%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU792^1 : 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 : n007.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 09:37:14 AM UTC 2026
% Result : Theorem 16.41s 4.01s
% Output : Refutation 16.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 116 ( 25 unt; 0 typ; 4 def)
% Number of atoms : 6265 (1613 equ; 0 cnn)
% Maximal formula atoms : 312 ( 54 avg)
% Number of connectives : 4448 ( 203 ~; 162 |;1022 &;1760 @)
% ( 14 <=>;1287 =>; 0 <=; 0 <~>)
% Maximal formula depth : 319 ( 24 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 551 ( 548 usr; 333 con; 0-6 aty)
% Number of variables : 214 ( 0 ^; 139 !; 75 ?; 214 :)
% 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_371,type,
sP1: $i > $i > $i > $o ).
thf(func_def_377,type,
sP7: $i > $i > $i > $o ).
thf(func_def_378,type,
sP8: $i > $i > $i > $i > $o ).
thf(func_def_381,type,
sP11: $i > $i > $o ).
thf(func_def_382,type,
sP12: $i > $o ).
thf(func_def_383,type,
sP13: $i > $i > $o ).
thf(func_def_384,type,
sP14: $i > $i > $o ).
thf(func_def_386,type,
sP16: $i > $o > $i > $i > $o ).
thf(func_def_403,type,
sK33: $i > $o ).
thf(func_def_405,type,
sK35: ( $i > $o ) > $i > $i > $i ).
thf(func_def_406,type,
sK36: ( $i > $o ) > $i > $i > $i ).
thf(func_def_417,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_419,type,
sK49: $i > $o ).
thf(func_def_435,type,
sK65: $i > ( $i > $i ) > $i > $i ).
thf(func_def_437,type,
sK67: $i > $i ).
thf(func_def_440,type,
sK70: $i > $o ).
thf(func_def_453,type,
sK83: $i > $o ).
thf(func_def_469,type,
sK99: ( $i > $o ) > $i > $i > $i ).
thf(func_def_470,type,
sK100: ( $i > $o ) > $i > $i > $i ).
thf(func_def_473,type,
sK103: $i > $o ).
thf(func_def_490,type,
sK120: $i > $i > $i > $i ).
thf(func_def_491,type,
sK121: $i > $i > $i > $i ).
thf(func_def_492,type,
sK122: $i > $i > $i > $i ).
thf(func_def_493,type,
sK123: $i > $i > $i > $i ).
thf(func_def_543,type,
sK173: $i > ( $i > $o ) > $i ).
thf(func_def_544,type,
sK174: $i > $o ).
thf(func_def_568,type,
sK198: $i > $o ).
thf(func_def_570,type,
sK200: $i > $i > $o ).
thf(func_def_586,type,
sK216: $i > $i ).
thf(func_def_595,type,
sK225: $i > $i > $o ).
thf(func_def_596,type,
sK226: $i > $i ).
thf(func_def_597,type,
sK227: $i > $i ).
thf(func_def_598,type,
sK228: ( $i > $i > $o ) > $i > $i ).
thf(func_def_599,type,
sK229: ( $i > $i > $o ) > $i > $i ).
thf(func_def_600,type,
sK230: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_601,type,
sK231: $i > $o ).
thf(func_def_602,type,
sK232: $i > $o ).
thf(func_def_603,type,
sK233: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_604,type,
sK234: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_625,type,
sK255: $i > $i > $i ).
thf(func_def_629,type,
sK259: $i > $o ).
thf(func_def_636,type,
sK266: $i > $i > $i ).
thf(func_def_637,type,
sK267: $i > $i > $i ).
thf(func_def_638,type,
sK268: $i > $i > $i ).
thf(func_def_647,type,
sK277: $i > $o ).
thf(func_def_661,type,
sK291: ( $i > $o ) > $i ).
thf(func_def_662,type,
sK292: $i > $o ).
thf(func_def_673,type,
sK303: $i > $i > $i > $i ).
thf(func_def_674,type,
sK304: $i > $i > $i > $i ).
thf(func_def_681,type,
sK311: $i > $o ).
thf(func_def_692,type,
sK322: $i > $i > $o ).
thf(func_def_704,type,
sK334: $i > $i > $i > $i > $i > $i ).
thf(func_def_711,type,
sK341: $i > $i ).
thf(func_def_714,type,
sK344: $i > ( $i > $i ) > $i > $i ).
thf(func_def_722,type,
sK352: $i > $i > $i > $i ).
thf(func_def_740,type,
sK370: $i > $i > $i ).
thf(func_def_753,type,
sK383: $i > $i > $i ).
thf(func_def_765,type,
sK395: $i > $i > $o ).
thf(func_def_781,type,
sK411: $i > $i > $o ).
thf(func_def_798,type,
sK428: $i > $o ).
thf(func_def_800,type,
sK430: ( $i > $o ) > $i > $i ).
thf(func_def_803,type,
sK433: $i > $i ).
thf(func_def_823,type,
sK453: $i > $i ).
thf(func_def_826,type,
sK456: $i > $i ).
thf(func_def_841,type,
sK471: $i > $i > $i > $i > $i ).
thf(func_def_842,type,
sK472: $i > ( $i > $o ) > $i ).
thf(func_def_843,type,
sK473: $i > $o ).
thf(func_def_850,type,
sK480: $i > $i > $i > $i > $i ).
thf(func_def_874,type,
sK504: $i > $i > $o ).
thf(func_def_875,type,
sK505: $i > $i ).
thf(func_def_878,type,
sK508: $i > $i > ( $i > $i ) > $i ).
thf(func_def_887,type,
sK517: $i > $o ).
thf(func_def_889,type,
sK519: $i > ( $i > $o ) > $i ).
thf(func_def_895,type,
sK525: $i > $o ).
thf(func_def_898,type,
sK528: $i > $i > ( $i > $o ) > $i ).
thf(func_def_918,type,
sK548: $i > ( $i > $i ) > $i > $i ).
thf(func_def_920,type,
sK550: $i > $i ).
thf(func_def_922,type,
sK552: $i > $o ).
thf(func_def_923,type,
sK553: $i > $i ).
thf(func_def_924,type,
sK554: ( $i > $o ) > $i ).
thf(func_def_925,type,
sK555: $i > $o ).
thf(func_def_940,type,
sK570: $i > $o ).
thf(func_def_942,type,
sK572: ( $i > $o ) > $i > $i ).
thf(func_def_943,type,
sK573: ( $i > $o ) > $i > $i ).
thf(func_def_949,type,
sK579: $i > $i > $o ).
thf(func_def_956,type,
sK586: $i > $i ).
thf(func_def_969,type,
sK599: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_970,type,
sK600: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_974,type,
sK604: $i > $o ).
thf(func_def_984,type,
sK614: $i > $i ).
thf(func_def_986,type,
sK616: $i > ( $i > $i ) > $i > $i ).
thf(func_def_987,type,
sK617: $i > $i > $i > $i ).
thf(func_def_991,type,
sK621: $i > $i > $i > $i ).
thf(func_def_1000,type,
sK630: $i > ( $i > $o ) > $i ).
thf(func_def_1001,type,
sK631: $i > $o ).
thf(func_def_1023,type,
sK653: $i > $i > $o ).
thf(func_def_1025,type,
sK655: $i > ( $i > $o ) > $i ).
thf(func_def_1026,type,
sK656: $i > $o ).
thf(func_def_1040,type,
sK670: $i > $i > $i ).
thf(func_def_1043,type,
sK673: $i > $i ).
thf(func_def_1044,type,
sK674: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1045,type,
sK675: $i > $i ).
thf(func_def_1049,type,
sK679: $i > $o ).
thf(func_def_1050,type,
sK680: $i > $o ).
thf(func_def_1051,type,
sK681: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1052,type,
sK682: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1063,type,
sK693: $i > $o ).
thf(func_def_1064,type,
sK694: $i > $o ).
thf(func_def_1105,type,
sK735: $i > $i > $i > $i > $i ).
thf(func_def_1106,type,
sK736: $i > $i > $i > $i > $i ).
thf(func_def_1107,type,
sK737: $i > $i > $i > $i > $i ).
thf(func_def_1108,type,
sK738: $i > $i > $i > $i > $i ).
thf(func_def_1120,type,
sK750: $i > $i > $i > $i > $i ).
thf(func_def_1121,type,
sK751: $i > $i > $i > $i > $i ).
thf(func_def_1131,type,
sK761: $i > $i > $i > $i ).
thf(func_def_1142,type,
sK772: $i > $i > $i ).
thf(func_def_1158,type,
sK788: $i > $o ).
thf(func_def_1160,type,
sK790: ( $i > $o ) > $i > $i ).
thf(func_def_1161,type,
sK791: ( $i > $o ) > $i > $i ).
thf(func_def_1179,type,
sK809: $o > $i > $i > $i ).
thf(func_def_1183,type,
sK813: $i > $i > $i ).
thf(func_def_1184,type,
sK814: $i > $i > $i ).
thf(func_def_1185,type,
sK815: $i > $i > $i ).
thf(func_def_1186,type,
sK816: $i > $i > $i ).
thf(func_def_1187,type,
sK817: $i > $i > $i ).
thf(func_def_1188,type,
sK818: $i > $i > $i > $i ).
thf(func_def_1189,type,
sK819: $i > $i ).
thf(func_def_1190,type,
sK820: $i > $i ).
thf(func_def_1191,type,
sK821: $i > $i ).
thf(func_def_1192,type,
sK822: $i > $i ).
thf(func_def_1193,type,
sK823: $i > $i > $i ).
thf(func_def_1194,type,
sK824: $i > $i > $i > $i ).
thf(func_def_1195,type,
sK825: $i > $i > $i > $i ).
thf(func_def_1196,type,
sK826: $i > $i > $i ).
thf(func_def_1197,type,
sK827: $i > $i > $i ).
thf(func_def_1198,type,
sK828: $i > $i ).
thf(func_def_1200,type,
sK830: $i > $i ).
thf(func_def_1201,type,
sK831: $i > $i ).
thf(func_def_1205,type,
sK835: $i > $o ).
thf(func_def_1207,type,
sK837: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1208,type,
sK838: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1256,type,
sK886: ( $i > $o ) > $i ).
thf(func_def_1257,type,
sK887: ( $i > $o ) > $i ).
thf(func_def_1258,type,
sK888: $i > $o ).
thf(func_def_1269,type,
sK899: $i > $o ).
thf(func_def_1271,type,
sK901: $i > ( $i > $o ) > $i ).
thf(func_def_1278,type,
sK908: $i > $i ).
thf(func_def_1280,type,
sK910: $i > $o ).
thf(func_def_1281,type,
sK911: $i > $o ).
thf(func_def_1282,type,
sK912: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1283,type,
sK913: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1284,type,
sK914: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1286,type,
sK916: $i > $i > $o ).
thf(func_def_1290,type,
sK920: $i > $i ).
thf(func_def_1295,type,
sK925: $i > $o ).
thf(func_def_1298,type,
sK928: $i > $i > $i > $i > $i ).
thf(func_def_1323,type,
sK953: $i > $i > $o ).
thf(func_def_1337,type,
sK967: $i > $i > $i ).
thf(func_def_1345,type,
sK975: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_1365,type,
sK995: $i > $o ).
thf(func_def_1369,type,
sK999: $i > $i > $i > $i ).
thf(func_def_1370,type,
sK1000: $i > $i > $i > $i ).
thf(func_def_1371,type,
sK1001: $i > $o ).
thf(func_def_1377,type,
sK1007: ( $i > $o ) > $i ).
thf(func_def_1378,type,
sK1008: $i > $o ).
thf(func_def_1379,type,
sK1009: $i > $i ).
thf(func_def_1382,type,
sK1012: $i > $o ).
thf(func_def_1385,type,
sK1015: $i > $i > $i ).
thf(func_def_1390,type,
sK1020: ( $i > $o ) > $i > $i ).
thf(func_def_1392,type,
sK1022: $i > $o ).
thf(func_def_1411,type,
ph1041:
!>[X0: $tType] : X0 ).
thf(f4953,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f4900,f4906,f4917,f4946,f4952]) ).
thf(f4952,plain,
spl1040_4,
inference(avatar_contradiction_clause,[status(thm)],[f4951]) ).
thf(f4951,plain,
( $false
| spl1040_4 ),
inference(subsumption_resolution,[status(thm)],[f4950,f4539]) ).
thf(f4539,plain,
( $true
= ( breln1 @ sK979 @ sK982 ) ),
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f2874,plain,
( ( prop2setE = $true )
& ( singletonsubset = $true )
& ( cartprodpairin = $true )
& ( funcext = $true )
& ( subsetTI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( cartprodpairmemER = $true )
& ( setminusI = $true )
& ( complementImpComplementIntersect = $true )
& ( dpsetconstrI = $true )
& ( funcGraphProp1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( complementTE1 = $true )
& ( setminusLsub = $true )
& ( binunionEcases = $true )
& ( nonemptyI = $true )
& ( cartprodfstpairEq = $true )
& ( demorgan1 = $true )
& ( cartprodfstin = $true )
& ( powersetAx = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( singletoninpowunion = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( woz1_4 = $true )
& ( upairequniteq = $true )
& ( inPowerset = $true )
& ( demorgan1a = $true )
& ( iffalse = $true )
& ( bs114d = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjR = $true )
& ( setextsub = $true )
& ( powersetE = $true )
& ( eta2 = $true )
& ( breln1SetBreln1 = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( subbreln = $true )
& ( dsetconstrEL = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( woz13rule0 = $true )
& ( ex1I2 = $true )
& ( binunionTE = $true )
& ( binintersectSubset2 = $true )
& ( upairset2IR = $true )
& ( funcinfuncset = $true )
& ( woz13rule4 = $true )
& ( brelnall1 = $true )
& ( breln1compI = $true )
& ( subsetE = $true )
& ( ifSingleton = $true )
& ( notequalI1 = $true )
& ( dpsetconstrSub = $true )
& ( breln1unionE = $true )
& ( dpsetconstrEL1 = $true )
& ( contrasubsetT1 = $true )
& ( notdexE = $true )
& ( in__Cong = $true )
& ( exuI3 = $true )
& ( setminusT_lem = $true )
& ( app = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( binintersectRsub = $true )
& ( ex1E2 = $true )
& ( dsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( complementTcontraSubset = $true )
& ( setminusIRneg = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( setextT = $true )
& ( $true
= ( breln1 @ sK979 @ sK981 ) )
& ( $true
= ( breln1 @ sK979 @ sK982 ) )
& ( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
& ( $true
= ( breln1 @ sK979 @ sK980 ) )
& ( exuE1 = $true )
& ( setminusELneg = $true )
& ( setunionI = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionTIRcontra = $true )
& ( emptyI = $true )
& ( woz2A = $true )
& ( woz1_1 = $true )
& ( breln1unionprop = $true )
& ( iftrueorfalse = $true )
& ( exuE3e = $true )
& ( woz1_2 = $true )
& ( funcGraphProp4 = $true )
& ( powersetsubset = $true )
& ( setadjoinE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eqbreln1 = $true )
& ( eqimpsubset2 = $true )
& ( singletonprop = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( cartprodmempair = $true )
& ( emptyinunitempty = $true )
& ( cartprodmempair1 = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( binintersectEL = $true )
& ( upairinpowunion = $true )
& ( eqbreln = $true )
& ( funcextLem = $true )
& ( setminusEL = $true )
& ( breln1unionEcases = $true )
& ( setukpairinjR1 = $true )
& ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ( iftrueProp2 = $true )
& ( demorgan2b = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( setextAx = $true )
& ( iffalseProp2 = $true )
& ( sepSubset = $true )
& ( ksndsingleton = $true )
& ( contrasubsetT3 = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairsurjEq = $true )
& ( iftrueProp1 = $true )
& ( subPowSU = $true )
& ( woz2Ex = $true )
& ( funcImageSingleton = $true )
& ( binunionRsub = $true )
& ( cartprodsndin = $true )
& ( breln1unionIL = $true )
& ( contrasubsetT2 = $true )
& ( exuE2 = $true )
& ( complementTI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( notdallE = $true )
& ( ex1E1 = $true )
& ( beta2 = $true )
& ( exuEu = $true )
& ( emptysetsubset = $true )
& ( powersetTI1 = $true )
& ( binintersectI = $true )
& ( subbreln1 = $true )
& ( cartprodmempaircEq = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( setunionE = $true )
& ( binunionTILcontra = $true )
& ( setukpairinjR11 = $true )
& ( lamp = $true )
& ( emptyE1 = $true )
& ( doubleComplementEq = $true )
& ( eta1 = $true )
& ( notequalI2 = $true )
& ( cartprodsndpairEq = $true )
& ( doubleComplementI1 = $true )
& ( powersetI = $true )
& ( binunionIL = $true )
& ( powerset__Cong = $true )
& ( demorgan2a1 = $true )
& ( funcGraphProp3 = $true )
& ( noeltsimpempty = $true )
& ( demorgan2a = $true )
& ( kpairp = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyImpWitness = $true )
& ( vacuousDall = $true )
& ( singletonsswitch = $true )
& ( notinemptyset = $true )
& ( subsetRefl = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset1 = $true )
& ( foundationAx = $true )
& ( exu__Cong = $true )
& ( setukpairIR = $true )
& ( prop2setI = $true )
& ( setadjoinIL = $true )
& ( singletoninpowerset = $true )
& ( upairset2E = $true )
& ( setadjoinSub = $true )
& ( setminusILneg = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem3 = $true )
& ( ksndpairEq = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( wellorderingAx = $true )
& ( ex1I = $true )
& ( kfstsingleton = $true )
& ( inCongP = $true )
& ( setunionE2 = $true )
& ( demorgan2b2 = $true )
& ( funcext2 = $true )
& ( descr__Cong = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( binintersectSubset4 = $true )
& ( binunionTEcontra = $true )
& ( upairsetE = $true )
& ( setukpairinjR2 = $true )
& ( kfstpairEq = $true )
& ( ap2p = $true )
& ( breln1all1 = $true )
& ( ifp = $true )
& ( upairsubunion = $true )
& ( breln1unionIR = $true )
& ( choice2fnsingleton = $true )
& ( brelnall2 = $true )
& ( inIntersectImpInUnion = $true )
& ( setunionsingleton1 = $true )
& ( setminusER = $true )
& ( setadjoinIR = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( binunionLsub = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( breln1compprop = $true )
& ( quantDeMorgan2 = $true )
& ( theprop = $true )
& ( exuI2 = $true )
& ( woz13rule3 = $true )
& ( subsetemptysetimpeq = $true )
& ( symdiffE = $true )
& ( sepInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( singletonsuniq = $true )
& ( breln1all2 = $true )
& ( secondinupair = $true )
& ( binintersectTELcontra = $true )
& ( subset2powerset = $true )
& ( notinsingleton = $true )
& ( infuncsetfunc = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrER = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( powersetT_lem = $true )
& ( woz1_5 = $true )
& ( binintersectSubset3 = $true )
& ( woz13rule2 = $true )
& ( dsetconstr__Cong = $true )
& ( breln1compE = $true )
& ( woz1_3 = $true )
& ( subsetTrans = $true )
& ( complementTnotintersectT = $true )
& ( setukpairinjL2 = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset5 = $true )
& ( binunionE = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub2 = $true )
& ( replAx = $true )
& ( contrasubsetT = $true )
& ( lam2lamEq = $true )
& ( symdiffI2 = $true )
& ( setext = $true )
& ( doubleComplementE1 = $true )
& ( cartprodpairmemEL = $true )
& ( breln1unionCommutes = $true )
& ( lamProp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( breln1unionI = $true )
& ( binunionIR = $true )
& ( binintersectLsub = $true )
& ( complementUnionInPowersetComplement = $true )
& ( iffalseProp1 = $true )
& ( demorgan2a2 = $true )
& ( exuE3u = $true )
& ( iftrue = $true )
& ( woz2W = $true )
& ( dpsetconstrEL2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffIneg1 = $true )
& ( breln1compEex = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( binintersectTERcontra = $true )
& ( breln1invE = $true )
& ( setadjoinAx = $true )
& ( binintersectT_lem = $true )
& ( lam2p = $true )
& ( descrp = $true )
& ( omega__Cong = $true )
& ( setminusSubset1 = $true )
& ( complementT_lem = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( setminusERneg = $true )
& ( woz13rule1 = $true )
& ( setadjoin__Cong = $true )
& ( contraSubsetComplement = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( funcGraphProp2 = $true )
& ( nonemptyE1 = $true )
& ( demorgan2 = $true )
& ( ap2apEq2 = $true )
& ( setbeta = $true )
& ( demorgan1b = $true )
& ( theeq = $true )
& ( omega0Ax = $true )
& ( binunionT_lem = $true )
& ( upairsetIR = $true )
& ( binintersectER = $true )
& ( beta1 = $true )
& ( eqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK979,sK980,sK981,sK982])],[f1205,f2873,f2872,f2871]) ).
thf(f2871,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( ( breln1 @ sK979 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK979 @ X3 ) )
& ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ X2 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) ) ) ) )
& ( $true
= ( breln1 @ sK979 @ sK980 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2872,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK979 @ X2 )
= $true )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK979 @ X3 ) )
& ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ X2 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK979 @ sK981 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ sK979 @ X3 ) )
& ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2873,plain,
( ? [X3: $i] :
( ( $true
= ( breln1 @ sK979 @ X3 ) )
& ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ X3 )
!= ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ X3 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK979 @ sK982 ) )
& ( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1205,plain,
( ( prop2setE = $true )
& ( singletonsubset = $true )
& ( cartprodpairin = $true )
& ( funcext = $true )
& ( subsetTI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( cartprodpairmemER = $true )
& ( setminusI = $true )
& ( complementImpComplementIntersect = $true )
& ( dpsetconstrI = $true )
& ( funcGraphProp1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( complementTE1 = $true )
& ( setminusLsub = $true )
& ( binunionEcases = $true )
& ( nonemptyI = $true )
& ( cartprodfstpairEq = $true )
& ( demorgan1 = $true )
& ( cartprodfstin = $true )
& ( powersetAx = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( singletoninpowunion = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( woz1_4 = $true )
& ( upairequniteq = $true )
& ( inPowerset = $true )
& ( demorgan1a = $true )
& ( iffalse = $true )
& ( bs114d = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjR = $true )
& ( setextsub = $true )
& ( powersetE = $true )
& ( eta2 = $true )
& ( breln1SetBreln1 = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( subbreln = $true )
& ( dsetconstrEL = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( woz13rule0 = $true )
& ( ex1I2 = $true )
& ( binunionTE = $true )
& ( binintersectSubset2 = $true )
& ( upairset2IR = $true )
& ( funcinfuncset = $true )
& ( woz13rule4 = $true )
& ( brelnall1 = $true )
& ( breln1compI = $true )
& ( subsetE = $true )
& ( ifSingleton = $true )
& ( notequalI1 = $true )
& ( dpsetconstrSub = $true )
& ( breln1unionE = $true )
& ( dpsetconstrEL1 = $true )
& ( contrasubsetT1 = $true )
& ( notdexE = $true )
& ( in__Cong = $true )
& ( exuI3 = $true )
& ( setminusT_lem = $true )
& ( app = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( binintersectRsub = $true )
& ( ex1E2 = $true )
& ( dsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( complementTcontraSubset = $true )
& ( setminusIRneg = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( setextT = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( exuE1 = $true )
& ( setminusELneg = $true )
& ( setunionI = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionTIRcontra = $true )
& ( emptyI = $true )
& ( woz2A = $true )
& ( woz1_1 = $true )
& ( breln1unionprop = $true )
& ( iftrueorfalse = $true )
& ( exuE3e = $true )
& ( woz1_2 = $true )
& ( funcGraphProp4 = $true )
& ( powersetsubset = $true )
& ( setadjoinE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( eqbreln1 = $true )
& ( eqimpsubset2 = $true )
& ( singletonprop = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( cartprodmempair = $true )
& ( emptyinunitempty = $true )
& ( cartprodmempair1 = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( binintersectEL = $true )
& ( upairinpowunion = $true )
& ( eqbreln = $true )
& ( funcextLem = $true )
& ( setminusEL = $true )
& ( breln1unionEcases = $true )
& ( setukpairinjR1 = $true )
& ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ( iftrueProp2 = $true )
& ( demorgan2b = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( setextAx = $true )
& ( iffalseProp2 = $true )
& ( sepSubset = $true )
& ( ksndsingleton = $true )
& ( contrasubsetT3 = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairsurjEq = $true )
& ( iftrueProp1 = $true )
& ( subPowSU = $true )
& ( woz2Ex = $true )
& ( funcImageSingleton = $true )
& ( binunionRsub = $true )
& ( cartprodsndin = $true )
& ( breln1unionIL = $true )
& ( contrasubsetT2 = $true )
& ( exuE2 = $true )
& ( complementTI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( notdallE = $true )
& ( ex1E1 = $true )
& ( beta2 = $true )
& ( exuEu = $true )
& ( emptysetsubset = $true )
& ( powersetTI1 = $true )
& ( binintersectI = $true )
& ( subbreln1 = $true )
& ( cartprodmempaircEq = $true )
& ( setminusSubset2 = $true )
& ( setukpairinjR12 = $true )
& ( setunionE = $true )
& ( binunionTILcontra = $true )
& ( setukpairinjR11 = $true )
& ( lamp = $true )
& ( emptyE1 = $true )
& ( doubleComplementEq = $true )
& ( eta1 = $true )
& ( notequalI2 = $true )
& ( cartprodsndpairEq = $true )
& ( doubleComplementI1 = $true )
& ( powersetI = $true )
& ( binunionIL = $true )
& ( powerset__Cong = $true )
& ( demorgan2a1 = $true )
& ( funcGraphProp3 = $true )
& ( noeltsimpempty = $true )
& ( demorgan2a = $true )
& ( kpairp = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyImpWitness = $true )
& ( vacuousDall = $true )
& ( singletonsswitch = $true )
& ( notinemptyset = $true )
& ( subsetRefl = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset1 = $true )
& ( foundationAx = $true )
& ( exu__Cong = $true )
& ( setukpairIR = $true )
& ( prop2setI = $true )
& ( setadjoinIL = $true )
& ( singletoninpowerset = $true )
& ( upairset2E = $true )
& ( setadjoinSub = $true )
& ( setminusILneg = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem3 = $true )
& ( ksndpairEq = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( wellorderingAx = $true )
& ( ex1I = $true )
& ( kfstsingleton = $true )
& ( inCongP = $true )
& ( setunionE2 = $true )
& ( demorgan2b2 = $true )
& ( funcext2 = $true )
& ( descr__Cong = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( binintersectSubset4 = $true )
& ( binunionTEcontra = $true )
& ( upairsetE = $true )
& ( setukpairinjR2 = $true )
& ( kfstpairEq = $true )
& ( ap2p = $true )
& ( breln1all1 = $true )
& ( ifp = $true )
& ( upairsubunion = $true )
& ( breln1unionIR = $true )
& ( choice2fnsingleton = $true )
& ( brelnall2 = $true )
& ( inIntersectImpInUnion = $true )
& ( setunionsingleton1 = $true )
& ( setminusER = $true )
& ( setadjoinIR = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( quantDeMorgan3 = $true )
& ( emptysetAx = $true )
& ( binunionLsub = $true )
& ( apProp = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( breln1compprop = $true )
& ( quantDeMorgan2 = $true )
& ( theprop = $true )
& ( exuI2 = $true )
& ( woz13rule3 = $true )
& ( subsetemptysetimpeq = $true )
& ( symdiffE = $true )
& ( sepInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( singletonsuniq = $true )
& ( breln1all2 = $true )
& ( secondinupair = $true )
& ( binintersectTELcontra = $true )
& ( subset2powerset = $true )
& ( notinsingleton = $true )
& ( infuncsetfunc = $true )
& ( ap2apEq1 = $true )
& ( dpsetconstrER = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( powersetT_lem = $true )
& ( woz1_5 = $true )
& ( binintersectSubset3 = $true )
& ( woz13rule2 = $true )
& ( dsetconstr__Cong = $true )
& ( breln1compE = $true )
& ( woz1_3 = $true )
& ( subsetTrans = $true )
& ( complementTnotintersectT = $true )
& ( setukpairinjL2 = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset5 = $true )
& ( binunionE = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub2 = $true )
& ( replAx = $true )
& ( contrasubsetT = $true )
& ( lam2lamEq = $true )
& ( symdiffI2 = $true )
& ( setext = $true )
& ( doubleComplementE1 = $true )
& ( cartprodpairmemEL = $true )
& ( breln1unionCommutes = $true )
& ( lamProp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( breln1unionI = $true )
& ( binunionIR = $true )
& ( binintersectLsub = $true )
& ( complementUnionInPowersetComplement = $true )
& ( iffalseProp1 = $true )
& ( demorgan2a2 = $true )
& ( exuE3u = $true )
& ( iftrue = $true )
& ( woz2W = $true )
& ( dpsetconstrEL2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffIneg1 = $true )
& ( breln1compEex = $true )
& ( notsubsetI = $true )
& ( subsetI1 = $true )
& ( binintersectTERcontra = $true )
& ( breln1invE = $true )
& ( setadjoinAx = $true )
& ( binintersectT_lem = $true )
& ( lam2p = $true )
& ( descrp = $true )
& ( omega__Cong = $true )
& ( setminusSubset1 = $true )
& ( complementT_lem = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( setminusERneg = $true )
& ( woz13rule1 = $true )
& ( setadjoin__Cong = $true )
& ( contraSubsetComplement = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( funcGraphProp2 = $true )
& ( nonemptyE1 = $true )
& ( demorgan2 = $true )
& ( ap2apEq2 = $true )
& ( setbeta = $true )
& ( demorgan1b = $true )
& ( theeq = $true )
& ( omega0Ax = $true )
& ( binunionT_lem = $true )
& ( upairsetIR = $true )
& ( binintersectER = $true )
& ( beta1 = $true )
& ( eqinunit = $true ) ),
inference(flattening,[status(thm)],[f1204]) ).
thf(f1204,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( 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)],[f663]) ).
thf(f663,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f662]) ).
thf(f662,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
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X2 ) ) ) @ ( breln1invset @ X0 @ ( breln1compset @ X0 @ ( breln1invset @ X0 @ X3 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f312]) ).
thf(f312,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
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X19: $i] :
( ( breln1 @ X3 @ X19 )
=> ( ( breln1compset @ X3 @ ( binunion @ X13 @ X15 ) @ X19 )
= ( binunion @ ( breln1invset @ X3 @ ( breln1compset @ X3 @ ( breln1invset @ X3 @ X19 ) @ ( breln1invset @ X3 @ X15 ) ) ) @ ( breln1invset @ X3 @ ( breln1compset @ X3 @ ( breln1invset @ X3 @ X19 ) @ ( breln1invset @ X3 @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f311]) ).
thf(f311,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
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X19: $i] :
( ( breln1 @ X3 @ X19 )
=> ( ( breln1compset @ X3 @ ( binunion @ X13 @ X15 ) @ X19 )
= ( binunion @ ( breln1invset @ X3 @ ( breln1compset @ X3 @ ( breln1invset @ X3 @ X19 ) @ ( breln1invset @ X3 @ X15 ) ) ) @ ( breln1invset @ X3 @ ( breln1compset @ X3 @ ( breln1invset @ X3 @ X19 ) @ ( breln1invset @ X3 @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2B) ).
thf(f4950,plain,
( ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_4 ),
inference(subsumption_resolution,[status(thm)],[f4949,f4392]) ).
thf(f4392,plain,
breln1compprop = $true,
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4949,plain,
( ( breln1compprop != $true )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_4 ),
inference(subsumption_resolution,[status(thm)],[f4948,f4537]) ).
thf(f4537,plain,
( $true
= ( breln1 @ sK979 @ sK980 ) ),
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4948,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( breln1compprop != $true )
| spl1040_4 ),
inference(trivial_inequality_removal,[status(thm)],[f4947]) ).
thf(f4947,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( breln1compprop != $true )
| ( $true != $true )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_4 ),
inference(superposition,[status(thm)],[f4916,f3463]) ).
thf(f3463,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( breln1 @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) ) )
| ( $true
!= ( breln1 @ X3 @ X5 ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) )
| ( breln1compprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f1953]) ).
thf(f1953,plain,
( ( ( breln1compprop = $true )
| ( ( $true
= ( breln1 @ sK375 @ sK377 ) )
& ( $true
!= ( breln1 @ sK375 @ ( breln1compset @ sK375 @ sK376 @ sK377 ) ) )
& ( $true
= ( breln1 @ sK375 @ sK376 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( breln1 @ X3 @ X5 ) )
| ( $true
= ( breln1 @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) ) ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) ) )
| ( breln1compprop != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK375,sK376,sK377])],[f1950,f1952,f1951]) ).
thf(f1951,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( ( breln1 @ sK375 @ X2 )
= $true )
& ( $true
!= ( breln1 @ sK375 @ ( breln1compset @ sK375 @ sK376 @ X2 ) ) ) )
& ( $true
= ( breln1 @ sK375 @ sK376 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1952,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK375 @ X2 )
= $true )
& ( $true
!= ( breln1 @ sK375 @ ( breln1compset @ sK375 @ sK376 @ X2 ) ) ) )
=> ( ( $true
= ( breln1 @ sK375 @ sK377 ) )
& ( $true
!= ( breln1 @ sK375 @ ( breln1compset @ sK375 @ sK376 @ sK377 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1950,plain,
( ( ( breln1compprop = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( breln1 @ X3 @ X5 ) )
| ( $true
= ( breln1 @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) ) ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) ) )
| ( breln1compprop != $true ) ) ),
inference(rectify,[status(thm)],[f1949]) ).
thf(f1949,plain,
( ( ( breln1compprop = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( $true
!= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ( $true
= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) )
| ( breln1compprop != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1241]) ).
thf(f1241,plain,
( ( breln1compprop = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ( $true
= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f522]) ).
thf(f522,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( $true
= ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) )
<=> ( breln1compprop = $true ) ),
inference(fool_elimination,[status(thm)],[f521]) ).
thf(f521,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
= breln1compprop ),
inference(rectify,[status(thm)],[f297]) ).
thf(f297,axiom,
! [X3: $i,X13: $i] :
( ( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ( breln1 @ X3 @ ( breln1compset @ X3 @ X13 @ X15 ) ) ) )
= breln1compprop ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',breln1compprop) ).
thf(f4916,plain,
( ( ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) )
!= $true )
| spl1040_4 ),
inference(avatar_component_clause,[status(thm)],[f4914]) ).
thf(f4914,definition,
( spl1040_4
<=> ( ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1040_4])],[avatar_definition]) ).
thf(f4946,plain,
spl1040_3,
inference(avatar_contradiction_clause,[status(thm)],[f4945]) ).
thf(f4945,plain,
( $false
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4944,f4537]) ).
thf(f4944,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| spl1040_3 ),
inference(trivial_inequality_removal,[status(thm)],[f4939]) ).
thf(f4939,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( $true != $true )
| spl1040_3 ),
inference(superposition,[status(thm)],[f4930,f4540]) ).
thf(f4540,plain,
( $true
= ( breln1 @ sK979 @ sK981 ) ),
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4930,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK981 ) )
| ( $true
!= ( breln1 @ X0 @ sK980 ) ) )
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4929,f4350]) ).
thf(f4350,plain,
breln1unionCommutes = $true,
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4929,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK980 ) )
| ( breln1unionCommutes != $true )
| ( $true
!= ( breln1 @ X0 @ sK981 ) ) )
| spl1040_3 ),
inference(trivial_inequality_removal,[status(thm)],[f4927]) ).
thf(f4927,plain,
( ! [X0: $i] :
( ( $true
!= ( breln1 @ X0 @ sK981 ) )
| ( breln1unionCommutes != $true )
| ( $true
!= ( breln1 @ X0 @ sK980 ) )
| ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ) )
| spl1040_3 ),
inference(superposition,[status(thm)],[f4924,f3235]) ).
thf(f3235,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( binunion @ X4 @ X5 )
= ( binunion @ X5 @ X4 ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) )
| ( breln1unionCommutes != $true )
| ( $true
!= ( breln1 @ X3 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f1693]) ).
thf(f1693,plain,
( ( ( breln1unionCommutes = $true )
| ( ( ( breln1 @ sK209 @ sK210 )
= $true )
& ( $true
= ( breln1 @ sK209 @ sK211 ) )
& ( ( binunion @ sK211 @ sK210 )
!= ( binunion @ sK210 @ sK211 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( breln1 @ X3 @ X4 ) )
| ! [X5: $i] :
( ( $true
!= ( breln1 @ X3 @ X5 ) )
| ( ( binunion @ X4 @ X5 )
= ( binunion @ X5 @ X4 ) ) ) )
| ( breln1unionCommutes != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK209,sK210,sK211])],[f1690,f1692,f1691]) ).
thf(f1691,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( ( binunion @ X2 @ X1 )
!= ( binunion @ X1 @ X2 ) ) ) )
=> ( ( ( breln1 @ sK209 @ sK210 )
= $true )
& ? [X2: $i] :
( ( $true
= ( breln1 @ sK209 @ X2 ) )
& ( ( binunion @ sK210 @ X2 )
!= ( binunion @ X2 @ sK210 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1692,plain,
( ? [X2: $i] :
( ( $true
= ( breln1 @ sK209 @ X2 ) )
& ( ( binunion @ sK210 @ X2 )
!= ( binunion @ X2 @ sK210 ) ) )
=> ( ( $true
= ( breln1 @ sK209 @ sK211 ) )
& ( ( binunion @ sK211 @ sK210 )
!= ( binunion @ sK210 @ sK211 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1690,plain,
( ( ( breln1unionCommutes = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( ( binunion @ X2 @ X1 )
!= ( binunion @ X1 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( $true
!= ( breln1 @ X3 @ X4 ) )
| ! [X5: $i] :
( ( $true
!= ( breln1 @ X3 @ X5 ) )
| ( ( binunion @ X4 @ X5 )
= ( binunion @ X5 @ X4 ) ) ) )
| ( breln1unionCommutes != $true ) ) ),
inference(rectify,[status(thm)],[f1689]) ).
thf(f1689,plain,
( ( ( breln1unionCommutes = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ( ( binunion @ X2 @ X1 )
!= ( binunion @ X1 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ( ( binunion @ X2 @ X1 )
= ( binunion @ X1 @ X2 ) ) ) )
| ( breln1unionCommutes != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1189]) ).
thf(f1189,plain,
( ( breln1unionCommutes = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ( ( binunion @ X2 @ X1 )
= ( binunion @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( ( breln1unionCommutes = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( ( binunion @ X2 @ X1 )
= ( binunion @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f626]) ).
thf(f626,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( binunion @ X2 @ X1 )
= ( binunion @ X1 @ X2 ) ) ) )
= breln1unionCommutes ),
inference(rectify,[status(thm)],[f307]) ).
thf(f307,axiom,
! [X3: $i,X13: $i] :
( ( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ( ( binunion @ X13 @ X15 )
= ( binunion @ X15 @ X13 ) ) ) )
= breln1unionCommutes ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',breln1unionCommutes) ).
thf(f4924,plain,
( ( ( breln1compset @ sK979 @ ( binunion @ sK981 @ sK980 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4923,f4530]) ).
thf(f4530,plain,
woz2A = $true,
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4923,plain,
( ( ( breln1compset @ sK979 @ ( binunion @ sK981 @ sK980 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( woz2A != $true )
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4922,f4539]) ).
thf(f4922,plain,
( ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( ( breln1compset @ sK979 @ ( binunion @ sK981 @ sK980 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( woz2A != $true )
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4921,f4537]) ).
thf(f4921,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( ( breln1compset @ sK979 @ ( binunion @ sK981 @ sK980 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( woz2A != $true )
| spl1040_3 ),
inference(subsumption_resolution,[status(thm)],[f4918,f4540]) ).
thf(f4918,plain,
( ( $true
!= ( breln1 @ sK979 @ sK981 ) )
| ( ( breln1compset @ sK979 @ ( binunion @ sK981 @ sK980 ) @ sK982 )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( woz2A != $true )
| spl1040_3 ),
inference(superposition,[status(thm)],[f4912,f4234]) ).
thf(f4234,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) )
| ( $true
!= ( breln1 @ X0 @ X3 ) )
| ( woz2A != $true )
| ( $true
!= ( breln1 @ X0 @ X2 ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f2796]) ).
thf(f2796,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( breln1 @ X0 @ X3 ) )
| ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
| ( woz2A != $true ) )
& ( ( woz2A = $true )
| ( ( $true
= ( breln1 @ sK921 @ sK922 ) )
& ( $true
= ( breln1 @ sK921 @ sK923 ) )
& ( $true
= ( breln1 @ sK921 @ sK924 ) )
& ( ( breln1compset @ sK921 @ ( binunion @ sK922 @ sK923 ) @ sK924 )
!= ( binunion @ ( breln1compset @ sK921 @ sK922 @ sK924 ) @ ( breln1compset @ sK921 @ sK923 @ sK924 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK921,sK922,sK923,sK924])],[f2792,f2795,f2794,f2793]) ).
thf(f2793,plain,
( ? [X4: $i,X5: $i] :
( ( $true
= ( breln1 @ X4 @ X5 ) )
& ? [X6: $i] :
( ( $true
= ( breln1 @ X4 @ X6 ) )
& ? [X7: $i] :
( ( $true
= ( breln1 @ X4 @ X7 ) )
& ( ( binunion @ ( breln1compset @ X4 @ X5 @ X7 ) @ ( breln1compset @ X4 @ X6 @ X7 ) )
!= ( breln1compset @ X4 @ ( binunion @ X5 @ X6 ) @ X7 ) ) ) ) )
=> ( ( $true
= ( breln1 @ sK921 @ sK922 ) )
& ? [X6: $i] :
( ( ( breln1 @ sK921 @ X6 )
= $true )
& ? [X7: $i] :
( ( $true
= ( breln1 @ sK921 @ X7 ) )
& ( ( binunion @ ( breln1compset @ sK921 @ sK922 @ X7 ) @ ( breln1compset @ sK921 @ X6 @ X7 ) )
!= ( breln1compset @ sK921 @ ( binunion @ sK922 @ X6 ) @ X7 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2794,plain,
( ? [X6: $i] :
( ( ( breln1 @ sK921 @ X6 )
= $true )
& ? [X7: $i] :
( ( $true
= ( breln1 @ sK921 @ X7 ) )
& ( ( binunion @ ( breln1compset @ sK921 @ sK922 @ X7 ) @ ( breln1compset @ sK921 @ X6 @ X7 ) )
!= ( breln1compset @ sK921 @ ( binunion @ sK922 @ X6 ) @ X7 ) ) ) )
=> ( ( $true
= ( breln1 @ sK921 @ sK923 ) )
& ? [X7: $i] :
( ( $true
= ( breln1 @ sK921 @ X7 ) )
& ( ( binunion @ ( breln1compset @ sK921 @ sK922 @ X7 ) @ ( breln1compset @ sK921 @ sK923 @ X7 ) )
!= ( breln1compset @ sK921 @ ( binunion @ sK922 @ sK923 ) @ X7 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2795,plain,
( ? [X7: $i] :
( ( $true
= ( breln1 @ sK921 @ X7 ) )
& ( ( binunion @ ( breln1compset @ sK921 @ sK922 @ X7 ) @ ( breln1compset @ sK921 @ sK923 @ X7 ) )
!= ( breln1compset @ sK921 @ ( binunion @ sK922 @ sK923 ) @ X7 ) ) )
=> ( ( $true
= ( breln1 @ sK921 @ sK924 ) )
& ( ( breln1compset @ sK921 @ ( binunion @ sK922 @ sK923 ) @ sK924 )
!= ( binunion @ ( breln1compset @ sK921 @ sK922 @ sK924 ) @ ( breln1compset @ sK921 @ sK923 @ sK924 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2792,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( breln1 @ X0 @ X3 ) )
| ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
| ( woz2A != $true ) )
& ( ( woz2A = $true )
| ? [X4: $i,X5: $i] :
( ( $true
= ( breln1 @ X4 @ X5 ) )
& ? [X6: $i] :
( ( $true
= ( breln1 @ X4 @ X6 ) )
& ? [X7: $i] :
( ( $true
= ( breln1 @ X4 @ X7 ) )
& ( ( binunion @ ( breln1compset @ X4 @ X5 @ X7 ) @ ( breln1compset @ X4 @ X6 @ X7 ) )
!= ( breln1compset @ X4 @ ( binunion @ X5 @ X6 ) @ X7 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2791]) ).
thf(f2791,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( breln1 @ X0 @ X3 ) )
| ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
| ( woz2A != $true ) )
& ( ( woz2A = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
& ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
!= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1168]) ).
thf(f1168,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ( $true
!= ( breln1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( breln1 @ X0 @ X3 ) )
| ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
<=> ( woz2A = $true ) ),
inference(ennf_transformation,[status(thm)],[f575]) ).
thf(f575,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( breln1 @ X0 @ X3 ) )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
<=> ( woz2A = $true ) ),
inference(fool_elimination,[status(thm)],[f574]) ).
thf(f574,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X0 @ X3 )
=> ( ( breln1compset @ X0 @ ( binunion @ X1 @ X2 ) @ X3 )
= ( binunion @ ( breln1compset @ X0 @ X1 @ X3 ) @ ( breln1compset @ X0 @ X2 @ X3 ) ) ) ) ) )
= woz2A ),
inference(rectify,[status(thm)],[f310]) ).
thf(f310,axiom,
! [X3: $i,X13: $i] :
( ( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X19: $i] :
( ( breln1 @ X3 @ X19 )
=> ( ( breln1compset @ X3 @ ( binunion @ X13 @ X15 ) @ X19 )
= ( binunion @ ( breln1compset @ X3 @ X13 @ X19 ) @ ( breln1compset @ X3 @ X15 @ X19 ) ) ) ) ) )
= woz2A ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2A) ).
