 s
% 34.33/6.42 % (22934)Instructions burned: 570 (million)
% 34.33/6.42 % (22934)------------------------------
% 34.33/6.42 % (22934)------------------------------
% 34.33/6.43 % (22932)Instruction limit reached!
% 34.33/6.43 % (22932)------------------------------
% 34.33/6.43 % (22932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.33/6.43 % (22932)Termination reason: Unknown
% 34.33/6.43 % (22932)Termination phase: Saturation
% 34.33/6.43
% 34.33/6.43 % (22932)Memory used [KB]: 10490
% 34.33/6.43 % (22932)Time elapsed: 0.221 s
% 34.33/6.43 % (22932)Instructions burned: 595 (million)
% 34.33/6.43 % (22932)------------------------------
% 34.33/6.43 % (22932)------------------------------
% 34.33/6.43 % (22936)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_22692 for (2954ds/562Mi)
% 34.33/6.44 % (22937)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22692 for (2954ds/406Mi)
% 34.91/6.52 % (22935)Instruction limit reached!
% 34.91/6.52 % (22935)------------------------------
% 34.91/6.52 % (22935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.52 % (22935)Termination reason: Unknown
% 34.91/6.52 % (22935)Termination phase: Saturation
% 34.91/6.52
% 34.91/6.52 % (22935)Memory used [KB]: 11001
% 34.91/6.52 % (22935)Time elapsed: 0.156 s
% 34.91/6.52 % (22935)Instructions burned: 502 (million)
% 34.91/6.52 % (22935)------------------------------
% 34.91/6.52 % (22935)------------------------------
% 34.91/6.53 % (22938)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_22692 for (2953ds/582Mi)
% 34.91/6.58 % (22937)Instruction limit reached!
% 34.91/6.58 % (22937)------------------------------
% 34.91/6.58 % (22937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.58 % (22937)Termination reason: Unknown
% 34.91/6.58 % (22937)Termination phase: Saturation
% 34.91/6.58
% 34.91/6.58 % (22937)Memory used [KB]: 7931
% 34.91/6.58 % (22937)Time elapsed: 0.133 s
% 34.91/6.58 % (22937)Instructions burned: 406 (million)
% 34.91/6.58 % (22937)------------------------------
% 34.91/6.58 % (22937)------------------------------
% 34.91/6.59 % (22939)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_22692 for (2952ds/456Mi)
% 34.91/6.59 % (22936)Instruction limit reached!
% 34.91/6.59 % (22936)------------------------------
% 34.91/6.59 % (22936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.91/6.59 % (22936)Termination reason: Unknown
% 34.91/6.59 % (22936)Termination phase: Saturation
% 34.91/6.59
% 34.91/6.59 % (22936)Memory used [KB]: 9338
% 34.91/6.59 % (22936)Time elapsed: 0.159 s
% 34.91/6.59 % (22936)Instructions burned: 562 (million)
% 34.91/6.59 % (22936)------------------------------
% 34.91/6.59 % (22936)------------------------------
% 35.58/6.60 % (22940)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_22692 for (2952ds/393Mi)
% 35.58/6.65 % (22928)Instruction limit reached!
% 35.58/6.65 % (22928)------------------------------
% 35.58/6.65 % (22928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.58/6.65 % (22928)Termination reason: Unknown
% 35.58/6.65 % (22928)Termination phase: Saturation
% 35.58/6.65
% 35.58/6.65 % (22928)Memory used [KB]: 21620
% 35.58/6.65 % (22928)Time elapsed: 0.513 s
% 35.58/6.65 % (22928)Instructions burned: 1765 (million)
% 35.58/6.65 % (22928)------------------------------
% 35.58/6.65 % (22928)------------------------------
% 35.58/6.66 % (22941)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_22692 for (2952ds/1335Mi)
% 36.31/6.71 % (22939)Instruction limit reached!
% 36.31/6.71 % (22939)------------------------------
% 36.31/6.71 % (22939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.31/6.71 % (22939)Termination reason: Unknown
% 36.31/6.71 % (22939)Termination phase: Saturation
% 36.31/6.71
% 36.31/6.71 % (22939)Memory used [KB]: 9850
% 36.31/6.71 % (22939)Time elapsed: 0.122 s
% 36.31/6.71 % (22939)Instructions burned: 457 (million)
% 36.31/6.71 % (22939)------------------------------
% 36.31/6.71 % (22939)------------------------------
% 36.31/6.71 % (22940)Instruction limit reached!
% 36.31/6.71 % (22940)------------------------------
% 36.31/6.71 % (22940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.31/6.71 % (22940)Termination reason: Unknown
% 36.31/6.71 % (22940)Termination phase: Saturation
% 36.31/6.71
% 36.31/6.71 % (22940)Memory used [KB]: 10362
% 36.31/6.71 % (22940)Time elapsed: 0.108 s
% 36.31/6.71 % (22940)Instructions burned: 393 (million)
% 36.31/6.71 % (22940)------------------------------
% 36.31/6.71 % (22940)------------------------------
% 36.31/6.71 % (22938)Instruction limit reached!
% 36.31/6.71 % (22938)------------------------------
% 36.31/6.71 % (22938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.31/6.71 % (22938)Termination reason: Unknown
% 36.31/6.71 % (22938)Termination phase: Saturation
% 36.31/6.71
% 36.31/6.71 % (22938)Memory used [KB]: 11257
% 36.31/6.71 % (22938)Time elapsed: 0.177 s
% 36.31/6.71 % (22938)Instructions burned: 584 (million)
% 36.31/6.71 % (22938)------------------------------
% 36.31/6.71 % (22938)------------------------------
% 36.31/6.72 % (22942)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_22692 for (2951ds/3373Mi)
% 36.31/6.72 % (22943)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_22692 for (2951ds/474Mi)
% 36.31/6.72 % (22944)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22692 for (2951ds/157Mi)
% 36.31/6.76 % (22944)Instruction limit reached!
% 36.31/6.76 % (22944)------------------------------
% 36.31/6.76 % (22944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.31/6.76 % (22944)Termination reason: Unknown
% 36.31/6.76 % (22944)Termination phase: Function definition elimination
% 36.31/6.76
% 36.31/6.76 % (22944)Memory used [KB]: 2814
% 36.31/6.76 % (22944)Time elapsed: 0.043 s
% 36.31/6.76 % (22944)Instructions burned: 158 (million)
% 36.31/6.76 % (22944)------------------------------
% 36.31/6.76 % (22944)------------------------------
% 36.31/6.77 % (22947)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_22692 for (2950ds/590Mi)
% 36.31/6.79 % (22933)Instruction limit reached!
% 36.31/6.79 % (22933)------------------------------
% 36.31/6.79 % (22933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.31/6.79 % (22933)Termination reason: Unknown
% 36.31/6.79 % (22933)Termination phase: Saturation
% 36.31/6.79
% 36.31/6.79 % (22933)Memory used [KB]: 13816
% 36.31/6.79 % (22933)Time elapsed: 0.548 s
% 36.31/6.79 % (22933)Instructions burned: 1513 (million)
% 36.31/6.79 % (22933)------------------------------
% 36.31/6.79 % (22933)------------------------------
% 37.55/6.80 % (22967)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_22692 for (2950ds/104Mi)
% 37.55/6.83 % (22967)Instruction limit reached!