thf(f4912,plain,
( ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 )
!= ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) )
| spl1040_3 ),
inference(avatar_component_clause,[status(thm)],[f4910]) ).
thf(f4910,definition,
( spl1040_3
<=> ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 )
= ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1040_3])],[avatar_definition]) ).
thf(f4917,plain,
( ~ spl1040_3
| ~ spl1040_4
| spl1040_2 ),
inference(avatar_split_clause,[status(thm)],[f4908,f4897,f4914,f4910]) ).
thf(f4897,definition,
( spl1040_2
<=> ( ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ) ),
introduced(definition,[new_symbols(naming,[spl1040_2])],[avatar_definition]) ).
thf(f4908,plain,
( ( ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) )
!= $true )
| ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 )
!= ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) )
| spl1040_2 ),
inference(subsumption_resolution,[status(thm)],[f4907,f4486]) ).
thf(f4486,plain,
woz2Ex = $true,
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4907,plain,
( ( ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) )
!= $true )
| ( ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 )
!= ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) )
| ( woz2Ex != $true )
| spl1040_2 ),
inference(superposition,[status(thm)],[f4899,f3410]) ).
thf(f3410,plain,
! [X2: $i,X3: $i] :
( ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X3 ) )
= X3 )
| ( $true
!= ( breln1 @ X2 @ X3 ) )
| ( woz2Ex != $true ) ),
inference(cnf_transformation,[status(thm)],[f1893]) ).
thf(f1893,plain,
( ( ( woz2Ex = $true )
| ( ( $true
= ( breln1 @ sK335 @ sK336 ) )
& ( sK336
!= ( breln1invset @ sK335 @ ( breln1invset @ sK335 @ sK336 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( breln1 @ X2 @ X3 ) )
| ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X3 ) )
= X3 ) )
| ( woz2Ex != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK335,sK336])],[f1891,f1892]) ).
thf(f1892,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= X1 ) )
=> ( ( $true
= ( breln1 @ sK335 @ sK336 ) )
& ( sK336
!= ( breln1invset @ sK335 @ ( breln1invset @ sK335 @ sK336 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1891,plain,
( ( ( woz2Ex = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( breln1 @ X2 @ X3 ) )
| ( ( breln1invset @ X2 @ ( breln1invset @ X2 @ X3 ) )
= X3 ) )
| ( woz2Ex != $true ) ) ),
inference(rectify,[status(thm)],[f1890]) ).
thf(f1890,plain,
( ( ( woz2Ex = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
!= X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) )
| ( woz2Ex != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1331]) ).
thf(f1331,plain,
( ( woz2Ex = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f530]) ).
thf(f530,plain,
( ( woz2Ex = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) ) ),
inference(fool_elimination,[status(thm)],[f529]) ).
thf(f529,plain,
! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
=> ( ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) )
= X1 ) )
= woz2Ex ),
inference(rectify,[status(thm)],[f308]) ).
thf(f308,axiom,
! [X3: $i,X13: $i] :
( ( ( breln1 @ X3 @ X13 )
=> ( ( breln1invset @ X3 @ ( breln1invset @ X3 @ X13 ) )
= X13 ) )
= woz2Ex ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2Ex) ).
thf(f4899,plain,
( ( ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| spl1040_2 ),
inference(avatar_component_clause,[status(thm)],[f4897]) ).
thf(f4906,plain,
spl1040_1,
inference(avatar_contradiction_clause,[status(thm)],[f4905]) ).
thf(f4905,plain,
( $false
| spl1040_1 ),
inference(subsumption_resolution,[status(thm)],[f4904,f4539]) ).
thf(f4904,plain,
( ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_1 ),
inference(subsumption_resolution,[status(thm)],[f4903,f4540]) ).
thf(f4903,plain,
( ( $true
!= ( breln1 @ sK979 @ sK981 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_1 ),
inference(subsumption_resolution,[status(thm)],[f4902,f4392]) ).
thf(f4902,plain,
( ( breln1compprop != $true )
| ( $true
!= ( breln1 @ sK979 @ sK981 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_1 ),
inference(trivial_inequality_removal,[status(thm)],[f4901]) ).
thf(f4901,plain,
( ( $true
!= ( breln1 @ sK979 @ sK981 ) )
| ( breln1compprop != $true )
| ( $true != $true )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| spl1040_1 ),
inference(superposition,[status(thm)],[f4895,f3463]) ).
thf(f4895,plain,
( ( $true
!= ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) )
| spl1040_1 ),
inference(avatar_component_clause,[status(thm)],[f4893]) ).
thf(f4893,definition,
( spl1040_1
<=> ( $true
= ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1040_1])],[avatar_definition]) ).
thf(f4900,plain,
( ~ spl1040_1
| ~ spl1040_2 ),
inference(avatar_split_clause,[status(thm)],[f4887,f4897,f4893]) ).
thf(f4887,plain,
( ( ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4883,f4486]) ).
thf(f4883,plain,
( ( woz2Ex != $true )
| ( ( binunion @ ( breln1compset @ sK979 @ sK981 @ sK982 ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) ),
inference(superposition,[status(thm)],[f4879,f3410]) ).
thf(f4879,plain,
( ( binunion @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ),
inference(subsumption_resolution,[status(thm)],[f4878,f4540]) ).
thf(f4878,plain,
( ( ( binunion @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK981 ) ) ),
inference(subsumption_resolution,[status(thm)],[f4877,f4539]) ).
thf(f4877,plain,
( ( ( binunion @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK981 ) ) ),
inference(subsumption_resolution,[status(thm)],[f4874,f4339]) ).
thf(f4339,plain,
woz2W = $true,
inference(cnf_transformation,[status(thm)],[f2874]) ).
thf(f4874,plain,
( ( ( binunion @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK981 @ sK982 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( woz2W != $true )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( $true
!= ( breln1 @ sK979 @ sK981 ) ) ),
inference(superposition,[status(thm)],[f4869,f3150]) ).
thf(f3150,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( breln1invset @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) )
= ( breln1compset @ X3 @ ( breln1invset @ X3 @ X5 ) @ ( breln1invset @ X3 @ X4 ) ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) )
| ( woz2W != $true )
| ( $true
!= ( breln1 @ X3 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f1599,plain,
( ( ( woz2W = $true )
| ( ( ( breln1compset @ sK149 @ ( breln1invset @ sK149 @ sK151 ) @ ( breln1invset @ sK149 @ sK150 ) )
!= ( breln1invset @ sK149 @ ( breln1compset @ sK149 @ sK150 @ sK151 ) ) )
& ( ( breln1 @ sK149 @ sK151 )
= $true )
& ( $true
= ( breln1 @ sK149 @ sK150 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( breln1invset @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) )
= ( breln1compset @ X3 @ ( breln1invset @ X3 @ X5 ) @ ( breln1invset @ X3 @ X4 ) ) )
| ( $true
!= ( breln1 @ X3 @ X5 ) ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) ) )
| ( woz2W != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150,sK151])],[f1596,f1598,f1597]) ).
thf(f1597,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
!= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ? [X2: $i] :
( ( ( breln1compset @ sK149 @ ( breln1invset @ sK149 @ X2 ) @ ( breln1invset @ sK149 @ sK150 ) )
!= ( breln1invset @ sK149 @ ( breln1compset @ sK149 @ sK150 @ X2 ) ) )
& ( $true
= ( breln1 @ sK149 @ X2 ) ) )
& ( $true
= ( breln1 @ sK149 @ sK150 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1598,plain,
( ? [X2: $i] :
( ( ( breln1compset @ sK149 @ ( breln1invset @ sK149 @ X2 ) @ ( breln1invset @ sK149 @ sK150 ) )
!= ( breln1invset @ sK149 @ ( breln1compset @ sK149 @ sK150 @ X2 ) ) )
& ( $true
= ( breln1 @ sK149 @ X2 ) ) )
=> ( ( ( breln1compset @ sK149 @ ( breln1invset @ sK149 @ sK151 ) @ ( breln1invset @ sK149 @ sK150 ) )
!= ( breln1invset @ sK149 @ ( breln1compset @ sK149 @ sK150 @ sK151 ) ) )
& ( ( breln1 @ sK149 @ sK151 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1596,plain,
( ( ( woz2W = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
!= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( breln1invset @ X3 @ ( breln1compset @ X3 @ X4 @ X5 ) )
= ( breln1compset @ X3 @ ( breln1invset @ X3 @ X5 ) @ ( breln1invset @ X3 @ X4 ) ) )
| ( $true
!= ( breln1 @ X3 @ X5 ) ) )
| ( $true
!= ( breln1 @ X3 @ X4 ) ) )
| ( woz2W != $true ) ) ),
inference(rectify,[status(thm)],[f1595]) ).
thf(f1595,plain,
( ( ( woz2W = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
!= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) )
| ( woz2W != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1134]) ).
thf(f1134,plain,
( ( woz2W = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f581]) ).
thf(f581,plain,
( ( woz2W = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f580]) ).
thf(f580,plain,
( woz2W
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( ( breln1invset @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= ( breln1compset @ X0 @ ( breln1invset @ X0 @ X2 ) @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f309]) ).
thf(f309,axiom,
( woz2W
= ( ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ( ( breln1invset @ X3 @ ( breln1compset @ X3 @ X13 @ X15 ) )
= ( breln1compset @ X3 @ ( breln1invset @ X3 @ X15 ) @ ( breln1invset @ X3 @ X13 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2W) ).
thf(f4869,plain,
( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ),
inference(subsumption_resolution,[status(thm)],[f4868,f4339]) ).
thf(f4868,plain,
( ( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) )
| ( woz2W != $true ) ),
inference(subsumption_resolution,[status(thm)],[f4867,f4539]) ).
thf(f4867,plain,
( ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( woz2W != $true )
| ( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ) ),
inference(subsumption_resolution,[status(thm)],[f4862,f4537]) ).
thf(f4862,plain,
( ( $true
!= ( breln1 @ sK979 @ sK980 ) )
| ( woz2W != $true )
| ( $true
!= ( breln1 @ sK979 @ sK982 ) )
| ( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ sK980 @ sK982 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ) ),
inference(superposition,[status(thm)],[f4538,f3150]) ).
thf(f4538,plain,
( ( binunion @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK981 ) ) ) @ ( breln1invset @ sK979 @ ( breln1compset @ sK979 @ ( breln1invset @ sK979 @ sK982 ) @ ( breln1invset @ sK979 @ sK980 ) ) ) )
!= ( breln1compset @ sK979 @ ( binunion @ sK980 @ sK981 ) @ sK982 ) ),
inference(cnf_transformation,[status(thm)],[f2874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU792^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n007.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:33:23 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU792^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : Binary Relations on a Set - Second Wizard of Oz Examples
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S ->
% 0.19/0.47 % (! T:i.breln1 A T -> breln1compset A (binunion R S) T =
% 0.19/0.47 % binunion (breln1invset A (breln1compset A (breln1invset A T)
% 0.19/0.47 % (breln1invset A S))) (breln1invset A (breln1compset A
% 0.19/0.47 % (breln1invset A T) (breln1invset A R))))))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC294g [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 1.00 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.19/0.47 % Syntax : Number of formulae : 667 ( 310 unt; 356 typ; 310 def)
% 0.19/0.47 % Number of atoms : 1917 ( 445 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 312 ( 6 avg)
% 0.19/0.47 % Number of connectives : 4236 ( 73 ~; 14 |; 48 &;3083 @)
% 0.19/0.47 % ( 14 <=>;1004 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 318 ( 2 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 359 ( 356 usr; 312 con; 0-4 aty)
% 0.19/0.47 % Number of variables : 1093 ( 71 ^; 985 !; 37 ?;1093 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=357
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(in_type,type,
% 0.19/0.47 in: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(exu_type,type,
% 0.19/0.47 exu: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(exu,definition,
% 0.19/0.47 ( exu
% 0.19/0.47 = ( ^ [Xphi: $i > $o] :
% 0.19/0.47 ? [Xx: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 & ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setextAx_type,type,
% 0.19/0.47 setextAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setextAx,definition,
% 0.19/0.47 ( setextAx
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 <=> ( in @ Xx @ B ) )
% 0.19/0.47 => ( A = B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyset_type,type,
% 0.19/0.47 emptyset: $i ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetAx_type,type,
% 0.19/0.47 emptysetAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetAx,definition,
% 0.19/0.47 ( emptysetAx
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin_type,type,
% 0.19/0.47 setadjoin: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinAx_type,type,
% 0.19/0.47 setadjoinAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinAx,definition,
% 0.19/0.47 ( setadjoinAx
% 0.19/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.47 <=> ( ( Xy = Xx )
% 0.19/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powerset_type,type,
% 0.19/0.47 powerset: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(powersetAx_type,type,
% 0.19/0.47 powersetAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetAx,definition,
% 0.19/0.47 ( powersetAx
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.47 <=> ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunion_type,type,
% 0.19/0.47 setunion: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setunionAx_type,type,
% 0.19/0.47 setunionAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionAx,definition,
% 0.19/0.47 ( setunionAx
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.47 <=> ? [B: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(omega_type,type,
% 0.19/0.47 omega: $i ).
% 0.19/0.47
% 0.19/0.47 thf(omega0Ax_type,type,
% 0.19/0.47 omega0Ax: $o ).
% 0.19/0.47
% 0.19/0.47 thf(omega0Ax,definition,
% 0.19/0.47 ( omega0Ax
% 0.19/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(omegaSAx_type,type,
% 0.19/0.47 omegaSAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(omegaSAx,definition,
% 0.19/0.47 ( omegaSAx
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ omega )
% 0.19/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(omegaIndAx_type,type,
% 0.19/0.47 omegaIndAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(omegaIndAx,definition,
% 0.19/0.47 ( omegaIndAx
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ( ( in @ emptyset @ A )
% 0.19/0.47 & ! [Xx: $i] :
% 0.19/0.47 ( ( ( in @ Xx @ omega )
% 0.19/0.47 & ( in @ Xx @ A ) )
% 0.19/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ omega )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(replAx_type,type,
% 0.19/0.47 replAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(replAx,definition,
% 0.19/0.47 ( replAx
% 0.19/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( exu
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.19/0.47 => ? [B: $i] :
% 0.19/0.47 ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 <=> ? [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(foundationAx_type,type,
% 0.19/0.47 foundationAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(foundationAx,definition,
% 0.19/0.47 ( foundationAx
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.47 => ? [B: $i] :
% 0.19/0.47 ( ( in @ B @ A )
% 0.19/0.47 & ~ ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(wellorderingAx_type,type,
% 0.19/0.47 wellorderingAx: $o ).
% 0.19/0.47
% 0.19/0.47 thf(wellorderingAx,definition,
% 0.19/0.47 ( wellorderingAx
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ? [B: $i] :
% 0.19/0.47 ( ! [C: $i] :
% 0.19/0.47 ( ( in @ C @ B )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ C )
% 0.19/0.47 => ( in @ Xx @ A ) ) )
% 0.19/0.47 & ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( ( in @ Xx @ A )
% 0.19/0.47 & ( in @ Xy @ A ) )
% 0.19/0.47 => ( ! [C: $i] :
% 0.19/0.47 ( ( in @ C @ B )
% 0.19/0.47 => ( ( in @ Xx @ C )
% 0.19/0.47 <=> ( in @ Xy @ C ) ) )
% 0.19/0.47 => ( Xx = Xy ) ) )
% 0.19/0.47 & ! [C: $i,D: $i] :
% 0.19/0.47 ( ( ( in @ C @ B )
% 0.19/0.47 & ( in @ D @ B ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ C )
% 0.19/0.47 => ( in @ Xx @ D ) )
% 0.19/0.47 | ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ D )
% 0.19/0.47 => ( in @ Xx @ C ) ) ) )
% 0.19/0.47 & ! [C: $i] :
% 0.19/0.47 ( ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ C )
% 0.19/0.47 => ( in @ Xx @ A ) )
% 0.19/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.19/0.47 => ? [D: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ D @ B )
% 0.19/0.47 & ( in @ Xx @ C )
% 0.19/0.47 & ~ ? [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ D )
% 0.19/0.47 & ( in @ Xy @ C ) )
% 0.19/0.47 & ! [E: $i] :
% 0.19/0.47 ( ( in @ E @ B )
% 0.19/0.47 => ( ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ E )
% 0.19/0.47 => ( in @ Xy @ D ) )
% 0.19/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(descr_type,type,
% 0.19/0.47 descr: ( $i > $o ) > $i ).
% 0.19/0.47
% 0.19/0.47 thf(descrp_type,type,
% 0.19/0.47 descrp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(descrp,definition,
% 0.19/0.47 ( descrp
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ( Xphi
% 0.19/0.47 @ ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstr_type,type,
% 0.19/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrI_type,type,
% 0.19/0.47 dsetconstrI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrI,definition,
% 0.19/0.47 ( dsetconstrI
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( in @ Xx
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrEL_type,type,
% 0.19/0.47 dsetconstrEL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrEL,definition,
% 0.19/0.47 ( dsetconstrEL
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrER_type,type,
% 0.19/0.47 dsetconstrER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstrER,definition,
% 0.19/0.47 ( dsetconstrER
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuE1_type,type,
% 0.19/0.47 exuE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuE1,definition,
% 0.19/0.47 ( exuE1
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 & ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(prop2set_type,type,
% 0.19/0.47 prop2set: $o > $i ).
% 0.19/0.47
% 0.19/0.47 thf(prop2setE_type,type,
% 0.19/0.47 prop2setE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(prop2setE,definition,
% 0.19/0.47 ( prop2setE
% 0.19/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.19/0.47 => Xphi ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetE_type,type,
% 0.19/0.47 emptysetE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetE,definition,
% 0.19/0.47 ( emptysetE
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ emptyset )
% 0.19/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetimpfalse_type,type,
% 0.19/0.47 emptysetimpfalse: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetimpfalse,definition,
% 0.19/0.47 ( emptysetimpfalse
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ emptyset )
% 0.19/0.47 => $false ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notinemptyset_type,type,
% 0.19/0.47 notinemptyset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notinemptyset,definition,
% 0.19/0.47 ( notinemptyset
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuE3e_type,type,
% 0.19/0.47 exuE3e: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuE3e,definition,
% 0.19/0.47 ( exuE3e
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setext_type,type,
% 0.19/0.47 setext: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setext,definition,
% 0.19/0.47 ( setext
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ A ) )
% 0.19/0.47 => ( A = B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyI_type,type,
% 0.19/0.47 emptyI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyI,definition,
% 0.19/0.47 ( emptyI
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ~ ( in @ Xx @ A )
% 0.19/0.47 => ( A = emptyset ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(noeltsimpempty_type,type,
% 0.19/0.47 noeltsimpempty: $o ).
% 0.19/0.47
% 0.19/0.47 thf(noeltsimpempty,definition,
% 0.19/0.47 ( noeltsimpempty
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ~ ( in @ Xx @ A )
% 0.19/0.47 => ( A = emptyset ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setbeta_type,type,
% 0.19/0.47 setbeta: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setbeta,definition,
% 0.19/0.47 ( setbeta
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(nonempty_type,type,
% 0.19/0.47 nonempty: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(nonempty,definition,
% 0.19/0.47 ( nonempty
% 0.19/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyE1_type,type,
% 0.19/0.47 nonemptyE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyE1,definition,
% 0.19/0.47 ( nonemptyE1
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ( nonempty @ A )
% 0.19/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyI_type,type,
% 0.19/0.47 nonemptyI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyI,definition,
% 0.19/0.47 ( nonemptyI
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( nonempty
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyI1_type,type,
% 0.19/0.47 nonemptyI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyI1,definition,
% 0.19/0.47 ( nonemptyI1
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIL_type,type,
% 0.19/0.47 setadjoinIL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIL,definition,
% 0.19/0.47 ( setadjoinIL
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyinunitempty_type,type,
% 0.19/0.47 emptyinunitempty: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyinunitempty,definition,
% 0.19/0.47 ( emptyinunitempty
% 0.19/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIR_type,type,
% 0.19/0.47 setadjoinIR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinIR,definition,
% 0.19/0.47 ( setadjoinIR
% 0.19/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinE_type,type,
% 0.19/0.47 setadjoinE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinE,definition,
% 0.19/0.47 ( setadjoinE
% 0.19/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.47 => ! [Xphi: $o] :
% 0.19/0.47 ( ( ( Xy = Xx )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => ( ( ( in @ Xy @ A )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinOr_type,type,
% 0.19/0.47 setadjoinOr: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinOr,definition,
% 0.19/0.47 ( setadjoinOr
% 0.19/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.47 => ( ( Xy = Xx )
% 0.19/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setoftrueEq_type,type,
% 0.19/0.47 setoftrueEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setoftrueEq,definition,
% 0.19/0.47 ( setoftrueEq
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : $true )
% 0.19/0.47 = A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetI_type,type,
% 0.19/0.47 powersetI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetI,definition,
% 0.19/0.47 ( powersetI
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ A ) )
% 0.19/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyinPowerset_type,type,
% 0.19/0.47 emptyinPowerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyinPowerset,definition,
% 0.19/0.47 ( emptyinPowerset
% 0.19/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyInPowerset_type,type,
% 0.19/0.47 emptyInPowerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyInPowerset,definition,
% 0.19/0.47 ( emptyInPowerset
% 0.19/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetE_type,type,
% 0.19/0.47 powersetE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetE,definition,
% 0.19/0.47 ( powersetE
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionI_type,type,
% 0.19/0.47 setunionI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionI,definition,
% 0.19/0.47 ( setunionI
% 0.19/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( ( in @ B @ A )
% 0.19/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionE_type,type,
% 0.19/0.47 setunionE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionE,definition,
% 0.19/0.47 ( setunionE
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.47 => ! [Xphi: $o] :
% 0.19/0.47 ( ! [B: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( ( in @ B @ A )
% 0.19/0.47 => Xphi ) )
% 0.19/0.47 => Xphi ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subPowSU_type,type,
% 0.19/0.47 subPowSU: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subPowSU,definition,
% 0.19/0.47 ( subPowSU
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuE2_type,type,
% 0.19/0.47 exuE2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuE2,definition,
% 0.19/0.47 ( exuE2
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyImpWitness_type,type,
% 0.19/0.47 nonemptyImpWitness: $o ).
% 0.19/0.47
% 0.19/0.47 thf(nonemptyImpWitness,definition,
% 0.19/0.47 ( nonemptyImpWitness
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ( nonempty @ A )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & $true ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(uniqinunit_type,type,
% 0.19/0.47 uniqinunit: $o ).
% 0.19/0.47
% 0.19/0.47 thf(uniqinunit,definition,
% 0.19/0.47 ( uniqinunit
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notinsingleton_type,type,
% 0.19/0.47 notinsingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notinsingleton,definition,
% 0.19/0.47 ( notinsingleton
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx != Xy )
% 0.19/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eqinunit_type,type,
% 0.19/0.47 eqinunit: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eqinunit,definition,
% 0.19/0.47 ( eqinunit
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsswitch_type,type,
% 0.19/0.47 singletonsswitch: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsswitch,definition,
% 0.19/0.47 ( singletonsswitch
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetE_type,type,
% 0.19/0.47 upairsetE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetE,definition,
% 0.19/0.47 ( upairsetE
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.47 => ( ( Xz = Xx )
% 0.19/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetIL_type,type,
% 0.19/0.47 upairsetIL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetIL,definition,
% 0.19/0.47 ( upairsetIL
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetIR_type,type,
% 0.19/0.47 upairsetIR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetIR,definition,
% 0.19/0.47 ( upairsetIR
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyE1_type,type,
% 0.19/0.47 emptyE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyE1,definition,
% 0.19/0.47 ( emptyE1
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) )
% 0.19/0.47 => ( ( ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 = emptyset )
% 0.19/0.47 => $false ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(vacuousDall_type,type,
% 0.19/0.47 vacuousDall: $o ).
% 0.19/0.47
% 0.19/0.47 thf(vacuousDall,definition,
% 0.19/0.47 ( vacuousDall
% 0.19/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ emptyset )
% 0.19/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan1_type,type,
% 0.19/0.47 quantDeMorgan1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan1,definition,
% 0.19/0.47 ( quantDeMorgan1
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ~ ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan2_type,type,
% 0.19/0.47 quantDeMorgan2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan2,definition,
% 0.19/0.47 ( quantDeMorgan2
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ~ ( Xphi @ Xx ) )
% 0.19/0.47 => ~ ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan3_type,type,
% 0.19/0.47 quantDeMorgan3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan3,definition,
% 0.19/0.47 ( quantDeMorgan3
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ~ ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan4_type,type,
% 0.19/0.47 quantDeMorgan4: $o ).
% 0.19/0.47
% 0.19/0.47 thf(quantDeMorgan4,definition,
% 0.19/0.47 ( quantDeMorgan4
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ~ ( Xphi @ Xx ) )
% 0.19/0.47 => ~ ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(prop2setI_type,type,
% 0.19/0.47 prop2setI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(prop2setI,definition,
% 0.19/0.47 ( prop2setI
% 0.19/0.47 = ( ! [Xphi: $o] :
% 0.19/0.47 ( Xphi
% 0.19/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(set2prop_type,type,
% 0.19/0.47 set2prop: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(prop2set2propI_type,type,
% 0.19/0.47 prop2set2propI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(prop2set2propI,definition,
% 0.19/0.47 ( prop2set2propI
% 0.19/0.47 = ( ! [Xphi: $o] :
% 0.19/0.47 ( Xphi
% 0.19/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notdexE_type,type,
% 0.19/0.47 notdexE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notdexE,definition,
% 0.19/0.47 ( notdexE
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ~ ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notdallE_type,type,
% 0.19/0.47 notdallE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notdallE,definition,
% 0.19/0.47 ( notdallE
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ~ ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuI1_type,type,
% 0.19/0.47 exuI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuI1,definition,
% 0.19/0.47 ( exuI1
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ? [Xx: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 & ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) )
% 0.19/0.47 => ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuI3_type,type,
% 0.19/0.47 exuI3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuI3,definition,
% 0.19/0.47 ( exuI3
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.19/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) )
% 0.19/0.47 => ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuI2_type,type,
% 0.19/0.47 exuI2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuI2,definition,
% 0.19/0.47 ( exuI2
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ? [Xx: $i] :
% 0.19/0.47 ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 <=> ( Xy = Xx ) )
% 0.19/0.47 => ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(inCongP_type,type,
% 0.19/0.47 inCongP: $o ).
% 0.19/0.47
% 0.19/0.47 thf(inCongP,definition,
% 0.19/0.47 ( inCongP
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(in__Cong_type,type,
% 0.19/0.47 in__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(in__Cong,definition,
% 0.19/0.47 ( in__Cong
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuE3u_type,type,
% 0.19/0.47 exuE3u: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuE3u,definition,
% 0.19/0.47 ( exuE3u
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exu__Cong_type,type,
% 0.19/0.47 exu__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exu__Cong,definition,
% 0.19/0.47 ( exu__Cong
% 0.19/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.47 => ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 <=> ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptyset__Cong_type,type,
% 0.19/0.47 emptyset__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptyset__Cong,definition,
% 0.19/0.47 ( emptyset__Cong
% 0.19/0.47 = ( emptyset = emptyset ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin__Cong_type,type,
% 0.19/0.47 setadjoin__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoin__Cong,definition,
% 0.19/0.47 ( setadjoin__Cong
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ! [Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( Xz = Xu )
% 0.19/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.19/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powerset__Cong_type,type,
% 0.19/0.47 powerset__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powerset__Cong,definition,
% 0.19/0.47 ( powerset__Cong
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ( ( powerset @ A )
% 0.19/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunion__Cong_type,type,
% 0.19/0.47 setunion__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunion__Cong,definition,
% 0.19/0.47 ( setunion__Cong
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ( ( setunion @ A )
% 0.19/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(omega__Cong_type,type,
% 0.19/0.47 omega__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(omega__Cong,definition,
% 0.19/0.47 ( omega__Cong
% 0.19/0.47 = ( omega = omega ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuEu_type,type,
% 0.19/0.47 exuEu: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuEu,definition,
% 0.19/0.47 ( exuEu
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(descr__Cong_type,type,
% 0.19/0.47 descr__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(descr__Cong,definition,
% 0.19/0.47 ( descr__Cong
% 0.19/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.47 => ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.47 => ( ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 = ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstr__Cong_type,type,
% 0.19/0.47 dsetconstr__Cong: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dsetconstr__Cong,definition,
% 0.19/0.47 ( dsetconstr__Cong
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( Xx = Xy )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.19/0.47 => ( ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 = ( dsetconstr @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subset_type,type,
% 0.19/0.47 subset: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(disjoint_type,type,
% 0.19/0.47 disjoint: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(setsmeet_type,type,
% 0.19/0.47 setsmeet: $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI1_type,type,
% 0.19/0.47 subsetI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI1,definition,
% 0.19/0.47 ( subsetI1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eqimpsubset2_type,type,
% 0.19/0.47 eqimpsubset2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eqimpsubset2,definition,
% 0.19/0.47 ( eqimpsubset2
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eqimpsubset1_type,type,
% 0.19/0.47 eqimpsubset1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eqimpsubset1,definition,
% 0.19/0.47 ( eqimpsubset1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( A = B )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI2_type,type,
% 0.19/0.47 subsetI2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetI2,definition,
% 0.19/0.47 ( subsetI2
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetsubset_type,type,
% 0.19/0.47 emptysetsubset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(emptysetsubset,definition,
% 0.19/0.47 ( emptysetsubset
% 0.19/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetE_type,type,
% 0.19/0.47 subsetE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetE,definition,
% 0.19/0.47 ( subsetE
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetE2_type,type,
% 0.19/0.47 subsetE2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetE2,definition,
% 0.19/0.47 ( subsetE2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notsubsetI_type,type,
% 0.19/0.47 notsubsetI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notsubsetI,definition,
% 0.19/0.47 ( notsubsetI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notequalI1_type,type,
% 0.19/0.47 notequalI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notequalI1,definition,
% 0.19/0.47 ( notequalI1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ~ ( subset @ A @ B )
% 0.19/0.47 => ( A != B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(notequalI2_type,type,
% 0.19/0.47 notequalI2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(notequalI2,definition,
% 0.19/0.47 ( notequalI2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ( A != B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetRefl_type,type,
% 0.19/0.47 subsetRefl: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetRefl,definition,
% 0.19/0.47 ( subsetRefl
% 0.19/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTrans_type,type,
% 0.19/0.47 subsetTrans: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTrans,definition,
% 0.19/0.47 ( subsetTrans
% 0.19/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ( subset @ B @ C )
% 0.19/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinSub_type,type,
% 0.19/0.47 setadjoinSub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinSub,definition,
% 0.19/0.47 ( setadjoinSub
% 0.19/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinSub2_type,type,
% 0.19/0.47 setadjoinSub2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setadjoinSub2,definition,
% 0.19/0.47 ( setadjoinSub2
% 0.19/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subset2powerset_type,type,
% 0.19/0.47 subset2powerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subset2powerset,definition,
% 0.19/0.47 ( subset2powerset
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setextsub_type,type,
% 0.19/0.47 setextsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setextsub,definition,
% 0.19/0.47 ( setextsub
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ( subset @ B @ A )
% 0.19/0.47 => ( A = B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetemptysetimpeq_type,type,
% 0.19/0.47 subsetemptysetimpeq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetemptysetimpeq,definition,
% 0.19/0.47 ( subsetemptysetimpeq
% 0.19/0.47 = ( ! [A: $i] :
% 0.19/0.47 ( ( subset @ A @ emptyset )
% 0.19/0.47 => ( A = emptyset ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetI1_type,type,
% 0.19/0.47 powersetI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetI1,definition,
% 0.19/0.47 ( powersetI1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ B @ A )
% 0.19/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetE1_type,type,
% 0.19/0.47 powersetE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetE1,definition,
% 0.19/0.47 ( powersetE1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(inPowerset_type,type,
% 0.19/0.47 inPowerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(inPowerset,definition,
% 0.19/0.47 ( inPowerset
% 0.19/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetsubset_type,type,
% 0.19/0.47 powersetsubset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetsubset,definition,
% 0.19/0.47 ( powersetsubset
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sepInPowerset_type,type,
% 0.19/0.47 sepInPowerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(sepInPowerset,definition,
% 0.19/0.47 ( sepInPowerset
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( in
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(sepSubset_type,type,
% 0.19/0.47 sepSubset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(sepSubset,definition,
% 0.19/0.47 ( sepSubset
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( subset
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunion_type,type,
% 0.19/0.47 binunion: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binunionIL_type,type,
% 0.19/0.47 binunionIL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionIL,definition,
% 0.19/0.47 ( binunionIL
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2IR_type,type,
% 0.19/0.47 upairset2IR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2IR,definition,
% 0.19/0.47 ( upairset2IR
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionIR_type,type,
% 0.19/0.47 binunionIR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionIR,definition,
% 0.19/0.47 ( binunionIR
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionEcases_type,type,
% 0.19/0.47 binunionEcases: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionEcases,definition,
% 0.19/0.47 ( binunionEcases
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.47 => ( ( ( in @ Xx @ A )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => ( ( ( in @ Xx @ B )
% 0.19/0.47 => Xphi )
% 0.19/0.47 => Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionE_type,type,
% 0.19/0.47 binunionE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionE,definition,
% 0.19/0.47 ( binunionE
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionLsub_type,type,
% 0.19/0.47 binunionLsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionLsub,definition,
% 0.19/0.47 ( binunionLsub
% 0.19/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionRsub_type,type,
% 0.19/0.47 binunionRsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionRsub,definition,
% 0.19/0.47 ( binunionRsub
% 0.19/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersect_type,type,
% 0.19/0.47 binintersect: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectI_type,type,
% 0.19/0.47 binintersectI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectI,definition,
% 0.19/0.47 ( binintersectI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset5_type,type,
% 0.19/0.47 binintersectSubset5: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset5,definition,
% 0.19/0.47 ( binintersectSubset5
% 0.19/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.47 ( ( subset @ C @ A )
% 0.19/0.47 => ( ( subset @ C @ B )
% 0.19/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectEL_type,type,
% 0.19/0.47 binintersectEL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectEL,definition,
% 0.19/0.47 ( binintersectEL
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectLsub_type,type,
% 0.19/0.47 binintersectLsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectLsub,definition,
% 0.19/0.47 ( binintersectLsub
% 0.19/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset2_type,type,
% 0.19/0.47 binintersectSubset2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset2,definition,
% 0.19/0.47 ( binintersectSubset2
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ( binintersect @ A @ B )
% 0.19/0.47 = A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset3_type,type,
% 0.19/0.47 binintersectSubset3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset3,definition,
% 0.19/0.47 ( binintersectSubset3
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( ( binintersect @ A @ B )
% 0.19/0.47 = B )
% 0.19/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectER_type,type,
% 0.19/0.47 binintersectER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectER,definition,
% 0.19/0.47 ( binintersectER
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(disjointsetsI1_type,type,
% 0.19/0.47 disjointsetsI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(disjointsetsI1,definition,
% 0.19/0.47 ( disjointsetsI1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ~ ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( in @ Xx @ B ) )
% 0.19/0.47 => ( ( binintersect @ A @ B )
% 0.19/0.47 = emptyset ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectRsub_type,type,
% 0.19/0.47 binintersectRsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectRsub,definition,
% 0.19/0.47 ( binintersectRsub
% 0.19/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset4_type,type,
% 0.19/0.47 binintersectSubset4: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset4,definition,
% 0.19/0.47 ( binintersectSubset4
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ B @ A )
% 0.19/0.47 => ( ( binintersect @ A @ B )
% 0.19/0.47 = B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset1_type,type,
% 0.19/0.47 binintersectSubset1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectSubset1,definition,
% 0.19/0.47 ( binintersectSubset1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( ( binintersect @ A @ B )
% 0.19/0.47 = A )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(bs114d_type,type,
% 0.19/0.47 bs114d: $o ).
% 0.19/0.47
% 0.19/0.47 thf(bs114d,definition,
% 0.19/0.47 ( bs114d
% 0.19/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.19/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(regular_type,type,
% 0.19/0.47 regular: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminus_type,type,
% 0.19/0.47 setminus: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(setminusI_type,type,
% 0.19/0.47 setminusI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusI,definition,
% 0.19/0.47 ( setminusI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusEL_type,type,
% 0.19/0.47 setminusEL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusEL,definition,
% 0.19/0.47 ( setminusEL
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusER_type,type,
% 0.19/0.47 setminusER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusER,definition,
% 0.19/0.47 ( setminusER
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusSubset2_type,type,
% 0.19/0.47 setminusSubset2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusSubset2,definition,
% 0.19/0.47 ( setminusSubset2
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( subset @ A @ B )
% 0.19/0.47 => ( ( setminus @ A @ B )
% 0.19/0.47 = emptyset ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusERneg_type,type,
% 0.19/0.47 setminusERneg: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusERneg,definition,
% 0.19/0.47 ( setminusERneg
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.47 => ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusELneg_type,type,
% 0.19/0.47 setminusELneg: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusELneg,definition,
% 0.19/0.47 ( setminusELneg
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusILneg_type,type,
% 0.19/0.47 setminusILneg: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusILneg,definition,
% 0.19/0.47 ( setminusILneg
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ~ ( in @ Xx @ A )
% 0.19/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusIRneg_type,type,
% 0.19/0.47 setminusIRneg: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusIRneg,definition,
% 0.19/0.47 ( setminusIRneg
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ B )
% 0.19/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusLsub_type,type,
% 0.19/0.47 setminusLsub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusLsub,definition,
% 0.19/0.47 ( setminusLsub
% 0.19/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusSubset1_type,type,
% 0.19/0.47 setminusSubset1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusSubset1,definition,
% 0.19/0.47 ( setminusSubset1
% 0.19/0.47 = ( ! [A: $i,B: $i] :
% 0.19/0.47 ( ( ( setminus @ A @ B )
% 0.19/0.47 = emptyset )
% 0.19/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(symdiff_type,type,
% 0.19/0.47 symdiff: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffE_type,type,
% 0.19/0.47 symdiffE: $o ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffE,definition,
% 0.19/0.47 ( symdiffE
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.19/0.47 => ! [Xphi: $o] :
% 0.19/0.47 ( ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => Xphi ) )
% 0.19/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => Xphi ) )
% 0.19/0.47 => Xphi ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffI1_type,type,
% 0.19/0.47 symdiffI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffI1,definition,
% 0.19/0.47 ( symdiffI1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffI2_type,type,
% 0.19/0.47 symdiffI2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffI2,definition,
% 0.19/0.47 ( symdiffI2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ~ ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffIneg1_type,type,
% 0.19/0.47 symdiffIneg1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffIneg1,definition,
% 0.19/0.47 ( symdiffIneg1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ B )
% 0.19/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffIneg2_type,type,
% 0.19/0.47 symdiffIneg2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(symdiffIneg2,definition,
% 0.19/0.47 ( symdiffIneg2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ~ ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ B )
% 0.19/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iskpair_type,type,
% 0.19/0.47 iskpair: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(secondinupair_type,type,
% 0.19/0.47 secondinupair: $o ).
% 0.19/0.47
% 0.19/0.47 thf(secondinupair,definition,
% 0.19/0.47 ( secondinupair
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairIL_type,type,
% 0.19/0.47 setukpairIL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairIL,definition,
% 0.19/0.47 ( setukpairIL
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairIR_type,type,
% 0.19/0.47 setukpairIR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairIR,definition,
% 0.19/0.47 ( setukpairIR
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(kpairiskpair_type,type,
% 0.19/0.47 kpairiskpair: $o ).
% 0.19/0.47
% 0.19/0.47 thf(kpairiskpair,definition,
% 0.19/0.47 ( kpairiskpair
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(kpair_type,type,
% 0.19/0.47 kpair: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(kpairp_type,type,
% 0.19/0.47 kpairp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(kpairp,definition,
% 0.19/0.47 ( kpairp
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprod_type,type,
% 0.19/0.47 cartprod: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsubset_type,type,
% 0.19/0.47 singletonsubset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsubset,definition,
% 0.19/0.47 ( singletonsubset
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singletoninpowerset_type,type,
% 0.19/0.47 singletoninpowerset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletoninpowerset,definition,
% 0.19/0.47 ( singletoninpowerset
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singletoninpowunion_type,type,
% 0.19/0.47 singletoninpowunion: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletoninpowunion,definition,
% 0.19/0.47 ( singletoninpowunion
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2E_type,type,
% 0.19/0.47 upairset2E: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairset2E,definition,
% 0.19/0.47 ( upairset2E
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.47 => ( ( Xz = Xx )
% 0.19/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairsubunion_type,type,
% 0.19/0.47 upairsubunion: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairsubunion,definition,
% 0.19/0.47 ( upairsubunion
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairinpowunion_type,type,
% 0.19/0.47 upairinpowunion: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairinpowunion,definition,
% 0.19/0.47 ( upairinpowunion
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem1_type,type,
% 0.19/0.47 ubforcartprodlem1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem1,definition,
% 0.19/0.47 ( ubforcartprodlem1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem2_type,type,
% 0.19/0.47 ubforcartprodlem2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem2,definition,
% 0.19/0.47 ( ubforcartprodlem2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem3_type,type,
% 0.19/0.47 ubforcartprodlem3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ubforcartprodlem3,definition,
% 0.19/0.47 ( ubforcartprodlem3
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairin_type,type,
% 0.19/0.47 cartprodpairin: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairin,definition,
% 0.19/0.47 ( cartprodpairin
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempair1_type,type,
% 0.19/0.47 cartprodmempair1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempair1,definition,
% 0.19/0.47 ( cartprodmempair1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ? [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 & ( Xu
% 0.19/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempair_type,type,
% 0.19/0.47 cartprodmempair: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempair,definition,
% 0.19/0.47 ( cartprodmempair
% 0.19/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionE2_type,type,
% 0.19/0.47 setunionE2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionE2,definition,
% 0.19/0.47 ( setunionE2
% 0.19/0.47 = ( ! [A: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.47 => ? [X: $i] :
% 0.19/0.47 ( ( in @ X @ A )
% 0.19/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton1_type,type,
% 0.19/0.47 setunionsingleton1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton1,definition,
% 0.19/0.47 ( setunionsingleton1
% 0.19/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton2_type,type,
% 0.19/0.47 setunionsingleton2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton2,definition,
% 0.19/0.47 ( setunionsingleton2
% 0.19/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton_type,type,
% 0.19/0.47 setunionsingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setunionsingleton,definition,
% 0.19/0.47 ( setunionsingleton
% 0.19/0.47 = ( ! [Xx: $i] :
% 0.19/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.19/0.47 = Xx ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singleton_type,type,
% 0.19/0.47 singleton: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletonprop_type,type,
% 0.19/0.47 singletonprop: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletonprop,definition,
% 0.19/0.47 ( singletonprop
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) )
% 0.19/0.47 => ( ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) )
% 0.19/0.47 => ( singleton
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ex1_type,type,
% 0.19/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(ex1E1_type,type,
% 0.19/0.47 ex1E1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ex1E1,definition,
% 0.19/0.47 ( ex1E1
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ( ex1 @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ex1I_type,type,
% 0.19/0.47 ex1I: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ex1I,definition,
% 0.19/0.47 ( ex1I
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xy = Xx ) ) )
% 0.19/0.47 => ( ex1 @ A
% 0.19/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ex1I2_type,type,
% 0.19/0.47 ex1I2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ex1I2,definition,
% 0.19/0.47 ( ex1I2
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) )
% 0.19/0.47 => ( ? [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 & ( Xphi @ Xx ) )
% 0.19/0.47 => ( ex1 @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsuniq_type,type,
% 0.19/0.47 singletonsuniq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(singletonsuniq,definition,
% 0.19/0.47 ( singletonsuniq
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.19/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(atmost1p_type,type,
% 0.19/0.47 atmost1p: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(atleast2p_type,type,
% 0.19/0.47 atleast2p: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(atmost2p_type,type,
% 0.19/0.47 atmost2p: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairsetp_type,type,
% 0.19/0.47 upairsetp: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL1_type,type,
% 0.19/0.47 setukpairinjL1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL1,definition,
% 0.19/0.47 ( setukpairinjL1
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(kfstsingleton_type,type,
% 0.19/0.47 kfstsingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(kfstsingleton,definition,
% 0.19/0.47 ( kfstsingleton
% 0.19/0.47 = ( ! [Xu: $i] :
% 0.19/0.47 ( ( iskpair @ Xu )
% 0.19/0.47 => ( singleton
% 0.19/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.19/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(theprop_type,type,
% 0.19/0.47 theprop: $o ).