% 37.55/6.83 % (22967)------------------------------
% 37.55/6.83 % (22967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.83 % (22967)Termination reason: Unknown
% 37.55/6.83 % (22967)Termination phase: Property scanning
% 37.55/6.83
% 37.55/6.83 % (22967)Memory used [KB]: 2942
% 37.55/6.83 % (22967)Time elapsed: 0.030 s
% 37.55/6.83 % (22967)Instructions burned: 107 (million)
% 37.55/6.83 % (22967)------------------------------
% 37.55/6.83 % (22967)------------------------------
% 37.55/6.84 % (22943)Instruction limit reached!
% 37.55/6.84 % (22943)------------------------------
% 37.55/6.84 % (22943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.55/6.84 % (22943)Termination reason: Unknown
% 37.55/6.84 % (22943)Termination phase: Saturation
% 37.55/6.84
% 37.55/6.84 % (22943)Memory used [KB]: 7803
% 37.55/6.84 % (22943)Time elapsed: 0.121 s
% 37.55/6.84 % (22943)Instructions burned: 476 (million)
% 37.55/6.84 % (22943)------------------------------
% 37.55/6.84 % (22943)------------------------------
% 37.55/6.84 % (22993)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_22692 for (2950ds/414Mi)
% 37.55/6.85 % (23000)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_22692 for (2950ds/715Mi)
% 37.92/6.94 % (22947)Instruction limit reached!
% 37.92/6.94 % (22947)------------------------------
% 37.92/6.94 % (22947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.92/6.94 % (22947)Termination reason: Unknown
% 37.92/6.94 % (22947)Termination phase: Saturation
% 37.92/6.94
% 37.92/6.94 % (22947)Memory used [KB]: 8955
% 37.92/6.94 % (22947)Time elapsed: 0.166 s
% 37.92/6.94 % (22947)Instructions burned: 591 (million)
% 37.92/6.94 % (22947)------------------------------
% 37.92/6.94 % (22947)------------------------------
% 37.92/6.95 % (22993)Instruction limit reached!
% 37.92/6.95 % (22993)------------------------------
% 37.92/6.95 % (22993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.92/6.95 % (22993)Termination reason: Unknown
% 37.92/6.95 % (22993)Termination phase: Saturation
% 37.92/6.95
% 37.92/6.95 % (22993)Memory used [KB]: 7803
% 37.92/6.95 % (22993)Time elapsed: 0.107 s
% 37.92/6.95 % (22993)Instructions burned: 417 (million)
% 37.92/6.95 % (22993)------------------------------
% 37.92/6.95 % (22993)------------------------------
% 37.92/6.95 % (23082)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_22692 for (2949ds/961Mi)
% 37.92/6.96 % (23089)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_22692 for (2949ds/1213Mi)
% 39.36/7.05 % (22941)Instruction limit reached!
% 39.36/7.05 % (22941)------------------------------
% 39.36/7.05 % (22941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.36/7.05 % (22941)Termination reason: Unknown
% 39.36/7.05 % (22941)Termination phase: Saturation
% 39.36/7.05
% 39.36/7.05 % (22941)Memory used [KB]: 10746
% 39.36/7.05 % (22941)Time elapsed: 0.397 s
% 39.36/7.05 % (22941)Instructions burned: 1336 (million)
% 39.36/7.05 % (22941)------------------------------
% 39.36/7.05 % (22941)------------------------------
% 39.36/7.06 % (23000)Instruction limit reached!
% 39.36/7.06 % (23000)------------------------------
% 39.36/7.06 % (23000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.36/7.06 % (23000)Termination reason: Unknown
% 39.36/7.06 % (23000)Termination phase: Saturation
% 39.36/7.06
% 39.36/7.06 % (23000)Memory used [KB]: 6012
% 39.36/7.06 % (23000)Time elapsed: 0.212 s
% 39.36/7.06 % (23000)Instructions burned: 717 (million)
% 39.36/7.06 % (23000)------------------------------
% 39.36/7.06 % (23000)------------------------------
% 39.36/7.07 % (23141)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_22692 for (2947ds/1979Mi)
% 39.36/7.07 % (23142)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_22692 for (2947ds/481Mi)
% 39.98/7.19 % (23142)Instruction limit reached!
% 39.98/7.19 % (23142)------------------------------
% 39.98/7.19 % (23142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.98/7.19 % (23142)Termination reason: Unknown
% 39.98/7.19 % (23142)Termination phase: Saturation
% 39.98/7.19
% 39.98/7.19 % (23142)Memory used [KB]: 7803
% 39.98/7.19 % (23142)Time elapsed: 0.120 s
% 39.98/7.19 % (23142)Instructions burned: 484 (million)
% 39.98/7.19 % (23142)------------------------------
% 39.98/7.19 % (23142)------------------------------
% 40.54/7.20 % (23182)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_22692 for (2946ds/783Mi)
% 40.54/7.23 % (23082)Instruction limit reached!
% 40.54/7.23 % (23082)------------------------------
% 40.54/7.23 % (23082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.54/7.23 % (23082)Termination reason: Unknown
% 40.54/7.23 % (23082)Termination phase: Saturation
% 40.54/7.23
% 40.54/7.23 % (23082)Memory used [KB]: 10746
% 40.54/7.23 % (23082)Time elapsed: 0.281 s
% 40.54/7.23 % (23082)Instructions burned: 963 (million)
% 40.54/7.23 % (23082)------------------------------
% 40.54/7.23 % (23082)------------------------------
% 40.54/7.24 % (23183)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_22692 for (2946ds/432Mi)
% 40.97/7.33 % (23089)Instruction limit reached!
% 40.97/7.33 % (23089)------------------------------
% 40.97/7.33 % (23089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.97/7.33 % (23089)Termination reason: Unknown
% 40.97/7.33 % (23089)Termination phase: Saturation
% 40.97/7.33
% 40.97/7.33 % (23089)Memory used [KB]: 15607
% 40.97/7.33 % (23089)Time elapsed: 0.376 s
% 40.97/7.33 % (23089)Instructions burned: 1215 (million)
% 40.97/7.33 % (23089)------------------------------
% 40.97/7.33 % (23089)------------------------------
% 40.97/7.34 % (23184)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_22692 for (2945ds/1670Mi)
% 40.97/7.35 % (23183)Instruction limit reached!
% 40.97/7.35 % (23183)------------------------------
% 40.97/7.35 % (23183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.97/7.35 % (23183)Termination reason: Unknown
% 40.97/7.35 % (23183)Termination phase: Saturation
% 40.97/7.35
% 40.97/7.35 % (23183)Memory used [KB]: 9850
% 40.97/7.35 % (23183)Time elapsed: 0.113 s
% 40.97/7.35 % (23183)Instructions burned: 432 (million)
% 40.97/7.35 % (23183)------------------------------
% 40.97/7.35 % (23183)------------------------------
% 40.97/7.36 % (23185)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_22692 for (2945ds/90Mi)
% 40.97/7.38 % (23185)Instruction limit reached!
% 40.97/7.38 % (23185)------------------------------
% 40.97/7.38 % (23185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.97/7.38 % (23185)Termination reason: Unknown
% 40.97/7.38 % (23185)Termination phase: Property scanning
% 40.97/7.38
% 40.97/7.38 % (23185)Memory used [KB]: 2814
% 40.97/7.38 % (23185)Time elapsed: 0.025 s
% 40.97/7.38 % (23185)Instructions burned: 93 (million)
% 40.97/7.38 % (23185)------------------------------
% 40.97/7.38 % (23185)------------------------------
% 40.97/7.39 % (23182)First to succeed.
% 40.97/7.39 % (23182)Refutation found. Thanks to Tanya!
% 40.97/7.39 % SZS status Theorem for DTF2THF_22692
% 40.97/7.39 % SZS output start Proof for DTF2THF_22692
% 40.97/7.39 thf(func_def_0, type, in: $i > $i > $o).
% 40.97/7.39 thf(func_def_1, type, exu: ($i > $o) > $o).
% 40.97/7.39 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 40.97/7.39 thf(func_def_8, type, powerset: $i > $i).
% 40.97/7.39 thf(func_def_10, type, setunion: $i > $i).
% 40.97/7.39 thf(func_def_19, type, descr: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_26, type, prop2set: $o > $i).
% 40.97/7.39 thf(func_def_36, type, nonempty: $i > $o).
% 40.97/7.39 thf(func_def_69, type, set2prop: $i > $o).
% 40.97/7.39 thf(func_def_88, type, subset: $i > $i > $o).
% 40.97/7.39 thf(func_def_89, type, disjoint: $i > $i > $o).
% 40.97/7.39 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 40.97/7.39 thf(func_def_114, type, binunion: $i > $i > $i).
% 40.97/7.39 thf(func_def_122, type, binintersect: $i > $i > $i).
% 40.97/7.39 thf(func_def_135, type, regular: $i > $o).
% 40.97/7.39 thf(func_def_136, type, setminus: $i > $i > $i).
% 40.97/7.39 thf(func_def_147, type, symdiff: $i > $i > $i).
% 40.97/7.39 thf(func_def_153, type, iskpair: $i > $o).
% 40.97/7.39 thf(func_def_158, type, kpair: $i > $i > $i).
% 40.97/7.39 thf(func_def_160, type, cartprod: $i > $i > $i).
% 40.97/7.39 thf(func_def_177, type, singleton: $i > $o).
% 40.97/7.39 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 40.97/7.39 thf(func_def_184, type, atmost1p: $i > $o).
% 40.97/7.39 thf(func_def_185, type, atleast2p: $i > $o).
% 40.97/7.39 thf(func_def_186, type, atmost2p: $i > $o).
% 40.97/7.39 thf(func_def_187, type, upairsetp: $i > $o).
% 40.97/7.39 thf(func_def_191, type, kfst: $i > $i).
% 40.97/7.39 thf(func_def_203, type, ksnd: $i > $i).
% 40.97/7.39 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 40.97/7.39 thf(func_def_222, type, func: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_223, type, funcSet: $i > $i > $i).
% 40.97/7.39 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 40.97/7.39 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 40.97/7.39 thf(func_def_323, type, breln1: $i > $i > $o).
% 40.97/7.39 thf(func_def_325, type, breln1Set: $i > $i).
% 40.97/7.39 thf(func_def_327, type, transitive: $i > $i > $o).
% 40.97/7.39 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 40.97/7.39 thf(func_def_329, type, reflexive: $i > $i > $o).
% 40.97/7.39 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 40.97/7.39 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 40.97/7.39 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 40.97/7.39 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 40.97/7.39 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 40.97/7.39 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 40.97/7.39 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 40.97/7.39 thf(func_def_388, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 40.97/7.39 thf(func_def_389, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 40.97/7.39 thf(func_def_390, type, sP2: $i > $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_393, type, sP5: $i > $i > $o).
% 40.97/7.39 thf(func_def_394, type, sP6: $i > $o).
% 40.97/7.39 thf(func_def_395, type, sP7: $i > $i > $o).
% 40.97/7.39 thf(func_def_396, type, sP8: $i > $i > $o).
% 40.97/7.39 thf(func_def_399, type, sP11: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_404, type, sP16: $o > $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_406, type, sP18: $i > $i > $i > $o).
% 40.97/7.39 thf(func_def_413, type, sK25: ($i > $o) > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_414, type, sK26: ($i > $o) > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_418, type, sK30: $i > $o).
% 40.97/7.39 thf(func_def_433, type, sK45: $i > $i > $o).
% 40.97/7.39 thf(func_def_444, type, sK56: $i > $o).
% 40.97/7.39 thf(func_def_446, type, sK58: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_447, type, sK59: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_448, type, sK60: $i > $o).
% 40.97/7.39 thf(func_def_460, type, sK72: $i > $o).
% 40.97/7.39 thf(func_def_462, type, sK74: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_465, type, sK77: $i > $o).
% 40.97/7.39 thf(func_def_466, type, sK78: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_471, type, sK83: $i > $i > $i).
% 40.97/7.39 thf(func_def_500, type, sK112: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_501, type, sK113: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_502, type, sK114: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_503, type, sK115: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_514, type, sK126: $i > $i).
% 40.97/7.39 thf(func_def_515, type, sK127: ($i > $i) > $i > $i > $i).
% 40.97/7.39 thf(func_def_522, type, sK134: $i > $o).
% 40.97/7.39 thf(func_def_524, type, sK136: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_525, type, sK137: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_555, type, sK167: $i > $i > $o).
% 40.97/7.39 thf(func_def_574, type, sK186: $i > $o).
% 40.97/7.39 thf(func_def_580, type, sK192: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_626, type, sK238: $i > $i).
% 40.97/7.39 thf(func_def_627, type, sK239: $i > $i).
% 40.97/7.39 thf(func_def_631, type, sK243: ($i > $o) > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_632, type, sK244: ($i > $o) > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_636, type, sK248: $i > $o).
% 40.97/7.39 thf(func_def_644, type, sK256: $i > $i > $o).
% 40.97/7.39 thf(func_def_658, type, sK270: $i > $o).
% 40.97/7.39 thf(func_def_660, type, sK272: ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_661, type, sK273: ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_683, type, sK295: $i > $i).
% 40.97/7.39 thf(func_def_690, type, sK302: $i > $i > $o).
% 40.97/7.39 thf(func_def_702, type, sK314: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_703, type, sK315: $i > $o).
% 40.97/7.39 thf(func_def_707, type, sK319: $i > $o).
% 40.97/7.39 thf(func_def_717, type, sK329: $i > $i > $i).
% 40.97/7.39 thf(func_def_720, type, sK332: ($i > $i) > $i > $i).
% 40.97/7.39 thf(func_def_721, type, sK333: $i > ($i > $i) > $i > $i).
% 40.97/7.39 thf(func_def_723, type, sK335: $i > $i).
% 40.97/7.39 thf(func_def_724, type, sK336: $i > $i).
% 40.97/7.39 thf(func_def_725, type, sK337: $i > $i).
% 40.97/7.39 thf(func_def_729, type, sK341: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_734, type, sK346: $i > $i > $i).
% 40.97/7.39 thf(func_def_735, type, sK347: $i > $i > $i).
% 40.97/7.39 thf(func_def_736, type, sK348: $i > $i > $i).
% 40.97/7.39 thf(func_def_737, type, sK349: $i > $i > $i).