% 0.19/0.47
% 0.19/0.47 thf(theprop,definition,
% 0.19/0.47 ( theprop
% 0.19/0.47 = ( ! [X: $i] :
% 0.19/0.47 ( ( singleton @ X )
% 0.19/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(kfst_type,type,
% 0.19/0.47 kfst: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(kfstpairEq_type,type,
% 0.19/0.47 kfstpairEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(kfstpairEq,definition,
% 0.19/0.47 ( kfstpairEq
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.19/0.47 = Xx ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodfstin_type,type,
% 0.19/0.47 cartprodfstin: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodfstin,definition,
% 0.19/0.47 ( cartprodfstin
% 0.19/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL2_type,type,
% 0.19/0.47 setukpairinjL2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL2,definition,
% 0.19/0.47 ( setukpairinjL2
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL_type,type,
% 0.19/0.47 setukpairinjL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjL,definition,
% 0.19/0.47 ( setukpairinjL
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.19/0.47 = ( kpair @ Xz @ Xu ) )
% 0.19/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR11_type,type,
% 0.19/0.47 setukpairinjR11: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR11,definition,
% 0.19/0.47 ( setukpairinjR11
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR12_type,type,
% 0.19/0.47 setukpairinjR12: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR12,definition,
% 0.19/0.47 ( setukpairinjR12
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR1_type,type,
% 0.19/0.47 setukpairinjR1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR1,definition,
% 0.19/0.47 ( setukpairinjR1
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.47 => ( ( Xz = Xu )
% 0.19/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(upairequniteq_type,type,
% 0.19/0.47 upairequniteq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(upairequniteq,definition,
% 0.19/0.47 ( upairequniteq
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR2_type,type,
% 0.19/0.47 setukpairinjR2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR2,definition,
% 0.19/0.47 ( setukpairinjR2
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR_type,type,
% 0.19/0.47 setukpairinjR: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setukpairinjR,definition,
% 0.19/0.47 ( setukpairinjR
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.19/0.47 = ( kpair @ Xz @ Xu ) )
% 0.19/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ksndsingleton_type,type,
% 0.19/0.47 ksndsingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ksndsingleton,definition,
% 0.19/0.47 ( ksndsingleton
% 0.19/0.47 = ( ! [Xu: $i] :
% 0.19/0.47 ( ( iskpair @ Xu )
% 0.19/0.47 => ( singleton
% 0.19/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.19/0.47 @ ^ [Xx: $i] :
% 0.19/0.47 ( Xu
% 0.19/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ksnd_type,type,
% 0.19/0.47 ksnd: $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(ksndpairEq_type,type,
% 0.19/0.47 ksndpairEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ksndpairEq,definition,
% 0.19/0.47 ( ksndpairEq
% 0.19/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.19/0.47 = Xy ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(kpairsurjEq_type,type,
% 0.19/0.47 kpairsurjEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(kpairsurjEq,definition,
% 0.19/0.47 ( kpairsurjEq
% 0.19/0.47 = ( ! [Xu: $i] :
% 0.19/0.47 ( ( iskpair @ Xu )
% 0.19/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.19/0.47 = Xu ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodsndin_type,type,
% 0.19/0.47 cartprodsndin: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodsndin,definition,
% 0.19/0.47 ( cartprodsndin
% 0.19/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairmemEL_type,type,
% 0.19/0.47 cartprodpairmemEL: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairmemEL,definition,
% 0.19/0.47 ( cartprodpairmemEL
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairmemER_type,type,
% 0.19/0.47 cartprodpairmemER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairmemER,definition,
% 0.19/0.47 ( cartprodpairmemER
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempaircEq_type,type,
% 0.19/0.47 cartprodmempaircEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodmempaircEq,definition,
% 0.19/0.47 ( cartprodmempaircEq
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( kpair @ Xx @ Xy )
% 0.19/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodfstpairEq_type,type,
% 0.19/0.47 cartprodfstpairEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodfstpairEq,definition,
% 0.19/0.47 ( cartprodfstpairEq
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.19/0.47 = Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodsndpairEq_type,type,
% 0.19/0.47 cartprodsndpairEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodsndpairEq,definition,
% 0.19/0.47 ( cartprodsndpairEq
% 0.19/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.19/0.47 = Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairsurjEq_type,type,
% 0.19/0.47 cartprodpairsurjEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(cartprodpairsurjEq,definition,
% 0.19/0.47 ( cartprodpairsurjEq
% 0.19/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.19/0.47 = Xu ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(breln_type,type,
% 0.19/0.47 breln: $i > $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstr_type,type,
% 0.19/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrI_type,type,
% 0.19/0.47 dpsetconstrI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrI,definition,
% 0.19/0.47 ( dpsetconstrI
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrSub_type,type,
% 0.19/0.47 dpsetconstrSub: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrSub,definition,
% 0.19/0.47 ( dpsetconstrSub
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.19/0.47 ( subset
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.19/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setOfPairsIsBReln_type,type,
% 0.19/0.47 setOfPairsIsBReln: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setOfPairsIsBReln,definition,
% 0.19/0.47 ( setOfPairsIsBReln
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.19/0.47 ( breln @ A @ B
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrERa_type,type,
% 0.19/0.47 dpsetconstrERa: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrERa,definition,
% 0.19/0.47 ( dpsetconstrERa
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrEL1_type,type,
% 0.19/0.47 dpsetconstrEL1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrEL1,definition,
% 0.19/0.47 ( dpsetconstrEL1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrEL2_type,type,
% 0.19/0.47 dpsetconstrEL2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrEL2,definition,
% 0.19/0.47 ( dpsetconstrEL2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrER_type,type,
% 0.19/0.47 dpsetconstrER: $o ).
% 0.19/0.47
% 0.19/0.47 thf(dpsetconstrER,definition,
% 0.19/0.47 ( dpsetconstrER
% 0.19/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(func_type,type,
% 0.19/0.47 func: $i > $i > $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcSet_type,type,
% 0.19/0.47 funcSet: $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(funcImageSingleton_type,type,
% 0.19/0.47 funcImageSingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcImageSingleton,definition,
% 0.19/0.47 ( funcImageSingleton
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( singleton
% 0.19/0.47 @ ( dsetconstr @ B
% 0.19/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(apProp_type,type,
% 0.19/0.47 apProp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(apProp,definition,
% 0.19/0.47 ( apProp
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in
% 0.19/0.47 @ ( setunion
% 0.19/0.47 @ ( dsetconstr @ B
% 0.19/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.19/0.47 @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ap_type,type,
% 0.19/0.47 ap: $i > $i > $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(app_type,type,
% 0.19/0.47 app: $o ).
% 0.19/0.47
% 0.19/0.47 thf(app,definition,
% 0.19/0.47 ( app
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(infuncsetfunc_type,type,
% 0.19/0.47 infuncsetfunc: $o ).
% 0.19/0.47
% 0.19/0.47 thf(infuncsetfunc,definition,
% 0.19/0.47 ( infuncsetfunc
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ap2p_type,type,
% 0.19/0.47 ap2p: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ap2p,definition,
% 0.19/0.47 ( ap2p
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcinfuncset_type,type,
% 0.19/0.47 funcinfuncset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcinfuncset,definition,
% 0.19/0.47 ( funcinfuncset
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(lamProp_type,type,
% 0.19/0.47 lamProp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lamProp,definition,
% 0.19/0.47 ( lamProp
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ( func @ A @ B
% 0.19/0.47 @ ( dpsetconstr @ A @ B
% 0.19/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xf @ Xx )
% 0.19/0.47 = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(lam_type,type,
% 0.19/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.19/0.47
% 0.19/0.47 thf(lamp_type,type,
% 0.19/0.47 lamp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lamp,definition,
% 0.19/0.47 ( lamp
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ( func @ A @ B
% 0.19/0.47 @ ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(lam2p_type,type,
% 0.19/0.47 lam2p: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lam2p,definition,
% 0.19/0.47 ( lam2p
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ( in
% 0.19/0.47 @ ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.19/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(brelnall1_type,type,
% 0.19/0.47 brelnall1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(brelnall1,definition,
% 0.19/0.47 ( brelnall1
% 0.19/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ R )
% 0.19/0.47 => ! [Xphi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ R )
% 0.19/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(brelnall2_type,type,
% 0.19/0.47 brelnall2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(brelnall2,definition,
% 0.19/0.47 ( brelnall2
% 0.19/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ R )
% 0.19/0.47 => ! [Xphi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ R )
% 0.19/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ex1E2_type,type,
% 0.19/0.47 ex1E2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ex1E2,definition,
% 0.19/0.47 ( ex1E2
% 0.19/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.47 ( ( ex1 @ A
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp1_type,type,
% 0.19/0.47 funcGraphProp1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp1,definition,
% 0.19/0.47 ( funcGraphProp1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp3_type,type,
% 0.19/0.47 funcGraphProp3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp3,definition,
% 0.19/0.47 ( funcGraphProp3
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp2_type,type,
% 0.19/0.47 funcGraphProp2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp2,definition,
% 0.19/0.47 ( funcGraphProp2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcextLem_type,type,
% 0.19/0.47 funcextLem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcextLem,definition,
% 0.19/0.47 ( funcextLem
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xg: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xg )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp4_type,type,
% 0.19/0.47 funcGraphProp4: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcGraphProp4,definition,
% 0.19/0.47 ( funcGraphProp4
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subbreln_type,type,
% 0.19/0.47 subbreln: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subbreln,definition,
% 0.19/0.47 ( subbreln
% 0.19/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ R )
% 0.19/0.47 => ! [S: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ S )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.19/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eqbreln_type,type,
% 0.19/0.47 eqbreln: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eqbreln,definition,
% 0.19/0.47 ( eqbreln
% 0.19/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ R )
% 0.19/0.47 => ! [S: $i] :
% 0.19/0.47 ( ( breln @ A @ B @ S )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ B )
% 0.19/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.19/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.19/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcext_type,type,
% 0.19/0.47 funcext: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcext,definition,
% 0.19/0.47 ( funcext
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xg: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xg )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(funcext2_type,type,
% 0.19/0.47 funcext2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(funcext2,definition,
% 0.19/0.47 ( funcext2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ! [Xg: $i] :
% 0.19/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ap2apEq1_type,type,
% 0.19/0.47 ap2apEq1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ap2apEq1,definition,
% 0.19/0.47 ( ap2apEq1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ap2apEq2_type,type,
% 0.19/0.47 ap2apEq2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ap2apEq2,definition,
% 0.19/0.47 ( ap2apEq2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(beta1_type,type,
% 0.19/0.47 beta1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(beta1,definition,
% 0.19/0.47 ( beta1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B
% 0.19/0.47 @ ( lam @ A @ B
% 0.19/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.19/0.47 @ Xx )
% 0.19/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eta1_type,type,
% 0.19/0.47 eta1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eta1,definition,
% 0.19/0.47 ( eta1
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( func @ A @ B @ Xf )
% 0.19/0.47 => ( ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.19/0.47 = Xf ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(lam2lamEq_type,type,
% 0.19/0.47 lam2lamEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(lam2lamEq,definition,
% 0.19/0.47 ( lam2lamEq
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ( ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.19/0.47 = ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(beta2_type,type,
% 0.19/0.47 beta2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(beta2,definition,
% 0.19/0.47 ( beta2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.47 ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( ap @ A @ B
% 0.19/0.47 @ ( lam @ A @ B
% 0.19/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.19/0.47 @ Xx )
% 0.19/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(eta2_type,type,
% 0.19/0.47 eta2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(eta2,definition,
% 0.19/0.47 ( eta2
% 0.19/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.47 => ( ( lam @ A @ B
% 0.19/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.19/0.47 = Xf ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iffalseProp1_type,type,
% 0.19/0.47 iffalseProp1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iffalseProp1,definition,
% 0.19/0.47 ( iffalseProp1
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ~ Xphi
% 0.19/0.47 => ( in @ Xy
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xz: $i] :
% 0.19/0.47 ( ( Xphi
% 0.19/0.47 & ( Xz = Xx ) )
% 0.19/0.47 | ( ~ Xphi
% 0.19/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iffalseProp2_type,type,
% 0.19/0.47 iffalseProp2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iffalseProp2,definition,
% 0.19/0.47 ( iffalseProp2
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ~ Xphi
% 0.19/0.47 => ( ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xz: $i] :
% 0.19/0.47 ( ( Xphi
% 0.19/0.47 & ( Xz = Xx ) )
% 0.19/0.47 | ( ~ Xphi
% 0.19/0.47 & ( Xz = Xy ) ) ) )
% 0.19/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueProp1_type,type,
% 0.19/0.47 iftrueProp1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueProp1,definition,
% 0.19/0.47 ( iftrueProp1
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( Xphi
% 0.19/0.47 => ( in @ Xx
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xz: $i] :
% 0.19/0.47 ( ( Xphi
% 0.19/0.47 & ( Xz = Xx ) )
% 0.19/0.47 | ( ~ Xphi
% 0.19/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueProp2_type,type,
% 0.19/0.47 iftrueProp2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueProp2,definition,
% 0.19/0.47 ( iftrueProp2
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( Xphi
% 0.19/0.47 => ( ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xz: $i] :
% 0.19/0.47 ( ( Xphi
% 0.19/0.47 & ( Xz = Xx ) )
% 0.19/0.47 | ( ~ Xphi
% 0.19/0.47 & ( Xz = Xy ) ) ) )
% 0.19/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(ifSingleton_type,type,
% 0.19/0.47 ifSingleton: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ifSingleton,definition,
% 0.19/0.47 ( ifSingleton
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( singleton
% 0.19/0.47 @ ( dsetconstr @ A
% 0.19/0.47 @ ^ [Xz: $i] :
% 0.19/0.47 ( ( Xphi
% 0.19/0.47 & ( Xz = Xx ) )
% 0.19/0.47 | ( ~ Xphi
% 0.19/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(if_type,type,
% 0.19/0.47 if: $i > $o > $i > $i > $i ).
% 0.19/0.47
% 0.19/0.47 thf(ifp_type,type,
% 0.19/0.47 ifp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(ifp,definition,
% 0.19/0.47 ( ifp
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(theeq_type,type,
% 0.19/0.47 theeq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(theeq,definition,
% 0.19/0.47 ( theeq
% 0.19/0.47 = ( ! [X: $i] :
% 0.19/0.47 ( ( singleton @ X )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ X )
% 0.19/0.47 => ( ( setunion @ X )
% 0.19/0.47 = Xx ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iftrue_type,type,
% 0.19/0.47 iftrue: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iftrue,definition,
% 0.19/0.47 ( iftrue
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( Xphi
% 0.19/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.19/0.47 = Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iffalse_type,type,
% 0.19/0.47 iffalse: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iffalse,definition,
% 0.19/0.47 ( iffalse
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( ~ Xphi
% 0.19/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.19/0.47 = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueorfalse_type,type,
% 0.19/0.47 iftrueorfalse: $o ).
% 0.19/0.47
% 0.19/0.47 thf(iftrueorfalse,definition,
% 0.19/0.47 ( iftrueorfalse
% 0.19/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ! [Xy: $i] :
% 0.19/0.47 ( ( in @ Xy @ A )
% 0.19/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectT_lem_type,type,
% 0.19/0.47 binintersectT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectT_lem,definition,
% 0.19/0.47 ( binintersectT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionT_lem_type,type,
% 0.19/0.47 binunionT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionT_lem,definition,
% 0.19/0.47 ( binunionT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetT_lem_type,type,
% 0.19/0.47 powersetT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetT_lem,definition,
% 0.19/0.47 ( powersetT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setminusT_lem_type,type,
% 0.19/0.47 setminusT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setminusT_lem,definition,
% 0.19/0.47 ( setminusT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementT_lem_type,type,
% 0.19/0.47 complementT_lem: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementT_lem,definition,
% 0.19/0.47 ( complementT_lem
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(setextT_type,type,
% 0.19/0.47 setextT: $o ).
% 0.19/0.47
% 0.19/0.47 thf(setextT,definition,
% 0.19/0.47 ( setextT
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ Y ) ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ Y )
% 0.19/0.47 => ( in @ Xx @ X ) ) )
% 0.19/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTI_type,type,
% 0.19/0.47 subsetTI: $o ).
% 0.19/0.47
% 0.19/0.47 thf(subsetTI,definition,
% 0.19/0.47 ( subsetTI
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ Y ) ) )
% 0.19/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetTI1_type,type,
% 0.19/0.47 powersetTI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetTI1,definition,
% 0.19/0.47 ( powersetTI1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ Y ) ) )
% 0.19/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(powersetTE1_type,type,
% 0.19/0.47 powersetTE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(powersetTE1,definition,
% 0.19/0.47 ( powersetTE1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementTI1_type,type,
% 0.19/0.47 complementTI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementTI1,definition,
% 0.19/0.47 ( complementTI1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementTE1_type,type,
% 0.19/0.47 complementTE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementTE1,definition,
% 0.19/0.47 ( complementTE1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectTELcontra_type,type,
% 0.19/0.47 binintersectTELcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectTELcontra,definition,
% 0.19/0.47 ( binintersectTELcontra
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ X )
% 0.19/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectTERcontra_type,type,
% 0.19/0.47 binintersectTERcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binintersectTERcontra,definition,
% 0.19/0.47 ( binintersectTERcontra
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ Y )
% 0.19/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT_type,type,
% 0.19/0.47 contrasubsetT: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT,definition,
% 0.19/0.47 ( contrasubsetT
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.47 => ( ( in @ Xx @ Y )
% 0.19/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT1_type,type,
% 0.19/0.47 contrasubsetT1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT1,definition,
% 0.19/0.47 ( contrasubsetT1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( subset @ X @ Y )
% 0.19/0.47 => ( ~ ( in @ Xx @ Y )
% 0.19/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT2_type,type,
% 0.19/0.47 contrasubsetT2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT2,definition,
% 0.19/0.47 ( contrasubsetT2
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ X @ Y )
% 0.19/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT3_type,type,
% 0.19/0.47 contrasubsetT3: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contrasubsetT3,definition,
% 0.19/0.47 ( contrasubsetT3
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.19/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementI1_type,type,
% 0.19/0.47 doubleComplementI1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementI1,definition,
% 0.19/0.47 ( doubleComplementI1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ X )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementE1_type,type,
% 0.19/0.47 doubleComplementE1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementE1,definition,
% 0.19/0.47 ( doubleComplementE1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.19/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementSub1_type,type,
% 0.19/0.47 doubleComplementSub1: $o ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementSub1,definition,
% 0.19/0.47 ( doubleComplementSub1
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementSub2_type,type,
% 0.19/0.47 doubleComplementSub2: $o ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementSub2,definition,
% 0.19/0.47 ( doubleComplementSub2
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementEq_type,type,
% 0.19/0.47 doubleComplementEq: $o ).
% 0.19/0.47
% 0.19/0.47 thf(doubleComplementEq,definition,
% 0.19/0.47 ( doubleComplementEq
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ( X
% 0.19/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementTnotintersectT_type,type,
% 0.19/0.47 complementTnotintersectT: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementTnotintersectT,definition,
% 0.19/0.47 ( complementTnotintersectT
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementImpComplementIntersect_type,type,
% 0.19/0.47 complementImpComplementIntersect: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementImpComplementIntersect,definition,
% 0.19/0.47 ( complementImpComplementIntersect
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.19/0.47 complementSubsetComplementIntersect: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.19/0.47 ( complementSubsetComplementIntersect
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.19/0.47 complementInPowersetComplementIntersect: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.19/0.47 ( complementInPowersetComplementIntersect
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(contraSubsetComplement_type,type,
% 0.19/0.47 contraSubsetComplement: $o ).
% 0.19/0.47
% 0.19/0.47 thf(contraSubsetComplement,definition,
% 0.19/0.47 ( contraSubsetComplement
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ( in @ Xx @ Y )
% 0.19/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(complementTcontraSubset_type,type,
% 0.19/0.47 complementTcontraSubset: $o ).
% 0.19/0.47
% 0.19/0.47 thf(complementTcontraSubset,definition,
% 0.19/0.47 ( complementTcontraSubset
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTILcontra_type,type,
% 0.19/0.47 binunionTILcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTILcontra,definition,
% 0.19/0.47 ( binunionTILcontra
% 0.19/0.47 = ( ! [A: $i,X: $i] :
% 0.19/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.47 => ! [Y: $i] :
% 0.19/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.47 => ! [Xx: $i] :
% 0.19/0.47 ( ( in @ Xx @ A )
% 0.19/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.19/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTIRcontra_type,type,
% 0.19/0.47 binunionTIRcontra: $o ).
% 0.19/0.47
% 0.19/0.47 thf(binunionTIRcontra,definition,
% 0.19/0.48 ( binunionTIRcontra
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.19/0.48 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInUnion_type,type,
% 0.19/0.48 inIntersectImpInUnion: $o ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInUnion,definition,
% 0.19/0.48 ( inIntersectImpInUnion
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.48 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInUnion2_type,type,
% 0.19/0.48 inIntersectImpInUnion2: $o ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInUnion2,definition,
% 0.19/0.48 ( inIntersectImpInUnion2
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.48 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInIntersectUnions_type,type,
% 0.19/0.48 inIntersectImpInIntersectUnions: $o ).
% 0.19/0.48
% 0.19/0.48 thf(inIntersectImpInIntersectUnions,definition,
% 0.19/0.48 ( inIntersectImpInIntersectUnions
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.48 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(intersectInPowersetIntersectUnions_type,type,
% 0.19/0.48 intersectInPowersetIntersectUnions: $o ).
% 0.19/0.48
% 0.19/0.48 thf(intersectInPowersetIntersectUnions,definition,
% 0.19/0.48 ( intersectInPowersetIntersectUnions
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(inComplementUnionImpNotIn1_type,type,
% 0.19/0.48 inComplementUnionImpNotIn1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(inComplementUnionImpNotIn1,definition,
% 0.19/0.48 ( inComplementUnionImpNotIn1
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(inComplementUnionImpInComplement1_type,type,
% 0.19/0.48 inComplementUnionImpInComplement1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(inComplementUnionImpInComplement1,definition,
% 0.19/0.48 ( inComplementUnionImpInComplement1
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(binunionTE_type,type,
% 0.19/0.48 binunionTE: $o ).
% 0.19/0.48
% 0.19/0.48 thf(binunionTE,definition,
% 0.19/0.48 ( binunionTE
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xphi: $o,Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.19/0.48 => ( ( ( in @ Xx @ X )
% 0.19/0.48 => Xphi )
% 0.19/0.48 => ( ( ( in @ Xx @ Y )
% 0.19/0.48 => Xphi )
% 0.19/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(binunionTEcontra_type,type,
% 0.19/0.48 binunionTEcontra: $o ).
% 0.19/0.48
% 0.19/0.48 thf(binunionTEcontra,definition,
% 0.19/0.48 ( binunionTEcontra
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ~ ( in @ Xx @ X )
% 0.19/0.48 => ( ~ ( in @ Xx @ Y )
% 0.19/0.48 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a1_type,type,
% 0.19/0.48 demorgan2a1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a1,definition,
% 0.19/0.48 ( demorgan2a1
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(complementUnionInPowersetComplement_type,type,
% 0.19/0.48 complementUnionInPowersetComplement: $o ).
% 0.19/0.48
% 0.19/0.48 thf(complementUnionInPowersetComplement,definition,
% 0.19/0.48 ( complementUnionInPowersetComplement
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a2_type,type,
% 0.19/0.48 demorgan2a2: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a2,definition,
% 0.19/0.48 ( demorgan2a2
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1a_type,type,
% 0.19/0.48 demorgan1a: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1a,definition,
% 0.19/0.48 ( demorgan1a
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1b_type,type,
% 0.19/0.48 demorgan1b: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1b,definition,
% 0.19/0.48 ( demorgan1b
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1_type,type,
% 0.19/0.48 demorgan1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan1,definition,
% 0.19/0.48 ( demorgan1
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.19/0.48 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a_type,type,
% 0.19/0.48 demorgan2a: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2a,definition,
% 0.19/0.48 ( demorgan2a
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2b2_type,type,
% 0.19/0.48 demorgan2b2: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2b2,definition,
% 0.19/0.48 ( demorgan2b2
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.48 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2b_type,type,
% 0.19/0.48 demorgan2b: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2b,definition,
% 0.19/0.48 ( demorgan2b
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ A )
% 0.19/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.19/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2_type,type,
% 0.19/0.48 demorgan2: $o ).
% 0.19/0.48
% 0.19/0.48 thf(demorgan2,definition,
% 0.19/0.48 ( demorgan2
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.19/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule0_type,type,
% 0.19/0.48 woz13rule0: $o ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule0,definition,
% 0.19/0.48 ( woz13rule0
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Xx: $i] :
% 0.19/0.48 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.19/0.48 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule1_type,type,
% 0.19/0.48 woz13rule1: $o ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule1,definition,
% 0.19/0.48 ( woz13rule1
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ( ( subset @ X @ Z )
% 0.19/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule2_type,type,
% 0.19/0.48 woz13rule2: $o ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule2,definition,
% 0.19/0.48 ( woz13rule2
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ( ( subset @ Y @ Z )
% 0.19/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule3_type,type,
% 0.19/0.48 woz13rule3: $o ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule3,definition,
% 0.19/0.48 ( woz13rule3
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.48 => ! [Z: $i] :
% 0.19/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.19/0.48 => ( ( subset @ X @ Y )
% 0.19/0.48 => ( ( subset @ X @ Z )
% 0.19/0.48 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule4_type,type,
% 0.19/0.48 woz13rule4: $o ).
% 0.19/0.48
% 0.19/0.48 thf(woz13rule4,definition,
% 0.19/0.48 ( woz13rule4
% 0.19/0.48 = ( ! [A: $i,X: $i] :
% 0.19/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.48 => ! [Y: $i] :
% 0.19/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [W: $i] :
% 0.31/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ Z )
% 0.31/0.48 => ( ( subset @ Y @ W )
% 0.31/0.48 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_1_type,type,
% 0.31/0.48 woz1_1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_1,definition,
% 0.31/0.48 ( woz1_1
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_2_type,type,
% 0.31/0.48 woz1_2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_2,definition,
% 0.31/0.48 ( woz1_2
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ! [W: $i] :
% 0.31/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.48 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.31/0.48 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_3_type,type,
% 0.31/0.48 woz1_3: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_3,definition,
% 0.31/0.48 ( woz1_3
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ! [Z: $i] :
% 0.31/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_4_type,type,
% 0.31/0.48 woz1_4: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_4,definition,
% 0.31/0.48 ( woz1_4
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_5_type,type,
% 0.31/0.48 woz1_5: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz1_5,definition,
% 0.31/0.48 ( woz1_5
% 0.31/0.48 = ( ! [A: $i,X: $i] :
% 0.31/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.48 => ! [Y: $i] :
% 0.31/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1_type,type,
% 0.31/0.48 breln1: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all2_type,type,
% 0.31/0.48 breln1all2: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all2,definition,
% 0.31/0.48 ( breln1all2
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ R )
% 0.31/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1Set_type,type,
% 0.31/0.48 breln1Set: $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(breln1SetBreln1_type,type,
% 0.31/0.48 breln1SetBreln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1SetBreln1,definition,
% 0.31/0.48 ( breln1SetBreln1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( in @ R @ ( breln1Set @ A ) )
% 0.31/0.48 => ( breln1 @ A @ R ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(transitive_type,type,
% 0.31/0.48 transitive: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(antisymmetric_type,type,
% 0.31/0.48 antisymmetric: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(reflexive_type,type,
% 0.31/0.48 reflexive: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(refltransitive_type,type,
% 0.31/0.48 refltransitive: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(refllinearorder_type,type,
% 0.31/0.48 refllinearorder: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(reflwellordering_type,type,
% 0.31/0.48 reflwellordering: $i > $i > $o ).
% 0.31/0.48
% 0.31/0.48 thf(choice2fnsingleton_type,type,
% 0.31/0.48 choice2fnsingleton: $o ).
% 0.31/0.48
% 0.31/0.48 thf(choice2fnsingleton,definition,
% 0.31/0.48 ( choice2fnsingleton
% 0.31/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ? [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 & ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.48 => ! [R: $i] :
% 0.31/0.48 ( ( in @ R @ ( breln1Set @ B ) )
% 0.31/0.48 => ( ( reflwellordering @ B @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ B
% 0.31/0.48 @ ^ [Xy: $i] :
% 0.31/0.48 ( ( Xphi @ Xx @ Xy )
% 0.31/0.48 & ! [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ B )
% 0.31/0.48 => ( ( Xphi @ Xx @ Xz )
% 0.31/0.48 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln1_type,type,
% 0.31/0.48 setOfPairsIsBReln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln1,definition,
% 0.31/0.48 ( setOfPairsIsBReln1
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.31/0.48 ( breln1 @ A
% 0.31/0.48 @ ( dpsetconstr @ A @ A
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all1_type,type,
% 0.31/0.48 breln1all1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all1,definition,
% 0.31/0.48 ( breln1all1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ R )
% 0.31/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln1_type,type,
% 0.31/0.48 subbreln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln1,definition,
% 0.31/0.48 ( subbreln1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln1_type,type,
% 0.31/0.48 eqbreln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln1,definition,
% 0.31/0.48 ( eqbreln1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.31/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invset_type,type,
% 0.31/0.48 breln1invset: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invprop_type,type,
% 0.31/0.48 breln1invprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invprop,definition,
% 0.31/0.48 ( breln1invprop
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invI_type,type,
% 0.31/0.48 breln1invI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invI,definition,
% 0.31/0.48 ( breln1invI
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invE_type,type,
% 0.31/0.48 breln1invE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invE,definition,
% 0.31/0.48 ( breln1invE
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compset_type,type,
% 0.31/0.48 breln1compset: $i > $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compprop_type,type,
% 0.31/0.48 breln1compprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compprop,definition,
% 0.31/0.48 ( breln1compprop
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compI_type,type,
% 0.31/0.48 breln1compI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compI,definition,
% 0.31/0.48 ( breln1compI
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ! [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.31/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compE_type,type,
% 0.31/0.48 breln1compE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compE,definition,
% 0.31/0.48 ( breln1compE
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.31/0.48 => ? [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ A )
% 0.31/0.48 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.31/0.48 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compEex_type,type,
% 0.31/0.48 breln1compEex: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compEex,definition,
% 0.31/0.48 ( breln1compEex
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.31/0.48 => ! [Xphi: $o] :
% 0.31/0.48 ( ! [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.31/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.31/0.48 => Xphi ) ) )
% 0.31/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionprop_type,type,
% 0.31/0.48 breln1unionprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionprop,definition,
% 0.31/0.48 ( breln1unionprop
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionIL_type,type,
% 0.31/0.48 breln1unionIL: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionIL,definition,
% 0.31/0.48 ( breln1unionIL
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionIR_type,type,
% 0.31/0.48 breln1unionIR: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionIR,definition,
% 0.31/0.48 ( breln1unionIR
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionI_type,type,
% 0.31/0.48 breln1unionI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionI,definition,
% 0.31/0.48 ( breln1unionI
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionE_type,type,
% 0.31/0.48 breln1unionE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionE,definition,
% 0.31/0.48 ( breln1unionE
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionEcases_type,type,
% 0.31/0.48 breln1unionEcases: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionEcases,definition,
% 0.31/0.48 ( breln1unionEcases
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.31/0.48 => ! [Xphi: $o] :
% 0.31/0.48 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.48 => Xphi )
% 0.31/0.48 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionCommutes_type,type,
% 0.31/0.48 breln1unionCommutes: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1unionCommutes,definition,
% 0.31/0.48 ( breln1unionCommutes
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ( binunion @ R @ S )
% 0.31/0.48 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz2Ex_type,type,
% 0.31/0.48 woz2Ex: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz2Ex,definition,
% 0.31/0.48 ( woz2Ex
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ( R
% 0.31/0.48 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz2W_type,type,
% 0.31/0.48 woz2W: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz2W,definition,
% 0.31/0.48 ( woz2W
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.31/0.48 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz2A_type,type,
% 0.31/0.48 woz2A: $o ).
% 0.31/0.48
% 0.31/0.48 thf(woz2A,definition,
% 0.31/0.48 ( woz2A
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [T: $i] :
% 0.31/0.48 ( ( breln1 @ A @ T )
% 0.31/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.31/0.48 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(woz2B,conjecture,
% 0.31/0.48 ( setextAx
% 0.31/0.48 => ( emptysetAx
% 0.31/0.48 => ( setadjoinAx
% 0.31/0.48 => ( powersetAx
% 0.31/0.48 => ( setunionAx
% 0.31/0.48 => ( omega0Ax
% 0.31/0.48 => ( omegaSAx
% 0.31/0.48 => ( omegaIndAx
% 0.31/0.48 => ( replAx
% 0.31/0.48 => ( foundationAx
% 0.31/0.48 => ( wellorderingAx
% 0.31/0.48 => ( descrp
% 0.31/0.48 => ( dsetconstrI
% 0.31/0.48 => ( dsetconstrEL
% 0.31/0.48 => ( dsetconstrER
% 0.31/0.48 => ( exuE1
% 0.31/0.48 => ( prop2setE
% 0.31/0.48 => ( emptysetE
% 0.31/0.48 => ( emptysetimpfalse
% 0.31/0.48 => ( notinemptyset
% 0.31/0.48 => ( exuE3e
% 0.31/0.48 => ( setext
% 0.31/0.48 => ( emptyI
% 0.31/0.48 => ( noeltsimpempty
% 0.31/0.48 => ( setbeta
% 0.31/0.48 => ( nonemptyE1
% 0.31/0.48 => ( nonemptyI
% 0.31/0.48 => ( nonemptyI1
% 0.31/0.48 => ( setadjoinIL
% 0.31/0.48 => ( emptyinunitempty
% 0.31/0.48 => ( setadjoinIR
% 0.31/0.48 => ( setadjoinE
% 0.31/0.48 => ( setadjoinOr
% 0.31/0.48 => ( setoftrueEq
% 0.31/0.48 => ( powersetI
% 0.31/0.48 => ( emptyinPowerset
% 0.31/0.48 => ( emptyInPowerset
% 0.31/0.48 => ( powersetE
% 0.31/0.48 => ( setunionI
% 0.31/0.48 => ( setunionE
% 0.31/0.48 => ( subPowSU
% 0.31/0.48 => ( exuE2
% 0.31/0.48 => ( nonemptyImpWitness
% 0.31/0.48 => ( uniqinunit
% 0.31/0.48 => ( notinsingleton
% 0.31/0.48 => ( eqinunit
% 0.31/0.48 => ( singletonsswitch
% 0.31/0.48 => ( upairsetE
% 0.31/0.48 => ( upairsetIL
% 0.31/0.48 => ( upairsetIR
% 0.31/0.48 => ( emptyE1
% 0.31/0.48 => ( vacuousDall
% 0.31/0.48 => ( quantDeMorgan1
% 0.31/0.48 => ( quantDeMorgan2
% 0.31/0.48 => ( quantDeMorgan3
% 0.31/0.48 => ( quantDeMorgan4
% 0.31/0.48 => ( prop2setI
% 0.31/0.48 => ( prop2set2propI
% 0.31/0.48 => ( notdexE
% 0.31/0.48 => ( notdallE
% 0.31/0.48 => ( exuI1
% 0.31/0.48 => ( exuI3
% 0.31/0.48 => ( exuI2
% 0.31/0.48 => ( inCongP
% 0.31/0.48 => ( in__Cong
% 0.31/0.48 => ( exuE3u
% 0.31/0.48 => ( exu__Cong
% 0.31/0.48 => ( emptyset__Cong
% 0.31/0.48 => ( setadjoin__Cong
% 0.31/0.48 => ( powerset__Cong
% 0.31/0.48 => ( setunion__Cong
% 0.31/0.48 => ( omega__Cong
% 0.31/0.48 => ( exuEu
% 0.31/0.48 => ( descr__Cong
% 0.31/0.48 => ( dsetconstr__Cong
% 0.31/0.48 => ( subsetI1
% 0.31/0.48 => ( eqimpsubset2
% 0.31/0.48 => ( eqimpsubset1
% 0.31/0.48 => ( subsetI2
% 0.31/0.48 => ( emptysetsubset
% 0.31/0.48 => ( subsetE
% 0.31/0.48 => ( subsetE2
% 0.31/0.48 => ( notsubsetI
% 0.31/0.48 => ( notequalI1
% 0.31/0.48 => ( notequalI2
% 0.31/0.48 => ( subsetRefl
% 0.31/0.48 => ( subsetTrans
% 0.31/0.48 => ( setadjoinSub
% 0.31/0.48 => ( setadjoinSub2
% 0.31/0.48 => ( subset2powerset
% 0.31/0.48 => ( setextsub
% 0.31/0.48 => ( subsetemptysetimpeq
% 0.31/0.48 => ( powersetI1
% 0.31/0.48 => ( powersetE1
% 0.31/0.48 => ( inPowerset
% 0.31/0.48 => ( powersetsubset
% 0.31/0.48 => ( sepInPowerset
% 0.31/0.48 => ( sepSubset
% 0.31/0.48 => ( binunionIL
% 0.31/0.48 => ( upairset2IR
% 0.31/0.48 => ( binunionIR
% 0.31/0.48 => ( binunionEcases
% 0.31/0.48 => ( binunionE
% 0.31/0.48 => ( binunionLsub
% 0.31/0.48 => ( binunionRsub
% 0.31/0.48 => ( binintersectI
% 0.31/0.48 => ( binintersectSubset5
% 0.31/0.48 => ( binintersectEL
% 0.31/0.48 => ( binintersectLsub
% 0.31/0.48 => ( binintersectSubset2
% 0.31/0.48 => ( binintersectSubset3
% 0.31/0.48 => ( binintersectER
% 0.31/0.48 => ( disjointsetsI1
% 0.31/0.48 => ( binintersectRsub
% 0.31/0.48 => ( binintersectSubset4
% 0.31/0.48 => ( binintersectSubset1
% 0.31/0.48 => ( bs114d
% 0.31/0.48 => ( setminusI
% 0.31/0.48 => ( setminusEL
% 0.31/0.48 => ( setminusER
% 0.31/0.48 => ( setminusSubset2
% 0.31/0.48 => ( setminusERneg
% 0.31/0.48 => ( setminusELneg
% 0.31/0.48 => ( setminusILneg
% 0.31/0.48 => ( setminusIRneg
% 0.31/0.48 => ( setminusLsub
% 0.31/0.48 => ( setminusSubset1
% 0.31/0.48 => ( symdiffE
% 0.31/0.48 => ( symdiffI1
% 0.31/0.48 => ( symdiffI2
% 0.31/0.48 => ( symdiffIneg1
% 0.31/0.48 => ( symdiffIneg2
% 0.31/0.48 => ( secondinupair
% 0.31/0.48 => ( setukpairIL
% 0.31/0.48 => ( setukpairIR
% 0.31/0.48 => ( kpairiskpair
% 0.31/0.48 => ( kpairp
% 0.31/0.48 => ( singletonsubset
% 0.31/0.48 => ( singletoninpowerset
% 0.31/0.48 => ( singletoninpowunion
% 0.31/0.48 => ( upairset2E
% 0.31/0.48 => ( upairsubunion
% 0.31/0.48 => ( upairinpowunion
% 0.31/0.48 => ( ubforcartprodlem1
% 0.31/0.48 => ( ubforcartprodlem2
% 0.31/0.48 => ( ubforcartprodlem3
% 0.31/0.48 => ( cartprodpairin
% 0.31/0.48 => ( cartprodmempair1
% 0.31/0.48 => ( cartprodmempair
% 0.31/0.48 => ( setunionE2
% 0.31/0.48 => ( setunionsingleton1
% 0.31/0.48 => ( setunionsingleton2
% 0.31/0.48 => ( setunionsingleton
% 0.31/0.48 => ( singletonprop
% 0.31/0.48 => ( ex1E1
% 0.31/0.48 => ( ex1I
% 0.31/0.48 => ( ex1I2
% 0.31/0.48 => ( singletonsuniq
% 0.31/0.48 => ( setukpairinjL1
% 0.31/0.48 => ( kfstsingleton
% 0.31/0.48 => ( theprop
% 0.31/0.48 => ( kfstpairEq
% 0.31/0.48 => ( cartprodfstin
% 0.31/0.48 => ( setukpairinjL2
% 0.31/0.48 => ( setukpairinjL
% 0.31/0.48 => ( setukpairinjR11
% 0.31/0.48 => ( setukpairinjR12
% 0.31/0.48 => ( setukpairinjR1
% 0.31/0.48 => ( upairequniteq
% 0.31/0.48 => ( setukpairinjR2
% 0.31/0.48 => ( setukpairinjR
% 0.31/0.48 => ( ksndsingleton
% 0.31/0.48 => ( ksndpairEq
% 0.31/0.48 => ( kpairsurjEq
% 0.31/0.48 => ( cartprodsndin
% 0.31/0.48 => ( cartprodpairmemEL
% 0.31/0.48 => ( cartprodpairmemER
% 0.31/0.48 => ( cartprodmempaircEq
% 0.31/0.48 => ( cartprodfstpairEq
% 0.31/0.48 => ( cartprodsndpairEq
% 0.31/0.48 => ( cartprodpairsurjEq
% 0.31/0.48 => ( dpsetconstrI
% 0.31/0.48 => ( dpsetconstrSub
% 0.31/0.48 => ( setOfPairsIsBReln
% 0.31/0.48 => ( dpsetconstrERa
% 0.31/0.48 => ( dpsetconstrEL1
% 0.31/0.48 => ( dpsetconstrEL2
% 0.31/0.48 => ( dpsetconstrER
% 0.31/0.48 => ( funcImageSingleton
% 0.31/0.48 => ( apProp
% 0.31/0.48 => ( app
% 0.31/0.48 => ( infuncsetfunc
% 0.31/0.48 => ( ap2p
% 0.31/0.48 => ( funcinfuncset
% 0.31/0.48 => ( lamProp
% 0.31/0.48 => ( lamp
% 0.31/0.48 => ( lam2p
% 0.31/0.48 => ( brelnall1
% 0.31/0.48 => ( brelnall2
% 0.31/0.48 => ( ex1E2
% 0.31/0.48 => ( funcGraphProp1
% 0.31/0.48 => ( funcGraphProp3
% 0.31/0.48 => ( funcGraphProp2
% 0.31/0.48 => ( funcextLem
% 0.31/0.48 => ( funcGraphProp4
% 0.31/0.48 => ( subbreln
% 0.31/0.48 => ( eqbreln
% 0.31/0.48 => ( funcext
% 0.31/0.48 => ( funcext2
% 0.31/0.48 => ( ap2apEq1
% 0.31/0.48 => ( ap2apEq2
% 0.31/0.48 => ( beta1
% 0.31/0.48 => ( eta1
% 0.31/0.48 => ( lam2lamEq
% 0.31/0.48 => ( beta2
% 0.31/0.48 => ( eta2
% 0.31/0.48 => ( iffalseProp1
% 0.31/0.48 => ( iffalseProp2
% 0.31/0.48 => ( iftrueProp1
% 0.31/0.48 => ( iftrueProp2
% 0.31/0.48 => ( ifSingleton
% 0.31/0.48 => ( ifp
% 0.31/0.48 => ( theeq
% 0.31/0.48 => ( iftrue
% 0.31/0.48 => ( iffalse
% 0.31/0.48 => ( iftrueorfalse
% 0.31/0.48 => ( binintersectT_lem
% 0.31/0.48 => ( binunionT_lem
% 0.31/0.48 => ( powersetT_lem
% 0.31/0.48 => ( setminusT_lem
% 0.31/0.48 => ( complementT_lem
% 0.31/0.48 => ( setextT
% 0.31/0.48 => ( subsetTI
% 0.31/0.48 => ( powersetTI1
% 0.31/0.48 => ( powersetTE1
% 0.31/0.48 => ( complementTI1
% 0.31/0.48 => ( complementTE1
% 0.31/0.48 => ( binintersectTELcontra
% 0.31/0.48 => ( binintersectTERcontra
% 0.31/0.48 => ( contrasubsetT
% 0.31/0.48 => ( contrasubsetT1
% 0.31/0.48 => ( contrasubsetT2
% 0.31/0.48 => ( contrasubsetT3
% 0.31/0.48 => ( doubleComplementI1
% 0.31/0.48 => ( doubleComplementE1
% 0.31/0.48 => ( doubleComplementSub1
% 0.31/0.48 => ( doubleComplementSub2
% 0.31/0.48 => ( doubleComplementEq
% 0.31/0.48 => ( complementTnotintersectT
% 0.31/0.48 => ( complementImpComplementIntersect
% 0.31/0.48 => ( complementSubsetComplementIntersect
% 0.31/0.48 => ( complementInPowersetComplementIntersect
% 0.31/0.48 => ( contraSubsetComplement
% 0.31/0.48 => ( complementTcontraSubset
% 0.31/0.48 => ( binunionTILcontra
% 0.31/0.48 => ( binunionTIRcontra
% 0.31/0.48 => ( inIntersectImpInUnion
% 0.31/0.48 => ( inIntersectImpInUnion2
% 0.31/0.48 => ( inIntersectImpInIntersectUnions
% 0.31/0.48 => ( intersectInPowersetIntersectUnions
% 0.31/0.48 => ( inComplementUnionImpNotIn1
% 0.31/0.48 => ( inComplementUnionImpInComplement1
% 0.31/0.48 => ( binunionTE
% 0.31/0.48 => ( binunionTEcontra
% 0.31/0.48 => ( demorgan2a1
% 0.31/0.48 => ( complementUnionInPowersetComplement
% 0.31/0.48 => ( demorgan2a2
% 0.31/0.48 => ( demorgan1a
% 0.31/0.48 => ( demorgan1b
% 0.31/0.48 => ( demorgan1
% 0.31/0.48 => ( demorgan2a
% 0.31/0.48 => ( demorgan2b2
% 0.31/0.48 => ( demorgan2b
% 0.31/0.48 => ( demorgan2
% 0.31/0.48 => ( woz13rule0
% 0.31/0.48 => ( woz13rule1
% 0.31/0.48 => ( woz13rule2
% 0.31/0.48 => ( woz13rule3
% 0.31/0.48 => ( woz13rule4
% 0.31/0.48 => ( woz1_1
% 0.31/0.48 => ( woz1_2
% 0.31/0.48 => ( woz1_3
% 0.31/0.48 => ( woz1_4
% 0.31/0.48 => ( woz1_5
% 0.31/0.48 => ( breln1all2
% 0.31/0.48 => ( breln1SetBreln1
% 0.31/0.48 => ( choice2fnsingleton
% 0.31/0.48 => ( setOfPairsIsBReln1
% 0.31/0.48 => ( breln1all1
% 0.31/0.48 => ( subbreln1
% 0.31/0.48 => ( eqbreln1
% 0.31/0.48 => ( breln1invprop
% 0.31/0.48 => ( breln1invI
% 0.31/0.48 => ( breln1invE
% 0.31/0.48 => ( breln1compprop
% 0.31/0.48 => ( breln1compI
% 0.31/0.48 => ( breln1compE
% 0.31/0.48 => ( breln1compEex
% 0.31/0.48 => ( breln1unionprop
% 0.31/0.48 => ( breln1unionIL
% 0.31/0.48 => ( breln1unionIR
% 0.31/0.48 => ( breln1unionI
% 0.31/0.48 => ( breln1unionE
% 0.31/0.48 => ( breln1unionEcases
% 0.31/0.48 => ( breln1unionCommutes
% 0.31/0.48 => ( woz2Ex
% 0.31/0.48 => ( woz2W
% 0.31/0.48 => ( woz2A
% 0.31/0.48 => ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [T: $i] :
% 0.31/0.48 ( ( breln1 @ A @ T )
% 0.31/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.31/0.48 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 3.29/1.61 ---- Embedded in THF ---
% 3.29/1.62 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.29/1.62 %%% Generated on Tue Feb 24 12:33:24 EST 2026
% 3.29/1.62 %%% using '$$dhol' embedding, version 1.3.0.
% 3.29/1.62 %%% Logic specification used:
% 3.29/1.62 %%% thf(spec, logic, $$dhol).
% 3.29/1.62
% 3.29/1.62 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2DTF18469.p
% See solution above
% 3.29/1.62 ------------------------
% 3.29/1.66 ---- Cleaned THF ---
% 3.29/1.66 thf(in_type,type,
% 3.29/1.66 in: $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(exu_type,type,
% 3.29/1.66 exu: ( $i > $o ) > $o ).
% 3.29/1.66
% 3.29/1.66 thf(exu,definition,
% 3.29/1.66 ( exu
% 3.29/1.66 = ( ^ [Xphi: $i > $o] :
% 3.29/1.66 ? [Xx: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 & ! [Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setextAx_type,type,
% 3.29/1.66 setextAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setextAx,definition,
% 3.29/1.66 ( setextAx
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 <=> ( in @ Xx @ B ) )
% 3.29/1.66 => ( A = B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyset_type,type,
% 3.29/1.66 emptyset: $i ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetAx_type,type,
% 3.29/1.66 emptysetAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetAx,definition,
% 3.29/1.66 ( emptysetAx
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoin_type,type,
% 3.29/1.66 setadjoin: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinAx_type,type,
% 3.29/1.66 setadjoinAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinAx,definition,
% 3.29/1.66 ( setadjoinAx
% 3.29/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.29/1.66 <=> ( ( Xy = Xx )
% 3.29/1.66 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powerset_type,type,
% 3.29/1.66 powerset: $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(powersetAx_type,type,
% 3.29/1.66 powersetAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetAx,definition,
% 3.29/1.66 ( powersetAx
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( in @ B @ ( powerset @ A ) )
% 3.29/1.66 <=> ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunion_type,type,
% 3.29/1.66 setunion: $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(setunionAx_type,type,
% 3.29/1.66 setunionAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionAx,definition,
% 3.29/1.66 ( setunionAx
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setunion @ A ) )
% 3.29/1.66 <=> ? [B: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 & ( in @ B @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(omega_type,type,
% 3.29/1.66 omega: $i ).
% 3.29/1.66
% 3.29/1.66 thf(omega0Ax_type,type,
% 3.29/1.66 omega0Ax: $o ).
% 3.29/1.66
% 3.29/1.66 thf(omega0Ax,definition,
% 3.29/1.66 ( omega0Ax
% 3.29/1.66 = ( in @ emptyset @ omega ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(omegaSAx_type,type,
% 3.29/1.66 omegaSAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(omegaSAx,definition,
% 3.29/1.66 ( omegaSAx
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ omega )
% 3.29/1.66 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(omegaIndAx_type,type,
% 3.29/1.66 omegaIndAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(omegaIndAx,definition,
% 3.29/1.66 ( omegaIndAx
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ( ( in @ emptyset @ A )
% 3.29/1.66 & ! [Xx: $i] :
% 3.29/1.66 ( ( ( in @ Xx @ omega )
% 3.29/1.66 & ( in @ Xx @ A ) )
% 3.29/1.66 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ omega )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(replAx_type,type,
% 3.29/1.66 replAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(replAx,definition,
% 3.29/1.66 ( replAx
% 3.29/1.66 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( exu
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.29/1.66 => ? [B: $i] :
% 3.29/1.66 ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 <=> ? [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ A )
% 3.29/1.66 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(foundationAx_type,type,
% 3.29/1.66 foundationAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(foundationAx,definition,
% 3.29/1.66 ( foundationAx
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.29/1.66 => ? [B: $i] :
% 3.29/1.66 ( ( in @ B @ A )
% 3.29/1.66 & ~ ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(wellorderingAx_type,type,
% 3.29/1.66 wellorderingAx: $o ).
% 3.29/1.66
% 3.29/1.66 thf(wellorderingAx,definition,
% 3.29/1.66 ( wellorderingAx
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ? [B: $i] :
% 3.29/1.66 ( ! [C: $i] :
% 3.29/1.66 ( ( in @ C @ B )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ C )
% 3.29/1.66 => ( in @ Xx @ A ) ) )
% 3.29/1.66 & ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( ( in @ Xx @ A )
% 3.29/1.66 & ( in @ Xy @ A ) )
% 3.29/1.66 => ( ! [C: $i] :
% 3.29/1.66 ( ( in @ C @ B )
% 3.29/1.66 => ( ( in @ Xx @ C )
% 3.29/1.66 <=> ( in @ Xy @ C ) ) )
% 3.29/1.66 => ( Xx = Xy ) ) )
% 3.29/1.66 & ! [C: $i,D: $i] :
% 3.29/1.66 ( ( ( in @ C @ B )
% 3.29/1.66 & ( in @ D @ B ) )
% 3.29/1.66 => ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ C )
% 3.29/1.66 => ( in @ Xx @ D ) )
% 3.29/1.66 | ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ D )
% 3.29/1.66 => ( in @ Xx @ C ) ) ) )
% 3.29/1.66 & ! [C: $i] :
% 3.29/1.66 ( ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ C )
% 3.29/1.66 => ( in @ Xx @ A ) )
% 3.29/1.66 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.29/1.66 => ? [D: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ D @ B )
% 3.29/1.66 & ( in @ Xx @ C )
% 3.29/1.66 & ~ ? [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ D )
% 3.29/1.66 & ( in @ Xy @ C ) )
% 3.29/1.66 & ! [E: $i] :
% 3.29/1.66 ( ( in @ E @ B )
% 3.29/1.66 => ( ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ E )
% 3.29/1.66 => ( in @ Xy @ D ) )
% 3.29/1.66 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(descr_type,type,
% 3.29/1.66 descr: ( $i > $o ) > $i ).
% 3.29/1.66
% 3.29/1.66 thf(descrp_type,type,
% 3.29/1.66 descrp: $o ).
% 3.29/1.66
% 3.29/1.66 thf(descrp,definition,
% 3.29/1.66 ( descrp
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ( Xphi
% 3.29/1.66 @ ( descr
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstr_type,type,
% 3.29/1.66 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrI_type,type,
% 3.29/1.66 dsetconstrI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrI,definition,
% 3.29/1.66 ( dsetconstrI
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 => ( in @ Xx
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrEL_type,type,
% 3.29/1.66 dsetconstrEL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrEL,definition,
% 3.29/1.66 ( dsetconstrEL
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrER_type,type,
% 3.29/1.66 dsetconstrER: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstrER,definition,
% 3.29/1.66 ( dsetconstrER
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.29/1.66 => ( Xphi @ Xx ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuE1_type,type,
% 3.29/1.66 exuE1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuE1,definition,
% 3.29/1.66 ( exuE1
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 & ! [Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(prop2set_type,type,
% 3.29/1.66 prop2set: $o > $i ).
% 3.29/1.66
% 3.29/1.66 thf(prop2setE_type,type,
% 3.29/1.66 prop2setE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(prop2setE,definition,
% 3.29/1.66 ( prop2setE
% 3.29/1.66 = ( ! [Xphi: $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.29/1.66 => Xphi ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetE_type,type,
% 3.29/1.66 emptysetE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetE,definition,
% 3.29/1.66 ( emptysetE
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ emptyset )
% 3.29/1.66 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetimpfalse_type,type,
% 3.29/1.66 emptysetimpfalse: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetimpfalse,definition,
% 3.29/1.66 ( emptysetimpfalse
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ emptyset )
% 3.29/1.66 => $false ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notinemptyset_type,type,
% 3.29/1.66 notinemptyset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notinemptyset,definition,
% 3.29/1.66 ( notinemptyset
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuE3e_type,type,
% 3.29/1.66 exuE3e: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuE3e,definition,
% 3.29/1.66 ( exuE3e
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setext_type,type,
% 3.29/1.66 setext: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setext,definition,
% 3.29/1.66 ( setext
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ B ) )
% 3.29/1.66 => ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ A ) )
% 3.29/1.66 => ( A = B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyI_type,type,
% 3.29/1.66 emptyI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyI,definition,
% 3.29/1.66 ( emptyI
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ~ ( in @ Xx @ A )
% 3.29/1.66 => ( A = emptyset ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(noeltsimpempty_type,type,
% 3.29/1.66 noeltsimpempty: $o ).
% 3.29/1.66
% 3.29/1.66 thf(noeltsimpempty,definition,
% 3.29/1.66 ( noeltsimpempty
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ~ ( in @ Xx @ A )
% 3.29/1.66 => ( A = emptyset ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setbeta_type,type,
% 3.29/1.66 setbeta: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setbeta,definition,
% 3.29/1.66 ( setbeta
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( in @ Xx
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.29/1.66 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(nonempty_type,type,
% 3.29/1.66 nonempty: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(nonempty,definition,
% 3.29/1.66 ( nonempty
% 3.29/1.66 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyE1_type,type,
% 3.29/1.66 nonemptyE1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyE1,definition,
% 3.29/1.66 ( nonemptyE1
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ( nonempty @ A )
% 3.29/1.66 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyI_type,type,
% 3.29/1.66 nonemptyI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyI,definition,
% 3.29/1.66 ( nonemptyI
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 => ( nonempty
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyI1_type,type,
% 3.29/1.66 nonemptyI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyI1,definition,
% 3.29/1.66 ( nonemptyI1
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.29/1.66 => ( nonempty @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinIL_type,type,
% 3.29/1.66 setadjoinIL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinIL,definition,
% 3.29/1.66 ( setadjoinIL
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyinunitempty_type,type,
% 3.29/1.66 emptyinunitempty: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyinunitempty,definition,
% 3.29/1.66 ( emptyinunitempty
% 3.29/1.66 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinIR_type,type,
% 3.29/1.66 setadjoinIR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinIR,definition,
% 3.29/1.66 ( setadjoinIR
% 3.29/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ A )
% 3.29/1.66 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinE_type,type,
% 3.29/1.66 setadjoinE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinE,definition,
% 3.29/1.66 ( setadjoinE
% 3.29/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.29/1.66 => ! [Xphi: $o] :
% 3.29/1.66 ( ( ( Xy = Xx )
% 3.29/1.66 => Xphi )
% 3.29/1.66 => ( ( ( in @ Xy @ A )
% 3.29/1.66 => Xphi )
% 3.29/1.66 => Xphi ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinOr_type,type,
% 3.29/1.66 setadjoinOr: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinOr,definition,
% 3.29/1.66 ( setadjoinOr
% 3.29/1.66 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.29/1.66 => ( ( Xy = Xx )
% 3.29/1.66 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setoftrueEq_type,type,
% 3.29/1.66 setoftrueEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setoftrueEq,definition,
% 3.29/1.66 ( setoftrueEq
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : $true )
% 3.29/1.66 = A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powersetI_type,type,
% 3.29/1.66 powersetI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetI,definition,
% 3.29/1.66 ( powersetI
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ A ) )
% 3.29/1.66 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyinPowerset_type,type,
% 3.29/1.66 emptyinPowerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyinPowerset,definition,
% 3.29/1.66 ( emptyinPowerset
% 3.29/1.66 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyInPowerset_type,type,
% 3.29/1.66 emptyInPowerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyInPowerset,definition,
% 3.29/1.66 ( emptyInPowerset
% 3.29/1.66 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powersetE_type,type,
% 3.29/1.66 powersetE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetE,definition,
% 3.29/1.66 ( powersetE
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ B @ ( powerset @ A ) )
% 3.29/1.66 => ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionI_type,type,
% 3.29/1.66 setunionI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionI,definition,
% 3.29/1.66 ( setunionI
% 3.29/1.66 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( ( in @ B @ A )
% 3.29/1.66 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionE_type,type,
% 3.29/1.66 setunionE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionE,definition,
% 3.29/1.66 ( setunionE
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setunion @ A ) )
% 3.29/1.66 => ! [Xphi: $o] :
% 3.29/1.66 ( ! [B: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( ( in @ B @ A )
% 3.29/1.66 => Xphi ) )
% 3.29/1.66 => Xphi ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subPowSU_type,type,
% 3.29/1.66 subPowSU: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subPowSU,definition,
% 3.29/1.66 ( subPowSU
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuE2_type,type,
% 3.29/1.66 exuE2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuE2,definition,
% 3.29/1.66 ( exuE2
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ! [Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xy )
% 3.29/1.66 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyImpWitness_type,type,
% 3.29/1.66 nonemptyImpWitness: $o ).
% 3.29/1.66
% 3.29/1.66 thf(nonemptyImpWitness,definition,
% 3.29/1.66 ( nonemptyImpWitness
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ( nonempty @ A )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & $true ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(uniqinunit_type,type,
% 3.29/1.66 uniqinunit: $o ).
% 3.29/1.66
% 3.29/1.66 thf(uniqinunit,definition,
% 3.29/1.66 ( uniqinunit
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notinsingleton_type,type,
% 3.29/1.66 notinsingleton: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notinsingleton,definition,
% 3.29/1.66 ( notinsingleton
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx != Xy )
% 3.29/1.66 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(eqinunit_type,type,
% 3.29/1.66 eqinunit: $o ).
% 3.29/1.66
% 3.29/1.66 thf(eqinunit,definition,
% 3.29/1.66 ( eqinunit
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsswitch_type,type,
% 3.29/1.66 singletonsswitch: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsswitch,definition,
% 3.29/1.66 ( singletonsswitch
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.29/1.66 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetE_type,type,
% 3.29/1.66 upairsetE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetE,definition,
% 3.29/1.66 ( upairsetE
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.29/1.66 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.29/1.66 => ( ( Xz = Xx )
% 3.29/1.66 | ( Xz = Xy ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetIL_type,type,
% 3.29/1.66 upairsetIL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetIL,definition,
% 3.29/1.66 ( upairsetIL
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetIR_type,type,
% 3.29/1.66 upairsetIR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetIR,definition,
% 3.29/1.66 ( upairsetIR
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyE1_type,type,
% 3.29/1.66 emptyE1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyE1,definition,
% 3.29/1.66 ( emptyE1
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) )
% 3.29/1.66 => ( ( ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 = emptyset )
% 3.29/1.66 => $false ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(vacuousDall_type,type,
% 3.29/1.66 vacuousDall: $o ).
% 3.29/1.66
% 3.29/1.66 thf(vacuousDall,definition,
% 3.29/1.66 ( vacuousDall
% 3.29/1.66 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ emptyset )
% 3.29/1.66 => ( Xphi @ Xx ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan1_type,type,
% 3.29/1.66 quantDeMorgan1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan1,definition,
% 3.29/1.66 ( quantDeMorgan1
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ~ ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan2_type,type,
% 3.29/1.66 quantDeMorgan2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan2,definition,
% 3.29/1.66 ( quantDeMorgan2
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ~ ( Xphi @ Xx ) )
% 3.29/1.66 => ~ ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan3_type,type,
% 3.29/1.66 quantDeMorgan3: $o ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan3,definition,
% 3.29/1.66 ( quantDeMorgan3
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ~ ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan4_type,type,
% 3.29/1.66 quantDeMorgan4: $o ).
% 3.29/1.66
% 3.29/1.66 thf(quantDeMorgan4,definition,
% 3.29/1.66 ( quantDeMorgan4
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ~ ( Xphi @ Xx ) )
% 3.29/1.66 => ~ ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(prop2setI_type,type,
% 3.29/1.66 prop2setI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(prop2setI,definition,
% 3.29/1.66 ( prop2setI
% 3.29/1.66 = ( ! [Xphi: $o] :
% 3.29/1.66 ( Xphi
% 3.29/1.66 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(set2prop_type,type,
% 3.29/1.66 set2prop: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(prop2set2propI_type,type,
% 3.29/1.66 prop2set2propI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(prop2set2propI,definition,
% 3.29/1.66 ( prop2set2propI
% 3.29/1.66 = ( ! [Xphi: $o] :
% 3.29/1.66 ( Xphi
% 3.29/1.66 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notdexE_type,type,
% 3.29/1.66 notdexE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notdexE,definition,
% 3.29/1.66 ( notdexE
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ~ ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notdallE_type,type,
% 3.29/1.66 notdallE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notdallE,definition,
% 3.29/1.66 ( notdallE
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ~ ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuI1_type,type,
% 3.29/1.66 exuI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuI1,definition,
% 3.29/1.66 ( exuI1
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ? [Xx: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 & ! [Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) )
% 3.29/1.66 => ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuI3_type,type,
% 3.29/1.66 exuI3: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuI3,definition,
% 3.29/1.66 ( exuI3
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.29/1.66 => ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) )
% 3.29/1.66 => ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuI2_type,type,
% 3.29/1.66 exuI2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuI2,definition,
% 3.29/1.66 ( exuI2
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ? [Xx: $i] :
% 3.29/1.66 ! [Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xy )
% 3.29/1.66 <=> ( Xy = Xx ) )
% 3.29/1.66 => ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(inCongP_type,type,
% 3.29/1.66 inCongP: $o ).
% 3.29/1.66
% 3.29/1.66 thf(inCongP,definition,
% 3.29/1.66 ( inCongP
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(in__Cong_type,type,
% 3.29/1.66 in__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(in__Cong,definition,
% 3.29/1.66 ( in__Cong
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( in @ Xx @ A )
% 3.29/1.66 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuE3u_type,type,
% 3.29/1.66 exuE3u: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuE3u,definition,
% 3.29/1.66 ( exuE3u
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exu__Cong_type,type,
% 3.29/1.66 exu__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exu__Cong,definition,
% 3.29/1.66 ( exu__Cong
% 3.29/1.66 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 <=> ( Xpsi @ Xy ) ) )
% 3.29/1.66 => ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 <=> ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptyset__Cong_type,type,
% 3.29/1.66 emptyset__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptyset__Cong,definition,
% 3.29/1.66 ( emptyset__Cong
% 3.29/1.66 = ( emptyset = emptyset ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoin__Cong_type,type,
% 3.29/1.66 setadjoin__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoin__Cong,definition,
% 3.29/1.66 ( setadjoin__Cong
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ! [Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( Xz = Xu )
% 3.29/1.66 => ( ( setadjoin @ Xx @ Xz )
% 3.29/1.66 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powerset__Cong_type,type,
% 3.29/1.66 powerset__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powerset__Cong,definition,
% 3.29/1.66 ( powerset__Cong
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ( ( powerset @ A )
% 3.29/1.66 = ( powerset @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunion__Cong_type,type,
% 3.29/1.66 setunion__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunion__Cong,definition,
% 3.29/1.66 ( setunion__Cong
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ( ( setunion @ A )
% 3.29/1.66 = ( setunion @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(omega__Cong_type,type,
% 3.29/1.66 omega__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(omega__Cong,definition,
% 3.29/1.66 ( omega__Cong
% 3.29/1.66 = ( omega = omega ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(exuEu_type,type,
% 3.29/1.66 exuEu: $o ).
% 3.29/1.66
% 3.29/1.66 thf(exuEu,definition,
% 3.29/1.66 ( exuEu
% 3.29/1.66 = ( ! [Xphi: $i > $o] :
% 3.29/1.66 ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xphi @ Xx )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(descr__Cong_type,type,
% 3.29/1.66 descr__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(descr__Cong,definition,
% 3.29/1.66 ( descr__Cong
% 3.29/1.66 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 <=> ( Xpsi @ Xy ) ) )
% 3.29/1.66 => ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ( ( exu
% 3.29/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.29/1.66 => ( ( descr
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 = ( descr
% 3.29/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstr__Cong_type,type,
% 3.29/1.66 dsetconstr__Cong: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dsetconstr__Cong,definition,
% 3.29/1.66 ( dsetconstr__Cong
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( Xx = Xy )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.29/1.66 => ( ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 = ( dsetconstr @ B
% 3.29/1.66 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subset_type,type,
% 3.29/1.66 subset: $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(disjoint_type,type,
% 3.29/1.66 disjoint: $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(setsmeet_type,type,
% 3.29/1.66 setsmeet: $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetI1_type,type,
% 3.29/1.66 subsetI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetI1,definition,
% 3.29/1.66 ( subsetI1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ B ) )
% 3.29/1.66 => ( subset @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(eqimpsubset2_type,type,
% 3.29/1.66 eqimpsubset2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(eqimpsubset2,definition,
% 3.29/1.66 ( eqimpsubset2
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ( subset @ B @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(eqimpsubset1_type,type,
% 3.29/1.66 eqimpsubset1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(eqimpsubset1,definition,
% 3.29/1.66 ( eqimpsubset1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( A = B )
% 3.29/1.66 => ( subset @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetI2_type,type,
% 3.29/1.66 subsetI2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetI2,definition,
% 3.29/1.66 ( subsetI2
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ B ) )
% 3.29/1.66 => ( subset @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetsubset_type,type,
% 3.29/1.66 emptysetsubset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(emptysetsubset,definition,
% 3.29/1.66 ( emptysetsubset
% 3.29/1.66 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetE_type,type,
% 3.29/1.66 subsetE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetE,definition,
% 3.29/1.66 ( subsetE
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetE2_type,type,
% 3.29/1.66 subsetE2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetE2,definition,
% 3.29/1.66 ( subsetE2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notsubsetI_type,type,
% 3.29/1.66 notsubsetI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notsubsetI,definition,
% 3.29/1.66 ( notsubsetI
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notequalI1_type,type,
% 3.29/1.66 notequalI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notequalI1,definition,
% 3.29/1.66 ( notequalI1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ~ ( subset @ A @ B )
% 3.29/1.66 => ( A != B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(notequalI2_type,type,
% 3.29/1.66 notequalI2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(notequalI2,definition,
% 3.29/1.66 ( notequalI2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ( A != B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetRefl_type,type,
% 3.29/1.66 subsetRefl: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetRefl,definition,
% 3.29/1.66 ( subsetRefl
% 3.29/1.66 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetTrans_type,type,
% 3.29/1.66 subsetTrans: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetTrans,definition,
% 3.29/1.66 ( subsetTrans
% 3.29/1.66 = ( ! [A: $i,B: $i,C: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ( subset @ B @ C )
% 3.29/1.66 => ( subset @ A @ C ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinSub_type,type,
% 3.29/1.66 setadjoinSub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinSub,definition,
% 3.29/1.66 ( setadjoinSub
% 3.29/1.66 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinSub2_type,type,
% 3.29/1.66 setadjoinSub2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setadjoinSub2,definition,
% 3.29/1.66 ( setadjoinSub2
% 3.29/1.66 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subset2powerset_type,type,
% 3.29/1.66 subset2powerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subset2powerset,definition,
% 3.29/1.66 ( subset2powerset
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setextsub_type,type,
% 3.29/1.66 setextsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setextsub,definition,
% 3.29/1.66 ( setextsub
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ( subset @ B @ A )
% 3.29/1.66 => ( A = B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(subsetemptysetimpeq_type,type,
% 3.29/1.66 subsetemptysetimpeq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(subsetemptysetimpeq,definition,
% 3.29/1.66 ( subsetemptysetimpeq
% 3.29/1.66 = ( ! [A: $i] :
% 3.29/1.66 ( ( subset @ A @ emptyset )
% 3.29/1.66 => ( A = emptyset ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powersetI1_type,type,
% 3.29/1.66 powersetI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetI1,definition,
% 3.29/1.66 ( powersetI1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ B @ A )
% 3.29/1.66 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powersetE1_type,type,
% 3.29/1.66 powersetE1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetE1,definition,
% 3.29/1.66 ( powersetE1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( in @ B @ ( powerset @ A ) )
% 3.29/1.66 => ( subset @ B @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(inPowerset_type,type,
% 3.29/1.66 inPowerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(inPowerset,definition,
% 3.29/1.66 ( inPowerset
% 3.29/1.66 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(powersetsubset_type,type,
% 3.29/1.66 powersetsubset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(powersetsubset,definition,
% 3.29/1.66 ( powersetsubset
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(sepInPowerset_type,type,
% 3.29/1.66 sepInPowerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(sepInPowerset,definition,
% 3.29/1.66 ( sepInPowerset
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( in
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 @ ( powerset @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(sepSubset_type,type,
% 3.29/1.66 sepSubset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(sepSubset,definition,
% 3.29/1.66 ( sepSubset
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( subset
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunion_type,type,
% 3.29/1.66 binunion: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(binunionIL_type,type,
% 3.29/1.66 binunionIL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionIL,definition,
% 3.29/1.66 ( binunionIL
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairset2IR_type,type,
% 3.29/1.66 upairset2IR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairset2IR,definition,
% 3.29/1.66 ( upairset2IR
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunionIR_type,type,
% 3.29/1.66 binunionIR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionIR,definition,
% 3.29/1.66 ( binunionIR
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunionEcases_type,type,
% 3.29/1.66 binunionEcases: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionEcases,definition,
% 3.29/1.66 ( binunionEcases
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.29/1.66 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.29/1.66 => ( ( ( in @ Xx @ A )
% 3.29/1.66 => Xphi )
% 3.29/1.66 => ( ( ( in @ Xx @ B )
% 3.29/1.66 => Xphi )
% 3.29/1.66 => Xphi ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunionE_type,type,
% 3.29/1.66 binunionE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionE,definition,
% 3.29/1.66 ( binunionE
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.29/1.66 => ( ( in @ Xx @ A )
% 3.29/1.66 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunionLsub_type,type,
% 3.29/1.66 binunionLsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionLsub,definition,
% 3.29/1.66 ( binunionLsub
% 3.29/1.66 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binunionRsub_type,type,
% 3.29/1.66 binunionRsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binunionRsub,definition,
% 3.29/1.66 ( binunionRsub
% 3.29/1.66 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersect_type,type,
% 3.29/1.66 binintersect: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectI_type,type,
% 3.29/1.66 binintersectI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectI,definition,
% 3.29/1.66 ( binintersectI
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset5_type,type,
% 3.29/1.66 binintersectSubset5: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset5,definition,
% 3.29/1.66 ( binintersectSubset5
% 3.29/1.66 = ( ! [A: $i,B: $i,C: $i] :
% 3.29/1.66 ( ( subset @ C @ A )
% 3.29/1.66 => ( ( subset @ C @ B )
% 3.29/1.66 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectEL_type,type,
% 3.29/1.66 binintersectEL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectEL,definition,
% 3.29/1.66 ( binintersectEL
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectLsub_type,type,
% 3.29/1.66 binintersectLsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectLsub,definition,
% 3.29/1.66 ( binintersectLsub
% 3.29/1.66 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset2_type,type,
% 3.29/1.66 binintersectSubset2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset2,definition,
% 3.29/1.66 ( binintersectSubset2
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ( binintersect @ A @ B )
% 3.29/1.66 = A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset3_type,type,
% 3.29/1.66 binintersectSubset3: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset3,definition,
% 3.29/1.66 ( binintersectSubset3
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( ( binintersect @ A @ B )
% 3.29/1.66 = B )
% 3.29/1.66 => ( subset @ B @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectER_type,type,
% 3.29/1.66 binintersectER: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectER,definition,
% 3.29/1.66 ( binintersectER
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.29/1.66 => ( in @ Xx @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(disjointsetsI1_type,type,
% 3.29/1.66 disjointsetsI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(disjointsetsI1,definition,
% 3.29/1.66 ( disjointsetsI1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ~ ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( in @ Xx @ B ) )
% 3.29/1.66 => ( ( binintersect @ A @ B )
% 3.29/1.66 = emptyset ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectRsub_type,type,
% 3.29/1.66 binintersectRsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectRsub,definition,
% 3.29/1.66 ( binintersectRsub
% 3.29/1.66 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset4_type,type,
% 3.29/1.66 binintersectSubset4: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset4,definition,
% 3.29/1.66 ( binintersectSubset4
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ B @ A )
% 3.29/1.66 => ( ( binintersect @ A @ B )
% 3.29/1.66 = B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset1_type,type,
% 3.29/1.66 binintersectSubset1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(binintersectSubset1,definition,
% 3.29/1.66 ( binintersectSubset1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( ( binintersect @ A @ B )
% 3.29/1.66 = A )
% 3.29/1.66 => ( subset @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(bs114d_type,type,
% 3.29/1.66 bs114d: $o ).
% 3.29/1.66
% 3.29/1.66 thf(bs114d,definition,
% 3.29/1.66 ( bs114d
% 3.29/1.66 = ( ! [A: $i,B: $i,C: $i] :
% 3.29/1.66 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.29/1.66 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(regular_type,type,
% 3.29/1.66 regular: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminus_type,type,
% 3.29/1.66 setminus: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(setminusI_type,type,
% 3.29/1.66 setminusI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusI,definition,
% 3.29/1.66 ( setminusI
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusEL_type,type,
% 3.29/1.66 setminusEL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusEL,definition,
% 3.29/1.66 ( setminusEL
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusER_type,type,
% 3.29/1.66 setminusER: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusER,definition,
% 3.29/1.66 ( setminusER
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.29/1.66 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusSubset2_type,type,
% 3.29/1.66 setminusSubset2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusSubset2,definition,
% 3.29/1.66 ( setminusSubset2
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( subset @ A @ B )
% 3.29/1.66 => ( ( setminus @ A @ B )
% 3.29/1.66 = emptyset ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusERneg_type,type,
% 3.29/1.66 setminusERneg: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusERneg,definition,
% 3.29/1.66 ( setminusERneg
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.29/1.66 => ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusELneg_type,type,
% 3.29/1.66 setminusELneg: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusELneg,definition,
% 3.29/1.66 ( setminusELneg
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusILneg_type,type,
% 3.29/1.66 setminusILneg: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusILneg,definition,
% 3.29/1.66 ( setminusILneg
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ~ ( in @ Xx @ A )
% 3.29/1.66 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusIRneg_type,type,
% 3.29/1.66 setminusIRneg: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusIRneg,definition,
% 3.29/1.66 ( setminusIRneg
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ B )
% 3.29/1.66 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusLsub_type,type,
% 3.29/1.66 setminusLsub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusLsub,definition,
% 3.29/1.66 ( setminusLsub
% 3.29/1.66 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setminusSubset1_type,type,
% 3.29/1.66 setminusSubset1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setminusSubset1,definition,
% 3.29/1.66 ( setminusSubset1
% 3.29/1.66 = ( ! [A: $i,B: $i] :
% 3.29/1.66 ( ( ( setminus @ A @ B )
% 3.29/1.66 = emptyset )
% 3.29/1.66 => ( subset @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(symdiff_type,type,
% 3.29/1.66 symdiff: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffE_type,type,
% 3.29/1.66 symdiffE: $o ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffE,definition,
% 3.29/1.66 ( symdiffE
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.29/1.66 => ! [Xphi: $o] :
% 3.29/1.66 ( ( ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => Xphi ) )
% 3.29/1.66 => ( ( ~ ( in @ Xx @ A )
% 3.29/1.66 => ( ( in @ Xx @ B )
% 3.29/1.66 => Xphi ) )
% 3.29/1.66 => Xphi ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffI1_type,type,
% 3.29/1.66 symdiffI1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffI1,definition,
% 3.29/1.66 ( symdiffI1
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffI2_type,type,
% 3.29/1.66 symdiffI2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffI2,definition,
% 3.29/1.66 ( symdiffI2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ~ ( in @ Xx @ A )
% 3.29/1.66 => ( ( in @ Xx @ B )
% 3.29/1.66 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffIneg1_type,type,
% 3.29/1.66 symdiffIneg1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffIneg1,definition,
% 3.29/1.66 ( symdiffIneg1
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( in @ Xx @ B )
% 3.29/1.66 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffIneg2_type,type,
% 3.29/1.66 symdiffIneg2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(symdiffIneg2,definition,
% 3.29/1.66 ( symdiffIneg2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ~ ( in @ Xx @ A )
% 3.29/1.66 => ( ~ ( in @ Xx @ B )
% 3.29/1.66 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(iskpair_type,type,
% 3.29/1.66 iskpair: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(secondinupair_type,type,
% 3.29/1.66 secondinupair: $o ).
% 3.29/1.66
% 3.29/1.66 thf(secondinupair,definition,
% 3.29/1.66 ( secondinupair
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairIL_type,type,
% 3.29/1.66 setukpairIL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairIL,definition,
% 3.29/1.66 ( setukpairIL
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairIR_type,type,
% 3.29/1.66 setukpairIR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairIR,definition,
% 3.29/1.66 ( setukpairIR
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(kpairiskpair_type,type,
% 3.29/1.66 kpairiskpair: $o ).
% 3.29/1.66
% 3.29/1.66 thf(kpairiskpair,definition,
% 3.29/1.66 ( kpairiskpair
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(kpair_type,type,
% 3.29/1.66 kpair: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(kpairp_type,type,
% 3.29/1.66 kpairp: $o ).
% 3.29/1.66
% 3.29/1.66 thf(kpairp,definition,
% 3.29/1.66 ( kpairp
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprod_type,type,
% 3.29/1.66 cartprod: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsubset_type,type,
% 3.29/1.66 singletonsubset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsubset,definition,
% 3.29/1.66 ( singletonsubset
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(singletoninpowerset_type,type,
% 3.29/1.66 singletoninpowerset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletoninpowerset,definition,
% 3.29/1.66 ( singletoninpowerset
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(singletoninpowunion_type,type,
% 3.29/1.66 singletoninpowunion: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletoninpowunion,definition,
% 3.29/1.66 ( singletoninpowunion
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairset2E_type,type,
% 3.29/1.66 upairset2E: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairset2E,definition,
% 3.29/1.66 ( upairset2E
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.29/1.66 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.29/1.66 => ( ( Xz = Xx )
% 3.29/1.66 | ( Xz = Xy ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairsubunion_type,type,
% 3.29/1.66 upairsubunion: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairsubunion,definition,
% 3.29/1.66 ( upairsubunion
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairinpowunion_type,type,
% 3.29/1.66 upairinpowunion: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairinpowunion,definition,
% 3.29/1.66 ( upairinpowunion
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem1_type,type,
% 3.29/1.66 ubforcartprodlem1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem1,definition,
% 3.29/1.66 ( ubforcartprodlem1
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem2_type,type,
% 3.29/1.66 ubforcartprodlem2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem2,definition,
% 3.29/1.66 ( ubforcartprodlem2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem3_type,type,
% 3.29/1.66 ubforcartprodlem3: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ubforcartprodlem3,definition,
% 3.29/1.66 ( ubforcartprodlem3
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairin_type,type,
% 3.29/1.66 cartprodpairin: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairin,definition,
% 3.29/1.66 ( cartprodpairin
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempair1_type,type,
% 3.29/1.66 cartprodmempair1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempair1,definition,
% 3.29/1.66 ( cartprodmempair1
% 3.29/1.66 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.29/1.66 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ? [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 & ( Xu
% 3.29/1.66 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempair_type,type,
% 3.29/1.66 cartprodmempair: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempair,definition,
% 3.29/1.66 ( cartprodmempair
% 3.29/1.66 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.29/1.66 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( iskpair @ Xu ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionE2_type,type,
% 3.29/1.66 setunionE2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionE2,definition,
% 3.29/1.66 ( setunionE2
% 3.29/1.66 = ( ! [A: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ ( setunion @ A ) )
% 3.29/1.66 => ? [X: $i] :
% 3.29/1.66 ( ( in @ X @ A )
% 3.29/1.66 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton1_type,type,
% 3.29/1.66 setunionsingleton1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton1,definition,
% 3.29/1.66 ( setunionsingleton1
% 3.29/1.66 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton2_type,type,
% 3.29/1.66 setunionsingleton2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton2,definition,
% 3.29/1.66 ( setunionsingleton2
% 3.29/1.66 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton_type,type,
% 3.29/1.66 setunionsingleton: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setunionsingleton,definition,
% 3.29/1.66 ( setunionsingleton
% 3.29/1.66 = ( ! [Xx: $i] :
% 3.29/1.66 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.29/1.66 = Xx ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(singleton_type,type,
% 3.29/1.66 singleton: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletonprop_type,type,
% 3.29/1.66 singletonprop: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletonprop,definition,
% 3.29/1.66 ( singletonprop
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ A )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) )
% 3.29/1.66 => ( ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) )
% 3.29/1.66 => ( singleton
% 3.29/1.66 @ ( dsetconstr @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ex1_type,type,
% 3.29/1.66 ex1: $i > ( $i > $o ) > $o ).
% 3.29/1.66
% 3.29/1.66 thf(ex1E1_type,type,
% 3.29/1.66 ex1E1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ex1E1,definition,
% 3.29/1.66 ( ex1E1
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ( ex1 @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.66 => ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ex1I_type,type,
% 3.29/1.66 ex1I: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ex1I,definition,
% 3.29/1.66 ( ex1I
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 => ( ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ A )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xy = Xx ) ) )
% 3.29/1.66 => ( ex1 @ A
% 3.29/1.66 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ex1I2_type,type,
% 3.29/1.66 ex1I2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ex1I2,definition,
% 3.29/1.66 ( ex1I2
% 3.29/1.66 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ A )
% 3.29/1.66 => ( ( Xphi @ Xx )
% 3.29/1.66 => ( ( Xphi @ Xy )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) )
% 3.29/1.66 => ( ? [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 & ( Xphi @ Xx ) )
% 3.29/1.66 => ( ex1 @ A
% 3.29/1.66 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsuniq_type,type,
% 3.29/1.66 singletonsuniq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(singletonsuniq,definition,
% 3.29/1.66 ( singletonsuniq
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( ( setadjoin @ Xx @ emptyset )
% 3.29/1.66 = ( setadjoin @ Xy @ emptyset ) )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(atmost1p_type,type,
% 3.29/1.66 atmost1p: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(atleast2p_type,type,
% 3.29/1.66 atleast2p: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(atmost2p_type,type,
% 3.29/1.66 atmost2p: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairsetp_type,type,
% 3.29/1.66 upairsetp: $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL1_type,type,
% 3.29/1.66 setukpairinjL1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL1,definition,
% 3.29/1.66 ( setukpairinjL1
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.29/1.66 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.29/1.66 => ( Xx = Xz ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(kfstsingleton_type,type,
% 3.29/1.66 kfstsingleton: $o ).
% 3.29/1.66
% 3.29/1.66 thf(kfstsingleton,definition,
% 3.29/1.66 ( kfstsingleton
% 3.29/1.66 = ( ! [Xu: $i] :
% 3.29/1.66 ( ( iskpair @ Xu )
% 3.29/1.66 => ( singleton
% 3.29/1.66 @ ( dsetconstr @ ( setunion @ Xu )
% 3.29/1.66 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(theprop_type,type,
% 3.29/1.66 theprop: $o ).
% 3.29/1.66
% 3.29/1.66 thf(theprop,definition,
% 3.29/1.66 ( theprop
% 3.29/1.66 = ( ! [X: $i] :
% 3.29/1.66 ( ( singleton @ X )
% 3.29/1.66 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(kfst_type,type,
% 3.29/1.66 kfst: $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(kfstpairEq_type,type,
% 3.29/1.66 kfstpairEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(kfstpairEq,definition,
% 3.29/1.66 ( kfstpairEq
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.29/1.66 = Xx ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodfstin_type,type,
% 3.29/1.66 cartprodfstin: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodfstin,definition,
% 3.29/1.66 ( cartprodfstin
% 3.29/1.66 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.29/1.66 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL2_type,type,
% 3.29/1.66 setukpairinjL2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL2,definition,
% 3.29/1.66 ( setukpairinjL2
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.29/1.66 => ( Xx = Xz ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL_type,type,
% 3.29/1.66 setukpairinjL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjL,definition,
% 3.29/1.66 ( setukpairinjL
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( ( kpair @ Xx @ Xy )
% 3.29/1.66 = ( kpair @ Xz @ Xu ) )
% 3.29/1.66 => ( Xx = Xz ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR11_type,type,
% 3.29/1.66 setukpairinjR11: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR11,definition,
% 3.29/1.66 ( setukpairinjR11
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR12_type,type,
% 3.29/1.66 setukpairinjR12: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR12,definition,
% 3.29/1.66 ( setukpairinjR12
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xx = Xy )
% 3.29/1.66 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR1_type,type,
% 3.29/1.66 setukpairinjR1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR1,definition,
% 3.29/1.66 ( setukpairinjR1
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.29/1.66 => ( ( Xz = Xu )
% 3.29/1.66 => ( Xy = Xu ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(upairequniteq_type,type,
% 3.29/1.66 upairequniteq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(upairequniteq,definition,
% 3.29/1.66 ( upairequniteq
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.29/1.66 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ Xz @ emptyset ) )
% 3.29/1.66 => ( Xx = Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR2_type,type,
% 3.29/1.66 setukpairinjR2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR2,definition,
% 3.29/1.66 ( setukpairinjR2
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.29/1.66 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.29/1.66 => ( Xy = Xu ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR_type,type,
% 3.29/1.66 setukpairinjR: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setukpairinjR,definition,
% 3.29/1.66 ( setukpairinjR
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.29/1.66 ( ( ( kpair @ Xx @ Xy )
% 3.29/1.66 = ( kpair @ Xz @ Xu ) )
% 3.29/1.66 => ( Xy = Xu ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ksndsingleton_type,type,
% 3.29/1.66 ksndsingleton: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ksndsingleton,definition,
% 3.29/1.66 ( ksndsingleton
% 3.29/1.66 = ( ! [Xu: $i] :
% 3.29/1.66 ( ( iskpair @ Xu )
% 3.29/1.66 => ( singleton
% 3.29/1.66 @ ( dsetconstr @ ( setunion @ Xu )
% 3.29/1.66 @ ^ [Xx: $i] :
% 3.29/1.66 ( Xu
% 3.29/1.66 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ksnd_type,type,
% 3.29/1.66 ksnd: $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(ksndpairEq_type,type,
% 3.29/1.66 ksndpairEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ksndpairEq,definition,
% 3.29/1.66 ( ksndpairEq
% 3.29/1.66 = ( ! [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.29/1.66 = Xy ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(kpairsurjEq_type,type,
% 3.29/1.66 kpairsurjEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(kpairsurjEq,definition,
% 3.29/1.66 ( kpairsurjEq
% 3.29/1.66 = ( ! [Xu: $i] :
% 3.29/1.66 ( ( iskpair @ Xu )
% 3.29/1.66 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.29/1.66 = Xu ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodsndin_type,type,
% 3.29/1.66 cartprodsndin: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodsndin,definition,
% 3.29/1.66 ( cartprodsndin
% 3.29/1.66 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.29/1.66 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairmemEL_type,type,
% 3.29/1.66 cartprodpairmemEL: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairmemEL,definition,
% 3.29/1.66 ( cartprodpairmemEL
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairmemER_type,type,
% 3.29/1.66 cartprodpairmemER: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairmemER,definition,
% 3.29/1.66 ( cartprodpairmemER
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( in @ Xy @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempaircEq_type,type,
% 3.29/1.66 cartprodmempaircEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodmempaircEq,definition,
% 3.29/1.66 ( cartprodmempaircEq
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( kpair @ Xx @ Xy )
% 3.29/1.66 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodfstpairEq_type,type,
% 3.29/1.66 cartprodfstpairEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodfstpairEq,definition,
% 3.29/1.66 ( cartprodfstpairEq
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.29/1.66 = Xx ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodsndpairEq_type,type,
% 3.29/1.66 cartprodsndpairEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodsndpairEq,definition,
% 3.29/1.66 ( cartprodsndpairEq
% 3.29/1.66 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.29/1.66 = Xy ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairsurjEq_type,type,
% 3.29/1.66 cartprodpairsurjEq: $o ).
% 3.29/1.66
% 3.29/1.66 thf(cartprodpairsurjEq,definition,
% 3.29/1.66 ( cartprodpairsurjEq
% 3.29/1.66 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.29/1.66 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.29/1.66 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.29/1.66 = Xu ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(breln_type,type,
% 3.29/1.66 breln: $i > $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstr_type,type,
% 3.29/1.66 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrI_type,type,
% 3.29/1.66 dpsetconstrI: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrI,definition,
% 3.29/1.66 ( dpsetconstrI
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( Xphi @ Xx @ Xy )
% 3.29/1.66 => ( in @ ( kpair @ Xx @ Xy )
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrSub_type,type,
% 3.29/1.66 dpsetconstrSub: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrSub,definition,
% 3.29/1.66 ( dpsetconstrSub
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.29/1.66 ( subset
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.29/1.66 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(setOfPairsIsBReln_type,type,
% 3.29/1.66 setOfPairsIsBReln: $o ).
% 3.29/1.66
% 3.29/1.66 thf(setOfPairsIsBReln,definition,
% 3.29/1.66 ( setOfPairsIsBReln
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.29/1.66 ( breln @ A @ B
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrERa_type,type,
% 3.29/1.66 dpsetconstrERa: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrERa,definition,
% 3.29/1.66 ( dpsetconstrERa
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.66 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.29/1.66 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrEL1_type,type,
% 3.29/1.66 dpsetconstrEL1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrEL1,definition,
% 3.29/1.66 ( dpsetconstrEL1
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ ( kpair @ Xx @ Xy )
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.29/1.66 => ( in @ Xx @ A ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrEL2_type,type,
% 3.29/1.66 dpsetconstrEL2: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrEL2,definition,
% 3.29/1.66 ( dpsetconstrEL2
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ ( kpair @ Xx @ Xy )
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.29/1.66 => ( in @ Xy @ B ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrER_type,type,
% 3.29/1.66 dpsetconstrER: $o ).