% 40.97/7.39 thf(func_def_738, type, sK350: $i > $i > $i).
% 40.97/7.39 thf(func_def_739, type, sK351: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_740, type, sK352: $i > $i).
% 40.97/7.39 thf(func_def_741, type, sK353: $i > $i).
% 40.97/7.39 thf(func_def_742, type, sK354: $i > $i).
% 40.97/7.39 thf(func_def_743, type, sK355: $i > $i).
% 40.97/7.39 thf(func_def_744, type, sK356: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_745, type, sK357: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_746, type, sK358: $i > $i > $i).
% 40.97/7.39 thf(func_def_747, type, sK359: $i > $i > $i).
% 40.97/7.39 thf(func_def_748, type, sK360: $i > $i > $i).
% 40.97/7.39 thf(func_def_750, type, sK362: $i > $i).
% 40.97/7.39 thf(func_def_751, type, sK363: $i > $i).
% 40.97/7.39 thf(func_def_752, type, sK364: $i > $i).
% 40.97/7.39 thf(func_def_769, type, sK381: $i > $i > $i).
% 40.97/7.39 thf(func_def_779, type, sK391: $i > $i).
% 40.97/7.39 thf(func_def_793, type, sK405: $i > $o).
% 40.97/7.39 thf(func_def_798, type, sK410: $i > $o).
% 40.97/7.39 thf(func_def_823, type, sK435: ($i > $o) > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_824, type, sK436: ($i > $o) > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_825, type, sK437: $i > $o).
% 40.97/7.39 thf(func_def_826, type, sK438: $i > $o).
% 40.97/7.39 thf(func_def_831, type, sK443: $i > $o).
% 40.97/7.39 thf(func_def_837, type, sK449: $i > $i).
% 40.97/7.39 thf(func_def_850, type, sK462: $i > $i > $o).
% 40.97/7.39 thf(func_def_852, type, sK464: $i > $i).
% 40.97/7.39 thf(func_def_853, type, sK465: $i > $i).
% 40.97/7.39 thf(func_def_854, type, sK466: $i > ($i > $i > $o) > $i).
% 40.97/7.39 thf(func_def_855, type, sK467: $i > $i > ($i > $i > $o) > $i).
% 40.97/7.39 thf(func_def_856, type, sK468: $i > ($i > $i > $o) > $i).
% 40.97/7.39 thf(func_def_871, type, sK483: $i > $o).
% 40.97/7.39 thf(func_def_872, type, sK484: $i > $o).
% 40.97/7.39 thf(func_def_873, type, sK485: ($i > $o) > ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_874, type, sK486: ($i > $o) > ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_881, type, sK493: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_882, type, sK494: $i > $o).
% 40.97/7.39 thf(func_def_885, type, sK497: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_901, type, sK513: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_902, type, sK514: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_903, type, sK515: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_904, type, sK516: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_905, type, sK517: $i > $i > ($i > $i) > $i).
% 40.97/7.39 thf(func_def_906, type, sK518: $i > $i).
% 40.97/7.39 thf(func_def_923, type, sK535: $i > $o).
% 40.97/7.39 thf(func_def_931, type, sK543: $i > $i).
% 40.97/7.39 thf(func_def_939, type, sK551: $i > $o).
% 40.97/7.39 thf(func_def_954, type, sK566: $i > $o).
% 40.97/7.39 thf(func_def_956, type, sK568: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_957, type, sK569: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_968, type, sK580: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_969, type, sK581: $i > $o).
% 40.97/7.39 thf(func_def_970, type, sK582: $i > $i).
% 40.97/7.39 thf(func_def_971, type, sK583: $i > $o).
% 40.97/7.39 thf(func_def_974, type, sK586: $i > $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_986, type, sK598: $i > $i > $i).
% 40.97/7.39 thf(func_def_1012, type, sK624: $o > $i > $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1013, type, sK625: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1014, type, sK626: $i > $o).
% 40.97/7.39 thf(func_def_1024, type, sK636: $i > $o).
% 40.97/7.39 thf(func_def_1027, type, sK639: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1044, type, sK656: $i > $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1056, type, sK668: $i > $i).
% 40.97/7.39 thf(func_def_1059, type, sK671: $i > $i).
% 40.97/7.39 thf(func_def_1061, type, sK673: $i > ($i > $i) > $i > $i).
% 40.97/7.39 thf(func_def_1065, type, sK677: $i > $i > $i).
% 40.97/7.39 thf(func_def_1078, type, sK690: $i > $i).
% 40.97/7.39 thf(func_def_1082, type, sK694: $i > $i > ($i > $i) > $i).
% 40.97/7.39 thf(func_def_1087, type, sK699: ($i > $i) > $i > $i > $i).
% 40.97/7.39 thf(func_def_1090, type, sK702: $i > $i).
% 40.97/7.39 thf(func_def_1097, type, sK709: ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_1098, type, sK710: ($i > $o) > $i > $i > $i).
% 40.97/7.39 thf(func_def_1101, type, sK713: $i > $o).
% 40.97/7.39 thf(func_def_1112, type, sK724: $i > $o).
% 40.97/7.39 thf(func_def_1114, type, sK726: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_1115, type, sK727: ($i > $o) > $i > $i).
% 40.97/7.39 thf(func_def_1132, type, sK744: $i > $o).
% 40.97/7.39 thf(func_def_1133, type, sK745: $i > $i).
% 40.97/7.39 thf(func_def_1134, type, sK746: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1139, type, sK751: $i > $i > $i).
% 40.97/7.39 thf(func_def_1148, type, sK760: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1149, type, sK761: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1172, type, sK784: $i > $o).
% 40.97/7.39 thf(func_def_1175, type, sK787: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1185, type, sK797: $i > $o).
% 40.97/7.39 thf(func_def_1188, type, sK800: $o > $i > $i > $i).
% 40.97/7.39 thf(func_def_1209, type, sK821: $i > $i).
% 40.97/7.39 thf(func_def_1210, type, sK822: ($i > $i) > $i > $i > $i).
% 40.97/7.39 thf(func_def_1220, type, sK832: ($i > $i) > $i > $i > $i).
% 40.97/7.39 thf(func_def_1223, type, sK835: $i > $i).
% 40.97/7.39 thf(func_def_1252, type, sK864: $i > $o).
% 40.97/7.39 thf(func_def_1255, type, sK867: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1259, type, sK871: $i > $i).
% 40.97/7.39 thf(func_def_1262, type, sK874: $i > $o).
% 40.97/7.39 thf(func_def_1264, type, sK876: $i > $i > ($i > $i) > $i).
% 40.97/7.39 thf(func_def_1265, type, sK877: $i > $i).
% 40.97/7.39 thf(func_def_1277, type, sK889: $i > $i > $o).
% 40.97/7.39 thf(func_def_1287, type, sK899: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1288, type, sK900: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1293, type, sK905: $i > $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1296, type, sK908: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1300, type, sK912: $i > $i > $i > $i).
% 40.97/7.39 thf(func_def_1303, type, sK915: $i > $i > $i).
% 40.97/7.39 thf(func_def_1304, type, sK916: $i > $i > $i).
% 40.97/7.39 thf(func_def_1312, type, sK924: ($i > $o) > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1313, type, sK925: ($i > $o) > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1314, type, sK926: $i > $o).