% 3.29/1.66
% 3.29/1.66 thf(dpsetconstrER,definition,
% 3.29/1.66 ( dpsetconstrER
% 3.29/1.66 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( in @ ( kpair @ Xx @ Xy )
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.29/1.66 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(func_type,type,
% 3.29/1.66 func: $i > $i > $i > $o ).
% 3.29/1.66
% 3.29/1.66 thf(funcSet_type,type,
% 3.29/1.66 funcSet: $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(funcImageSingleton_type,type,
% 3.29/1.66 funcImageSingleton: $o ).
% 3.29/1.66
% 3.29/1.66 thf(funcImageSingleton,definition,
% 3.29/1.66 ( funcImageSingleton
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( func @ A @ B @ Xf )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( singleton
% 3.29/1.66 @ ( dsetconstr @ B
% 3.29/1.66 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(apProp_type,type,
% 3.29/1.66 apProp: $o ).
% 3.29/1.66
% 3.29/1.66 thf(apProp,definition,
% 3.29/1.66 ( apProp
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( func @ A @ B @ Xf )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in
% 3.29/1.66 @ ( setunion
% 3.29/1.66 @ ( dsetconstr @ B
% 3.29/1.66 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.29/1.66 @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ap_type,type,
% 3.29/1.66 ap: $i > $i > $i > $i > $i ).
% 3.29/1.66
% 3.29/1.66 thf(app_type,type,
% 3.29/1.66 app: $o ).
% 3.29/1.66
% 3.29/1.66 thf(app,definition,
% 3.29/1.66 ( app
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( func @ A @ B @ Xf )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(infuncsetfunc_type,type,
% 3.29/1.66 infuncsetfunc: $o ).
% 3.29/1.66
% 3.29/1.66 thf(infuncsetfunc,definition,
% 3.29/1.66 ( infuncsetfunc
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.66 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(ap2p_type,type,
% 3.29/1.66 ap2p: $o ).
% 3.29/1.66
% 3.29/1.66 thf(ap2p,definition,
% 3.29/1.66 ( ap2p
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.66 => ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(funcinfuncset_type,type,
% 3.29/1.66 funcinfuncset: $o ).
% 3.29/1.66
% 3.29/1.66 thf(funcinfuncset,definition,
% 3.29/1.66 ( funcinfuncset
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.66 ( ( func @ A @ B @ Xf )
% 3.29/1.66 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(lamProp_type,type,
% 3.29/1.66 lamProp: $o ).
% 3.29/1.66
% 3.29/1.66 thf(lamProp,definition,
% 3.29/1.66 ( lamProp
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.66 => ( func @ A @ B
% 3.29/1.66 @ ( dpsetconstr @ A @ B
% 3.29/1.66 @ ^ [Xx: $i,Xy: $i] :
% 3.29/1.66 ( ( Xf @ Xx )
% 3.29/1.66 = Xy ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(lam_type,type,
% 3.29/1.66 lam: $i > $i > ( $i > $i ) > $i ).
% 3.29/1.66
% 3.29/1.66 thf(lamp_type,type,
% 3.29/1.66 lamp: $o ).
% 3.29/1.66
% 3.29/1.66 thf(lamp,definition,
% 3.29/1.66 ( lamp
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.66 => ( func @ A @ B
% 3.29/1.66 @ ( lam @ A @ B
% 3.29/1.66 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(lam2p_type,type,
% 3.29/1.66 lam2p: $o ).
% 3.29/1.66
% 3.29/1.66 thf(lam2p,definition,
% 3.29/1.66 ( lam2p
% 3.29/1.66 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.66 => ( in
% 3.29/1.66 @ ( lam @ A @ B
% 3.29/1.66 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.29/1.66 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.29/1.66
% 3.29/1.66 thf(brelnall1_type,type,
% 3.29/1.66 brelnall1: $o ).
% 3.29/1.66
% 3.29/1.66 thf(brelnall1,definition,
% 3.29/1.66 ( brelnall1
% 3.29/1.66 = ( ! [A: $i,B: $i,R: $i] :
% 3.29/1.66 ( ( breln @ A @ B @ R )
% 3.29/1.66 => ! [Xphi: $i > $o] :
% 3.29/1.66 ( ! [Xx: $i] :
% 3.29/1.66 ( ( in @ Xx @ A )
% 3.29/1.66 => ! [Xy: $i] :
% 3.29/1.66 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ R )
% 3.29/1.67 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(brelnall2_type,type,
% 3.29/1.67 brelnall2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(brelnall2,definition,
% 3.29/1.67 ( brelnall2
% 3.29/1.67 = ( ! [A: $i,B: $i,R: $i] :
% 3.29/1.67 ( ( breln @ A @ B @ R )
% 3.29/1.67 => ! [Xphi: $i > $o] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ R )
% 3.29/1.67 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(ex1E2_type,type,
% 3.29/1.67 ex1E2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(ex1E2,definition,
% 3.29/1.67 ( ex1E2
% 3.29/1.67 = ( ! [A: $i,Xphi: $i > $o] :
% 3.29/1.67 ( ( ex1 @ A
% 3.29/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( Xphi @ Xx )
% 3.29/1.67 => ( ( Xphi @ Xy )
% 3.29/1.67 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp1_type,type,
% 3.29/1.67 funcGraphProp1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp1,definition,
% 3.29/1.67 ( funcGraphProp1
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp3_type,type,
% 3.29/1.67 funcGraphProp3: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp3,definition,
% 3.29/1.67 ( funcGraphProp3
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp2_type,type,
% 3.29/1.67 funcGraphProp2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp2,definition,
% 3.29/1.67 ( funcGraphProp2
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = Xy ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcextLem_type,type,
% 3.29/1.67 funcextLem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcextLem,definition,
% 3.29/1.67 ( funcextLem
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ! [Xg: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xg )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp4_type,type,
% 3.29/1.67 funcGraphProp4: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcGraphProp4,definition,
% 3.29/1.67 ( funcGraphProp4
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = Xy ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(subbreln_type,type,
% 3.29/1.67 subbreln: $o ).
% 3.29/1.67
% 3.29/1.67 thf(subbreln,definition,
% 3.29/1.67 ( subbreln
% 3.29/1.67 = ( ! [A: $i,B: $i,R: $i] :
% 3.29/1.67 ( ( breln @ A @ B @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln @ A @ B @ S )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.29/1.67 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(eqbreln_type,type,
% 3.29/1.67 eqbreln: $o ).
% 3.29/1.67
% 3.29/1.67 thf(eqbreln,definition,
% 3.29/1.67 ( eqbreln
% 3.29/1.67 = ( ! [A: $i,B: $i,R: $i] :
% 3.29/1.67 ( ( breln @ A @ B @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln @ A @ B @ S )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.29/1.67 => ( R = S ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcext_type,type,
% 3.29/1.67 funcext: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcext,definition,
% 3.29/1.67 ( funcext
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ! [Xg: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xg )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.29/1.67 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(funcext2_type,type,
% 3.29/1.67 funcext2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(funcext2,definition,
% 3.29/1.67 ( funcext2
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ! [Xg: $i] :
% 3.29/1.67 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.29/1.67 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(ap2apEq1_type,type,
% 3.29/1.67 ap2apEq1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(ap2apEq1,definition,
% 3.29/1.67 ( ap2apEq1
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(ap2apEq2_type,type,
% 3.29/1.67 ap2apEq2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(ap2apEq2,definition,
% 3.29/1.67 ( ap2apEq2
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.29/1.67 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(beta1_type,type,
% 3.29/1.67 beta1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(beta1,definition,
% 3.29/1.67 ( beta1
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B
% 3.29/1.67 @ ( lam @ A @ B
% 3.29/1.67 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.29/1.67 @ Xx )
% 3.29/1.67 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(eta1_type,type,
% 3.29/1.67 eta1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(eta1,definition,
% 3.29/1.67 ( eta1
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( func @ A @ B @ Xf )
% 3.29/1.67 => ( ( lam @ A @ B
% 3.29/1.67 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.29/1.67 = Xf ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(lam2lamEq_type,type,
% 3.29/1.67 lam2lamEq: $o ).
% 3.29/1.67
% 3.29/1.67 thf(lam2lamEq,definition,
% 3.29/1.67 ( lam2lamEq
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.67 => ( ( lam @ A @ B
% 3.29/1.67 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.29/1.67 = ( lam @ A @ B
% 3.29/1.67 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(beta2_type,type,
% 3.29/1.67 beta2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(beta2,definition,
% 3.29/1.67 ( beta2
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( ap @ A @ B
% 3.29/1.67 @ ( lam @ A @ B
% 3.29/1.67 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.29/1.67 @ Xx )
% 3.29/1.67 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(eta2_type,type,
% 3.29/1.67 eta2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(eta2,definition,
% 3.29/1.67 ( eta2
% 3.29/1.67 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.29/1.67 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.29/1.67 => ( ( lam @ A @ B
% 3.29/1.67 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.29/1.67 = Xf ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iffalseProp1_type,type,
% 3.29/1.67 iffalseProp1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iffalseProp1,definition,
% 3.29/1.67 ( iffalseProp1
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ~ Xphi
% 3.29/1.67 => ( in @ Xy
% 3.29/1.67 @ ( dsetconstr @ A
% 3.29/1.67 @ ^ [Xz: $i] :
% 3.29/1.67 ( ( Xphi
% 3.29/1.67 & ( Xz = Xx ) )
% 3.29/1.67 | ( ~ Xphi
% 3.29/1.67 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iffalseProp2_type,type,
% 3.29/1.67 iffalseProp2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iffalseProp2,definition,
% 3.29/1.67 ( iffalseProp2
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ~ Xphi
% 3.29/1.67 => ( ( dsetconstr @ A
% 3.29/1.67 @ ^ [Xz: $i] :
% 3.29/1.67 ( ( Xphi
% 3.29/1.67 & ( Xz = Xx ) )
% 3.29/1.67 | ( ~ Xphi
% 3.29/1.67 & ( Xz = Xy ) ) ) )
% 3.29/1.67 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueProp1_type,type,
% 3.29/1.67 iftrueProp1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueProp1,definition,
% 3.29/1.67 ( iftrueProp1
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( Xphi
% 3.29/1.67 => ( in @ Xx
% 3.29/1.67 @ ( dsetconstr @ A
% 3.29/1.67 @ ^ [Xz: $i] :
% 3.29/1.67 ( ( Xphi
% 3.29/1.67 & ( Xz = Xx ) )
% 3.29/1.67 | ( ~ Xphi
% 3.29/1.67 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueProp2_type,type,
% 3.29/1.67 iftrueProp2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueProp2,definition,
% 3.29/1.67 ( iftrueProp2
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( Xphi
% 3.29/1.67 => ( ( dsetconstr @ A
% 3.29/1.67 @ ^ [Xz: $i] :
% 3.29/1.67 ( ( Xphi
% 3.29/1.67 & ( Xz = Xx ) )
% 3.29/1.67 | ( ~ Xphi
% 3.29/1.67 & ( Xz = Xy ) ) ) )
% 3.29/1.67 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(ifSingleton_type,type,
% 3.29/1.67 ifSingleton: $o ).
% 3.29/1.67
% 3.29/1.67 thf(ifSingleton,definition,
% 3.29/1.67 ( ifSingleton
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( singleton
% 3.29/1.67 @ ( dsetconstr @ A
% 3.29/1.67 @ ^ [Xz: $i] :
% 3.29/1.67 ( ( Xphi
% 3.29/1.67 & ( Xz = Xx ) )
% 3.29/1.67 | ( ~ Xphi
% 3.29/1.67 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(if_type,type,
% 3.29/1.67 if: $i > $o > $i > $i > $i ).
% 3.29/1.67
% 3.29/1.67 thf(ifp_type,type,
% 3.29/1.67 ifp: $o ).
% 3.29/1.67
% 3.29/1.67 thf(ifp,definition,
% 3.29/1.67 ( ifp
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(theeq_type,type,
% 3.29/1.67 theeq: $o ).
% 3.29/1.67
% 3.29/1.67 thf(theeq,definition,
% 3.29/1.67 ( theeq
% 3.29/1.67 = ( ! [X: $i] :
% 3.29/1.67 ( ( singleton @ X )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ X )
% 3.29/1.67 => ( ( setunion @ X )
% 3.29/1.67 = Xx ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iftrue_type,type,
% 3.29/1.67 iftrue: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iftrue,definition,
% 3.29/1.67 ( iftrue
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( Xphi
% 3.29/1.67 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.29/1.67 = Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iffalse_type,type,
% 3.29/1.67 iffalse: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iffalse,definition,
% 3.29/1.67 ( iffalse
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ~ Xphi
% 3.29/1.67 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.29/1.67 = Xy ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueorfalse_type,type,
% 3.29/1.67 iftrueorfalse: $o ).
% 3.29/1.67
% 3.29/1.67 thf(iftrueorfalse,definition,
% 3.29/1.67 ( iftrueorfalse
% 3.29/1.67 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectT_lem_type,type,
% 3.29/1.67 binintersectT_lem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectT_lem,definition,
% 3.29/1.67 ( binintersectT_lem
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binunionT_lem_type,type,
% 3.29/1.67 binunionT_lem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binunionT_lem,definition,
% 3.29/1.67 ( binunionT_lem
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(powersetT_lem_type,type,
% 3.29/1.67 powersetT_lem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(powersetT_lem,definition,
% 3.29/1.67 ( powersetT_lem
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(setminusT_lem_type,type,
% 3.29/1.67 setminusT_lem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(setminusT_lem,definition,
% 3.29/1.67 ( setminusT_lem
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementT_lem_type,type,
% 3.29/1.67 complementT_lem: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementT_lem,definition,
% 3.29/1.67 ( complementT_lem
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(setextT_type,type,
% 3.29/1.67 setextT: $o ).
% 3.29/1.67
% 3.29/1.67 thf(setextT,definition,
% 3.29/1.67 ( setextT
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ( in @ Xx @ Y ) ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ Y )
% 3.29/1.67 => ( in @ Xx @ X ) ) )
% 3.29/1.67 => ( X = Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(subsetTI_type,type,
% 3.29/1.67 subsetTI: $o ).
% 3.29/1.67
% 3.29/1.67 thf(subsetTI,definition,
% 3.29/1.67 ( subsetTI
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ( in @ Xx @ Y ) ) )
% 3.29/1.67 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(powersetTI1_type,type,
% 3.29/1.67 powersetTI1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(powersetTI1,definition,
% 3.29/1.67 ( powersetTI1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ( in @ Xx @ Y ) ) )
% 3.29/1.67 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(powersetTE1_type,type,
% 3.29/1.67 powersetTE1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(powersetTE1,definition,
% 3.29/1.67 ( powersetTE1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ X @ ( powerset @ Y ) )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementTI1_type,type,
% 3.29/1.67 complementTI1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementTI1,definition,
% 3.29/1.67 ( complementTI1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementTE1_type,type,
% 3.29/1.67 complementTE1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementTE1,definition,
% 3.29/1.67 ( complementTE1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.29/1.67 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectTELcontra_type,type,
% 3.29/1.67 binintersectTELcontra: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectTELcontra,definition,
% 3.29/1.67 ( binintersectTELcontra
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ X )
% 3.29/1.67 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectTERcontra_type,type,
% 3.29/1.67 binintersectTERcontra: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binintersectTERcontra,definition,
% 3.29/1.67 ( binintersectTERcontra
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ Y )
% 3.29/1.67 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT_type,type,
% 3.29/1.67 contrasubsetT: $o ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT,definition,
% 3.29/1.67 ( contrasubsetT
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.29/1.67 => ( ( in @ Xx @ Y )
% 3.29/1.67 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT1_type,type,
% 3.29/1.67 contrasubsetT1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT1,definition,
% 3.29/1.67 ( contrasubsetT1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( subset @ X @ Y )
% 3.29/1.67 => ( ~ ( in @ Xx @ Y )
% 3.29/1.67 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT2_type,type,
% 3.29/1.67 contrasubsetT2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT2,definition,
% 3.29/1.67 ( contrasubsetT2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ Y )
% 3.29/1.67 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT3_type,type,
% 3.29/1.67 contrasubsetT3: $o ).
% 3.29/1.67
% 3.29/1.67 thf(contrasubsetT3,definition,
% 3.29/1.67 ( contrasubsetT3
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.29/1.67 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementI1_type,type,
% 3.29/1.67 doubleComplementI1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementI1,definition,
% 3.29/1.67 ( doubleComplementI1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ X )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementE1_type,type,
% 3.29/1.67 doubleComplementE1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementE1,definition,
% 3.29/1.67 ( doubleComplementE1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.29/1.67 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementSub1_type,type,
% 3.29/1.67 doubleComplementSub1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementSub1,definition,
% 3.29/1.67 ( doubleComplementSub1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementSub2_type,type,
% 3.29/1.67 doubleComplementSub2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementSub2,definition,
% 3.29/1.67 ( doubleComplementSub2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementEq_type,type,
% 3.29/1.67 doubleComplementEq: $o ).
% 3.29/1.67
% 3.29/1.67 thf(doubleComplementEq,definition,
% 3.29/1.67 ( doubleComplementEq
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ( X
% 3.29/1.67 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementTnotintersectT_type,type,
% 3.29/1.67 complementTnotintersectT: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementTnotintersectT,definition,
% 3.29/1.67 ( complementTnotintersectT
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.29/1.67 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementImpComplementIntersect_type,type,
% 3.29/1.67 complementImpComplementIntersect: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementImpComplementIntersect,definition,
% 3.29/1.67 ( complementImpComplementIntersect
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementSubsetComplementIntersect_type,type,
% 3.29/1.67 complementSubsetComplementIntersect: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementSubsetComplementIntersect,definition,
% 3.29/1.67 ( complementSubsetComplementIntersect
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementInPowersetComplementIntersect_type,type,
% 3.29/1.67 complementInPowersetComplementIntersect: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementInPowersetComplementIntersect,definition,
% 3.29/1.67 ( complementInPowersetComplementIntersect
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(contraSubsetComplement_type,type,
% 3.29/1.67 contraSubsetComplement: $o ).
% 3.29/1.67
% 3.29/1.67 thf(contraSubsetComplement,definition,
% 3.29/1.67 ( contraSubsetComplement
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ Y )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementTcontraSubset_type,type,
% 3.29/1.67 complementTcontraSubset: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementTcontraSubset,definition,
% 3.29/1.67 ( complementTcontraSubset
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.29/1.67 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTILcontra_type,type,
% 3.29/1.67 binunionTILcontra: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTILcontra,definition,
% 3.29/1.67 ( binunionTILcontra
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.29/1.67 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTIRcontra_type,type,
% 3.29/1.67 binunionTIRcontra: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTIRcontra,definition,
% 3.29/1.67 ( binunionTIRcontra
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.29/1.67 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInUnion_type,type,
% 3.29/1.67 inIntersectImpInUnion: $o ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInUnion,definition,
% 3.29/1.67 ( inIntersectImpInUnion
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.29/1.67 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInUnion2_type,type,
% 3.29/1.67 inIntersectImpInUnion2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInUnion2,definition,
% 3.29/1.67 ( inIntersectImpInUnion2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.29/1.67 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInIntersectUnions_type,type,
% 3.29/1.67 inIntersectImpInIntersectUnions: $o ).
% 3.29/1.67
% 3.29/1.67 thf(inIntersectImpInIntersectUnions,definition,
% 3.29/1.67 ( inIntersectImpInIntersectUnions
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.29/1.67 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(intersectInPowersetIntersectUnions_type,type,
% 3.29/1.67 intersectInPowersetIntersectUnions: $o ).
% 3.29/1.67
% 3.29/1.67 thf(intersectInPowersetIntersectUnions,definition,
% 3.29/1.67 ( intersectInPowersetIntersectUnions
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(inComplementUnionImpNotIn1_type,type,
% 3.29/1.67 inComplementUnionImpNotIn1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(inComplementUnionImpNotIn1,definition,
% 3.29/1.67 ( inComplementUnionImpNotIn1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.29/1.67 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(inComplementUnionImpInComplement1_type,type,
% 3.29/1.67 inComplementUnionImpInComplement1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(inComplementUnionImpInComplement1,definition,
% 3.29/1.67 ( inComplementUnionImpInComplement1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTE_type,type,
% 3.29/1.67 binunionTE: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTE,definition,
% 3.29/1.67 ( binunionTE
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xphi: $o,Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.29/1.67 => ( ( ( in @ Xx @ X )
% 3.29/1.67 => Xphi )
% 3.29/1.67 => ( ( ( in @ Xx @ Y )
% 3.29/1.67 => Xphi )
% 3.29/1.67 => Xphi ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTEcontra_type,type,
% 3.29/1.67 binunionTEcontra: $o ).
% 3.29/1.67
% 3.29/1.67 thf(binunionTEcontra,definition,
% 3.29/1.67 ( binunionTEcontra
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ~ ( in @ Xx @ X )
% 3.29/1.67 => ( ~ ( in @ Xx @ Y )
% 3.29/1.67 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a1_type,type,
% 3.29/1.67 demorgan2a1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a1,definition,
% 3.29/1.67 ( demorgan2a1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(complementUnionInPowersetComplement_type,type,
% 3.29/1.67 complementUnionInPowersetComplement: $o ).
% 3.29/1.67
% 3.29/1.67 thf(complementUnionInPowersetComplement,definition,
% 3.29/1.67 ( complementUnionInPowersetComplement
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a2_type,type,
% 3.29/1.67 demorgan2a2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a2,definition,
% 3.29/1.67 ( demorgan2a2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1a_type,type,
% 3.29/1.67 demorgan1a: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1a,definition,
% 3.29/1.67 ( demorgan1a
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1b_type,type,
% 3.29/1.67 demorgan1b: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1b,definition,
% 3.29/1.67 ( demorgan1b
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1_type,type,
% 3.29/1.67 demorgan1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan1,definition,
% 3.29/1.67 ( demorgan1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.29/1.67 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a_type,type,
% 3.29/1.67 demorgan2a: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2a,definition,
% 3.29/1.67 ( demorgan2a
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2b2_type,type,
% 3.29/1.67 demorgan2b2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2b2,definition,
% 3.29/1.67 ( demorgan2b2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.29/1.67 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2b_type,type,
% 3.29/1.67 demorgan2b: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2b,definition,
% 3.29/1.67 ( demorgan2b
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.29/1.67 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2_type,type,
% 3.29/1.67 demorgan2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(demorgan2,definition,
% 3.29/1.67 ( demorgan2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.29/1.67 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule0_type,type,
% 3.29/1.67 woz13rule0: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule0,definition,
% 3.29/1.67 ( woz13rule0
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.29/1.67 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule1_type,type,
% 3.29/1.67 woz13rule1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule1,definition,
% 3.29/1.67 ( woz13rule1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ Z )
% 3.29/1.67 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule2_type,type,
% 3.29/1.67 woz13rule2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule2,definition,
% 3.29/1.67 ( woz13rule2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ Y @ Z )
% 3.29/1.67 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule3_type,type,
% 3.29/1.67 woz13rule3: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule3,definition,
% 3.29/1.67 ( woz13rule3
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ Y )
% 3.29/1.67 => ( ( subset @ X @ Z )
% 3.29/1.67 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule4_type,type,
% 3.29/1.67 woz13rule4: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz13rule4,definition,
% 3.29/1.67 ( woz13rule4
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ! [W: $i] :
% 3.29/1.67 ( ( in @ W @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ Z )
% 3.29/1.67 => ( ( subset @ Y @ W )
% 3.29/1.67 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_1_type,type,
% 3.29/1.67 woz1_1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_1,definition,
% 3.29/1.67 ( woz1_1
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_2_type,type,
% 3.29/1.67 woz1_2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_2,definition,
% 3.29/1.67 ( woz1_2
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ! [W: $i] :
% 3.29/1.67 ( ( in @ W @ ( powerset @ A ) )
% 3.29/1.67 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.29/1.67 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_3_type,type,
% 3.29/1.67 woz1_3: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_3,definition,
% 3.29/1.67 ( woz1_3
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ! [Z: $i] :
% 3.29/1.67 ( ( in @ Z @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_4_type,type,
% 3.29/1.67 woz1_4: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_4,definition,
% 3.29/1.67 ( woz1_4
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.29/1.67 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_5_type,type,
% 3.29/1.67 woz1_5: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz1_5,definition,
% 3.29/1.67 ( woz1_5
% 3.29/1.67 = ( ! [A: $i,X: $i] :
% 3.29/1.67 ( ( in @ X @ ( powerset @ A ) )
% 3.29/1.67 => ! [Y: $i] :
% 3.29/1.67 ( ( in @ Y @ ( powerset @ A ) )
% 3.29/1.67 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1_type,type,
% 3.29/1.67 breln1: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1all2_type,type,
% 3.29/1.67 breln1all2: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1all2,definition,
% 3.29/1.67 ( breln1all2
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [Xphi: $i > $o] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ R )
% 3.29/1.67 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1Set_type,type,
% 3.29/1.67 breln1Set: $i > $i ).
% 3.29/1.67
% 3.29/1.67 thf(breln1SetBreln1_type,type,
% 3.29/1.67 breln1SetBreln1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1SetBreln1,definition,
% 3.29/1.67 ( breln1SetBreln1
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( in @ R @ ( breln1Set @ A ) )
% 3.29/1.67 => ( breln1 @ A @ R ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(transitive_type,type,
% 3.29/1.67 transitive: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(antisymmetric_type,type,
% 3.29/1.67 antisymmetric: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(reflexive_type,type,
% 3.29/1.67 reflexive: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(refltransitive_type,type,
% 3.29/1.67 refltransitive: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(refllinearorder_type,type,
% 3.29/1.67 refllinearorder: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(reflwellordering_type,type,
% 3.29/1.67 reflwellordering: $i > $i > $o ).
% 3.29/1.67
% 3.29/1.67 thf(choice2fnsingleton_type,type,
% 3.29/1.67 choice2fnsingleton: $o ).
% 3.29/1.67
% 3.29/1.67 thf(choice2fnsingleton,definition,
% 3.29/1.67 ( choice2fnsingleton
% 3.29/1.67 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ? [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ B )
% 3.29/1.67 & ( Xphi @ Xx @ Xy ) ) )
% 3.29/1.67 => ! [R: $i] :
% 3.29/1.67 ( ( in @ R @ ( breln1Set @ B ) )
% 3.29/1.67 => ( ( reflwellordering @ B @ R )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ( singleton
% 3.29/1.67 @ ( dsetconstr @ B
% 3.29/1.67 @ ^ [Xy: $i] :
% 3.29/1.67 ( ( Xphi @ Xx @ Xy )
% 3.29/1.67 & ! [Xz: $i] :
% 3.29/1.67 ( ( in @ Xz @ B )
% 3.29/1.67 => ( ( Xphi @ Xx @ Xz )
% 3.29/1.67 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(setOfPairsIsBReln1_type,type,
% 3.29/1.67 setOfPairsIsBReln1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(setOfPairsIsBReln1,definition,
% 3.29/1.67 ( setOfPairsIsBReln1
% 3.29/1.67 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.29/1.67 ( breln1 @ A
% 3.29/1.67 @ ( dpsetconstr @ A @ A
% 3.29/1.67 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1all1_type,type,
% 3.29/1.67 breln1all1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1all1,definition,
% 3.29/1.67 ( breln1all1
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [Xphi: $i > $o] :
% 3.29/1.67 ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ R )
% 3.29/1.67 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(subbreln1_type,type,
% 3.29/1.67 subbreln1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(subbreln1,definition,
% 3.29/1.67 ( subbreln1
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.29/1.67 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(eqbreln1_type,type,
% 3.29/1.67 eqbreln1: $o ).
% 3.29/1.67
% 3.29/1.67 thf(eqbreln1,definition,
% 3.29/1.67 ( eqbreln1
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.29/1.67 => ( ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.29/1.67 => ( R = S ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invset_type,type,
% 3.29/1.67 breln1invset: $i > $i > $i ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invprop_type,type,
% 3.29/1.67 breln1invprop: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invprop,definition,
% 3.29/1.67 ( breln1invprop
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invI_type,type,
% 3.29/1.67 breln1invI: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invI,definition,
% 3.29/1.67 ( breln1invI
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invE_type,type,
% 3.29/1.67 breln1invE: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1invE,definition,
% 3.29/1.67 ( breln1invE
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compset_type,type,
% 3.29/1.67 breln1compset: $i > $i > $i > $i ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compprop_type,type,
% 3.29/1.67 breln1compprop: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compprop,definition,
% 3.29/1.67 ( breln1compprop
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compI_type,type,
% 3.29/1.67 breln1compI: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compI,definition,
% 3.29/1.67 ( breln1compI
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ! [Xz: $i] :
% 3.29/1.67 ( ( in @ Xz @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.29/1.67 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compE_type,type,
% 3.29/1.67 breln1compE: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compE,definition,
% 3.29/1.67 ( breln1compE
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.29/1.67 => ? [Xz: $i] :
% 3.29/1.67 ( ( in @ Xz @ A )
% 3.29/1.67 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.29/1.67 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compEex_type,type,
% 3.29/1.67 breln1compEex: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1compEex,definition,
% 3.29/1.67 ( breln1compEex
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.29/1.67 => ! [Xphi: $o] :
% 3.29/1.67 ( ! [Xz: $i] :
% 3.29/1.67 ( ( in @ Xz @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.29/1.67 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.29/1.67 => Xphi ) ) )
% 3.29/1.67 => Xphi ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionprop_type,type,
% 3.29/1.67 breln1unionprop: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionprop,definition,
% 3.29/1.67 ( breln1unionprop
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionIL_type,type,
% 3.29/1.67 breln1unionIL: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionIL,definition,
% 3.29/1.67 ( breln1unionIL
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionIR_type,type,
% 3.29/1.67 breln1unionIR: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionIR,definition,
% 3.29/1.67 ( breln1unionIR
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionI_type,type,
% 3.29/1.67 breln1unionI: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionI,definition,
% 3.29/1.67 ( breln1unionI
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.29/1.67 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionE_type,type,
% 3.29/1.67 breln1unionE: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionE,definition,
% 3.29/1.67 ( breln1unionE
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionEcases_type,type,
% 3.29/1.67 breln1unionEcases: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionEcases,definition,
% 3.29/1.67 ( breln1unionEcases
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [Xx: $i] :
% 3.29/1.67 ( ( in @ Xx @ A )
% 3.29/1.67 => ! [Xy: $i] :
% 3.29/1.67 ( ( in @ Xy @ A )
% 3.29/1.67 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.29/1.67 => ! [Xphi: $o] :
% 3.29/1.67 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.29/1.67 => Xphi )
% 3.29/1.67 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.29/1.67 => Xphi )
% 3.29/1.67 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionCommutes_type,type,
% 3.29/1.67 breln1unionCommutes: $o ).
% 3.29/1.67
% 3.29/1.67 thf(breln1unionCommutes,definition,
% 3.29/1.67 ( breln1unionCommutes
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( ( binunion @ R @ S )
% 3.29/1.67 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz2Ex_type,type,
% 3.29/1.67 woz2Ex: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz2Ex,definition,
% 3.29/1.67 ( woz2Ex
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ( R
% 3.29/1.67 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz2W_type,type,
% 3.29/1.67 woz2W: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz2W,definition,
% 3.29/1.67 ( woz2W
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.29/1.67 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz2A_type,type,
% 3.29/1.67 woz2A: $o ).
% 3.29/1.67
% 3.29/1.67 thf(woz2A,definition,
% 3.29/1.67 ( woz2A
% 3.29/1.67 = ( ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [T: $i] :
% 3.29/1.67 ( ( breln1 @ A @ T )
% 3.29/1.67 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.29/1.67 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.29/1.67
% 3.29/1.67 thf(woz2B,conjecture,
% 3.29/1.67 ( setextAx
% 3.29/1.67 => ( emptysetAx
% 3.29/1.67 => ( setadjoinAx
% 3.29/1.67 => ( powersetAx
% 3.29/1.67 => ( setunionAx
% 3.29/1.67 => ( omega0Ax
% 3.29/1.67 => ( omegaSAx
% 3.29/1.67 => ( omegaIndAx
% 3.29/1.67 => ( replAx
% 3.29/1.67 => ( foundationAx
% 3.29/1.67 => ( wellorderingAx
% 3.29/1.67 => ( descrp
% 3.29/1.67 => ( dsetconstrI
% 3.29/1.67 => ( dsetconstrEL
% 3.29/1.67 => ( dsetconstrER
% 3.29/1.67 => ( exuE1
% 3.29/1.67 => ( prop2setE
% 3.29/1.67 => ( emptysetE
% 3.29/1.67 => ( emptysetimpfalse
% 3.29/1.67 => ( notinemptyset
% 3.29/1.67 => ( exuE3e
% 3.29/1.67 => ( setext
% 3.29/1.67 => ( emptyI
% 3.29/1.67 => ( noeltsimpempty
% 3.29/1.67 => ( setbeta
% 3.29/1.67 => ( nonemptyE1
% 3.29/1.67 => ( nonemptyI
% 3.29/1.67 => ( nonemptyI1
% 3.29/1.67 => ( setadjoinIL
% 3.29/1.67 => ( emptyinunitempty
% 3.29/1.67 => ( setadjoinIR
% 3.29/1.67 => ( setadjoinE
% 3.29/1.67 => ( setadjoinOr
% 3.29/1.67 => ( setoftrueEq
% 3.29/1.67 => ( powersetI
% 3.29/1.67 => ( emptyinPowerset
% 3.29/1.67 => ( emptyInPowerset
% 3.29/1.67 => ( powersetE
% 3.29/1.67 => ( setunionI
% 3.29/1.67 => ( setunionE
% 3.29/1.67 => ( subPowSU
% 3.29/1.67 => ( exuE2
% 3.29/1.67 => ( nonemptyImpWitness
% 3.29/1.67 => ( uniqinunit
% 3.29/1.67 => ( notinsingleton
% 3.29/1.67 => ( eqinunit
% 3.29/1.67 => ( singletonsswitch
% 3.29/1.67 => ( upairsetE
% 3.29/1.67 => ( upairsetIL
% 3.29/1.67 => ( upairsetIR
% 3.29/1.67 => ( emptyE1
% 3.29/1.67 => ( vacuousDall
% 3.29/1.67 => ( quantDeMorgan1
% 3.29/1.67 => ( quantDeMorgan2
% 3.29/1.67 => ( quantDeMorgan3
% 3.29/1.67 => ( quantDeMorgan4
% 3.29/1.67 => ( prop2setI
% 3.29/1.67 => ( prop2set2propI
% 3.29/1.67 => ( notdexE
% 3.29/1.67 => ( notdallE
% 3.29/1.67 => ( exuI1
% 3.29/1.67 => ( exuI3
% 3.29/1.67 => ( exuI2
% 3.29/1.67 => ( inCongP
% 3.29/1.67 => ( in__Cong
% 3.29/1.67 => ( exuE3u
% 3.29/1.67 => ( exu__Cong
% 3.29/1.67 => ( emptyset__Cong
% 3.29/1.67 => ( setadjoin__Cong
% 3.29/1.67 => ( powerset__Cong
% 3.29/1.67 => ( setunion__Cong
% 3.29/1.67 => ( omega__Cong
% 3.29/1.67 => ( exuEu
% 3.29/1.67 => ( descr__Cong
% 3.29/1.67 => ( dsetconstr__Cong
% 3.29/1.67 => ( subsetI1
% 3.29/1.67 => ( eqimpsubset2
% 3.29/1.67 => ( eqimpsubset1
% 3.29/1.67 => ( subsetI2
% 3.29/1.67 => ( emptysetsubset
% 3.29/1.67 => ( subsetE
% 3.29/1.67 => ( subsetE2
% 3.29/1.67 => ( notsubsetI
% 3.29/1.67 => ( notequalI1
% 3.29/1.67 => ( notequalI2
% 3.29/1.67 => ( subsetRefl
% 3.29/1.67 => ( subsetTrans
% 3.29/1.67 => ( setadjoinSub
% 3.29/1.67 => ( setadjoinSub2
% 3.29/1.67 => ( subset2powerset
% 3.29/1.67 => ( setextsub
% 3.29/1.67 => ( subsetemptysetimpeq
% 3.29/1.67 => ( powersetI1
% 3.29/1.67 => ( powersetE1
% 3.29/1.67 => ( inPowerset
% 3.29/1.67 => ( powersetsubset
% 3.29/1.67 => ( sepInPowerset
% 3.29/1.67 => ( sepSubset
% 3.29/1.67 => ( binunionIL
% 3.29/1.67 => ( upairset2IR
% 3.29/1.67 => ( binunionIR
% 3.29/1.67 => ( binunionEcases
% 3.29/1.67 => ( binunionE
% 3.29/1.67 => ( binunionLsub
% 3.29/1.67 => ( binunionRsub
% 3.29/1.67 => ( binintersectI
% 3.29/1.67 => ( binintersectSubset5
% 3.29/1.67 => ( binintersectEL
% 3.29/1.67 => ( binintersectLsub
% 3.29/1.67 => ( binintersectSubset2
% 3.29/1.67 => ( binintersectSubset3
% 3.29/1.67 => ( binintersectER
% 3.29/1.67 => ( disjointsetsI1
% 3.29/1.67 => ( binintersectRsub
% 3.29/1.67 => ( binintersectSubset4
% 3.29/1.67 => ( binintersectSubset1
% 3.29/1.67 => ( bs114d
% 3.29/1.67 => ( setminusI
% 3.29/1.67 => ( setminusEL
% 3.29/1.67 => ( setminusER
% 3.29/1.67 => ( setminusSubset2
% 3.29/1.67 => ( setminusERneg
% 3.29/1.67 => ( setminusELneg
% 3.29/1.67 => ( setminusILneg
% 3.29/1.67 => ( setminusIRneg
% 3.29/1.67 => ( setminusLsub
% 3.29/1.67 => ( setminusSubset1
% 3.29/1.67 => ( symdiffE
% 3.29/1.67 => ( symdiffI1
% 3.29/1.67 => ( symdiffI2
% 3.29/1.67 => ( symdiffIneg1
% 3.29/1.67 => ( symdiffIneg2
% 3.29/1.67 => ( secondinupair
% 3.29/1.67 => ( setukpairIL
% 3.29/1.67 => ( setukpairIR
% 3.29/1.67 => ( kpairiskpair
% 3.29/1.67 => ( kpairp
% 3.29/1.67 => ( singletonsubset
% 3.29/1.67 => ( singletoninpowerset
% 3.29/1.67 => ( singletoninpowunion
% 3.29/1.67 => ( upairset2E
% 3.29/1.67 => ( upairsubunion
% 3.29/1.67 => ( upairinpowunion
% 3.29/1.67 => ( ubforcartprodlem1
% 3.29/1.67 => ( ubforcartprodlem2
% 3.29/1.67 => ( ubforcartprodlem3
% 3.29/1.67 => ( cartprodpairin
% 3.29/1.67 => ( cartprodmempair1
% 3.29/1.67 => ( cartprodmempair
% 3.29/1.67 => ( setunionE2
% 3.29/1.67 => ( setunionsingleton1
% 3.29/1.67 => ( setunionsingleton2
% 3.29/1.67 => ( setunionsingleton
% 3.29/1.67 => ( singletonprop
% 3.29/1.67 => ( ex1E1
% 3.29/1.67 => ( ex1I
% 3.29/1.67 => ( ex1I2
% 3.29/1.67 => ( singletonsuniq
% 3.29/1.67 => ( setukpairinjL1
% 3.29/1.67 => ( kfstsingleton
% 3.29/1.67 => ( theprop
% 3.29/1.67 => ( kfstpairEq
% 3.29/1.67 => ( cartprodfstin
% 3.29/1.67 => ( setukpairinjL2
% 3.29/1.67 => ( setukpairinjL
% 3.29/1.67 => ( setukpairinjR11
% 3.29/1.67 => ( setukpairinjR12
% 3.29/1.67 => ( setukpairinjR1
% 3.29/1.67 => ( upairequniteq
% 3.29/1.67 => ( setukpairinjR2
% 3.29/1.67 => ( setukpairinjR
% 3.29/1.67 => ( ksndsingleton
% 3.29/1.67 => ( ksndpairEq
% 3.29/1.67 => ( kpairsurjEq
% 3.29/1.67 => ( cartprodsndin
% 3.29/1.67 => ( cartprodpairmemEL
% 3.29/1.67 => ( cartprodpairmemER
% 3.29/1.67 => ( cartprodmempaircEq
% 3.29/1.67 => ( cartprodfstpairEq
% 3.29/1.67 => ( cartprodsndpairEq
% 3.29/1.67 => ( cartprodpairsurjEq
% 3.29/1.67 => ( dpsetconstrI
% 3.29/1.67 => ( dpsetconstrSub
% 3.29/1.67 => ( setOfPairsIsBReln
% 3.29/1.67 => ( dpsetconstrERa
% 3.29/1.67 => ( dpsetconstrEL1
% 3.29/1.67 => ( dpsetconstrEL2
% 3.29/1.67 => ( dpsetconstrER
% 3.29/1.67 => ( funcImageSingleton
% 3.29/1.67 => ( apProp
% 3.29/1.67 => ( app
% 3.29/1.67 => ( infuncsetfunc
% 3.29/1.67 => ( ap2p
% 3.29/1.67 => ( funcinfuncset
% 3.29/1.67 => ( lamProp
% 3.29/1.67 => ( lamp
% 3.29/1.67 => ( lam2p
% 3.29/1.67 => ( brelnall1
% 3.29/1.67 => ( brelnall2
% 3.29/1.67 => ( ex1E2
% 3.29/1.67 => ( funcGraphProp1
% 3.29/1.67 => ( funcGraphProp3
% 3.29/1.67 => ( funcGraphProp2
% 3.29/1.67 => ( funcextLem
% 3.29/1.67 => ( funcGraphProp4
% 3.29/1.67 => ( subbreln
% 3.29/1.67 => ( eqbreln
% 3.29/1.67 => ( funcext
% 3.29/1.67 => ( funcext2
% 3.29/1.67 => ( ap2apEq1
% 3.29/1.67 => ( ap2apEq2
% 3.29/1.67 => ( beta1
% 3.29/1.67 => ( eta1
% 3.29/1.67 => ( lam2lamEq
% 3.29/1.67 => ( beta2
% 3.29/1.67 => ( eta2
% 3.29/1.67 => ( iffalseProp1
% 3.29/1.67 => ( iffalseProp2
% 3.29/1.67 => ( iftrueProp1
% 3.29/1.67 => ( iftrueProp2
% 3.29/1.67 => ( ifSingleton
% 3.29/1.67 => ( ifp
% 3.29/1.67 => ( theeq
% 3.29/1.67 => ( iftrue
% 3.29/1.67 => ( iffalse
% 3.29/1.67 => ( iftrueorfalse
% 3.29/1.67 => ( binintersectT_lem
% 3.29/1.67 => ( binunionT_lem
% 3.29/1.67 => ( powersetT_lem
% 3.29/1.67 => ( setminusT_lem
% 3.29/1.67 => ( complementT_lem
% 3.29/1.67 => ( setextT
% 3.29/1.67 => ( subsetTI
% 3.29/1.67 => ( powersetTI1
% 3.29/1.67 => ( powersetTE1
% 3.29/1.67 => ( complementTI1
% 3.29/1.67 => ( complementTE1
% 3.29/1.67 => ( binintersectTELcontra
% 3.29/1.67 => ( binintersectTERcontra
% 3.29/1.67 => ( contrasubsetT
% 3.29/1.67 => ( contrasubsetT1
% 3.29/1.67 => ( contrasubsetT2
% 3.29/1.67 => ( contrasubsetT3
% 3.29/1.67 => ( doubleComplementI1
% 3.29/1.67 => ( doubleComplementE1
% 3.29/1.67 => ( doubleComplementSub1
% 3.29/1.67 => ( doubleComplementSub2
% 3.29/1.67 => ( doubleComplementEq
% 3.29/1.67 => ( complementTnotintersectT
% 3.29/1.67 => ( complementImpComplementIntersect
% 3.29/1.67 => ( complementSubsetComplementIntersect
% 3.29/1.67 => ( complementInPowersetComplementIntersect
% 3.29/1.67 => ( contraSubsetComplement
% 3.29/1.67 => ( complementTcontraSubset
% 3.29/1.67 => ( binunionTILcontra
% 3.29/1.67 => ( binunionTIRcontra
% 3.29/1.67 => ( inIntersectImpInUnion
% 3.29/1.67 => ( inIntersectImpInUnion2
% 3.29/1.67 => ( inIntersectImpInIntersectUnions
% 3.29/1.67 => ( intersectInPowersetIntersectUnions
% 3.29/1.67 => ( inComplementUnionImpNotIn1
% 3.29/1.67 => ( inComplementUnionImpInComplement1
% 3.29/1.67 => ( binunionTE
% 3.29/1.67 => ( binunionTEcontra
% 3.29/1.67 => ( demorgan2a1
% 3.29/1.67 => ( complementUnionInPowersetComplement
% 3.29/1.67 => ( demorgan2a2
% 3.29/1.67 => ( demorgan1a
% 3.29/1.67 => ( demorgan1b
% 3.29/1.67 => ( demorgan1
% 3.29/1.67 => ( demorgan2a
% 3.29/1.67 => ( demorgan2b2
% 3.29/1.67 => ( demorgan2b
% 3.29/1.67 => ( demorgan2
% 3.29/1.67 => ( woz13rule0
% 3.29/1.67 => ( woz13rule1
% 3.29/1.67 => ( woz13rule2
% 3.29/1.67 => ( woz13rule3
% 3.29/1.67 => ( woz13rule4
% 3.29/1.67 => ( woz1_1
% 3.29/1.67 => ( woz1_2
% 3.29/1.67 => ( woz1_3
% 3.29/1.67 => ( woz1_4
% 3.29/1.67 => ( woz1_5
% 3.29/1.67 => ( breln1all2
% 3.29/1.67 => ( breln1SetBreln1
% 3.29/1.67 => ( choice2fnsingleton
% 3.29/1.67 => ( setOfPairsIsBReln1
% 3.29/1.67 => ( breln1all1
% 3.29/1.67 => ( subbreln1
% 3.29/1.67 => ( eqbreln1
% 3.29/1.67 => ( breln1invprop
% 3.29/1.67 => ( breln1invI
% 3.29/1.67 => ( breln1invE
% 3.29/1.67 => ( breln1compprop
% 3.29/1.67 => ( breln1compI
% 3.29/1.67 => ( breln1compE
% 3.29/1.67 => ( breln1compEex
% 3.29/1.67 => ( breln1unionprop
% 3.29/1.67 => ( breln1unionIL
% 3.29/1.67 => ( breln1unionIR
% 3.29/1.67 => ( breln1unionI
% 3.29/1.67 => ( breln1unionE
% 3.29/1.67 => ( breln1unionEcases
% 3.29/1.67 => ( breln1unionCommutes
% 3.29/1.67 => ( woz2Ex
% 3.29/1.67 => ( woz2W
% 3.29/1.67 => ( woz2A
% 3.29/1.67 => ! [A: $i,R: $i] :
% 3.29/1.67 ( ( breln1 @ A @ R )
% 3.29/1.67 => ! [S: $i] :
% 3.29/1.67 ( ( breln1 @ A @ S )
% 3.29/1.67 => ! [T: $i] :
% 3.29/1.67 ( ( breln1 @ A @ T )
% 3.29/1.67 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.29/1.67 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.29/1.67 ------------------------
% 3.36/1.70 % (18673)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/183Mi)
% 3.36/1.70 % (18677)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_18469 for (2999ds/2Mi)
% 3.36/1.70 % (18674)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_18469 for (2999ds/4Mi)
% 3.36/1.70 % (18676)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/2Mi)
% 3.36/1.70 % (18675)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_18469 for (2999ds/27Mi)
% 3.36/1.70 % (18678)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_18469 for (2999ds/275Mi)
% 3.36/1.70 % (18679)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/18Mi)
% 3.36/1.71 % (18676)Instruction limit reached!