% 40.97/7.39 thf(func_def_1315, type, sK927: $i > $o).
% 40.97/7.39 thf(func_def_1332, type, sK944: $i > $i > $o).
% 40.97/7.39 thf(func_def_1339, type, sK951: $i > $i > $o).
% 40.97/7.39 thf(func_def_1353, type, sK965: $i > $o).
% 40.97/7.39 thf(func_def_1355, type, sK967: $i > ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1386, type, sK998: $i > $o).
% 40.97/7.39 thf(func_def_1400, type, sK1012: $i > $o).
% 40.97/7.39 thf(func_def_1403, type, sK1015: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1404, type, sK1016: ($i > $o) > $i).
% 40.97/7.39 thf(func_def_1405, type, sK1017: $i > $o).
% 40.97/7.39 thf(func_def_1409, type, sK1021: $i > $i > $i).
% 40.97/7.39 thf(func_def_1436, type, sK1048: $i > $i > $o).
% 40.97/7.39 thf(func_def_1449, type, sK1061: $i > $i > $i).
% 40.97/7.39 thf(func_def_1457, type, ph1069: !>[X0: $tType]:(X0)).
% 40.97/7.39 thf(f8211,plain,(
% 40.97/7.39 $false),
% 40.97/7.39 inference(subsumption_resolution,[status(thm)],[f8186,f3423])).
% 40.97/7.39 thf(f3423,plain,(
% 40.97/7.39 ($true != (surjective @ sK212 @ sK214 @ sK213))),
% 40.97/7.39 inference(cnf_transformation,[status(thm)],[f1753])).
% 40.97/7.39 thf(f1753,plain,(
% 40.97/7.39 (binintersectSubset3 = $true) & (ubforcartprodlem2 = $true) & (inCongP = $true) & (demorgan1a = $true) & (subsetemptysetimpeq = $true) & (breln1compEex = $true) & (exuE3u = $true) & (subsetTrans = $true) & (funcext = $true) & (cartprodmempair = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectEL = $true) & (ex1E1 = $true) & (ubforcartprodlem1 = $true) & (nonemptyImpWitness = $true) & (theprop = $true) & (inPowerset = $true) & (notdexE = $true) & (symdiffIneg1 = $true) & (emptyE1 = $true) & (intersectInPowersetIntersectUnions = $true) & (breln1compI = $true) & (emptyset__Cong = $true) & (demorgan1 = $true) & (complementInPowersetComplementIntersect = $true) & (powersetI1 = $true) & (eqinunit = $true) & (demorgan2b2 = $true) & (cartprodfstpairEq = $true) & (setunionE = $true) & (doubleComplementSub2 = $true) & (breln1unionprop = $true) & (nonemptyE1 = $true) & (injFuncSetFuncIn = $true) & (setminusER = $true) & (emptyinunitempty = $true) & (powersetT_lem = $true) & (binintersectER = $true) & (breln1unionE = $true) & (breln1compprop = $true) & (ksndsingleton = $true) & (setminusEL = $true) & (powersetE = $true) & (setext = $true) & (symdiffI2 = $true) & (demorgan2a2 = $true) & (ap2apEq2 = $true) & (image1Ex1 = $true) & (complementTI1 = $true) & (doubleComplementSub1 = $true) & (subPowSU = $true) & (kpairiskpair = $true) & (lamProp = $true) & (doubleComplementI1 = $true) & (exu__Cong = $true) & (subbreln1 = $true) & (setunion__Cong = $true) & (iffalseProp1 = $true) & (descr__Cong = $true) & (iftrueProp1 = $true) & (dsetconstrI = $true) & (breln1unionEcases = $true) & (secondinupair = $true) & (singletonsubset = $true) & (setunionI = $true) & (binintersectI = $true) & (woz13rule1 = $true) & (binintersectRsub = $true) & (setukpairinjL = $true) & (dsetconstrEL = $true) & (beta2 = $true) & (inIntersectImpInUnion = $true) & (setbeta = $true) & (iftrueProp2 = $true) & (app = $true) & (doubleComplementEq = $true) & (binunionRsub = $true) & (breln1all1 = $true) & (subset2powerset = $true) & (eqimpsubset2 = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (complementSubsetComplementIntersect = $true) & (nonemptyI1 = $true) & (dpsetconstrEL2 = $true) & (funcinfuncset = $true) & (eqimpsubset1 = $true) & (powersetsubset = $true) & (setukpairinjR11 = $true) & (subsetI1 = $true) & (setukpairinjR12 = $true) & (upairsubunion = $true) & (funcGraphProp3 = $true) & (quantDeMorgan2 = $true) & (emptysetimpfalse = $true) & (lam2lamEq = $true) & (notsubsetI = $true) & (replAx = $true) & (binintersectLsub = $true) & (iftrueorfalse = $true) & (notequalI1 = $true) & (ex1I = $true) & (lamp = $true) & (singletonprop = $true) & (binintersectSubset2 = $true) & (upairsetE = $true) & (setextAx = $true) & (woz1_1 = $true) & (prop2set2propI = $true) & (setminusERneg = $true) & (contrasubsetT2 = $true) & (upairsetIR = $true) & (emptyI = $true) & (breln1invE = $true) & (ifSingleton = $true) & (setukpairIL = $true) & (kfstpairEq = $true) & (notinemptyset = $true) & (complementTnotintersectT = $true) & (image1I = $true) & (injFuncSetFuncInj = $true) & (foundationAx = $true) & (singletoninpowunion = $true) & (woz13rule4 = $true) & (surjFuncSetFuncIn = $true) & (dpsetconstrERa = $true) & (woz2B = $true) & (dpsetconstrEL1 = $true) & (emptysetE = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (image1E = $true) & (woz13rule2 = $true) & (bs114d = $true) & (kfstsingleton = $true) & (setukpairinjR = $true) & (subsetE2 = $true) & (woz2W = $true) & (eqbreln = $true) & (binintersectTELcontra = $true) & (quantDeMorgan3 = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (iffalse = $true) & (complementImpComplementIntersect = $true) & (iftrue = $true) & (beta1 = $true) & (setadjoinIL = $true) & (image1Ex = $true) & (binintersectT_lem = $true) & (setminusT_lem = $true) & (woz2Ex = $true) & (binunionT_lem = $true) & (image1Equiv = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (ap2p = $true) & (binunionTILcontra = $true) & (setminusSubset1 = $true) & (powersetTI1 = $true) & (dsetconstr__Cong = $true) & (omega0Ax = $true) & (kpairsurjEq = $true) & (breln1unionCommutes = $true) & (setminusI = $true) & (woz13rule0 = $true) & (complementUnionInPowersetComplement = $true) & (breln1invI = $true) & (setunionsingleton1 = $true) & (exuE1 = $true) & (prop2setI = $true) & (upairset2IR = $true) & (cartprodsndin = $true) & (wellorderingAx = $true) & (binunionIR = $true) & (woz1_4 = $true) & (complementT_lem = $true) & (setextT = $true) & (setunionsingleton = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (vacuousDall = $true) & (dsetconstrER = $true) & (exuE3e = $true) & (woz13rule3 = $true) & (symdiffE = $true) & (binunionEcases = $true) & (cartprodpairsurjEq = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (cartprodpairmemEL = $true) & (subsetTI = $true) & (cartprodsndpairEq = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (breln1SetBreln1 = $true) & (notinsingleton = $true) & (cartprodfstin = $true) & (eta1 = $true) & (powersetTE1 = $true) & (cartprodmempair1 = $true) & (subbreln = $true) & (funcGraphProp1 = $true) & (subsetE = $true) & (brelnall1 = $true) & (setukpairIR = $true) & (in__Cong = $true) & (ksndpairEq = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & (($true != (surjective @ sK212 @ sK214 @ sK213)) & ($true = (in @ sK213 @ (surjFuncSet @ sK212 @ sK214)))) & (singletonsuniq = $true) & (woz1_2 = $true) & (quantDeMorgan1 = $true) & (demorgan2a1 = $true) & (demorgan1b = $true) & (breln1unionI = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (binunionLsub = $true) & (powersetAx = $true) & (binintersectSubset4 = $true) & (injFuncInInjFuncSet = $true) & (apProp = $true) & (demorgan2a = $true) & (setminusIRneg = $true) & (breln1unionIL = $true) & (ap2apEq1 = $true) & (dpsetconstrI = $true) & (funcGraphProp4 = $true) & (cartprodmempaircEq = $true) & (ifp = $true) & (sepInPowerset = $true) & (singletonsswitch = $true) & (binunionTEcontra = $true) & (setminusELneg = $true) & (quantDeMorgan4 = $true) & (demorgan2b = $true) & (omegaSAx = $true) & (iffalseProp2 = $true) & (singletoninpowerset = $true) & (setukpairinjL1 = $true) & (binunionIL = $true) & (complementTcontraSubset = $true) & (brelnall2 = $true) & (infuncsetfunc = $true) & (setextsub = $true) & (setadjoin__Cong = $true) & (contrasubsetT3 = $true) & (choice2fnsingleton = $true) & (breln1compE = $true) & (disjointsetsI1 = $true) & (demorgan2 = $true) & (complementTE1 = $true) & (binintersectSubset5 = $true) & (setukpairinjL2 = $true) & (upairinpowunion = $true) & (prop2setE = $true) & (ex1E2 = $true) & (binunionTIRcontra = $true) & (setunionAx = $true) & (cartprodpairin = $true) & (woz1_3 = $true) & (woz2A = $true) & (inIntersectImpInUnion2 = $true) & (inComplementUnionImpNotIn1 = $true) & (emptyinPowerset = $true) & (woz1_5 = $true) & (setadjoinSub = $true) & (binunionE = $true) & (nonemptyI = $true) & (exuE2 = $true) & (setoftrueEq = $true) & (breln1all2 = $true) & (omega__Cong = $true) & (cartprodpairmemER = $true) & (setminusILneg = $true) & (breln1unionIR = $true) & (powersetE1 = $true) & (ex1I2 = $true) & (lam2p = $true) & (setminusSubset2 = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (contrasubsetT = $true) & (setukpairinjR2 = $true) & (ubforcartprodlem3 = $true) & (subsetRefl = $true) & (breln1invprop = $true) & (eta2 = $true) & (emptysetsubset = $true) & (binintersectSubset1 = $true) & (sepSubset = $true) & (powerset__Cong = $true) & (notdallE = $true) & (dpsetconstrER = $true) & (subsetI2 = $true) & (contrasubsetT1 = $true) & (symdiffI1 = $true) & (descrp = $true) & (setunionE2 = $true) & (upairsetIL = $true) & (exuI3 = $true) & (setOfPairsIsBReln1 = $true) & (funcGraphProp2 = $true) & (upairequniteq = $true) & (funcImageSingleton = $true) & (kpairp = $true) & (upairset2E = $true) & (binintersectTERcontra = $true) & (funcextLem = $true) & (eqbreln1 = $true) & (setunionsingleton2 = $true) & (theeq = $true) & (powersetI = $true) & (funcext2 = $true) & (doubleComplementE1 = $true) & (contraSubsetComplement = $true) & (symdiffIneg2 = $true)),
% 40.97/7.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK212,sK213,sK214])],[f1281,f1752])).
% 40.97/7.39 thf(f1752,plain,(
% 40.97/7.39 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (surjective @ X0 @ X2 @ X1)) & ($true = (in @ X1 @ (surjFuncSet @ X0 @ X2)))) => (($true != (surjective @ sK212 @ sK214 @ sK213)) & ($true = (in @ sK213 @ (surjFuncSet @ sK212 @ sK214))))),
% 40.97/7.39 introduced(definition,[],[choice_axiom])).
% 40.97/7.39 thf(f1281,plain,(
% 40.97/7.39 (binintersectSubset3 = $true) & (ubforcartprodlem2 = $true) & (inCongP = $true) & (demorgan1a = $true) & (subsetemptysetimpeq = $true) & (breln1compEex = $true) & (exuE3u = $true) & (subsetTrans = $true) & (funcext = $true) & (cartprodmempair = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectEL = $true) & (ex1E1 = $true) & (ubforcartprodlem1 = $true) & (nonemptyImpWitness = $true) & (theprop = $true) & (inPowerset = $true) & (notdexE = $true) & (symdiffIneg1 = $true) & (emptyE1 = $true) & (intersectInPowersetIntersectUnions = $true) & (breln1compI = $true) & (emptyset__Cong = $true) & (demorgan1 = $true) & (complementInPowersetComplementIntersect = $true) & (powersetI1 = $true) & (eqinunit = $true) & (demorgan2b2 = $true) & (cartprodfstpairEq = $true) & (setunionE = $true) & (doubleComplementSub2 = $true) & (breln1unionprop = $true) & (nonemptyE1 = $true) & (injFuncSetFuncIn = $true) & (setminusER = $true) & (emptyinunitempty = $true) & (powersetT_lem = $true) & (binintersectER = $true) & (breln1unionE = $true) & (breln1compprop = $true) & (ksndsingleton = $true) & (setminusEL = $true) & (powersetE = $true) & (setext = $true) & (symdiffI2 = $true) & (demorgan2a2 = $true) & (ap2apEq2 = $true) & (image1Ex1 = $true) & (complementTI1 = $true) & (doubleComplementSub1 = $true) & (subPowSU = $true) & (kpairiskpair = $true) & (lamProp = $true) & (doubleComplementI1 = $true) & (exu__Cong = $true) & (subbreln1 = $true) & (setunion__Cong = $true) & (iffalseProp1 = $true) & (descr__Cong = $true) & (iftrueProp1 = $true) & (dsetconstrI = $true) & (breln1unionEcases = $true) & (secondinupair = $true) & (singletonsubset = $true) & (setunionI = $true) & (binintersectI = $true) & (woz13rule1 = $true) & (binintersectRsub = $true) & (setukpairinjL = $true) & (dsetconstrEL = $true) & (beta2 = $true) & (inIntersectImpInUnion = $true) & (setbeta = $true) & (iftrueProp2 = $true) & (app = $true) & (doubleComplementEq = $true) & (binunionRsub = $true) & (breln1all1 = $true) & (subset2powerset = $true) & (eqimpsubset2 = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (complementSubsetComplementIntersect = $true) & (nonemptyI1 = $true) & (dpsetconstrEL2 = $true) & (funcinfuncset = $true) & (eqimpsubset1 = $true) & (powersetsubset = $true) & (setukpairinjR11 = $true) & (subsetI1 = $true) & (setukpairinjR12 = $true) & (upairsubunion = $true) & (funcGraphProp3 = $true) & (quantDeMorgan2 = $true) & (emptysetimpfalse = $true) & (lam2lamEq = $true) & (notsubsetI = $true) & (replAx = $true) & (binintersectLsub = $true) & (iftrueorfalse = $true) & (notequalI1 = $true) & (ex1I = $true) & (lamp = $true) & (singletonprop = $true) & (binintersectSubset2 = $true) & (upairsetE = $true) & (setextAx = $true) & (woz1_1 = $true) & (prop2set2propI = $true) & (setminusERneg = $true) & (contrasubsetT2 = $true) & (upairsetIR = $true) & (emptyI = $true) & (breln1invE = $true) & (ifSingleton = $true) & (setukpairIL = $true) & (kfstpairEq = $true) & (notinemptyset = $true) & (complementTnotintersectT = $true) & (image1I = $true) & (injFuncSetFuncInj = $true) & (foundationAx = $true) & (singletoninpowunion = $true) & (woz13rule4 = $true) & (surjFuncSetFuncIn = $true) & (dpsetconstrERa = $true) & (woz2B = $true) & (dpsetconstrEL1 = $true) & (emptysetE = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (image1E = $true) & (woz13rule2 = $true) & (bs114d = $true) & (kfstsingleton = $true) & (setukpairinjR = $true) & (subsetE2 = $true) & (woz2W = $true) & (eqbreln = $true) & (binintersectTELcontra = $true) & (quantDeMorgan3 = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (iffalse = $true) & (complementImpComplementIntersect = $true) & (iftrue = $true) & (beta1 = $true) & (setadjoinIL = $true) & (image1Ex = $true) & (binintersectT_lem = $true) & (setminusT_lem = $true) & (woz2Ex = $true) & (binunionT_lem = $true) & (image1Equiv = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (ap2p = $true) & (binunionTILcontra = $true) & (setminusSubset1 = $true) & (powersetTI1 = $true) & (dsetconstr__Cong = $true) & (omega0Ax = $true) & (kpairsurjEq = $true) & (breln1unionCommutes = $true) & (setminusI = $true) & (woz13rule0 = $true) & (complementUnionInPowersetComplement = $true) & (breln1invI = $true) & (setunionsingleton1 = $true) & (exuE1 = $true) & (prop2setI = $true) & (upairset2IR = $true) & (cartprodsndin = $true) & (wellorderingAx = $true) & (binunionIR = $true) & (woz1_4 = $true) & (complementT_lem = $true) & (setextT = $true) & (setunionsingleton = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (vacuousDall = $true) & (dsetconstrER = $true) & (exuE3e = $true) & (woz13rule3 = $true) & (symdiffE = $true) & (binunionEcases = $true) & (cartprodpairsurjEq = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (cartprodpairmemEL = $true) & (subsetTI = $true) & (cartprodsndpairEq = $true) & (emptyInPowerset = $true) & (setadjoinSub2 = $true) & (breln1SetBreln1 = $true) & (notinsingleton = $true) & (cartprodfstin = $true) & (eta1 = $true) & (powersetTE1 = $true) & (cartprodmempair1 = $true) & (subbreln = $true) & (funcGraphProp1 = $true) & (subsetE = $true) & (brelnall1 = $true) & (setukpairIR = $true) & (in__Cong = $true) & (ksndpairEq = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (surjective @ X0 @ X2 @ X1)) & ($true = (in @ X1 @ (surjFuncSet @ X0 @ X2)))) & (singletonsuniq = $true) & (woz1_2 = $true) & (quantDeMorgan1 = $true) & (demorgan2a1 = $true) & (demorgan1b = $true) & (breln1unionI = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (binunionLsub = $true) & (powersetAx = $true) & (binintersectSubset4 = $true) & (injFuncInInjFuncSet = $true) & (apProp = $true) & (demorgan2a = $true) & (setminusIRneg = $true) & (breln1unionIL = $true) & (ap2apEq1 = $true) & (dpsetconstrI = $true) & (funcGraphProp4 = $true) & (cartprodmempaircEq = $true) & (ifp = $true) & (sepInPowerset = $true) & (singletonsswitch = $true) & (binunionTEcontra = $true) & (setminusELneg = $true) & (quantDeMorgan4 = $true) & (demorgan2b = $true) & (omegaSAx = $true) & (iffalseProp2 = $true) & (singletoninpowerset = $true) & (setukpairinjL1 = $true) & (binunionIL = $true) & (complementTcontraSubset = $true) & (brelnall2 = $true) & (infuncsetfunc = $true) & (setextsub = $true) & (setadjoin__Cong = $true) & (contrasubsetT3 = $true) & (choice2fnsingleton = $true) & (breln1compE = $true) & (disjointsetsI1 = $true) & (demorgan2 = $true) & (complementTE1 = $true) & (binintersectSubset5 = $true) & (setukpairinjL2 = $true) & (upairinpowunion = $true) & (prop2setE = $true) & (ex1E2 = $true) & (binunionTIRcontra = $true) & (setunionAx = $true) & (cartprodpairin = $true) & (woz1_3 = $true) & (woz2A = $true) & (inIntersectImpInUnion2 = $true) & (inComplementUnionImpNotIn1 = $true) & (emptyinPowerset = $true) & (woz1_5 = $true) & (setadjoinSub = $true) & (binunionE = $true) & (nonemptyI = $true) & (exuE2 = $true) & (setoftrueEq = $true) & (breln1all2 = $true) & (omega__Cong = $true) & (cartprodpairmemER = $true) & (setminusILneg = $true) & (breln1unionIR = $true) & (powersetE1 = $true) & (ex1I2 = $true) & (lam2p = $true) & (setminusSubset2 = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (contrasubsetT = $true) & (setukpairinjR2 = $true) & (ubforcartprodlem3 = $true) & (subsetRefl = $true) & (breln1invprop = $true) & (eta2 = $true) & (emptysetsubset = $true) & (binintersectSubset1 = $true) & (sepSubset = $true) & (powerset__Cong = $true) & (notdallE = $true) & (dpsetconstrER = $true) & (subsetI2 = $true) & (contrasubsetT1 = $true) & (symdiffI1 = $true) & (descrp = $true) & (setunionE2 = $true) & (upairsetIL = $true) & (exuI3 = $true) & (setOfPairsIsBReln1 = $true) & (funcGraphProp2 = $true) & (upairequniteq = $true) & (funcImageSingleton = $true) & (kpairp = $true) & (upairset2E = $true) & (binintersectTERcontra = $true) & (funcextLem = $true) & (eqbreln1 = $true) & (setunionsingleton2 = $true) & (theeq = $true) & (powersetI = $true) & (funcext2 = $true) & (doubleComplementE1 = $true) & (contraSubsetComplement = $true) & (symdiffIneg2 = $true)),
% 40.97/7.39 inference(flattening,[status(thm)],[f1280])).
% 40.97/7.39 thf(f1280,plain,(
% 40.97/7.39 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true != (surjective @ X0 @ X2 @ X1)) & ($true = (in @ X1 @ (surjFuncSet @ X0 @ X2)))) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (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)),
% 40.97/7.39 inference(ennf_transformation,[status(thm)],[f427])).