% 3.36/1.71 % (18676)------------------------------
% 3.36/1.71 % (18676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.71 % (18676)Termination reason: Unknown
% 3.36/1.71 % (18677)Instruction limit reached!
% 3.36/1.71 % (18677)------------------------------
% 3.36/1.71 % (18677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.71 % (18677)Termination reason: Unknown
% 3.36/1.71 % (18677)Termination phase: shuffling
% 3.36/1.71
% 3.36/1.71 % (18677)Memory used [KB]: 1535
% 3.36/1.71 % (18677)Time elapsed: 0.003 s
% 3.36/1.71 % (18677)Instructions burned: 3 (million)
% 3.36/1.71 % (18677)------------------------------
% 3.36/1.71 % (18677)------------------------------
% 3.36/1.71 % (18676)Termination phase: shuffling
% 3.36/1.71
% 3.36/1.71 % (18676)Memory used [KB]: 1535
% 3.36/1.71 % (18676)Time elapsed: 0.003 s
% 3.36/1.71 % (18676)Instructions burned: 3 (million)
% 3.36/1.71 % (18676)------------------------------
% 3.36/1.71 % (18676)------------------------------
% 3.36/1.71 % (18674)Instruction limit reached!
% 3.36/1.71 % (18674)------------------------------
% 3.36/1.71 % (18674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.71 % (18674)Termination reason: Unknown
% 3.36/1.71 % (18674)Termination phase: shuffling
% 3.36/1.71
% 3.36/1.71 % (18674)Memory used [KB]: 1535
% 3.36/1.71 % (18674)Time elapsed: 0.004 s
% 3.36/1.71 % (18674)Instructions burned: 5 (million)
% 3.36/1.71 % (18674)------------------------------
% 3.36/1.71 % (18674)------------------------------
% 3.36/1.71 % (18679)Instruction limit reached!
% 3.36/1.71 % (18679)------------------------------
% 3.36/1.71 % (18679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.71 % (18679)Termination reason: Unknown
% 3.36/1.71 % (18679)Termination phase: shuffling
% 3.36/1.71
% 3.36/1.71 % (18679)Memory used [KB]: 1791
% 3.36/1.71 % (18679)Time elapsed: 0.011 s
% 3.36/1.71 % (18679)Instructions burned: 19 (million)
% 3.36/1.71 % (18679)------------------------------
% 3.36/1.71 % (18679)------------------------------
% 3.36/1.72 % (18675)Instruction limit reached!
% 3.36/1.72 % (18675)------------------------------
% 3.36/1.72 % (18675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.72 % (18675)Termination reason: Unknown
% 3.36/1.72 % (18675)Termination phase: shuffling
% 3.36/1.72
% 3.36/1.72 % (18675)Memory used [KB]: 2046
% 3.36/1.72 % (18675)Time elapsed: 0.013 s
% 3.36/1.72 % (18675)Instructions burned: 28 (million)
% 3.36/1.72 % (18675)------------------------------
% 3.36/1.72 % (18675)------------------------------
% 3.36/1.72 % (18681)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/3Mi)
% 3.36/1.72 % (18682)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_18469 for (2999ds/37Mi)
% 3.36/1.72 % (18683)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_18469 for (2999ds/15Mi)
% 3.36/1.72 % (18681)Instruction limit reached!
% 3.36/1.72 % (18681)------------------------------
% 3.36/1.72 % (18681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.72 % (18681)Termination reason: Unknown
% 3.36/1.72 % (18681)Termination phase: shuffling
% 3.36/1.72
% 3.36/1.72 % (18681)Memory used [KB]: 1535
% 3.36/1.72 % (18681)Time elapsed: 0.003 s
% 3.36/1.72 % (18681)Instructions burned: 3 (million)
% 3.36/1.72 % (18681)------------------------------
% 3.36/1.72 % (18681)------------------------------
% 3.36/1.73 % (18687)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_18469 for (2999ds/1041Mi)
% 3.36/1.73 % (18683)Instruction limit reached!
% 3.36/1.73 % (18683)------------------------------
% 3.36/1.73 % (18683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.73 % (18683)Termination reason: Unknown
% 3.36/1.73 % (18683)Termination phase: shuffling
% 3.36/1.73
% 3.36/1.73 % (18683)Memory used [KB]: 1791
% 3.36/1.73 % (18683)Time elapsed: 0.006 s
% 3.36/1.73 % (18683)Instructions burned: 16 (million)
% 3.36/1.73 % (18683)------------------------------
% 3.36/1.73 % (18683)------------------------------
% 3.36/1.74 % (18682)Instruction limit reached!
% 3.36/1.74 % (18682)------------------------------
% 3.36/1.74 % (18682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.74 % (18682)Termination reason: Unknown
% 3.36/1.74 % (18682)Termination phase: shuffling
% 3.36/1.74
% 3.36/1.74 % (18682)Memory used [KB]: 2302
% 3.36/1.74 % (18682)Time elapsed: 0.018 s
% 3.36/1.74 % (18682)Instructions burned: 40 (million)
% 3.36/1.74 % (18682)------------------------------
% 3.36/1.74 % (18682)------------------------------
% 3.36/1.74 % (18689)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/7Mi)
% 3.36/1.74 % (18686)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_18469 for (2999ds/3Mi)
% 3.36/1.74 % (18690)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/16Mi)
% 3.36/1.74 % (18686)Instruction limit reached!
% 3.36/1.74 % (18686)------------------------------
% 3.36/1.74 % (18686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.74 % (18686)Termination reason: Unknown
% 3.36/1.74 % (18686)Termination phase: shuffling
% 3.36/1.74
% 3.36/1.74 % (18686)Memory used [KB]: 1535
% 3.36/1.74 % (18686)Time elapsed: 0.003 s
% 3.36/1.74 % (18686)Instructions burned: 4 (million)
% 3.36/1.74 % (18686)------------------------------
% 3.36/1.74 % (18686)------------------------------
% 3.36/1.74 % (18689)Instruction limit reached!
% 3.36/1.74 % (18689)------------------------------
% 3.36/1.74 % (18689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.74 % (18689)Termination reason: Unknown
% 3.36/1.74 % (18689)Termination phase: shuffling
% 3.36/1.74
% 3.36/1.74 % (18689)Memory used [KB]: 1663
% 3.36/1.74 % (18689)Time elapsed: 0.005 s
% 3.36/1.74 % (18689)Instructions burned: 7 (million)
% 3.36/1.74 % (18689)------------------------------
% 3.36/1.74 % (18689)------------------------------
% 3.36/1.75 % (18690)Instruction limit reached!
% 3.36/1.75 % (18690)------------------------------
% 3.36/1.75 % (18690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.75 % (18690)Termination reason: Unknown
% 3.36/1.75 % (18690)Termination phase: shuffling
% 3.36/1.75
% 3.36/1.75 % (18690)Memory used [KB]: 1918
% 3.36/1.75 % (18690)Time elapsed: 0.009 s
% 3.36/1.75 % (18690)Instructions burned: 17 (million)
% 3.36/1.75 % (18690)------------------------------
% 3.36/1.75 % (18690)------------------------------
% 3.36/1.75 % (18693)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_18469 for (2999ds/3Mi)
% 3.36/1.75 % (18694)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_18469 for (2999ds/3Mi)
% 3.36/1.75 % (18694)Instruction limit reached!
% 3.36/1.75 % (18694)------------------------------
% 3.36/1.75 % (18694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.75 % (18694)Termination reason: Unknown
% 3.36/1.75 % (18694)Termination phase: shuffling
% 3.36/1.75
% 3.36/1.75 % (18694)Memory used [KB]: 1663
% 3.36/1.75 % (18694)Time elapsed: 0.003 s
% 3.36/1.75 % (18694)Instructions burned: 6 (million)
% 3.36/1.75 % (18694)------------------------------
% 3.36/1.75 % (18694)------------------------------
% 3.36/1.75 % (18693)Instruction limit reached!
% 3.36/1.75 % (18693)------------------------------
% 3.36/1.75 % (18693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.75 % (18693)Termination reason: Unknown
% 3.36/1.75 % (18693)Termination phase: shuffling
% 3.36/1.75
% 3.36/1.75 % (18693)Memory used [KB]: 1535
% 3.36/1.75 % (18693)Time elapsed: 0.004 s
% 3.36/1.75 % (18693)Instructions burned: 5 (million)
% 3.36/1.75 % (18693)------------------------------
% 3.36/1.75 % (18693)------------------------------
% 3.36/1.76 % (18673)Instruction limit reached!
% 3.36/1.76 % (18673)------------------------------
% 3.36/1.76 % (18673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.76 % (18673)Termination reason: Unknown
% 3.36/1.76 % (18673)Termination phase: Property scanning
% 3.36/1.76
% 3.36/1.76 % (18673)Memory used [KB]: 3070
% 3.36/1.76 % (18673)Time elapsed: 0.060 s
% 3.36/1.76 % (18673)Instructions burned: 184 (million)
% 3.36/1.76 % (18673)------------------------------
% 3.36/1.76 % (18673)------------------------------
% 3.36/1.76 % (18696)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/7Mi)
% 3.36/1.76 % (18698)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/4Mi)
% 3.36/1.76 % (18696)Instruction limit reached!
% 3.36/1.76 % (18696)------------------------------
% 3.36/1.76 % (18696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.76 % (18696)Termination reason: Unknown
% 3.36/1.76 % (18696)Termination phase: shuffling
% 3.36/1.76
% 3.36/1.76 % (18696)Memory used [KB]: 1663
% 3.36/1.76 % (18696)Time elapsed: 0.005 s
% 3.36/1.76 % (18696)Instructions burned: 8 (million)
% 3.36/1.76 % (18696)------------------------------
% 3.36/1.76 % (18696)------------------------------
% 3.36/1.76 % (18698)Instruction limit reached!
% 3.36/1.76 % (18698)------------------------------
% 3.36/1.76 % (18698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.76 % (18698)Termination reason: Unknown
% 3.36/1.76 % (18698)Termination phase: shuffling
% 3.36/1.76
% 3.36/1.76 % (18698)Memory used [KB]: 1663
% 3.36/1.76 % (18698)Time elapsed: 0.003 s
% 3.36/1.76 % (18698)Instructions burned: 6 (million)
% 3.36/1.76 % (18698)------------------------------
% 3.36/1.76 % (18698)------------------------------
% 3.36/1.77 % (18697)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/3Mi)
% 3.36/1.77 % (18697)Instruction limit reached!
% 3.36/1.77 % (18697)------------------------------
% 3.36/1.77 % (18697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.77 % (18697)Termination reason: Unknown
% 3.36/1.77 % (18697)Termination phase: shuffling
% 3.36/1.77
% 3.36/1.77 % (18697)Memory used [KB]: 1535
% 3.36/1.77 % (18697)Time elapsed: 0.003 s
% 3.36/1.77 % (18697)Instructions burned: 3 (million)
% 3.36/1.77 % (18697)------------------------------
% 3.36/1.77 % (18697)------------------------------
% 3.36/1.77 % (18699)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/18Mi)
% 3.36/1.77 % (18700)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/710Mi)
% 3.36/1.77 % (18702)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_18469 for (2999ds/902Mi)
% 3.36/1.78 % (18699)Instruction limit reached!
% 3.36/1.78 % (18699)------------------------------
% 3.36/1.78 % (18699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.78 % (18699)Termination reason: Unknown
% 3.36/1.78 % (18699)Termination phase: shuffling
% 3.36/1.78
% 3.36/1.78 % (18699)Memory used [KB]: 1791
% 3.36/1.78 % (18699)Time elapsed: 0.010 s
% 3.36/1.78 % (18699)Instructions burned: 19 (million)
% 3.36/1.78 % (18699)------------------------------
% 3.36/1.78 % (18699)------------------------------
% 3.36/1.78 % (18701)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/6Mi)
% 3.36/1.78 % (18701)Instruction limit reached!
% 3.36/1.78 % (18701)------------------------------
% 3.36/1.78 % (18701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.78 % (18701)Termination reason: Unknown
% 3.36/1.78 % (18701)Termination phase: shuffling
% 3.36/1.78
% 3.36/1.78 % (18701)Memory used [KB]: 1663
% 3.36/1.78 % (18701)Time elapsed: 0.004 s
% 3.36/1.78 % (18701)Instructions burned: 6 (million)
% 3.36/1.78 % (18701)------------------------------
% 3.36/1.78 % (18701)------------------------------
% 3.36/1.78 % (18703)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_18469 for (2999ds/21Mi)
% 3.36/1.79 % (18703)Instruction limit reached!
% 3.36/1.79 % (18703)------------------------------
% 3.36/1.79 % (18703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.79 % (18703)Termination reason: Unknown
% 3.36/1.79 % (18703)Termination phase: shuffling
% 3.36/1.79
% 3.36/1.79 % (18703)Memory used [KB]: 1918
% 3.36/1.79 % (18703)Time elapsed: 0.011 s
% 3.36/1.79 % (18703)Instructions burned: 21 (million)
% 3.36/1.79 % (18703)------------------------------
% 3.36/1.79 % (18703)------------------------------
% 3.36/1.79 % (18704)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18469 for (2999ds/5Mi)
% 3.36/1.80 % (18704)Instruction limit reached!
% 3.36/1.80 % (18704)------------------------------
% 3.36/1.80 % (18704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.80 % (18704)Termination reason: Unknown
% 3.36/1.80 % (18704)Termination phase: shuffling
% 3.36/1.80
% 3.36/1.80 % (18704)Memory used [KB]: 1535
% 3.36/1.80 % (18704)Time elapsed: 0.004 s
% 3.36/1.80 % (18704)Instructions burned: 5 (million)
% 3.36/1.80 % (18704)------------------------------
% 3.36/1.80 % (18704)------------------------------
% 3.36/1.80 % (18705)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_18469 for (2999ds/6Mi)
% 3.36/1.80 % (18705)Instruction limit reached!
% 3.36/1.80 % (18705)------------------------------
% 3.36/1.80 % (18705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.80 % (18705)Termination reason: Unknown
% 3.36/1.80 % (18705)Termination phase: shuffling
% 3.36/1.80
% 3.36/1.80 % (18705)Memory used [KB]: 1663
% 3.36/1.80 % (18705)Time elapsed: 0.004 s
% 3.36/1.80 % (18705)Instructions burned: 6 (million)
% 3.36/1.80 % (18705)------------------------------
% 3.36/1.80 % (18705)------------------------------
% 3.36/1.81 % (18706)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/377Mi)
% 3.36/1.81 % (18708)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_18469 for (2998ds/779Mi)
% 3.36/1.82 % (18709)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_18469 for (2998ds/19Mi)
% 3.36/1.82 % (18709)Instruction limit reached!
% 3.36/1.82 % (18709)------------------------------
% 3.36/1.82 % (18709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.82 % (18709)Termination reason: Unknown
% 3.36/1.82 % (18709)Termination phase: shuffling
% 3.36/1.82
% 3.36/1.82 % (18709)Memory used [KB]: 1918
% 3.36/1.82 % (18709)Time elapsed: 0.010 s
% 3.36/1.82 % (18709)Instructions burned: 19 (million)
% 3.36/1.82 % (18709)------------------------------
% 3.36/1.82 % (18709)------------------------------
% 3.36/1.83 % (18678)Instruction limit reached!
% 3.36/1.83 % (18678)------------------------------
% 3.36/1.83 % (18678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83 % (18678)Termination reason: Unknown
% 3.36/1.83 % (18678)Termination phase: Saturation
% 3.36/1.83
% 3.36/1.83 % (18678)Memory used [KB]: 5884
% 3.36/1.83 % (18678)Time elapsed: 0.124 s
% 3.36/1.83 % (18678)Instructions burned: 276 (million)
% 3.36/1.83 % (18678)------------------------------
% 3.36/1.83 % (18678)------------------------------
% 3.36/1.84 % (18714)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/17Mi)
% 3.36/1.84 % (18713)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/879Mi)
% 3.36/1.85 % (18714)Instruction limit reached!
% 3.36/1.85 % (18714)------------------------------
% 3.36/1.85 % (18714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (18714)Termination reason: Unknown
% 3.36/1.85 % (18714)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (18714)Memory used [KB]: 1918
% 3.36/1.85 % (18714)Time elapsed: 0.010 s
% 3.36/1.85 % (18714)Instructions burned: 18 (million)
% 3.36/1.85 % (18714)------------------------------
% 3.36/1.85 % (18714)------------------------------
% 3.36/1.86 % (18715)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/3Mi)
% 3.36/1.86 % (18715)Instruction limit reached!
% 3.36/1.86 % (18715)------------------------------
% 3.36/1.86 % (18715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (18715)Termination reason: Unknown
% 3.36/1.86 % (18715)Termination phase: shuffling
% 3.36/1.86
% 3.36/1.86 % (18715)Memory used [KB]: 1535
% 3.36/1.86 % (18715)Time elapsed: 0.003 s
% 3.36/1.86 % (18715)Instructions burned: 4 (million)
% 3.36/1.86 % (18715)------------------------------
% 3.36/1.86 % (18715)------------------------------
% 3.36/1.87 % (18716)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/30Mi)
% 3.36/1.88 % (18716)Instruction limit reached!
% 3.36/1.88 % (18716)------------------------------
% 3.36/1.88 % (18716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (18716)Termination reason: Unknown
% 3.36/1.88 % (18716)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (18716)Memory used [KB]: 2174
% 3.36/1.88 % (18716)Time elapsed: 0.010 s
% 3.36/1.88 % (18716)Instructions burned: 31 (million)
% 3.36/1.88 % (18716)------------------------------
% 3.36/1.88 % (18716)------------------------------
% 3.36/1.90 % (18719)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18469 for (2998ds/127Mi)
% 3.36/1.95 % (18719)Instruction limit reached!
% 3.36/1.95 % (18719)------------------------------
% 3.36/1.95 % (18719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.95 % (18719)Termination reason: Unknown
% 3.36/1.95 % (18719)Termination phase: Property scanning
% 3.36/1.95
% 3.36/1.95 % (18719)Memory used [KB]: 2814
% 3.36/1.95 % (18719)Time elapsed: 0.057 s
% 3.36/1.95 % (18719)Instructions burned: 128 (million)
% 3.36/1.95 % (18719)------------------------------
% 3.36/1.95 % (18719)------------------------------
% 3.36/1.96 % (18723)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18469 for (2997ds/100Mi)
% 3.36/1.97 % (18706)Instruction limit reached!
% 3.36/1.97 % (18706)------------------------------
% 3.36/1.97 % (18706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.97 % (18706)Termination reason: Unknown
% 3.36/1.97 % (18706)Termination phase: Saturation
% 3.36/1.97
% 3.36/1.97 % (18706)Memory used [KB]: 9466
% 3.36/1.97 % (18706)Time elapsed: 0.161 s
% 3.36/1.97 % (18706)Instructions burned: 377 (million)
% 3.36/1.97 % (18706)------------------------------
% 3.36/1.97 % (18706)------------------------------
% 3.36/1.99 % (18723)Instruction limit reached!
% 3.36/1.99 % (18723)------------------------------
% 3.36/1.99 % (18723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.99 % (18723)Termination reason: Unknown
% 3.36/1.99 % (18723)Termination phase: Property scanning
% 3.36/1.99
% 3.36/1.99 % (18723)Memory used [KB]: 2814
% 3.36/1.99 % (18723)Time elapsed: 0.028 s
% 3.36/1.99 % (18723)Instructions burned: 101 (million)
% 3.36/1.99 % (18723)------------------------------
% 3.36/1.99 % (18723)------------------------------
% 3.36/2.00 % (18724)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_18469 for (2997ds/3Mi)
% 3.36/2.00 % (18725)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_18469 for (2997ds/20Mi)
% 3.36/2.00 % (18724)Instruction limit reached!
% 3.36/2.00 % (18724)------------------------------
% 3.36/2.00 % (18724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/2.00 % (18724)Termination reason: Unknown
% 3.36/2.00 % (18724)Termination phase: shuffling
% 3.36/2.00
% 3.36/2.00 % (18724)Memory used [KB]: 1535
% 3.36/2.00 % (18724)Time elapsed: 0.004 s
% 3.36/2.00 % (18724)Instructions burned: 4 (million)
% 3.36/2.00 % (18724)------------------------------
% 3.36/2.00 % (18724)------------------------------
% 3.36/2.00 % (18725)Instruction limit reached!
% 3.36/2.00 % (18725)------------------------------
% 3.36/2.00 % (18725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/2.00 % (18725)Termination reason: Unknown
% 3.36/2.00 % (18725)Termination phase: shuffling
% 3.36/2.00
% 3.36/2.00 % (18725)Memory used [KB]: 1918
% 3.36/2.00 % (18725)Time elapsed: 0.008 s
% 3.36/2.00 % (18725)Instructions burned: 20 (million)
% 3.36/2.00 % (18725)------------------------------
% 3.36/2.00 % (18725)------------------------------
% 3.36/2.01 % (18727)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_18469 for (2996ds/86Mi)
% 3.36/2.02 % (18728)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_18469 for (2996ds/107Mi)
% 5.59/2.04 % (18727)Instruction limit reached!
% 5.59/2.04 % (18727)------------------------------
% 5.59/2.04 % (18727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.04 % (18727)Termination reason: Unknown
% 5.59/2.04 % (18727)Termination phase: Property scanning
% 5.59/2.04
% 5.59/2.04 % (18727)Memory used [KB]: 2686
% 5.59/2.04 % (18727)Time elapsed: 0.028 s
% 5.59/2.04 % (18727)Instructions burned: 87 (million)
% 5.59/2.04 % (18727)------------------------------
% 5.59/2.04 % (18727)------------------------------
% 5.59/2.06 % (18733)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_18469 for (2996ds/39Mi)
% 5.59/2.07 % (18728)Instruction limit reached!
% 5.59/2.07 % (18728)------------------------------
% 5.59/2.07 % (18728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.07 % (18728)Termination reason: Unknown
% 5.59/2.07 % (18728)Termination phase: SInE selection
% 5.59/2.07
% 5.59/2.07 % (18728)Memory used [KB]: 2686
% 5.59/2.07 % (18728)Time elapsed: 0.050 s
% 5.59/2.07 % (18728)Instructions burned: 108 (million)
% 5.59/2.07 % (18728)------------------------------
% 5.59/2.07 % (18728)------------------------------
% 5.59/2.07 % (18733)Instruction limit reached!
% 5.59/2.07 % (18733)------------------------------
% 5.59/2.07 % (18733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.07 % (18733)Termination reason: Unknown
% 5.59/2.07 % (18733)Termination phase: shuffling
% 5.59/2.07
% 5.59/2.07 % (18733)Memory used [KB]: 2302
% 5.59/2.07 % (18733)Time elapsed: 0.019 s
% 5.59/2.07 % (18733)Instructions burned: 39 (million)
% 5.59/2.07 % (18733)------------------------------
% 5.59/2.07 % (18733)------------------------------
% 5.59/2.08 % (18737)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_18469 for (2995ds/448Mi)
% 5.59/2.08 % (18700)Instruction limit reached!
% 5.59/2.08 % (18700)------------------------------
% 5.59/2.08 % (18700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.08 % (18700)Termination reason: Unknown
% 5.59/2.08 % (18700)Termination phase: Saturation
% 5.59/2.08
% 5.59/2.08 % (18700)Memory used [KB]: 12281
% 5.59/2.08 % (18700)Time elapsed: 0.311 s
% 5.59/2.08 % (18700)Instructions burned: 710 (million)
% 5.59/2.08 % (18700)------------------------------
% 5.59/2.08 % (18700)------------------------------
% 5.59/2.09 % (18739)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_18469 for (2995ds/46Mi)
% 5.59/2.10 % (18740)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_18469 for (2995ds/98Mi)
% 5.59/2.11 % (18708)Instruction limit reached!
% 5.59/2.11 % (18708)------------------------------
% 5.59/2.11 % (18708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.11 % (18708)Termination reason: Unknown
% 5.59/2.11 % (18708)Termination phase: Saturation
% 5.59/2.11
% 5.59/2.11 % (18708)Memory used [KB]: 7803
% 5.59/2.11 % (18708)Time elapsed: 0.300 s
% 5.59/2.11 % (18708)Instructions burned: 781 (million)
% 5.59/2.11 % (18708)------------------------------
% 5.59/2.11 % (18708)------------------------------
% 5.59/2.11 % (18687)Instruction limit reached!
% 5.59/2.11 % (18687)------------------------------
% 5.59/2.11 % (18687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.11 % (18687)Termination reason: Unknown
% 5.59/2.11 % (18687)Termination phase: Saturation
% 5.59/2.11
% 5.59/2.11 % (18687)Memory used [KB]: 17526
% 5.59/2.11 % (18687)Time elapsed: 0.386 s
% 5.59/2.11 % (18687)Instructions burned: 1044 (million)
% 5.59/2.11 % (18687)------------------------------
% 5.59/2.11 % (18687)------------------------------
% 5.59/2.11 % (18739)Instruction limit reached!
% 5.59/2.11 % (18739)------------------------------
% 5.59/2.11 % (18739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.59/2.11 % (18739)Termination reason: Unknown
% 5.59/2.11 % (18739)Termination phase: shuffling
% 5.59/2.11
% 5.59/2.11 % (18739)Memory used [KB]: 2430
% 5.59/2.11 % (18739)Time elapsed: 0.023 s
% 5.59/2.11 % (18739)Instructions burned: 47 (million)
% 5.59/2.11 % (18739)------------------------------
% 5.59/2.11 % (18739)------------------------------
% 5.59/2.12 % (18742)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_18469 for (2995ds/149Mi)
% 6.23/2.13 % (18741)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_18469 for (2995ds/507Mi)
% 6.23/2.13 % (18743)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_18469 for (2995ds/39Mi)
% 6.23/2.14 % (18740)Instruction limit reached!
% 6.23/2.14 % (18740)------------------------------
% 6.23/2.14 % (18740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.14 % (18740)Termination reason: Unknown
% 6.23/2.14 % (18740)Termination phase: Property scanning
% 6.23/2.14
% 6.23/2.14 % (18740)Memory used [KB]: 2686
% 6.23/2.14 % (18740)Time elapsed: 0.045 s
% 6.23/2.14 % (18740)Instructions burned: 99 (million)
% 6.23/2.14 % (18740)------------------------------
% 6.23/2.14 % (18740)------------------------------
% 6.23/2.15 % (18743)Instruction limit reached!
% 6.23/2.15 % (18743)------------------------------
% 6.23/2.15 % (18743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.15 % (18743)Termination reason: Unknown
% 6.23/2.15 % (18743)Termination phase: shuffling
% 6.23/2.15
% 6.23/2.15 % (18743)Memory used [KB]: 2430
% 6.23/2.15 % (18743)Time elapsed: 0.020 s
% 6.23/2.15 % (18743)Instructions burned: 41 (million)
% 6.23/2.15 % (18743)------------------------------
% 6.23/2.15 % (18743)------------------------------
% 6.23/2.16 % (18745)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_18469 for (2995ds/6Mi)
% 6.23/2.16 % (18742)Instruction limit reached!
% 6.23/2.16 % (18742)------------------------------
% 6.23/2.16 % (18742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.16 % (18742)Termination reason: Unknown
% 6.23/2.16 % (18742)Termination phase: Function definition elimination
% 6.23/2.16
% 6.23/2.16 % (18742)Memory used [KB]: 2942
% 6.23/2.16 % (18742)Time elapsed: 0.039 s
% 6.23/2.16 % (18742)Instructions burned: 150 (million)
% 6.23/2.16 % (18742)------------------------------
% 6.23/2.16 % (18742)------------------------------
% 6.23/2.16 % (18745)Instruction limit reached!
% 6.23/2.16 % (18745)------------------------------
% 6.23/2.16 % (18745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.16 % (18745)Termination reason: Unknown
% 6.23/2.16 % (18745)Termination phase: shuffling
% 6.23/2.16
% 6.23/2.16 % (18745)Memory used [KB]: 1663
% 6.23/2.16 % (18745)Time elapsed: 0.005 s
% 6.23/2.16 % (18745)Instructions burned: 6 (million)
% 6.23/2.16 % (18745)------------------------------
% 6.23/2.16 % (18745)------------------------------
% 6.23/2.16 % (18747)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_18469 for (2995ds/1087Mi)
% 6.23/2.17 % (18702)Instruction limit reached!
% 6.23/2.17 % (18702)------------------------------
% 6.23/2.17 % (18702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.17 % (18702)Termination reason: Unknown
% 6.23/2.17 % (18702)Termination phase: Saturation
% 6.23/2.17
% 6.23/2.17 % (18702)Memory used [KB]: 12920
% 6.23/2.17 % (18702)Time elapsed: 0.398 s
% 6.23/2.17 % (18702)Instructions burned: 902 (million)
% 6.23/2.17 % (18702)------------------------------
% 6.23/2.17 % (18702)------------------------------
% 6.23/2.18 % (18748)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_18469 for (2995ds/47Mi)
% 6.23/2.18 % (18751)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_18469 for (2995ds/44Mi)
% 6.23/2.18 % (18753)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_18469 for (2994ds/432Mi)
% 6.51/2.20 % (18751)Instruction limit reached!
% 6.51/2.20 % (18751)------------------------------
% 6.51/2.20 % (18751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.20 % (18751)Termination reason: Unknown
% 6.51/2.20 % (18751)Termination phase: shuffling
% 6.51/2.20
% 6.51/2.20 % (18751)Memory used [KB]: 2430
% 6.51/2.20 % (18751)Time elapsed: 0.022 s
% 6.51/2.20 % (18751)Instructions burned: 46 (million)
% 6.51/2.20 % (18751)------------------------------
% 6.51/2.20 % (18751)------------------------------
% 6.51/2.20 % (18748)Instruction limit reached!
% 6.51/2.20 % (18748)------------------------------
% 6.51/2.20 % (18748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.20 % (18748)Termination reason: Unknown
% 6.51/2.20 % (18748)Termination phase: shuffling
% 6.51/2.20
% 6.51/2.20 % (18748)Memory used [KB]: 2558
% 6.51/2.20 % (18748)Time elapsed: 0.024 s
% 6.51/2.20 % (18748)Instructions burned: 48 (million)
% 6.51/2.20 % (18748)------------------------------
% 6.51/2.20 % (18748)------------------------------
% 6.51/2.22 % (18755)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_18469 for (2994ds/62Mi)
% 6.51/2.22 % (18756)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_18469 for (2994ds/31Mi)
% 6.51/2.23 % (18713)Instruction limit reached!
% 6.51/2.23 % (18713)------------------------------
% 6.51/2.23 % (18713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.23 % (18713)Termination reason: Unknown
% 6.51/2.23 % (18713)Termination phase: Saturation
% 6.51/2.23
% 6.51/2.23 % (18713)Memory used [KB]: 10490
% 6.51/2.23 % (18713)Time elapsed: 0.386 s
% 6.51/2.23 % (18713)Instructions burned: 880 (million)
% 6.51/2.23 % (18713)------------------------------
% 6.51/2.23 % (18713)------------------------------
% 6.51/2.23 % (18756)Instruction limit reached!
% 6.51/2.23 % (18756)------------------------------
% 6.51/2.23 % (18756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.23 % (18756)Termination reason: Unknown
% 6.51/2.23 % (18756)Termination phase: shuffling
% 6.51/2.23
% 6.51/2.23 % (18756)Memory used [KB]: 2174
% 6.51/2.23 % (18756)Time elapsed: 0.016 s
% 6.51/2.23 % (18756)Instructions burned: 32 (million)
% 6.51/2.23 % (18756)------------------------------
% 6.51/2.23 % (18756)------------------------------
% 6.51/2.24 % (18755)Instruction limit reached!
% 6.51/2.24 % (18755)------------------------------
% 6.51/2.24 % (18755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.24 % (18737)Instruction limit reached!
% 6.51/2.24 % (18737)------------------------------
% 6.51/2.24 % (18737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.24 % (18737)Termination reason: Unknown
% 6.51/2.24 % (18755)Termination reason: Unknown
% 6.51/2.24 % (18737)Termination phase: Saturation
% 6.51/2.24
% 6.51/2.24 % (18755)Termination phase: Property scanning
% 6.51/2.24
% 6.51/2.24 % (18737)Memory used [KB]: 7675
% 6.51/2.24 % (18755)Memory used [KB]: 2686
% 6.51/2.24 % (18737)Time elapsed: 0.164 s
% 6.51/2.24 % (18755)Time elapsed: 0.029 s
% 6.51/2.24 % (18755)Instructions burned: 63 (million)
% 6.51/2.24 % (18737)Instructions burned: 448 (million)
% 6.51/2.24 % (18755)------------------------------
% 6.51/2.24 % (18755)------------------------------
% 6.51/2.24 % (18737)------------------------------
% 6.51/2.24 % (18737)------------------------------
% 6.51/2.25 % (18758)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_18469 for (2994ds/453Mi)
% 6.51/2.25 % (18757)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_18469 for (2994ds/96Mi)
% 6.51/2.26 % (18762)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_18469 for (2994ds/83Mi)
% 6.51/2.26 % (18761)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_18469 for (2994ds/71Mi)
% 6.51/2.28 % (18762)Instruction limit reached!
% 6.51/2.28 % (18762)------------------------------
% 6.51/2.28 % (18762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.28 % (18762)Termination reason: Unknown
% 6.51/2.28 % (18762)Termination phase: Property scanning
% 6.51/2.28
% 6.51/2.28 % (18762)Memory used [KB]: 2686
% 6.51/2.28 % (18762)Time elapsed: 0.023 s
% 6.51/2.28 % (18762)Instructions burned: 83 (million)
% 6.51/2.28 % (18762)------------------------------
% 6.51/2.28 % (18762)------------------------------
% 6.51/2.29 % (18768)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_18469 for (2993ds/11Mi)
% 6.51/2.29 % (18761)Instruction limit reached!
% 6.51/2.29 % (18761)------------------------------
% 6.51/2.29 % (18761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.29 % (18761)Termination reason: Unknown
% 6.51/2.29 % (18761)Termination phase: Property scanning
% 6.51/2.29
% 6.51/2.29 % (18761)Memory used [KB]: 2686
% 6.51/2.29 % (18761)Time elapsed: 0.034 s
% 6.51/2.29 % (18761)Instructions burned: 71 (million)
% 6.51/2.29 % (18761)------------------------------
% 6.51/2.29 % (18761)------------------------------
% 6.51/2.29 % (18757)Instruction limit reached!
% 6.51/2.29 % (18757)------------------------------
% 6.51/2.29 % (18757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.29 % (18757)Termination reason: Unknown
% 6.51/2.29 % (18757)Termination phase: Property scanning
% 6.51/2.29
% 6.51/2.29 % (18757)Memory used [KB]: 2686
% 6.51/2.29 % (18757)Time elapsed: 0.045 s
% 6.51/2.29 % (18757)Instructions burned: 97 (million)
% 6.51/2.29 % (18757)------------------------------
% 6.51/2.29 % (18757)------------------------------
% 6.51/2.29 % (18768)Instruction limit reached!
% 6.51/2.29 % (18768)------------------------------
% 6.51/2.29 % (18768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.51/2.29 % (18768)Termination reason: Unknown
% 6.51/2.29 % (18768)Termination phase: shuffling
% 6.51/2.29
% 6.51/2.29 % (18768)Memory used [KB]: 1791
% 6.51/2.29 % (18768)Time elapsed: 0.005 s
% 6.51/2.29 % (18768)Instructions burned: 13 (million)
% 6.51/2.29 % (18768)------------------------------
% 6.51/2.29 % (18768)------------------------------
% 7.04/2.30 % (18770)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18469 for (2993ds/6Mi)
% 7.04/2.31 % (18770)Instruction limit reached!
% 7.04/2.31 % (18770)------------------------------
% 7.04/2.31 % (18770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.31 % (18770)Termination reason: Unknown
% 7.04/2.31 % (18770)Termination phase: shuffling
% 7.04/2.31
% 7.04/2.31 % (18770)Memory used [KB]: 1663
% 7.04/2.31 % (18770)Time elapsed: 0.003 s
% 7.04/2.31 % (18770)Instructions burned: 7 (million)
% 7.04/2.31 % (18770)------------------------------
% 7.04/2.31 % (18770)------------------------------
% 7.04/2.31 % (18769)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_18469 for (2993ds/41Mi)
% 7.04/2.31 % (18771)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_18469 for (2993ds/150Mi)
% 7.04/2.32 % (18772)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_18469 for (2993ds/343Mi)
% 7.04/2.32 % (18769)Instruction limit reached!
% 7.04/2.32 % (18769)------------------------------
% 7.04/2.32 % (18769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.32 % (18769)Termination reason: Unknown
% 7.04/2.32 % (18769)Termination phase: shuffling
% 7.04/2.32
% 7.04/2.32 % (18769)Memory used [KB]: 2430
% 7.04/2.32 % (18769)Time elapsed: 0.013 s
% 7.04/2.32 % (18769)Instructions burned: 43 (million)
% 7.04/2.32 % (18769)------------------------------
% 7.04/2.32 % (18769)------------------------------
% 7.04/2.33 % (18741)Instruction limit reached!
% 7.04/2.33 % (18741)------------------------------
% 7.04/2.33 % (18741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.33 % (18741)Termination reason: Unknown
% 7.04/2.33 % (18741)Termination phase: Saturation
% 7.04/2.33
% 7.04/2.33 % (18741)Memory used [KB]: 8187
% 7.04/2.33 % (18741)Time elapsed: 0.200 s
% 7.04/2.33 % (18741)Instructions burned: 508 (million)
% 7.04/2.33 % (18741)------------------------------
% 7.04/2.33 % (18741)------------------------------
% 7.04/2.33 % (18774)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_18469 for (2993ds/109Mi)
% 7.04/2.34 % (18753)Instruction limit reached!
% 7.04/2.34 % (18753)------------------------------
% 7.04/2.34 % (18753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.34 % (18753)Termination reason: Unknown
% 7.04/2.34 % (18753)Termination phase: Saturation
% 7.04/2.34
% 7.04/2.34 % (18753)Memory used [KB]: 3198
% 7.04/2.34 % (18753)Time elapsed: 0.164 s
% 7.04/2.34 % (18753)Instructions burned: 432 (million)
% 7.04/2.34 % (18753)------------------------------
% 7.04/2.34 % (18753)------------------------------
% 7.04/2.35 % (18775)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_18469 for (2993ds/253Mi)
% 7.04/2.36 % (18776)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_18469 for (2993ds/140Mi)
% 7.04/2.38 % (18774)Instruction limit reached!
% 7.04/2.38 % (18774)------------------------------
% 7.04/2.38 % (18774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.38 % (18774)Termination reason: Unknown
% 7.04/2.38 % (18774)Termination phase: SInE selection
% 7.04/2.38
% 7.04/2.38 % (18774)Memory used [KB]: 2686
% 7.04/2.38 % (18774)Time elapsed: 0.044 s
% 7.04/2.38 % (18774)Instructions burned: 111 (million)
% 7.04/2.38 % (18774)------------------------------
% 7.04/2.38 % (18774)------------------------------
% 7.04/2.38 % (18771)Instruction limit reached!
% 7.04/2.38 % (18771)------------------------------
% 7.04/2.38 % (18771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.04/2.38 % (18771)Termination reason: Unknown
% 7.04/2.38 % (18771)Termination phase: Property scanning
% 7.04/2.38
% 7.04/2.38 % (18771)Memory used [KB]: 5373
% 7.04/2.38 % (18771)Time elapsed: 0.074 s
% 7.04/2.38 % (18771)Instructions burned: 152 (million)
% 7.04/2.38 % (18771)------------------------------
% 7.04/2.38 % (18771)------------------------------
% 7.04/2.39 % (18778)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_18469 for (2993ds/614Mi)
% 7.61/2.41 % (18779)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_18469 for (2992ds/202Mi)
% 7.61/2.42 % (18776)Instruction limit reached!
% 7.61/2.42 % (18776)------------------------------
% 7.61/2.42 % (18776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.42 % (18776)Termination reason: Unknown
% 7.61/2.42 % (18776)Termination phase: Property scanning
% 7.61/2.42
% 7.61/2.42 % (18776)Memory used [KB]: 2942
% 7.61/2.42 % (18776)Time elapsed: 0.062 s
% 7.61/2.42 % (18776)Instructions burned: 140 (million)
% 7.61/2.42 % (18776)------------------------------
% 7.61/2.42 % (18776)------------------------------
% 7.61/2.43 % (18758)Instruction limit reached!
% 7.61/2.43 % (18758)------------------------------
% 7.61/2.43 % (18758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.43 % (18758)Termination reason: Unknown
% 7.61/2.43 % (18758)Termination phase: Saturation
% 7.61/2.43
% 7.61/2.43 % (18758)Memory used [KB]: 7675
% 7.61/2.43 % (18758)Time elapsed: 0.186 s
% 7.61/2.43 % (18758)Instructions burned: 454 (million)
% 7.61/2.43 % (18758)------------------------------
% 7.61/2.43 % (18758)------------------------------
% 7.61/2.43 % (18775)Instruction limit reached!
% 7.61/2.43 % (18775)------------------------------
% 7.61/2.43 % (18775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.43 % (18775)Termination reason: Unknown
% 7.61/2.43 % (18775)Termination phase: Property scanning
% 7.61/2.43
% 7.61/2.43 % (18775)Memory used [KB]: 5628
% 7.61/2.43 % (18775)Time elapsed: 0.086 s
% 7.61/2.43 % (18775)Instructions burned: 253 (million)
% 7.61/2.43 % (18775)------------------------------
% 7.61/2.43 % (18775)------------------------------
% 7.61/2.44 % (18783)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_18469 for (2992ds/339Mi)
% 7.61/2.45 % (18785)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_18469 for (2992ds/134Mi)
% 7.61/2.45 % (18784)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_18469 for (2992ds/283Mi)
% 7.61/2.47 % (18772)Instruction limit reached!
% 7.61/2.47 % (18772)------------------------------
% 7.61/2.47 % (18772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.47 % (18772)Termination reason: Unknown
% 7.61/2.47 % (18772)Termination phase: Saturation
% 7.61/2.47
% 7.61/2.47 % (18772)Memory used [KB]: 8315
% 7.61/2.47 % (18772)Time elapsed: 0.148 s
% 7.61/2.47 % (18772)Instructions burned: 344 (million)
% 7.61/2.47 % (18772)------------------------------
% 7.61/2.47 % (18772)------------------------------
% 7.61/2.49 % (18787)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_18469 for (2992ds/298Mi)
% 8.14/2.50 % (18779)Instruction limit reached!
% 8.14/2.50 % (18779)------------------------------
% 8.14/2.50 % (18779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.50 % (18779)Termination reason: Unknown
% 8.14/2.50 % (18779)Termination phase: Property scanning
% 8.14/2.50
% 8.14/2.50 % (18779)Memory used [KB]: 5500
% 8.14/2.50 % (18779)Time elapsed: 0.090 s
% 8.14/2.50 % (18779)Instructions burned: 203 (million)
% 8.14/2.50 % (18779)------------------------------
% 8.14/2.50 % (18779)------------------------------
% 8.14/2.51 % (18785)Instruction limit reached!
% 8.14/2.51 % (18785)------------------------------
% 8.14/2.51 % (18785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.51 % (18785)Termination reason: Unknown
% 8.14/2.51 % (18785)Termination phase: Property scanning
% 8.14/2.51
% 8.14/2.51 % (18785)Memory used [KB]: 2942
% 8.14/2.51 % (18785)Time elapsed: 0.061 s
% 8.14/2.51 % (18785)Instructions burned: 135 (million)
% 8.14/2.51 % (18785)------------------------------
% 8.14/2.51 % (18785)------------------------------
% 8.14/2.51 % (18788)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_18469 for (2991ds/192Mi)
% 8.14/2.54 % (18789)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_18469 for (2991ds/258Mi)
% 8.14/2.57 % (18784)Instruction limit reached!
% 8.14/2.57 % (18784)------------------------------
% 8.14/2.57 % (18784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.57 % (18784)Termination reason: Unknown
% 8.14/2.57 % (18784)Termination phase: Saturation
% 8.14/2.57
% 8.14/2.57 % (18784)Memory used [KB]: 7547
% 8.14/2.57 % (18784)Time elapsed: 0.120 s
% 8.14/2.57 % (18784)Instructions burned: 284 (million)
% 8.14/2.57 % (18784)------------------------------
% 8.14/2.57 % (18784)------------------------------
% 8.14/2.59 % (18791)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_18469 for (2991ds/90Mi)
% 8.14/2.59 % (18783)Instruction limit reached!
% 8.14/2.59 % (18783)------------------------------
% 8.14/2.59 % (18783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.59 % (18783)Termination reason: Unknown
% 8.14/2.59 % (18783)Termination phase: Saturation
% 8.14/2.59
% 8.14/2.59 % (18783)Memory used [KB]: 7931
% 8.14/2.59 % (18783)Time elapsed: 0.152 s
% 8.14/2.59 % (18783)Instructions burned: 339 (million)
% 8.14/2.59 % (18783)------------------------------
% 8.14/2.59 % (18783)------------------------------
% 8.62/2.60 % (18788)Instruction limit reached!
% 8.62/2.60 % (18788)------------------------------
% 8.62/2.60 % (18788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.60 % (18788)Termination reason: Unknown
% 8.62/2.60 % (18788)Termination phase: Saturation
% 8.62/2.60
% 8.62/2.60 % (18788)Memory used [KB]: 7547
% 8.62/2.60 % (18788)Time elapsed: 0.085 s
% 8.62/2.60 % (18788)Instructions burned: 192 (million)
% 8.62/2.60 % (18788)------------------------------
% 8.62/2.60 % (18788)------------------------------
% 8.62/2.60 % (18793)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_18469 for (2990ds/231Mi)
% 8.62/2.61 % (18794)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_18469 for (2990ds/458Mi)
% 8.62/2.62 % (18787)Instruction limit reached!
% 8.62/2.62 % (18787)------------------------------
% 8.62/2.62 % (18787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.62 % (18787)Termination reason: Unknown
% 8.62/2.62 % (18787)Termination phase: Saturation
% 8.62/2.62
% 8.62/2.62 % (18787)Memory used [KB]: 7547
% 8.62/2.62 % (18787)Time elapsed: 0.125 s
% 8.62/2.62 % (18787)Instructions burned: 299 (million)
% 8.62/2.62 % (18787)------------------------------
% 8.62/2.62 % (18787)------------------------------
% 8.62/2.63 % (18791)Instruction limit reached!
% 8.62/2.63 % (18791)------------------------------
% 8.62/2.63 % (18791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.63 % (18791)Termination reason: Unknown
% 8.62/2.63 % (18791)Termination phase: Property scanning
% 8.62/2.63
% 8.62/2.63 % (18791)Memory used [KB]: 2686
% 8.62/2.63 % (18791)Time elapsed: 0.043 s
% 8.62/2.63 % (18791)Instructions burned: 92 (million)
% 8.62/2.63 % (18791)------------------------------
% 8.62/2.63 % (18791)------------------------------
% 8.62/2.64 % (18795)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_18469 for (2990ds/31Mi)
% 8.62/2.64 % (18796)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_18469 for (2990ds/297Mi)
% 8.62/2.65 % (18795)Instruction limit reached!
% 8.62/2.65 % (18795)------------------------------
% 8.62/2.65 % (18795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.65 % (18795)Termination reason: Unknown
% 8.62/2.65 % (18795)Termination phase: shuffling
% 8.62/2.65
% 8.62/2.65 % (18795)Memory used [KB]: 2174
% 8.62/2.65 % (18795)Time elapsed: 0.016 s
% 8.62/2.65 % (18795)Instructions burned: 32 (million)
% 8.62/2.65 % (18795)------------------------------
% 8.62/2.65 % (18795)------------------------------
% 8.62/2.67 % (18797)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_18469 for (2990ds/987Mi)
% 8.62/2.67 % (18789)Instruction limit reached!
% 8.62/2.67 % (18789)------------------------------
% 8.62/2.67 % (18789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.67 % (18789)Termination reason: Unknown
% 8.62/2.67 % (18789)Termination phase: Saturation
% 8.62/2.67
% 8.62/2.67 % (18789)Memory used [KB]: 7931
% 8.62/2.67 % (18789)Time elapsed: 0.073 s
% 8.62/2.67 % (18789)Instructions burned: 259 (million)
% 8.62/2.67 % (18789)------------------------------
% 8.62/2.67 % (18789)------------------------------
% 8.62/2.68 % (18778)Instruction limit reached!
% 8.62/2.68 % (18778)------------------------------
% 8.62/2.68 % (18778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.68 % (18778)Termination reason: Unknown
% 8.62/2.68 % (18778)Termination phase: Saturation
% 8.62/2.68
% 8.62/2.68 % (18778)Memory used [KB]: 10234
% 8.62/2.68 % (18778)Time elapsed: 0.285 s
% 8.62/2.68 % (18778)Instructions burned: 614 (million)
% 8.62/2.68 % (18778)------------------------------
% 8.62/2.68 % (18778)------------------------------
% 8.62/2.69 % (18798)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_18469 for (2990ds/182Mi)
% 8.62/2.69 % (18747)Instruction limit reached!
% 8.62/2.69 % (18747)------------------------------
% 8.62/2.69 % (18747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.69 % (18747)Termination reason: Unknown
% 8.62/2.69 % (18747)Termination phase: Saturation
% 8.62/2.69
% 8.62/2.69 % (18747)Memory used [KB]: 12792
% 8.62/2.69 % (18747)Time elapsed: 0.520 s
% 8.62/2.69 % (18747)Instructions burned: 1089 (million)
% 8.62/2.69 % (18747)------------------------------
% 8.62/2.69 % (18747)------------------------------
% 8.62/2.69 % (18799)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_18469 for (2989ds/182Mi)
% 9.77/2.70 % (18801)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_18469 for (2989ds/154Mi)
% 9.77/2.70 % (18793)Instruction limit reached!
% 9.77/2.70 % (18793)------------------------------
% 9.77/2.70 % (18793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.70 % (18793)Termination reason: Unknown
% 9.77/2.70 % (18793)Termination phase: Property scanning
% 9.77/2.70
% 9.77/2.70 % (18793)Memory used [KB]: 3965
% 9.77/2.70 % (18793)Time elapsed: 0.101 s
% 9.77/2.70 % (18793)Instructions burned: 232 (million)
% 9.77/2.70 % (18793)------------------------------
% 9.77/2.70 % (18793)------------------------------
% 9.77/2.72 % (18802)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_18469 for (2989ds/79Mi)
% 9.77/2.75 % (18799)Instruction limit reached!
% 9.77/2.75 % (18799)------------------------------
% 9.77/2.75 % (18799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.75 % (18799)Termination reason: Unknown
% 9.77/2.75 % (18799)Termination phase: Property scanning
% 9.77/2.75
% 9.77/2.75 % (18799)Memory used [KB]: 5500
% 9.77/2.75 % (18799)Time elapsed: 0.059 s
% 9.77/2.75 % (18799)Instructions burned: 186 (million)
% 9.77/2.75 % (18799)------------------------------
% 9.77/2.75 % (18799)------------------------------
% 9.77/2.76 % (18802)Instruction limit reached!
% 9.77/2.76 % (18802)------------------------------
% 9.77/2.76 % (18802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.76 % (18802)Termination reason: Unknown
% 9.77/2.76 % (18802)Termination phase: Property scanning
% 9.77/2.76
% 9.77/2.76 % (18802)Memory used [KB]: 2686
% 9.77/2.76 % (18802)Time elapsed: 0.037 s
% 9.77/2.76 % (18802)Instructions burned: 80 (million)
% 9.77/2.76 % (18802)------------------------------
% 9.77/2.76 % (18802)------------------------------
% 9.77/2.76 % (18801)Instruction limit reached!
% 9.77/2.76 % (18801)------------------------------
% 9.77/2.76 % (18801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.76 % (18801)Termination reason: Unknown
% 9.77/2.76 % (18801)Termination phase: Function definition elimination
% 9.77/2.76
% 9.77/2.76 % (18801)Memory used [KB]: 2814
% 9.77/2.76 % (18801)Time elapsed: 0.061 s
% 9.77/2.76 % (18801)Instructions burned: 154 (million)
% 9.77/2.76 % (18801)------------------------------
% 9.77/2.76 % (18801)------------------------------
% 9.77/2.76 % (18796)Instruction limit reached!
% 9.77/2.76 % (18796)------------------------------
% 9.77/2.76 % (18796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.76 % (18796)Termination reason: Unknown
% 9.77/2.76 % (18796)Termination phase: Saturation
% 9.77/2.76
% 9.77/2.76 % (18796)Memory used [KB]: 7547
% 9.77/2.76 % (18796)Time elapsed: 0.123 s
% 9.77/2.76 % (18796)Instructions burned: 298 (million)
% 9.77/2.76 % (18796)------------------------------
% 9.77/2.76 % (18796)------------------------------
% 9.77/2.77 % (18806)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_18469 for (2989ds/114Mi)
% 9.77/2.77 % (18805)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_18469 for (2989ds/216Mi)
% 9.77/2.77 % (18798)Instruction limit reached!
% 9.77/2.77 % (18798)------------------------------
% 9.77/2.77 % (18798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.77 % (18798)Termination reason: Unknown
% 9.77/2.77 % (18798)Termination phase: Property scanning
% 9.77/2.77
% 9.77/2.77 % (18798)Memory used [KB]: 2942
% 9.77/2.77 % (18798)Time elapsed: 0.081 s
% 9.77/2.77 % (18798)Instructions burned: 183 (million)
% 9.77/2.77 % (18798)------------------------------
% 9.77/2.77 % (18798)------------------------------
% 9.77/2.78 % (18808)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_18469 for (2989ds/182Mi)
% 9.77/2.78 % (18807)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_18469 for (2989ds/922Mi)
% 9.77/2.78 % (18809)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_18469 for (2989ds/164Mi)
% 9.77/2.80 % (18806)Instruction limit reached!
% 9.77/2.80 % (18806)------------------------------
% 9.77/2.80 % (18806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.80 % (18806)Termination reason: Unknown
% 9.77/2.80 % (18806)Termination phase: Property scanning
% 9.77/2.80
% 9.77/2.80 % (18806)Memory used [KB]: 2814
% 9.77/2.80 % (18806)Time elapsed: 0.031 s
% 9.77/2.80 % (18806)Instructions burned: 115 (million)
% 9.77/2.80 % (18806)------------------------------
% 9.77/2.80 % (18806)------------------------------
% 10.35/2.80 % (18810)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_18469 for (2988ds/50Mi)
% 10.35/2.81 % (18794)Instruction limit reached!
% 10.35/2.81 % (18794)------------------------------
% 10.35/2.81 % (18794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.81 % (18794)Termination reason: Unknown
% 10.35/2.81 % (18794)Termination phase: Saturation
% 10.35/2.81
% 10.35/2.81 % (18794)Memory used [KB]: 9722
% 10.35/2.81 % (18794)Time elapsed: 0.201 s
% 10.35/2.81 % (18794)Instructions burned: 458 (million)
% 10.35/2.81 % (18794)------------------------------
% 10.35/2.81 % (18794)------------------------------
% 10.35/2.82 % (18810)Instruction limit reached!
% 10.35/2.82 % (18810)------------------------------
% 10.35/2.82 % (18810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.82 % (18810)Termination reason: Unknown
% 10.35/2.82 % (18810)Termination phase: shuffling
% 10.35/2.82
% 10.35/2.82 % (18810)Memory used [KB]: 2430
% 10.35/2.82 % (18810)Time elapsed: 0.018 s
% 10.35/2.82 % (18810)Instructions burned: 51 (million)
% 10.35/2.82 % (18810)------------------------------
% 10.35/2.82 % (18810)------------------------------
% 10.35/2.83 % (18811)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_18469 for (2988ds/368Mi)
% 10.35/2.84 % (18813)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_18469 for (2988ds/1021Mi)
% 10.35/2.84 % (18805)Instruction limit reached!
% 10.35/2.84 % (18805)------------------------------
% 10.35/2.84 % (18805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.84 % (18805)Termination reason: Unknown
% 10.35/2.84 % (18805)Termination phase: Property scanning
% 10.35/2.84
% 10.35/2.84 % (18805)Memory used [KB]: 3070
% 10.35/2.84 % (18805)Time elapsed: 0.079 s
% 10.35/2.84 % (18805)Instructions burned: 216 (million)
% 10.35/2.84 % (18805)------------------------------
% 10.35/2.84 % (18805)------------------------------
% 10.35/2.84 % (18809)Instruction limit reached!
% 10.35/2.84 % (18809)------------------------------
% 10.35/2.84 % (18809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.84 % (18809)Termination reason: Unknown
% 10.35/2.84 % (18809)Termination phase: Property scanning
% 10.35/2.84
% 10.35/2.84 % (18809)Memory used [KB]: 2942
% 10.35/2.84 % (18809)Time elapsed: 0.062 s
% 10.35/2.84 % (18809)Instructions burned: 164 (million)
% 10.35/2.84 % (18809)------------------------------
% 10.35/2.84 % (18809)------------------------------
% 10.35/2.86 % (18808)Instruction limit reached!
% 10.35/2.86 % (18808)------------------------------
% 10.35/2.86 % (18808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.86 % (18808)Termination reason: Unknown
% 10.35/2.86 % (18808)Termination phase: Property scanning
% 10.35/2.86
% 10.35/2.86 % (18808)Memory used [KB]: 3070
% 10.35/2.86 % (18808)Time elapsed: 0.078 s
% 10.35/2.86 % (18808)Instructions burned: 182 (million)
% 10.35/2.86 % (18808)------------------------------
% 10.35/2.86 % (18808)------------------------------
% 10.35/2.86 % (18815)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_18469 for (2988ds/267Mi)
% 10.35/2.86 % (18816)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_18469 for (2988ds/204Mi)
% 10.35/2.88 % (18818)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_18469 for (2988ds/26Mi)
% 10.85/2.90 % (18818)Instruction limit reached!
% 10.85/2.90 % (18818)------------------------------
% 10.85/2.90 % (18818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.85/2.90 % (18818)Termination reason: Unknown
% 10.85/2.90 % (18818)Termination phase: shuffling
% 10.85/2.90
% 10.85/2.90 % (18818)Memory used [KB]: 2174
% 10.85/2.90 % (18818)Time elapsed: 0.010 s
% 10.85/2.90 % (18818)Instructions burned: 28 (million)
% 10.85/2.90 % (18818)------------------------------
% 10.85/2.90 % (18818)------------------------------
% 10.85/2.92 % (18819)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_18469 for (2987ds/53Mi)
% 10.85/2.94 % (18819)Instruction limit reached!
% 10.85/2.94 % (18819)------------------------------
% 10.85/2.94 % (18819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.85/2.94 % (18819)Termination reason: Unknown
% 10.85/2.94 % (18819)Termination phase: shuffling
% 10.85/2.94
% 10.85/2.94 % (18819)Memory used [KB]: 2558
% 10.85/2.94 % (18819)Time elapsed: 0.025 s
% 10.85/2.94 % (18819)Instructions burned: 53 (million)
% 10.85/2.94 % (18819)------------------------------
% 10.85/2.94 % (18819)------------------------------
% 10.85/2.95 % (18816)Instruction limit reached!
% 10.85/2.95 % (18816)------------------------------
% 10.85/2.95 % (18816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.85/2.95 % (18816)Termination reason: Unknown
% 10.85/2.95 % (18816)Termination phase: Property scanning
% 10.85/2.95
% 10.85/2.95 % (18816)Memory used [KB]: 2942
% 10.85/2.95 % (18816)Time elapsed: 0.087 s
% 10.85/2.95 % (18816)Instructions burned: 206 (million)
% 10.85/2.95 % (18816)------------------------------
% 10.85/2.95 % (18816)------------------------------
% 10.85/2.95 % (18811)Instruction limit reached!
% 10.85/2.95 % (18811)------------------------------
% 10.85/2.95 % (18811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.85/2.95 % (18811)Termination reason: Unknown
% 10.85/2.95 % (18811)Termination phase: Saturation
% 10.85/2.95
% 10.85/2.95 % (18811)Memory used [KB]: 9338
% 10.85/2.95 % (18811)Time elapsed: 0.103 s
% 10.85/2.95 % (18811)Instructions burned: 368 (million)
% 10.85/2.95 % (18811)------------------------------
% 10.85/2.95 % (18811)------------------------------
% 10.85/2.96 % (18820)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_18469 for (2987ds/4436Mi)
% 10.85/2.96 % (18821)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_18469 for (2987ds/1539Mi)
% 10.85/2.96 % (18822)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_18469 for (2987ds/408Mi)
% 10.85/2.97 % (18815)Instruction limit reached!
% 10.85/2.97 % (18815)------------------------------
% 10.85/2.97 % (18815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.85/2.97 % (18815)Termination reason: Unknown
% 10.85/2.97 % (18815)Termination phase: Saturation
% 10.85/2.97
% 10.85/2.97 % (18815)Memory used [KB]: 7547
% 10.85/2.97 % (18815)Time elapsed: 0.114 s
% 10.85/2.97 % (18815)Instructions burned: 267 (million)
% 10.85/2.97 % (18815)------------------------------
% 10.85/2.97 % (18815)------------------------------
% 10.85/2.98 % (18823)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_18469 for (2987ds/5205Mi)
% 12.29/3.04 % (18797)Instruction limit reached!
% 12.29/3.04 % (18797)------------------------------
% 12.29/3.04 % (18797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.29/3.04 % (18797)Termination reason: Unknown
% 12.29/3.04 % (18797)Termination phase: Saturation
% 12.29/3.04
% 12.29/3.04 % (18797)Memory used [KB]: 15863
% 12.29/3.04 % (18797)Time elapsed: 0.405 s
% 12.29/3.04 % (18797)Instructions burned: 989 (million)
% 12.29/3.04 % (18797)------------------------------
% 12.29/3.04 % (18797)------------------------------
% 12.29/3.06 % (18827)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_18469 for (2986ds/1913Mi)
% 12.93/3.13 % (18822)Instruction limit reached!
% 12.93/3.13 % (18822)------------------------------
% 12.93/3.13 % (18822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.13 % (18822)Termination reason: Unknown
% 12.93/3.13 % (18822)Termination phase: Saturation
% 12.93/3.13
% 12.93/3.13 % (18822)Memory used [KB]: 11769
% 12.93/3.13 % (18822)Time elapsed: 0.172 s
% 12.93/3.13 % (18822)Instructions burned: 410 (million)
% 12.93/3.13 % (18822)------------------------------
% 12.93/3.13 % (18822)------------------------------
% 12.93/3.14 % (18828)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_18469 for (2985ds/4350Mi)
% 13.30/3.23 % (18807)Instruction limit reached!
% 13.30/3.23 % (18807)------------------------------
% 13.30/3.23 % (18807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.30/3.23 % (18807)Termination reason: Unknown
% 13.30/3.23 % (18807)Termination phase: Saturation
% 13.30/3.23
% 13.30/3.23 % (18807)Memory used [KB]: 12537
% 13.30/3.23 % (18807)Time elapsed: 0.452 s
% 13.30/3.23 % (18807)Instructions burned: 922 (million)
% 13.30/3.23 % (18807)------------------------------
% 13.30/3.23 % (18807)------------------------------
% 13.30/3.25 % (18831)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_18469 for (2984ds/68Mi)
% 13.30/3.28 % (18831)Instruction limit reached!
% 13.30/3.28 % (18831)------------------------------
% 13.30/3.28 % (18831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.30/3.28 % (18831)Termination reason: Unknown
% 13.30/3.28 % (18831)Termination phase: Property scanning
% 13.30/3.28
% 13.30/3.28 % (18831)Memory used [KB]: 2686
% 13.30/3.28 % (18831)Time elapsed: 0.031 s
% 13.30/3.28 % (18831)Instructions burned: 69 (million)
% 13.30/3.28 % (18831)------------------------------
% 13.30/3.28 % (18831)------------------------------
% 13.30/3.29 % (18834)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_18469 for (2983ds/358Mi)
% 13.81/3.31 % (18813)Instruction limit reached!
% 13.81/3.31 % (18813)------------------------------
% 13.81/3.31 % (18813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.31 % (18813)Termination reason: Unknown
% 13.81/3.31 % (18813)Termination phase: Saturation
% 13.81/3.31
% 13.81/3.31 % (18813)Memory used [KB]: 13048
% 13.81/3.31 % (18813)Time elapsed: 0.474 s
% 13.81/3.31 % (18813)Instructions burned: 1021 (million)
% 13.81/3.31 % (18813)------------------------------
% 13.81/3.31 % (18813)------------------------------
% 13.81/3.33 % (18836)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_18469 for (2983ds/31Mi)
% 13.81/3.34 % (18836)Instruction limit reached!
% 13.81/3.34 % (18836)------------------------------
% 13.81/3.34 % (18836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.81/3.34 % (18836)Termination reason: Unknown
% 13.81/3.34 % (18836)Termination phase: shuffling
% 13.81/3.34
% 13.81/3.34 % (18836)Memory used [KB]: 2174
% 13.81/3.34 % (18836)Time elapsed: 0.016 s
% 13.81/3.34 % (18836)Instructions burned: 31 (million)
% 13.81/3.34 % (18836)------------------------------
% 13.81/3.34 % (18836)------------------------------
% 13.81/3.36 % (18838)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_18469 for (2983ds/279Mi)
% 14.18/3.42 % (18834)Instruction limit reached!
% 14.18/3.42 % (18834)------------------------------
% 14.18/3.42 % (18834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.18/3.42 % (18834)Termination reason: Unknown
% 14.18/3.42 % (18834)Termination phase: Saturation
% 14.18/3.42
% 14.18/3.42 % (18834)Memory used [KB]: 8315
% 14.18/3.42 % (18834)Time elapsed: 0.127 s
% 14.18/3.42 % (18834)Instructions burned: 359 (million)
% 14.18/3.42 % (18834)------------------------------
% 14.18/3.42 % (18834)------------------------------
% 14.18/3.44 % (18841)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_18469 for (2982ds/258Mi)
% 14.18/3.47 % (18838)Instruction limit reached!
% 14.18/3.47 % (18838)------------------------------
% 14.18/3.47 % (18838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.18/3.47 % (18838)Termination reason: Unknown
% 14.18/3.47 % (18838)Termination phase: Saturation
% 14.18/3.47
% 14.18/3.47 % (18838)Memory used [KB]: 7547
% 14.18/3.47 % (18838)Time elapsed: 0.117 s
% 14.18/3.47 % (18838)Instructions burned: 279 (million)
% 14.18/3.47 % (18838)------------------------------
% 14.18/3.47 % (18838)------------------------------
% 14.72/3.50 % (18843)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_18469 for (2981ds/26Mi)
% 14.72/3.50 % (18843)Instruction limit reached!
% 14.72/3.50 % (18843)------------------------------
% 14.72/3.50 % (18843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.50 % (18843)Termination reason: Unknown
% 14.72/3.50 % (18843)Termination phase: shuffling
% 14.72/3.50
% 14.72/3.50 % (18843)Memory used [KB]: 2174
% 14.72/3.50 % (18843)Time elapsed: 0.009 s
% 14.72/3.50 % (18843)Instructions burned: 28 (million)
% 14.72/3.50 % (18843)------------------------------
% 14.72/3.50 % (18843)------------------------------
% 14.72/3.51 % (18845)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_18469 for (2981ds/995Mi)
% 14.72/3.57 % (18841)Instruction limit reached!
% 14.72/3.57 % (18841)------------------------------
% 14.72/3.57 % (18841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.57 % (18841)Termination reason: Unknown
% 14.72/3.57 % (18841)Termination phase: Saturation
% 14.72/3.57
% 14.72/3.57 % (18841)Memory used [KB]: 8315
% 14.72/3.57 % (18841)Time elapsed: 0.113 s
% 14.72/3.57 % (18841)Instructions burned: 258 (million)
% 14.72/3.57 % (18841)------------------------------
% 14.72/3.57 % (18841)------------------------------
% 14.72/3.58 % (18821)Instruction limit reached!
% 14.72/3.58 % (18821)------------------------------
% 14.72/3.58 % (18821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.58 % (18821)Termination reason: Unknown
% 14.72/3.58 % (18821)Termination phase: Saturation
% 14.72/3.58
% 14.72/3.58 % (18821)Memory used [KB]: 10746
% 14.72/3.58 % (18821)Time elapsed: 0.634 s
% 14.72/3.58 % (18821)Instructions burned: 1539 (million)
% 14.72/3.58 % (18821)------------------------------
% 14.72/3.58 % (18821)------------------------------
% 14.72/3.59 % (18846)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_18469 for (2980ds/373Mi)
% 14.72/3.59 % (18847)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_18469 for (2980ds/253Mi)
% 15.16/3.69 % (18847)Instruction limit reached!
% 15.16/3.69 % (18847)------------------------------
% 15.16/3.69 % (18847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.16/3.69 % (18847)Termination reason: Unknown
% 15.16/3.69 % (18847)Termination phase: Saturation
% 15.16/3.69
% 15.16/3.69 % (18847)Memory used [KB]: 7547
% 15.16/3.69 % (18847)Time elapsed: 0.102 s
% 15.16/3.69 % (18847)Instructions burned: 254 (million)
% 15.16/3.69 % (18847)------------------------------
% 15.16/3.69 % (18847)------------------------------
% 15.47/3.72 % (18848)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_18469 for (2979ds/832Mi)
% 15.47/3.76 % (18846)Instruction limit reached!
% 15.47/3.76 % (18846)------------------------------
% 15.47/3.76 % (18846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.47/3.76 % (18846)Termination reason: Unknown
% 15.47/3.76 % (18846)Termination phase: Saturation
% 15.47/3.76
% 15.47/3.76 % (18846)Memory used [KB]: 9466
% 15.47/3.76 % (18846)Time elapsed: 0.166 s
% 15.47/3.76 % (18846)Instructions burned: 373 (million)
% 15.47/3.76 % (18846)------------------------------
% 15.47/3.76 % (18846)------------------------------
% 15.47/3.77 % (18849)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_18469 for (2979ds/668Mi)
% 15.85/3.84 % (18845)Instruction limit reached!
% 15.85/3.84 % (18845)------------------------------
% 15.85/3.84 % (18845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.85/3.84 % (18845)Termination reason: Unknown
% 15.85/3.84 % (18845)Termination phase: Saturation
% 15.85/3.84
% 15.85/3.84 % (18845)Memory used [KB]: 17654
% 15.85/3.84 % (18845)Time elapsed: 0.328 s
% 15.85/3.84 % (18845)Instructions burned: 996 (million)
% 15.85/3.84 % (18845)------------------------------
% 15.85/3.84 % (18845)------------------------------
% 15.85/3.86 % (18851)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_18469 for (2978ds/40Mi)
% 15.85/3.88 % (18851)Instruction limit reached!
% 15.85/3.88 % (18851)------------------------------
% 15.85/3.88 % (18851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.85/3.88 % (18851)Termination reason: Unknown
% 15.85/3.88 % (18851)Termination phase: shuffling
% 15.85/3.88
% 15.85/3.88 % (18851)Memory used [KB]: 2302
% 15.85/3.88 % (18851)Time elapsed: 0.020 s
% 15.85/3.88 % (18851)Instructions burned: 40 (million)
% 15.85/3.88 % (18851)------------------------------
% 15.85/3.88 % (18851)------------------------------
% 15.85/3.90 % (18852)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_18469 for (2977ds/294Mi)
% 16.41/3.97 % (18827)Instruction limit reached!
% 16.41/3.97 % (18827)------------------------------
% 16.41/3.97 % (18827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.41/3.97 % (18827)Termination reason: Unknown
% 16.41/3.97 % (18827)Termination phase: Saturation
% 16.41/3.97
% 16.41/3.97 % (18827)Memory used [KB]: 6396
% 16.41/3.97 % (18827)Time elapsed: 0.910 s
% 16.41/3.97 % (18827)Instructions burned: 1913 (million)
% 16.41/3.97 % (18827)------------------------------
% 16.41/3.97 % (18827)------------------------------
% 16.41/3.98 % (18854)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_18469 for (2977ds/187Mi)
% 16.41/4.00 % (18848)First to succeed.
% 16.41/4.01 % (18848)Refutation found. Thanks to Tanya!
% 16.41/4.01 % SZS status Theorem for DTF2THF_18469
% 16.41/4.01 % SZS output start Proof for DTF2THF_18469
% 16.41/4.01 thf(func_def_0, type, in: $i > $i > $o).
% 16.41/4.01 thf(func_def_1, type, exu: ($i > $o) > $o).
% 16.41/4.01 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 16.41/4.01 thf(func_def_8, type, powerset: $i > $i).
% 16.41/4.01 thf(func_def_10, type, setunion: $i > $i).
% 16.41/4.01 thf(func_def_19, type, descr: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_26, type, prop2set: $o > $i).
% 16.41/4.01 thf(func_def_36, type, nonempty: $i > $o).
% 16.41/4.01 thf(func_def_69, type, set2prop: $i > $o).
% 16.41/4.01 thf(func_def_88, type, subset: $i > $i > $o).
% 16.41/4.01 thf(func_def_89, type, disjoint: $i > $i > $o).
% 16.41/4.01 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 16.41/4.01 thf(func_def_114, type, binunion: $i > $i > $i).
% 16.41/4.01 thf(func_def_122, type, binintersect: $i > $i > $i).
% 16.41/4.01 thf(func_def_135, type, regular: $i > $o).
% 16.41/4.01 thf(func_def_136, type, setminus: $i > $i > $i).
% 16.41/4.01 thf(func_def_147, type, symdiff: $i > $i > $i).
% 16.41/4.01 thf(func_def_153, type, iskpair: $i > $o).
% 16.41/4.01 thf(func_def_158, type, kpair: $i > $i > $i).
% 16.41/4.01 thf(func_def_160, type, cartprod: $i > $i > $i).
% 16.41/4.01 thf(func_def_177, type, singleton: $i > $o).
% 16.41/4.01 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 16.41/4.01 thf(func_def_184, type, atmost1p: $i > $o).
% 16.41/4.01 thf(func_def_185, type, atleast2p: $i > $o).
% 16.41/4.01 thf(func_def_186, type, atmost2p: $i > $o).
% 16.41/4.01 thf(func_def_187, type, upairsetp: $i > $o).
% 16.41/4.01 thf(func_def_191, type, kfst: $i > $i).
% 16.41/4.01 thf(func_def_203, type, ksnd: $i > $i).
% 16.41/4.01 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 16.41/4.01 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 16.41/4.01 thf(func_def_222, type, func: $i > $i > $i > $o).
% 16.41/4.01 thf(func_def_223, type, funcSet: $i > $i > $i).
% 16.41/4.01 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 16.41/4.01 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 16.41/4.01 thf(func_def_323, type, breln1: $i > $i > $o).
% 16.41/4.01 thf(func_def_325, type, breln1Set: $i > $i).
% 16.41/4.01 thf(func_def_327, type, transitive: $i > $i > $o).
% 16.41/4.01 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 16.41/4.01 thf(func_def_329, type, reflexive: $i > $i > $o).
% 16.41/4.01 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 16.41/4.01 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 16.41/4.01 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 16.41/4.01 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 16.41/4.01 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_371, type, sP1: $i > $i > $i > $o).
% 16.41/4.01 thf(func_def_377, type, sP7: $i > $i > $i > $o).
% 16.41/4.01 thf(func_def_378, type, sP8: $i > $i > $i > $i > $o).
% 16.41/4.01 thf(func_def_381, type, sP11: $i > $i > $o).
% 16.41/4.01 thf(func_def_382, type, sP12: $i > $o).
% 16.41/4.01 thf(func_def_383, type, sP13: $i > $i > $o).
% 16.41/4.01 thf(func_def_384, type, sP14: $i > $i > $o).
% 16.41/4.01 thf(func_def_386, type, sP16: $i > $o > $i > $i > $o).
% 16.41/4.01 thf(func_def_403, type, sK33: $i > $o).
% 16.41/4.01 thf(func_def_405, type, sK35: ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_406, type, sK36: ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_417, type, sK47: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_419, type, sK49: $i > $o).
% 16.41/4.01 thf(func_def_435, type, sK65: $i > ($i > $i) > $i > $i).
% 16.41/4.01 thf(func_def_437, type, sK67: $i > $i).
% 16.41/4.01 thf(func_def_440, type, sK70: $i > $o).
% 16.41/4.01 thf(func_def_453, type, sK83: $i > $o).
% 16.41/4.01 thf(func_def_469, type, sK99: ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_470, type, sK100: ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_473, type, sK103: $i > $o).
% 16.41/4.01 thf(func_def_490, type, sK120: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_491, type, sK121: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_492, type, sK122: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_493, type, sK123: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_543, type, sK173: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_544, type, sK174: $i > $o).
% 16.41/4.01 thf(func_def_568, type, sK198: $i > $o).
% 16.41/4.01 thf(func_def_570, type, sK200: $i > $i > $o).
% 16.41/4.01 thf(func_def_586, type, sK216: $i > $i).
% 16.41/4.01 thf(func_def_595, type, sK225: $i > $i > $o).
% 16.41/4.01 thf(func_def_596, type, sK226: $i > $i).
% 16.41/4.01 thf(func_def_597, type, sK227: $i > $i).
% 16.41/4.01 thf(func_def_598, type, sK228: ($i > $i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_599, type, sK229: ($i > $i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_600, type, sK230: $i > ($i > $i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_601, type, sK231: $i > $o).
% 16.41/4.01 thf(func_def_602, type, sK232: $i > $o).
% 16.41/4.01 thf(func_def_603, type, sK233: ($i > $o) > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_604, type, sK234: ($i > $o) > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_625, type, sK255: $i > $i > $i).
% 16.41/4.01 thf(func_def_629, type, sK259: $i > $o).
% 16.41/4.01 thf(func_def_636, type, sK266: $i > $i > $i).
% 16.41/4.01 thf(func_def_637, type, sK267: $i > $i > $i).
% 16.41/4.01 thf(func_def_638, type, sK268: $i > $i > $i).
% 16.41/4.01 thf(func_def_647, type, sK277: $i > $o).
% 16.41/4.01 thf(func_def_661, type, sK291: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_662, type, sK292: $i > $o).
% 16.41/4.01 thf(func_def_673, type, sK303: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_674, type, sK304: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_681, type, sK311: $i > $o).
% 16.41/4.01 thf(func_def_692, type, sK322: $i > $i > $o).
% 16.41/4.01 thf(func_def_704, type, sK334: $i > $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_711, type, sK341: $i > $i).
% 16.41/4.01 thf(func_def_714, type, sK344: $i > ($i > $i) > $i > $i).
% 16.41/4.01 thf(func_def_722, type, sK352: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_740, type, sK370: $i > $i > $i).
% 16.41/4.01 thf(func_def_753, type, sK383: $i > $i > $i).
% 16.41/4.01 thf(func_def_765, type, sK395: $i > $i > $o).
% 16.41/4.01 thf(func_def_781, type, sK411: $i > $i > $o).
% 16.41/4.01 thf(func_def_798, type, sK428: $i > $o).
% 16.41/4.01 thf(func_def_800, type, sK430: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_803, type, sK433: $i > $i).
% 16.41/4.01 thf(func_def_823, type, sK453: $i > $i).
% 16.41/4.01 thf(func_def_826, type, sK456: $i > $i).
% 16.41/4.01 thf(func_def_841, type, sK471: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_842, type, sK472: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_843, type, sK473: $i > $o).
% 16.41/4.01 thf(func_def_850, type, sK480: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_874, type, sK504: $i > $i > $o).
% 16.41/4.01 thf(func_def_875, type, sK505: $i > $i).
% 16.41/4.01 thf(func_def_878, type, sK508: $i > $i > ($i > $i) > $i).
% 16.41/4.01 thf(func_def_887, type, sK517: $i > $o).
% 16.41/4.01 thf(func_def_889, type, sK519: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_895, type, sK525: $i > $o).
% 16.41/4.01 thf(func_def_898, type, sK528: $i > $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_918, type, sK548: $i > ($i > $i) > $i > $i).
% 16.41/4.01 thf(func_def_920, type, sK550: $i > $i).
% 16.41/4.01 thf(func_def_922, type, sK552: $i > $o).
% 16.41/4.01 thf(func_def_923, type, sK553: $i > $i).
% 16.41/4.01 thf(func_def_924, type, sK554: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_925, type, sK555: $i > $o).
% 16.41/4.01 thf(func_def_940, type, sK570: $i > $o).
% 16.41/4.01 thf(func_def_942, type, sK572: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_943, type, sK573: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_949, type, sK579: $i > $i > $o).
% 16.41/4.01 thf(func_def_956, type, sK586: $i > $i).
% 16.41/4.01 thf(func_def_969, type, sK599: ($i > $o) > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_970, type, sK600: ($i > $o) > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_974, type, sK604: $i > $o).
% 16.41/4.01 thf(func_def_984, type, sK614: $i > $i).
% 16.41/4.01 thf(func_def_986, type, sK616: $i > ($i > $i) > $i > $i).
% 16.41/4.01 thf(func_def_987, type, sK617: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_991, type, sK621: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1000, type, sK630: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1001, type, sK631: $i > $o).
% 16.41/4.01 thf(func_def_1023, type, sK653: $i > $i > $o).
% 16.41/4.01 thf(func_def_1025, type, sK655: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1026, type, sK656: $i > $o).
% 16.41/4.01 thf(func_def_1040, type, sK670: $i > $i > $i).
% 16.41/4.01 thf(func_def_1043, type, sK673: $i > $i).
% 16.41/4.01 thf(func_def_1044, type, sK674: ($i > $i) > $i > $i > $i).
% 16.41/4.01 thf(func_def_1045, type, sK675: $i > $i).
% 16.41/4.01 thf(func_def_1049, type, sK679: $i > $o).
% 16.41/4.01 thf(func_def_1050, type, sK680: $i > $o).
% 16.41/4.01 thf(func_def_1051, type, sK681: ($i > $o) > ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_1052, type, sK682: ($i > $o) > ($i > $o) > $i > $i > $i).
% 16.41/4.01 thf(func_def_1063, type, sK693: $i > $o).
% 16.41/4.01 thf(func_def_1064, type, sK694: $i > $o).
% 16.41/4.01 thf(func_def_1105, type, sK735: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1106, type, sK736: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1107, type, sK737: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1108, type, sK738: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1120, type, sK750: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1121, type, sK751: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1131, type, sK761: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1142, type, sK772: $i > $i > $i).
% 16.41/4.01 thf(func_def_1158, type, sK788: $i > $o).
% 16.41/4.01 thf(func_def_1160, type, sK790: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_1161, type, sK791: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_1179, type, sK809: $o > $i > $i > $i).
% 16.41/4.01 thf(func_def_1183, type, sK813: $i > $i > $i).
% 16.41/4.01 thf(func_def_1184, type, sK814: $i > $i > $i).
% 16.41/4.01 thf(func_def_1185, type, sK815: $i > $i > $i).
% 16.41/4.01 thf(func_def_1186, type, sK816: $i > $i > $i).
% 16.41/4.01 thf(func_def_1187, type, sK817: $i > $i > $i).
% 16.41/4.01 thf(func_def_1188, type, sK818: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1189, type, sK819: $i > $i).
% 16.41/4.01 thf(func_def_1190, type, sK820: $i > $i).
% 16.41/4.01 thf(func_def_1191, type, sK821: $i > $i).
% 16.41/4.01 thf(func_def_1192, type, sK822: $i > $i).
% 16.41/4.01 thf(func_def_1193, type, sK823: $i > $i > $i).
% 16.41/4.01 thf(func_def_1194, type, sK824: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1195, type, sK825: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1196, type, sK826: $i > $i > $i).
% 16.41/4.01 thf(func_def_1197, type, sK827: $i > $i > $i).
% 16.41/4.01 thf(func_def_1198, type, sK828: $i > $i).
% 16.41/4.01 thf(func_def_1200, type, sK830: $i > $i).
% 16.41/4.01 thf(func_def_1201, type, sK831: $i > $i).
% 16.41/4.01 thf(func_def_1205, type, sK835: $i > $o).
% 16.41/4.01 thf(func_def_1207, type, sK837: ($i > $o) > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1208, type, sK838: ($i > $o) > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1256, type, sK886: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1257, type, sK887: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1258, type, sK888: $i > $o).
% 16.41/4.01 thf(func_def_1269, type, sK899: $i > $o).
% 16.41/4.01 thf(func_def_1271, type, sK901: $i > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1278, type, sK908: $i > $i).
% 16.41/4.01 thf(func_def_1280, type, sK910: $i > $o).
% 16.41/4.01 thf(func_def_1281, type, sK911: $i > $o).
% 16.41/4.01 thf(func_def_1282, type, sK912: ($i > $o) > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1283, type, sK913: ($i > $o) > ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1284, type, sK914: $i > ($i > $i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_1286, type, sK916: $i > $i > $o).
% 16.41/4.01 thf(func_def_1290, type, sK920: $i > $i).
% 16.41/4.01 thf(func_def_1295, type, sK925: $i > $o).
% 16.41/4.01 thf(func_def_1298, type, sK928: $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1323, type, sK953: $i > $i > $o).
% 16.41/4.01 thf(func_def_1337, type, sK967: $i > $i > $i).
% 16.41/4.01 thf(func_def_1345, type, sK975: $o > $i > $i > $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1365, type, sK995: $i > $o).
% 16.41/4.01 thf(func_def_1369, type, sK999: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1370, type, sK1000: $i > $i > $i > $i).
% 16.41/4.01 thf(func_def_1371, type, sK1001: $i > $o).
% 16.41/4.01 thf(func_def_1377, type, sK1007: ($i > $o) > $i).
% 16.41/4.01 thf(func_def_1378, type, sK1008: $i > $o).
% 16.41/4.01 thf(func_def_1379, type, sK1009: $i > $i).
% 16.41/4.01 thf(func_def_1382, type, sK1012: $i > $o).
% 16.41/4.01 thf(func_def_1385, type, sK1015: $i > $i > $i).
% 16.41/4.01 thf(func_def_1390, type, sK1020: ($i > $o) > $i > $i).
% 16.41/4.01 thf(func_def_1392, type, sK1022: $i > $o).
% 16.41/4.01 thf(func_def_1411, type, ph1041: !>[X0: $tType]:(X0)).
% 16.41/4.01 thf(f4953,plain,(
% 16.41/4.01 $false),
% 16.41/4.01 inference(avatar_sat_refutation,[status(thm)],[f4900,f4906,f4917,f4946,f4952])).
% 16.41/4.01 thf(f4952,plain,(
% 16.41/4.01 spl1040_4),
% 16.41/4.01 inference(avatar_contradiction_clause,[status(thm)],[f4951])).
% 16.41/4.01 thf(f4951,plain,(
% 16.41/4.01 $false | spl1040_4),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4950,f4539])).