% 40.97/7.39 thf(f427,plain,(
% 40.97/7.39 ~((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) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (surjFuncSet @ X0 @ X2))) => ($true = (surjective @ X0 @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 40.97/7.39 inference(fool_elimination,[status(thm)],[f426])).
% 40.97/7.39 thf(f426,plain,(
% 40.97/7.39 ~(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 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (surjFuncSet @ X0 @ X2)) => (surjective @ X0 @ X2 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 40.97/7.39 inference(rectify,[status(thm)],[f324])).
% 40.97/7.39 thf(f324,negated_conjecture,(
% 40.97/7.39 ~(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 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => ! [X1 : $i,X12 : $i,X2 : $i] : ((in @ X12 @ (surjFuncSet @ X1 @ X2)) => (surjective @ X1 @ X2 @ X12))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 40.97/7.39 inference(negated_conjecture,[status(cth)],[f323])).
% 40.97/7.39 thf(f323,conjecture,(
% 40.97/7.39 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 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => ! [X1 : $i,X12 : $i,X2 : $i] : ((in @ X12 @ (surjFuncSet @ X1 @ X2)) => (surjective @ X1 @ X2 @ X12)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 40.97/7.39 file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',surjFuncSetFuncSurj)).
% 40.97/7.39 thf(f8186,plain,(
% 40.97/7.39 ($true = (surjective @ sK212 @ sK214 @ sK213))),
% 40.97/7.39 inference(trivial_inequality_removal,[status(thm)],[f8144])).
% 40.97/7.39 thf(f8144,plain,(
% 40.97/7.39 ($true = (surjective @ sK212 @ sK214 @ sK213)) | ($true != $true)),
% 40.97/7.39 inference(superposition,[status(thm)],[f6252,f6209])).
% 40.97/7.39 thf(f6209,plain,(
% 40.97/7.39 ((in @ sK213 @ (dsetconstr @ (funcSet @ sK212 @ sK214) @ (surjective @ sK212 @ sK214))) = $true)),
% 40.97/7.39 inference(beta_eta_normalization,[status(thm)],[f5060])).
% 40.97/7.39 thf(f5060,plain,(
% 40.97/7.39 ($true = (in @ sK213 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))) @ sK212 @ sK214)))),
% 40.97/7.39 inference(definition_unfolding,[status(thm)],[f3422,f4322])).
% 40.97/7.39 thf(f4322,plain,(
% 40.97/7.39 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 40.97/7.39 inference(cnf_transformation,[status(thm)],[f409])).
% 40.97/7.39 thf(f409,plain,(
% 40.97/7.39 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 40.97/7.39 inference(fool_elimination,[status(thm)],[f408])).
% 40.97/7.39 thf(f408,plain,(
% 40.97/7.39 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (surjective @ X0 @ X1 @ X2)))) = surjFuncSet)),
% 40.97/7.39 inference(rectify,[status(thm)],[f321])).
% 40.97/7.39 thf(f321,axiom,(
% 40.97/7.39 ((^[X3 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X3 @ X4) @ (^[X12 : $i] : (surjective @ X3 @ X4 @ X12)))) = surjFuncSet)),
% 40.97/7.39 file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',surjFuncSet)).
% 40.97/7.39 thf(f3422,plain,(
% 40.97/7.39 ($true = (in @ sK213 @ (surjFuncSet @ sK212 @ sK214)))),
% 40.97/7.39 inference(cnf_transformation,[status(thm)],[f1753])).
% 40.97/7.39 thf(f6252,plain,(
% 40.97/7.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X2 @ X0))) | ((X0 @ X1) = $true)) )),
% 40.97/7.39 inference(beta_eta_normalization,[status(thm)],[f6251])).
% 40.97/7.39 thf(f6251,plain,(
% 40.97/7.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) | ((X0 @ X1) = $true)) )),
% 40.97/7.39 inference(trivial_inequality_removal,[status(thm)],[f5562])).
% 40.97/7.39 thf(f5562,plain,(
% 40.97/7.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) | ((X0 @ X1) = $true)) )),
% 40.97/7.39 inference(definition_unfolding,[status(thm)],[f4229,f3451])).
% 40.97/7.39 thf(f3451,plain,(
% 40.97/7.39 (dsetconstrER = $true)),
% 40.97/7.39 inference(cnf_transformation,[status(thm)],[f1753])).
% 40.97/7.39 thf(f4229,plain,(
% 40.97/7.39 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) | (dsetconstrER != $true)) )),
% 40.97/7.39 inference(cnf_transformation,[status(thm)],[f2400])).
% 40.97/7.39 thf(f2400,plain,(
% 40.97/7.39 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK636 @ sK637) != $true) & ($true = (in @ sK637 @ (dsetconstr @ sK638 @ (^[Y0 : $i]: (sK636 @ Y0)))))))),
% 40.97/7.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK636,sK637,sK638])],[f2398,f2399])).
% 40.97/7.39 thf(f2399,plain,(
% 40.97/7.39 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X4)) & ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))))) => (((sK636 @ sK637) != $true) & ($true = (in @ sK637 @ (dsetconstr @ sK638 @ (^[Y0 : $i]: (sK636 @ Y0))))))),
% 40.97/7.39 introduced(definition,[],[choice_axiom])).
% 40.97/7.39 thf(f2398,plain,(
% 40.97/7.39 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != (X3 @ X4)) & ($true = (in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))))))),
% 40.97/7.39 inference(rectify,[status(thm)],[f2397])).
% 40.97/7.39 thf(f2397,plain,(
% 40.97/7.39 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) != $true) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))))),
% 40.97/7.39 inference(nnf_transformation,[status(thm)],[f1336])).
% 40.97/7.39 thf(f1336,plain,(
% 40.97/7.39 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((X0 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) <=> (dsetconstrER = $true)),
% 40.97/7.39 inference(ennf_transformation,[status(thm)],[f627])).
% 40.97/7.39 thf(f627,plain,(
% 40.97/7.39 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) => ((X0 @ X1) = $true))),
% 40.97/7.39 inference(fool_elimination,[status(thm)],[f626])).
% 40.97/7.39 thf(f626,plain,(
% 40.97/7.39 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)) = dsetconstrER)),
% 40.97/7.39 inference(rectify,[status(thm)],[f16])).
% 40.97/7.39 thf(f16,axiom,(
% 40.97/7.39 (! [X0 : $i > $o,X1 : $i,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 40.97/7.39 file('/export/starexec/sandbox2/tmp/tmp.NQWvkmZhlf/DTF2THF_22692.p',dsetconstrER)).
% 40.97/7.39 % SZS output end Proof for DTF2THF_22692
% 40.97/7.39 % (23182)------------------------------
% 40.97/7.39 % (23182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.97/7.39 % (23182)Termination reason: Refutation
% 40.97/7.39
% 40.97/7.39 % (23182)Memory used [KB]: 12281
% 40.97/7.39 % (23182)Time elapsed: 0.193 s
% 40.97/7.39 % (23182)Instructions burned: 633 (million)
% 40.97/7.39 % (23182)------------------------------
% 40.97/7.39 % (23182)------------------------------
% 40.97/7.39 % (22793)Success in time 5.531 s
%------------------------------------------------------------------------------