% 16.41/4.01 thf(f4539,plain,(
% 16.41/4.01 ($true = (breln1 @ sK979 @ sK982))),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f2874,plain,(
% 16.41/4.01 (prop2setE = $true) & (singletonsubset = $true) & (cartprodpairin = $true) & (funcext = $true) & (subsetTI = $true) & (inComplementUnionImpInComplement1 = $true) & (cartprodpairmemER = $true) & (setminusI = $true) & (complementImpComplementIntersect = $true) & (dpsetconstrI = $true) & (funcGraphProp1 = $true) & (setOfPairsIsBReln1 = $true) & (complementTE1 = $true) & (setminusLsub = $true) & (binunionEcases = $true) & (nonemptyI = $true) & (cartprodfstpairEq = $true) & (demorgan1 = $true) & (cartprodfstin = $true) & (powersetAx = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (singletoninpowunion = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (woz1_4 = $true) & (upairequniteq = $true) & (inPowerset = $true) & (demorgan1a = $true) & (iffalse = $true) & (bs114d = $true) & (symdiffIneg2 = $true) & (setukpairinjR = $true) & (setextsub = $true) & (powersetE = $true) & (eta2 = $true) & (breln1SetBreln1 = $true) & (exuI1 = $true) & (subsetE2 = $true) & (subbreln = $true) & (dsetconstrEL = $true) & (complementInPowersetComplementIntersect = $true) & (woz13rule0 = $true) & (ex1I2 = $true) & (binunionTE = $true) & (binintersectSubset2 = $true) & (upairset2IR = $true) & (funcinfuncset = $true) & (woz13rule4 = $true) & (brelnall1 = $true) & (breln1compI = $true) & (subsetE = $true) & (ifSingleton = $true) & (notequalI1 = $true) & (dpsetconstrSub = $true) & (breln1unionE = $true) & (dpsetconstrEL1 = $true) & (contrasubsetT1 = $true) & (notdexE = $true) & (in__Cong = $true) & (exuI3 = $true) & (setminusT_lem = $true) & (app = $true) & (symdiffI1 = $true) & (kpairsurjEq = $true) & (binintersectRsub = $true) & (ex1E2 = $true) & (dsetconstrI = $true) & (emptyinPowerset = $true) & (complementTcontraSubset = $true) & (setminusIRneg = $true) & (emptysetE = $true) & (upairsetIL = $true) & (setextT = $true) & ((($true = (breln1 @ sK979 @ sK981)) & (($true = (breln1 @ sK979 @ sK982)) & ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK980)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)))) & ($true = (breln1 @ sK979 @ sK980))) & (exuE1 = $true) & (setminusELneg = $true) & (setunionI = $true) & (ubforcartprodlem1 = $true) & (binunionTIRcontra = $true) & (emptyI = $true) & (woz2A = $true) & (woz1_1 = $true) & (breln1unionprop = $true) & (iftrueorfalse = $true) & (exuE3e = $true) & (woz1_2 = $true) & (funcGraphProp4 = $true) & (powersetsubset = $true) & (setadjoinE = $true) & (complementSubsetComplementIntersect = $true) & (eqbreln1 = $true) & (eqimpsubset2 = $true) & (singletonprop = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (cartprodmempair = $true) & (emptyinunitempty = $true) & (cartprodmempair1 = $true) & (dsetconstrER = $true) & (nonemptyI1 = $true) & (binintersectEL = $true) & (upairinpowunion = $true) & (eqbreln = $true) & (funcextLem = $true) & (setminusEL = $true) & (breln1unionEcases = $true) & (setukpairinjR1 = $true) & (uniqinunit = $true) & (setunionsingleton = $true) & (iftrueProp2 = $true) & (demorgan2b = $true) & (setunionAx = $true) & (emptysetimpfalse = $true) & (setextAx = $true) & (iffalseProp2 = $true) & (sepSubset = $true) & (ksndsingleton = $true) & (contrasubsetT3 = $true) & (setOfPairsIsBReln = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (cartprodpairsurjEq = $true) & (iftrueProp1 = $true) & (subPowSU = $true) & (woz2Ex = $true) & (funcImageSingleton = $true) & (binunionRsub = $true) & (cartprodsndin = $true) & (breln1unionIL = $true) & (contrasubsetT2 = $true) & (exuE2 = $true) & (complementTI1 = $true) & (inIntersectImpInUnion2 = $true) & (notdallE = $true) & (ex1E1 = $true) & (beta2 = $true) & (exuEu = $true) & (emptysetsubset = $true) & (powersetTI1 = $true) & (binintersectI = $true) & (subbreln1 = $true) & (cartprodmempaircEq = $true) & (setminusSubset2 = $true) & (setukpairinjR12 = $true) & (setunionE = $true) & (binunionTILcontra = $true) & (setukpairinjR11 = $true) & (lamp = $true) & (emptyE1 = $true) & (doubleComplementEq = $true) & (eta1 = $true) & (notequalI2 = $true) & (cartprodsndpairEq = $true) & (doubleComplementI1 = $true) & (powersetI = $true) & (binunionIL = $true) & (powerset__Cong = $true) & (demorgan2a1 = $true) & (funcGraphProp3 = $true) & (noeltsimpempty = $true) & (demorgan2a = $true) & (kpairp = $true) & (disjointsetsI1 = $true) & (nonemptyImpWitness = $true) & (vacuousDall = $true) & (singletonsswitch = $true) & (notinemptyset = $true) & (subsetRefl = $true) & (powersetTE1 = $true) & (binintersectSubset1 = $true) & (foundationAx = $true) & (exu__Cong = $true) & (setukpairIR = $true) & (prop2setI = $true) & (setadjoinIL = $true) & (singletoninpowerset = $true) & (upairset2E = $true) & (setadjoinSub = $true) & (setminusILneg = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem3 = $true) & (ksndpairEq = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (wellorderingAx = $true) & (ex1I = $true) & (kfstsingleton = $true) & (inCongP = $true) & (setunionE2 = $true) & (demorgan2b2 = $true) & (funcext2 = $true) & (descr__Cong = $true) & (setunion__Cong = $true) & (setukpairinjL = $true) & (binintersectSubset4 = $true) & (binunionTEcontra = $true) & (upairsetE = $true) & (setukpairinjR2 = $true) & (kfstpairEq = $true) & (ap2p = $true) & (breln1all1 = $true) & (ifp = $true) & (upairsubunion = $true) & (breln1unionIR = $true) & (choice2fnsingleton = $true) & (brelnall2 = $true) & (inIntersectImpInUnion = $true) & (setunionsingleton1 = $true) & (setminusER = $true) & (setadjoinIR = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (quantDeMorgan3 = $true) & (emptysetAx = $true) & (binunionLsub = $true) & (apProp = $true) & (setadjoinOr = $true) & (eqimpsubset1 = $true) & (breln1compprop = $true) & (quantDeMorgan2 = $true) & (theprop = $true) & (exuI2 = $true) & (woz13rule3 = $true) & (subsetemptysetimpeq = $true) & (symdiffE = $true) & (sepInPowerset = $true) & (setadjoinSub2 = $true) & (doubleComplementSub1 = $true) & (singletonsuniq = $true) & (breln1all2 = $true) & (secondinupair = $true) & (binintersectTELcontra = $true) & (subset2powerset = $true) & (notinsingleton = $true) & (infuncsetfunc = $true) & (ap2apEq1 = $true) & (dpsetconstrER = $true) & (intersectInPowersetIntersectUnions = $true) & (powersetT_lem = $true) & (woz1_5 = $true) & (binintersectSubset3 = $true) & (woz13rule2 = $true) & (dsetconstr__Cong = $true) & (breln1compE = $true) & (woz1_3 = $true) & (subsetTrans = $true) & (complementTnotintersectT = $true) & (setukpairinjL2 = $true) & (emptyset__Cong = $true) & (binintersectSubset5 = $true) & (binunionE = $true) & (dpsetconstrERa = $true) & (doubleComplementSub2 = $true) & (replAx = $true) & (contrasubsetT = $true) & (lam2lamEq = $true) & (symdiffI2 = $true) & (setext = $true) & (doubleComplementE1 = $true) & (cartprodpairmemEL = $true) & (breln1unionCommutes = $true) & (lamProp = $true) & (inComplementUnionImpNotIn1 = $true) & (breln1unionI = $true) & (binunionIR = $true) & (binintersectLsub = $true) & (complementUnionInPowersetComplement = $true) & (iffalseProp1 = $true) & (demorgan2a2 = $true) & (exuE3u = $true) & (iftrue = $true) & (woz2W = $true) & (dpsetconstrEL2 = $true) & (inIntersectImpInIntersectUnions = $true) & (symdiffIneg1 = $true) & (breln1compEex = $true) & (notsubsetI = $true) & (subsetI1 = $true) & (binintersectTERcontra = $true) & (breln1invE = $true) & (setadjoinAx = $true) & (binintersectT_lem = $true) & (lam2p = $true) & (descrp = $true) & (omega__Cong = $true) & (setminusSubset1 = $true) & (complementT_lem = $true) & (breln1invI = $true) & (breln1invprop = $true) & (setminusERneg = $true) & (woz13rule1 = $true) & (setadjoin__Cong = $true) & (contraSubsetComplement = $true) & (emptyInPowerset = $true) & (setukpairIL = $true) & (funcGraphProp2 = $true) & (nonemptyE1 = $true) & (demorgan2 = $true) & (ap2apEq2 = $true) & (setbeta = $true) & (demorgan1b = $true) & (theeq = $true) & (omega0Ax = $true) & (binunionT_lem = $true) & (upairsetIR = $true) & (binintersectER = $true) & (beta1 = $true) & (eqinunit = $true)),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK979,sK980,sK981,sK982])],[f1205,f2873,f2872,f2871])).
% 16.41/4.01 thf(f2871,plain,(
% 16.41/4.01 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ X0 @ X3)) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : (((breln1 @ sK979 @ X2) = $true) & ? [X3 : $i] : (($true = (breln1 @ sK979 @ X3)) & ((breln1compset @ sK979 @ (binunion @ sK980 @ X2) @ X3) != (binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ X2))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK980))))))) & ($true = (breln1 @ sK979 @ sK980)))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f2872,plain,(
% 16.41/4.01 ? [X2 : $i] : (((breln1 @ sK979 @ X2) = $true) & ? [X3 : $i] : (($true = (breln1 @ sK979 @ X3)) & ((breln1compset @ sK979 @ (binunion @ sK980 @ X2) @ X3) != (binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ X2))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK980))))))) => (($true = (breln1 @ sK979 @ sK981)) & ? [X3 : $i] : (($true = (breln1 @ sK979 @ X3)) & ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ X3) != (binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK980)))))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f2873,plain,(
% 16.41/4.01 ? [X3 : $i] : (($true = (breln1 @ sK979 @ X3)) & ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ X3) != (binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ X3) @ (breln1invset @ sK979 @ sK980)))))) => (($true = (breln1 @ sK979 @ sK982)) & ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK980)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1205,plain,(
% 16.41/4.01 (prop2setE = $true) & (singletonsubset = $true) & (cartprodpairin = $true) & (funcext = $true) & (subsetTI = $true) & (inComplementUnionImpInComplement1 = $true) & (cartprodpairmemER = $true) & (setminusI = $true) & (complementImpComplementIntersect = $true) & (dpsetconstrI = $true) & (funcGraphProp1 = $true) & (setOfPairsIsBReln1 = $true) & (complementTE1 = $true) & (setminusLsub = $true) & (binunionEcases = $true) & (nonemptyI = $true) & (cartprodfstpairEq = $true) & (demorgan1 = $true) & (cartprodfstin = $true) & (powersetAx = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (singletoninpowunion = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (woz1_4 = $true) & (upairequniteq = $true) & (inPowerset = $true) & (demorgan1a = $true) & (iffalse = $true) & (bs114d = $true) & (symdiffIneg2 = $true) & (setukpairinjR = $true) & (setextsub = $true) & (powersetE = $true) & (eta2 = $true) & (breln1SetBreln1 = $true) & (exuI1 = $true) & (subsetE2 = $true) & (subbreln = $true) & (dsetconstrEL = $true) & (complementInPowersetComplementIntersect = $true) & (woz13rule0 = $true) & (ex1I2 = $true) & (binunionTE = $true) & (binintersectSubset2 = $true) & (upairset2IR = $true) & (funcinfuncset = $true) & (woz13rule4 = $true) & (brelnall1 = $true) & (breln1compI = $true) & (subsetE = $true) & (ifSingleton = $true) & (notequalI1 = $true) & (dpsetconstrSub = $true) & (breln1unionE = $true) & (dpsetconstrEL1 = $true) & (contrasubsetT1 = $true) & (notdexE = $true) & (in__Cong = $true) & (exuI3 = $true) & (setminusT_lem = $true) & (app = $true) & (symdiffI1 = $true) & (kpairsurjEq = $true) & (binintersectRsub = $true) & (ex1E2 = $true) & (dsetconstrI = $true) & (emptyinPowerset = $true) & (complementTcontraSubset = $true) & (setminusIRneg = $true) & (emptysetE = $true) & (upairsetIL = $true) & (setextT = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ X0 @ X3)) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))) & ($true = (breln1 @ X0 @ X1))) & (exuE1 = $true) & (setminusELneg = $true) & (setunionI = $true) & (ubforcartprodlem1 = $true) & (binunionTIRcontra = $true) & (emptyI = $true) & (woz2A = $true) & (woz1_1 = $true) & (breln1unionprop = $true) & (iftrueorfalse = $true) & (exuE3e = $true) & (woz1_2 = $true) & (funcGraphProp4 = $true) & (powersetsubset = $true) & (setadjoinE = $true) & (complementSubsetComplementIntersect = $true) & (eqbreln1 = $true) & (eqimpsubset2 = $true) & (singletonprop = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (cartprodmempair = $true) & (emptyinunitempty = $true) & (cartprodmempair1 = $true) & (dsetconstrER = $true) & (nonemptyI1 = $true) & (binintersectEL = $true) & (upairinpowunion = $true) & (eqbreln = $true) & (funcextLem = $true) & (setminusEL = $true) & (breln1unionEcases = $true) & (setukpairinjR1 = $true) & (uniqinunit = $true) & (setunionsingleton = $true) & (iftrueProp2 = $true) & (demorgan2b = $true) & (setunionAx = $true) & (emptysetimpfalse = $true) & (setextAx = $true) & (iffalseProp2 = $true) & (sepSubset = $true) & (ksndsingleton = $true) & (contrasubsetT3 = $true) & (setOfPairsIsBReln = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (cartprodpairsurjEq = $true) & (iftrueProp1 = $true) & (subPowSU = $true) & (woz2Ex = $true) & (funcImageSingleton = $true) & (binunionRsub = $true) & (cartprodsndin = $true) & (breln1unionIL = $true) & (contrasubsetT2 = $true) & (exuE2 = $true) & (complementTI1 = $true) & (inIntersectImpInUnion2 = $true) & (notdallE = $true) & (ex1E1 = $true) & (beta2 = $true) & (exuEu = $true) & (emptysetsubset = $true) & (powersetTI1 = $true) & (binintersectI = $true) & (subbreln1 = $true) & (cartprodmempaircEq = $true) & (setminusSubset2 = $true) & (setukpairinjR12 = $true) & (setunionE = $true) & (binunionTILcontra = $true) & (setukpairinjR11 = $true) & (lamp = $true) & (emptyE1 = $true) & (doubleComplementEq = $true) & (eta1 = $true) & (notequalI2 = $true) & (cartprodsndpairEq = $true) & (doubleComplementI1 = $true) & (powersetI = $true) & (binunionIL = $true) & (powerset__Cong = $true) & (demorgan2a1 = $true) & (funcGraphProp3 = $true) & (noeltsimpempty = $true) & (demorgan2a = $true) & (kpairp = $true) & (disjointsetsI1 = $true) & (nonemptyImpWitness = $true) & (vacuousDall = $true) & (singletonsswitch = $true) & (notinemptyset = $true) & (subsetRefl = $true) & (powersetTE1 = $true) & (binintersectSubset1 = $true) & (foundationAx = $true) & (exu__Cong = $true) & (setukpairIR = $true) & (prop2setI = $true) & (setadjoinIL = $true) & (singletoninpowerset = $true) & (upairset2E = $true) & (setadjoinSub = $true) & (setminusILneg = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem3 = $true) & (ksndpairEq = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (wellorderingAx = $true) & (ex1I = $true) & (kfstsingleton = $true) & (inCongP = $true) & (setunionE2 = $true) & (demorgan2b2 = $true) & (funcext2 = $true) & (descr__Cong = $true) & (setunion__Cong = $true) & (setukpairinjL = $true) & (binintersectSubset4 = $true) & (binunionTEcontra = $true) & (upairsetE = $true) & (setukpairinjR2 = $true) & (kfstpairEq = $true) & (ap2p = $true) & (breln1all1 = $true) & (ifp = $true) & (upairsubunion = $true) & (breln1unionIR = $true) & (choice2fnsingleton = $true) & (brelnall2 = $true) & (inIntersectImpInUnion = $true) & (setunionsingleton1 = $true) & (setminusER = $true) & (setadjoinIR = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (quantDeMorgan3 = $true) & (emptysetAx = $true) & (binunionLsub = $true) & (apProp = $true) & (setadjoinOr = $true) & (eqimpsubset1 = $true) & (breln1compprop = $true) & (quantDeMorgan2 = $true) & (theprop = $true) & (exuI2 = $true) & (woz13rule3 = $true) & (subsetemptysetimpeq = $true) & (symdiffE = $true) & (sepInPowerset = $true) & (setadjoinSub2 = $true) & (doubleComplementSub1 = $true) & (singletonsuniq = $true) & (breln1all2 = $true) & (secondinupair = $true) & (binintersectTELcontra = $true) & (subset2powerset = $true) & (notinsingleton = $true) & (infuncsetfunc = $true) & (ap2apEq1 = $true) & (dpsetconstrER = $true) & (intersectInPowersetIntersectUnions = $true) & (powersetT_lem = $true) & (woz1_5 = $true) & (binintersectSubset3 = $true) & (woz13rule2 = $true) & (dsetconstr__Cong = $true) & (breln1compE = $true) & (woz1_3 = $true) & (subsetTrans = $true) & (complementTnotintersectT = $true) & (setukpairinjL2 = $true) & (emptyset__Cong = $true) & (binintersectSubset5 = $true) & (binunionE = $true) & (dpsetconstrERa = $true) & (doubleComplementSub2 = $true) & (replAx = $true) & (contrasubsetT = $true) & (lam2lamEq = $true) & (symdiffI2 = $true) & (setext = $true) & (doubleComplementE1 = $true) & (cartprodpairmemEL = $true) & (breln1unionCommutes = $true) & (lamProp = $true) & (inComplementUnionImpNotIn1 = $true) & (breln1unionI = $true) & (binunionIR = $true) & (binintersectLsub = $true) & (complementUnionInPowersetComplement = $true) & (iffalseProp1 = $true) & (demorgan2a2 = $true) & (exuE3u = $true) & (iftrue = $true) & (woz2W = $true) & (dpsetconstrEL2 = $true) & (inIntersectImpInIntersectUnions = $true) & (symdiffIneg1 = $true) & (breln1compEex = $true) & (notsubsetI = $true) & (subsetI1 = $true) & (binintersectTERcontra = $true) & (breln1invE = $true) & (setadjoinAx = $true) & (binintersectT_lem = $true) & (lam2p = $true) & (descrp = $true) & (omega__Cong = $true) & (setminusSubset1 = $true) & (complementT_lem = $true) & (breln1invI = $true) & (breln1invprop = $true) & (setminusERneg = $true) & (woz13rule1 = $true) & (setadjoin__Cong = $true) & (contraSubsetComplement = $true) & (emptyInPowerset = $true) & (setukpairIL = $true) & (funcGraphProp2 = $true) & (nonemptyE1 = $true) & (demorgan2 = $true) & (ap2apEq2 = $true) & (setbeta = $true) & (demorgan1b = $true) & (theeq = $true) & (omega0Ax = $true) & (binunionT_lem = $true) & (upairsetIR = $true) & (binintersectER = $true) & (beta1 = $true) & (eqinunit = $true)),
% 16.41/4.01 inference(flattening,[status(thm)],[f1204])).
% 16.41/4.01 thf(f1204,plain,(
% 16.41/4.01 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ X0 @ X3)) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))) & ($true = (breln1 @ X0 @ X1))) & (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)),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f663])).
% 16.41/4.01 thf(f663,plain,(
% 16.41/4.01 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (breln1 @ X0 @ X3)) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f662])).
% 16.41/4.01 thf(f662,plain,(
% 16.41/4.01 ~(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 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X2))) @ (breln1invset @ X0 @ (breln1compset @ X0 @ (breln1invset @ X0 @ X3) @ (breln1invset @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.41/4.01 inference(rectify,[status(thm)],[f312])).
% 16.41/4.01 thf(f312,negated_conjecture,(
% 16.41/4.01 ~(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 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X19 : $i] : ((breln1 @ X3 @ X19) => ((breln1compset @ X3 @ (binunion @ X13 @ X15) @ X19) = (binunion @ (breln1invset @ X3 @ (breln1compset @ X3 @ (breln1invset @ X3 @ X19) @ (breln1invset @ X3 @ X15))) @ (breln1invset @ X3 @ (breln1compset @ X3 @ (breln1invset @ X3 @ X19) @ (breln1invset @ X3 @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.41/4.01 inference(negated_conjecture,[status(cth)],[f311])).
% 16.41/4.01 thf(f311,conjecture,(
% 16.41/4.01 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 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X19 : $i] : ((breln1 @ X3 @ X19) => ((breln1compset @ X3 @ (binunion @ X13 @ X15) @ X19) = (binunion @ (breln1invset @ X3 @ (breln1compset @ X3 @ (breln1invset @ X3 @ X19) @ (breln1invset @ X3 @ X15))) @ (breln1invset @ X3 @ (breln1compset @ X3 @ (breln1invset @ X3 @ X19) @ (breln1invset @ X3 @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2B)).
% 16.41/4.01 thf(f4950,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK982)) | spl1040_4),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4949,f4392])).
% 16.41/4.01 thf(f4392,plain,(
% 16.41/4.01 (breln1compprop = $true)),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4949,plain,(
% 16.41/4.01 (breln1compprop != $true) | ($true != (breln1 @ sK979 @ sK982)) | spl1040_4),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4948,f4537])).
% 16.41/4.01 thf(f4537,plain,(
% 16.41/4.01 ($true = (breln1 @ sK979 @ sK980))),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4948,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | ($true != (breln1 @ sK979 @ sK982)) | (breln1compprop != $true) | spl1040_4),
% 16.41/4.01 inference(trivial_inequality_removal,[status(thm)],[f4947])).
% 16.41/4.01 thf(f4947,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | (breln1compprop != $true) | ($true != $true) | ($true != (breln1 @ sK979 @ sK982)) | spl1040_4),
% 16.41/4.01 inference(superposition,[status(thm)],[f4916,f3463])).
% 16.41/4.01 thf(f3463,plain,(
% 16.41/4.01 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (breln1 @ X3 @ (breln1compset @ X3 @ X4 @ X5))) | ($true != (breln1 @ X3 @ X5)) | ($true != (breln1 @ X3 @ X4)) | (breln1compprop != $true)) )),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f1953])).
% 16.41/4.01 thf(f1953,plain,(
% 16.41/4.01 ((breln1compprop = $true) | ((($true = (breln1 @ sK375 @ sK377)) & ($true != (breln1 @ sK375 @ (breln1compset @ sK375 @ sK376 @ sK377)))) & ($true = (breln1 @ sK375 @ sK376)))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true != (breln1 @ X3 @ X5)) | ($true = (breln1 @ X3 @ (breln1compset @ X3 @ X4 @ X5)))) | ($true != (breln1 @ X3 @ X4))) | (breln1compprop != $true))),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK375,sK376,sK377])],[f1950,f1952,f1951])).
% 16.41/4.01 thf(f1951,plain,(
% 16.41/4.01 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : (((breln1 @ sK375 @ X2) = $true) & ($true != (breln1 @ sK375 @ (breln1compset @ sK375 @ sK376 @ X2)))) & ($true = (breln1 @ sK375 @ sK376)))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1952,plain,(
% 16.41/4.01 ? [X2 : $i] : (((breln1 @ sK375 @ X2) = $true) & ($true != (breln1 @ sK375 @ (breln1compset @ sK375 @ sK376 @ X2)))) => (($true = (breln1 @ sK375 @ sK377)) & ($true != (breln1 @ sK375 @ (breln1compset @ sK375 @ sK376 @ sK377))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1950,plain,(
% 16.41/4.01 ((breln1compprop = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1)))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true != (breln1 @ X3 @ X5)) | ($true = (breln1 @ X3 @ (breln1compset @ X3 @ X4 @ X5)))) | ($true != (breln1 @ X3 @ X4))) | (breln1compprop != $true))),
% 16.41/4.01 inference(rectify,[status(thm)],[f1949])).
% 16.41/4.01 thf(f1949,plain,(
% 16.41/4.01 ((breln1compprop = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ($true != (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (breln1 @ X0 @ X1)))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ($true = (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (breln1 @ X0 @ X1))) | (breln1compprop != $true))),
% 16.41/4.01 inference(nnf_transformation,[status(thm)],[f1241])).
% 16.41/4.01 thf(f1241,plain,(
% 16.41/4.01 (breln1compprop = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ($true = (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (breln1 @ X0 @ X1)))),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f522])).
% 16.41/4.01 thf(f522,plain,(
% 16.41/4.01 ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ($true = (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2))))) <=> (breln1compprop = $true)),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f521])).
% 16.41/4.01 thf(f521,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (breln1 @ X0 @ (breln1compset @ X0 @ X1 @ X2)))) = breln1compprop)),
% 16.41/4.01 inference(rectify,[status(thm)],[f297])).
% 16.41/4.01 thf(f297,axiom,(
% 16.41/4.01 (! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => (breln1 @ X3 @ (breln1compset @ X3 @ X13 @ X15)))) = breln1compprop)),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',breln1compprop)).
% 16.41/4.01 thf(f4916,plain,(
% 16.41/4.01 ((breln1 @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)) != $true) | spl1040_4),
% 16.41/4.01 inference(avatar_component_clause,[status(thm)],[f4914])).
% 16.41/4.01 thf(f4914,definition,(
% 16.41/4.01 spl1040_4 <=> ((breln1 @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)) = $true)),
% 16.41/4.01 introduced(definition,[new_symbols(naming,[spl1040_4])],[avatar_definition])).
% 16.41/4.01 thf(f4946,plain,(
% 16.41/4.01 spl1040_3),
% 16.41/4.01 inference(avatar_contradiction_clause,[status(thm)],[f4945])).
% 16.41/4.01 thf(f4945,plain,(
% 16.41/4.01 $false | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4944,f4537])).
% 16.41/4.01 thf(f4944,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | spl1040_3),
% 16.41/4.01 inference(trivial_inequality_removal,[status(thm)],[f4939])).
% 16.41/4.01 thf(f4939,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | ($true != $true) | spl1040_3),
% 16.41/4.01 inference(superposition,[status(thm)],[f4930,f4540])).
% 16.41/4.01 thf(f4540,plain,(
% 16.41/4.01 ($true = (breln1 @ sK979 @ sK981))),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4930,plain,(
% 16.41/4.01 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK981)) | ($true != (breln1 @ X0 @ sK980))) ) | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4929,f4350])).
% 16.41/4.01 thf(f4350,plain,(
% 16.41/4.01 (breln1unionCommutes = $true)),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4929,plain,(
% 16.41/4.01 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK980)) | (breln1unionCommutes != $true) | ($true != (breln1 @ X0 @ sK981))) ) | spl1040_3),
% 16.41/4.01 inference(trivial_inequality_removal,[status(thm)],[f4927])).
% 16.41/4.01 thf(f4927,plain,(
% 16.41/4.01 ( ! [X0 : $i] : (($true != (breln1 @ X0 @ sK981)) | (breln1unionCommutes != $true) | ($true != (breln1 @ X0 @ sK980)) | ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))) ) | spl1040_3),
% 16.41/4.01 inference(superposition,[status(thm)],[f4924,f3235])).
% 16.41/4.01 thf(f3235,plain,(
% 16.41/4.01 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((binunion @ X4 @ X5) = (binunion @ X5 @ X4)) | ($true != (breln1 @ X3 @ X4)) | (breln1unionCommutes != $true) | ($true != (breln1 @ X3 @ X5))) )),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f1693])).
% 16.41/4.01 thf(f1693,plain,(
% 16.41/4.01 ((breln1unionCommutes = $true) | (((breln1 @ sK209 @ sK210) = $true) & (($true = (breln1 @ sK209 @ sK211)) & ((binunion @ sK211 @ sK210) != (binunion @ sK210 @ sK211))))) & (! [X3 : $i,X4 : $i] : (($true != (breln1 @ X3 @ X4)) | ! [X5 : $i] : (($true != (breln1 @ X3 @ X5)) | ((binunion @ X4 @ X5) = (binunion @ X5 @ X4)))) | (breln1unionCommutes != $true))),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK209,sK210,sK211])],[f1690,f1692,f1691])).
% 16.41/4.01 thf(f1691,plain,(
% 16.41/4.01 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ((binunion @ X2 @ X1) != (binunion @ X1 @ X2)))) => (((breln1 @ sK209 @ sK210) = $true) & ? [X2 : $i] : (($true = (breln1 @ sK209 @ X2)) & ((binunion @ sK210 @ X2) != (binunion @ X2 @ sK210))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1692,plain,(
% 16.41/4.01 ? [X2 : $i] : (($true = (breln1 @ sK209 @ X2)) & ((binunion @ sK210 @ X2) != (binunion @ X2 @ sK210))) => (($true = (breln1 @ sK209 @ sK211)) & ((binunion @ sK211 @ sK210) != (binunion @ sK210 @ sK211)))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1690,plain,(
% 16.41/4.01 ((breln1unionCommutes = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ((binunion @ X2 @ X1) != (binunion @ X1 @ X2))))) & (! [X3 : $i,X4 : $i] : (($true != (breln1 @ X3 @ X4)) | ! [X5 : $i] : (($true != (breln1 @ X3 @ X5)) | ((binunion @ X4 @ X5) = (binunion @ X5 @ X4)))) | (breln1unionCommutes != $true))),
% 16.41/4.01 inference(rectify,[status(thm)],[f1689])).
% 16.41/4.01 thf(f1689,plain,(
% 16.41/4.01 ((breln1unionCommutes = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ((binunion @ X2 @ X1) != (binunion @ X1 @ X2))))) & (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ((binunion @ X2 @ X1) = (binunion @ X1 @ X2)))) | (breln1unionCommutes != $true))),
% 16.41/4.01 inference(nnf_transformation,[status(thm)],[f1189])).
% 16.41/4.01 thf(f1189,plain,(
% 16.41/4.01 (breln1unionCommutes = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ((binunion @ X2 @ X1) = (binunion @ X1 @ X2))))),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f627])).
% 16.41/4.01 thf(f627,plain,(
% 16.41/4.01 (breln1unionCommutes = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ((binunion @ X2 @ X1) = (binunion @ X1 @ X2))))),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f626])).
% 16.41/4.01 thf(f626,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ((binunion @ X2 @ X1) = (binunion @ X1 @ X2)))) = breln1unionCommutes)),
% 16.41/4.01 inference(rectify,[status(thm)],[f307])).
% 16.41/4.01 thf(f307,axiom,(
% 16.41/4.01 (! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ((binunion @ X13 @ X15) = (binunion @ X15 @ X13)))) = breln1unionCommutes)),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',breln1unionCommutes)).
% 16.41/4.01 thf(f4924,plain,(
% 16.41/4.01 ((breln1compset @ sK979 @ (binunion @ sK981 @ sK980) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4923,f4530])).
% 16.41/4.01 thf(f4530,plain,(
% 16.41/4.01 (woz2A = $true)),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4923,plain,(
% 16.41/4.01 ((breln1compset @ sK979 @ (binunion @ sK981 @ sK980) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | (woz2A != $true) | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4922,f4539])).
% 16.41/4.01 thf(f4922,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK982)) | ((breln1compset @ sK979 @ (binunion @ sK981 @ sK980) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | (woz2A != $true) | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4921,f4537])).
% 16.41/4.01 thf(f4921,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | ((breln1compset @ sK979 @ (binunion @ sK981 @ sK980) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ sK982)) | (woz2A != $true) | spl1040_3),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4918,f4540])).
% 16.41/4.01 thf(f4918,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK981)) | ((breln1compset @ sK979 @ (binunion @ sK981 @ sK980) @ sK982) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ sK980)) | ($true != (breln1 @ sK979 @ sK982)) | (woz2A != $true) | spl1040_3),
% 16.41/4.01 inference(superposition,[status(thm)],[f4912,f4234])).
% 16.41/4.01 thf(f4234,plain,(
% 16.41/4.01 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3))) | ($true != (breln1 @ X0 @ X3)) | (woz2A != $true) | ($true != (breln1 @ X0 @ X2)) | ($true != (breln1 @ X0 @ X1))) )),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2796])).
% 16.41/4.01 thf(f2796,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (($true != (breln1 @ X0 @ X3)) | ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) | (woz2A != $true)) & ((woz2A = $true) | (($true = (breln1 @ sK921 @ sK922)) & (($true = (breln1 @ sK921 @ sK923)) & (($true = (breln1 @ sK921 @ sK924)) & ((breln1compset @ sK921 @ (binunion @ sK922 @ sK923) @ sK924) != (binunion @ (breln1compset @ sK921 @ sK922 @ sK924) @ (breln1compset @ sK921 @ sK923 @ sK924)))))))),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK921,sK922,sK923,sK924])],[f2792,f2795,f2794,f2793])).
% 16.41/4.01 thf(f2793,plain,(
% 16.41/4.01 ? [X4 : $i,X5 : $i] : (($true = (breln1 @ X4 @ X5)) & ? [X6 : $i] : (($true = (breln1 @ X4 @ X6)) & ? [X7 : $i] : (($true = (breln1 @ X4 @ X7)) & ((binunion @ (breln1compset @ X4 @ X5 @ X7) @ (breln1compset @ X4 @ X6 @ X7)) != (breln1compset @ X4 @ (binunion @ X5 @ X6) @ X7))))) => (($true = (breln1 @ sK921 @ sK922)) & ? [X6 : $i] : (((breln1 @ sK921 @ X6) = $true) & ? [X7 : $i] : (($true = (breln1 @ sK921 @ X7)) & ((binunion @ (breln1compset @ sK921 @ sK922 @ X7) @ (breln1compset @ sK921 @ X6 @ X7)) != (breln1compset @ sK921 @ (binunion @ sK922 @ X6) @ X7)))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f2794,plain,(
% 16.41/4.01 ? [X6 : $i] : (((breln1 @ sK921 @ X6) = $true) & ? [X7 : $i] : (($true = (breln1 @ sK921 @ X7)) & ((binunion @ (breln1compset @ sK921 @ sK922 @ X7) @ (breln1compset @ sK921 @ X6 @ X7)) != (breln1compset @ sK921 @ (binunion @ sK922 @ X6) @ X7)))) => (($true = (breln1 @ sK921 @ sK923)) & ? [X7 : $i] : (($true = (breln1 @ sK921 @ X7)) & ((binunion @ (breln1compset @ sK921 @ sK922 @ X7) @ (breln1compset @ sK921 @ sK923 @ X7)) != (breln1compset @ sK921 @ (binunion @ sK922 @ sK923) @ X7))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f2795,plain,(
% 16.41/4.01 ? [X7 : $i] : (($true = (breln1 @ sK921 @ X7)) & ((binunion @ (breln1compset @ sK921 @ sK922 @ X7) @ (breln1compset @ sK921 @ sK923 @ X7)) != (breln1compset @ sK921 @ (binunion @ sK922 @ sK923) @ X7))) => (($true = (breln1 @ sK921 @ sK924)) & ((breln1compset @ sK921 @ (binunion @ sK922 @ sK923) @ sK924) != (binunion @ (breln1compset @ sK921 @ sK922 @ sK924) @ (breln1compset @ sK921 @ sK923 @ sK924))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f2792,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (($true != (breln1 @ X0 @ X3)) | ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) | (woz2A != $true)) & ((woz2A = $true) | ? [X4 : $i,X5 : $i] : (($true = (breln1 @ X4 @ X5)) & ? [X6 : $i] : (($true = (breln1 @ X4 @ X6)) & ? [X7 : $i] : (($true = (breln1 @ X4 @ X7)) & ((binunion @ (breln1compset @ X4 @ X5 @ X7) @ (breln1compset @ X4 @ X6 @ X7)) != (breln1compset @ X4 @ (binunion @ X5 @ X6) @ X7))))))),
% 16.41/4.01 inference(rectify,[status(thm)],[f2791])).
% 16.41/4.01 thf(f2791,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (($true != (breln1 @ X0 @ X3)) | ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) | (woz2A != $true)) & ((woz2A = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (breln1 @ X0 @ X2)) & ? [X3 : $i] : (($true = (breln1 @ X0 @ X3)) & ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) != (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))))),
% 16.41/4.01 inference(nnf_transformation,[status(thm)],[f1168])).
% 16.41/4.01 thf(f1168,plain,(
% 16.41/4.01 ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (($true != (breln1 @ X0 @ X2)) | ! [X3 : $i] : (($true != (breln1 @ X0 @ X3)) | ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) <=> (woz2A = $true)),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f575])).
% 16.41/4.01 thf(f575,plain,(
% 16.41/4.01 ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (breln1 @ X0 @ X3)) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) <=> (woz2A = $true)),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f574])).
% 16.41/4.01 thf(f574,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((breln1 @ X0 @ X3) => ((breln1compset @ X0 @ (binunion @ X1 @ X2) @ X3) = (binunion @ (breln1compset @ X0 @ X1 @ X3) @ (breln1compset @ X0 @ X2 @ X3)))))) = woz2A)),
% 16.41/4.01 inference(rectify,[status(thm)],[f310])).
% 16.41/4.01 thf(f310,axiom,(
% 16.41/4.01 (! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X19 : $i] : ((breln1 @ X3 @ X19) => ((breln1compset @ X3 @ (binunion @ X13 @ X15) @ X19) = (binunion @ (breln1compset @ X3 @ X13 @ X19) @ (breln1compset @ X3 @ X15 @ X19)))))) = woz2A)),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2A)).
% 16.41/4.01 thf(f4912,plain,(
% 16.41/4.01 ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982) != (binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1compset @ sK979 @ sK980 @ sK982))) | spl1040_3),
% 16.41/4.01 inference(avatar_component_clause,[status(thm)],[f4910])).
% 16.41/4.01 thf(f4910,definition,(
% 16.41/4.01 spl1040_3 <=> ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982) = (binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1compset @ sK979 @ sK980 @ sK982)))),
% 16.41/4.01 introduced(definition,[new_symbols(naming,[spl1040_3])],[avatar_definition])).
% 16.41/4.01 thf(f4917,plain,(
% 16.41/4.01 ~spl1040_3 | ~spl1040_4 | spl1040_2),
% 16.41/4.01 inference(avatar_split_clause,[status(thm)],[f4908,f4897,f4914,f4910])).
% 16.41/4.01 thf(f4897,definition,(
% 16.41/4.01 spl1040_2 <=> ((binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) = (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 introduced(definition,[new_symbols(naming,[spl1040_2])],[avatar_definition])).
% 16.41/4.01 thf(f4908,plain,(
% 16.41/4.01 ((breln1 @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)) != $true) | ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982) != (binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1compset @ sK979 @ sK980 @ sK982))) | spl1040_2),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4907,f4486])).
% 16.41/4.01 thf(f4486,plain,(
% 16.41/4.01 (woz2Ex = $true)),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4907,plain,(
% 16.41/4.01 ((breln1 @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)) != $true) | ((breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982) != (binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1compset @ sK979 @ sK980 @ sK982))) | (woz2Ex != $true) | spl1040_2),
% 16.41/4.01 inference(superposition,[status(thm)],[f4899,f3410])).
% 16.41/4.01 thf(f3410,plain,(
% 16.41/4.01 ( ! [X2 : $i,X3 : $i] : (((breln1invset @ X2 @ (breln1invset @ X2 @ X3)) = X3) | ($true != (breln1 @ X2 @ X3)) | (woz2Ex != $true)) )),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f1893])).
% 16.41/4.01 thf(f1893,plain,(
% 16.41/4.01 ((woz2Ex = $true) | (($true = (breln1 @ sK335 @ sK336)) & (sK336 != (breln1invset @ sK335 @ (breln1invset @ sK335 @ sK336))))) & (! [X2 : $i,X3 : $i] : (($true != (breln1 @ X2 @ X3)) | ((breln1invset @ X2 @ (breln1invset @ X2 @ X3)) = X3)) | (woz2Ex != $true))),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK335,sK336])],[f1891,f1892])).
% 16.41/4.01 thf(f1892,plain,(
% 16.41/4.01 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) != X1)) => (($true = (breln1 @ sK335 @ sK336)) & (sK336 != (breln1invset @ sK335 @ (breln1invset @ sK335 @ sK336))))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1891,plain,(
% 16.41/4.01 ((woz2Ex = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) != X1))) & (! [X2 : $i,X3 : $i] : (($true != (breln1 @ X2 @ X3)) | ((breln1invset @ X2 @ (breln1invset @ X2 @ X3)) = X3)) | (woz2Ex != $true))),
% 16.41/4.01 inference(rectify,[status(thm)],[f1890])).
% 16.41/4.01 thf(f1890,plain,(
% 16.41/4.01 ((woz2Ex = $true) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) != X1))) & (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1)) | (woz2Ex != $true))),
% 16.41/4.01 inference(nnf_transformation,[status(thm)],[f1331])).
% 16.41/4.01 thf(f1331,plain,(
% 16.41/4.01 (woz2Ex = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1))),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f530])).
% 16.41/4.01 thf(f530,plain,(
% 16.41/4.01 (woz2Ex = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1))),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f529])).
% 16.41/4.01 thf(f529,plain,(
% 16.41/4.01 (! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ((breln1invset @ X0 @ (breln1invset @ X0 @ X1)) = X1)) = woz2Ex)),
% 16.41/4.01 inference(rectify,[status(thm)],[f308])).
% 16.41/4.01 thf(f308,axiom,(
% 16.41/4.01 (! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ((breln1invset @ X3 @ (breln1invset @ X3 @ X13)) = X13)) = woz2Ex)),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2Ex)).
% 16.41/4.01 thf(f4899,plain,(
% 16.41/4.01 ((binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | spl1040_2),
% 16.41/4.01 inference(avatar_component_clause,[status(thm)],[f4897])).
% 16.41/4.01 thf(f4906,plain,(
% 16.41/4.01 spl1040_1),
% 16.41/4.01 inference(avatar_contradiction_clause,[status(thm)],[f4905])).
% 16.41/4.01 thf(f4905,plain,(
% 16.41/4.01 $false | spl1040_1),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4904,f4539])).
% 16.41/4.01 thf(f4904,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK982)) | spl1040_1),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4903,f4540])).
% 16.41/4.01 thf(f4903,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK981)) | ($true != (breln1 @ sK979 @ sK982)) | spl1040_1),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4902,f4392])).
% 16.41/4.01 thf(f4902,plain,(
% 16.41/4.01 (breln1compprop != $true) | ($true != (breln1 @ sK979 @ sK981)) | ($true != (breln1 @ sK979 @ sK982)) | spl1040_1),
% 16.41/4.01 inference(trivial_inequality_removal,[status(thm)],[f4901])).
% 16.41/4.01 thf(f4901,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK981)) | (breln1compprop != $true) | ($true != $true) | ($true != (breln1 @ sK979 @ sK982)) | spl1040_1),
% 16.41/4.01 inference(superposition,[status(thm)],[f4895,f3463])).
% 16.41/4.01 thf(f4895,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982))) | spl1040_1),
% 16.41/4.01 inference(avatar_component_clause,[status(thm)],[f4893])).
% 16.41/4.01 thf(f4893,definition,(
% 16.41/4.01 spl1040_1 <=> ($true = (breln1 @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982)))),
% 16.41/4.01 introduced(definition,[new_symbols(naming,[spl1040_1])],[avatar_definition])).
% 16.41/4.01 thf(f4900,plain,(
% 16.41/4.01 ~spl1040_1 | ~spl1040_2),
% 16.41/4.01 inference(avatar_split_clause,[status(thm)],[f4887,f4897,f4893])).
% 16.41/4.01 thf(f4887,plain,(
% 16.41/4.01 ((binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982)))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4883,f4486])).
% 16.41/4.01 thf(f4883,plain,(
% 16.41/4.01 (woz2Ex != $true) | ((binunion @ (breln1compset @ sK979 @ sK981 @ sK982) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982)))),
% 16.41/4.01 inference(superposition,[status(thm)],[f4879,f3410])).
% 16.41/4.01 thf(f4879,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4878,f4540])).
% 16.41/4.01 thf(f4878,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ sK981))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4877,f4539])).
% 16.41/4.01 thf(f4877,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | ($true != (breln1 @ sK979 @ sK982)) | ($true != (breln1 @ sK979 @ sK981))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4874,f4339])).
% 16.41/4.01 thf(f4339,plain,(
% 16.41/4.01 (woz2W = $true)),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 thf(f4874,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK981 @ sK982))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | (woz2W != $true) | ($true != (breln1 @ sK979 @ sK982)) | ($true != (breln1 @ sK979 @ sK981))),
% 16.41/4.01 inference(superposition,[status(thm)],[f4869,f3150])).
% 16.41/4.01 thf(f3150,plain,(
% 16.41/4.01 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((breln1invset @ X3 @ (breln1compset @ X3 @ X4 @ X5)) = (breln1compset @ X3 @ (breln1invset @ X3 @ X5) @ (breln1invset @ X3 @ X4))) | ($true != (breln1 @ X3 @ X4)) | (woz2W != $true) | ($true != (breln1 @ X3 @ X5))) )),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f1599])).
% 16.41/4.01 thf(f1599,plain,(
% 16.41/4.01 ((woz2W = $true) | ((((breln1compset @ sK149 @ (breln1invset @ sK149 @ sK151) @ (breln1invset @ sK149 @ sK150)) != (breln1invset @ sK149 @ (breln1compset @ sK149 @ sK150 @ sK151))) & ((breln1 @ sK149 @ sK151) = $true)) & ($true = (breln1 @ sK149 @ sK150)))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (((breln1invset @ X3 @ (breln1compset @ X3 @ X4 @ X5)) = (breln1compset @ X3 @ (breln1invset @ X3 @ X5) @ (breln1invset @ X3 @ X4))) | ($true != (breln1 @ X3 @ X5))) | ($true != (breln1 @ X3 @ X4))) | (woz2W != $true))),
% 16.41/4.01 inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150,sK151])],[f1596,f1598,f1597])).
% 16.41/4.01 thf(f1597,plain,(
% 16.41/4.01 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) != (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) => (? [X2 : $i] : (((breln1compset @ sK149 @ (breln1invset @ sK149 @ X2) @ (breln1invset @ sK149 @ sK150)) != (breln1invset @ sK149 @ (breln1compset @ sK149 @ sK150 @ X2))) & ($true = (breln1 @ sK149 @ X2))) & ($true = (breln1 @ sK149 @ sK150)))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1598,plain,(
% 16.41/4.01 ? [X2 : $i] : (((breln1compset @ sK149 @ (breln1invset @ sK149 @ X2) @ (breln1invset @ sK149 @ sK150)) != (breln1invset @ sK149 @ (breln1compset @ sK149 @ sK150 @ X2))) & ($true = (breln1 @ sK149 @ X2))) => (((breln1compset @ sK149 @ (breln1invset @ sK149 @ sK151) @ (breln1invset @ sK149 @ sK150)) != (breln1invset @ sK149 @ (breln1compset @ sK149 @ sK150 @ sK151))) & ((breln1 @ sK149 @ sK151) = $true))),
% 16.41/4.01 introduced(definition,[],[choice_axiom])).
% 16.41/4.01 thf(f1596,plain,(
% 16.41/4.01 ((woz2W = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) != (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1)))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (((breln1invset @ X3 @ (breln1compset @ X3 @ X4 @ X5)) = (breln1compset @ X3 @ (breln1invset @ X3 @ X5) @ (breln1invset @ X3 @ X4))) | ($true != (breln1 @ X3 @ X5))) | ($true != (breln1 @ X3 @ X4))) | (woz2W != $true))),
% 16.41/4.01 inference(rectify,[status(thm)],[f1595])).
% 16.41/4.01 thf(f1595,plain,(
% 16.41/4.01 ((woz2W = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) != (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1)))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) = (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))) | ($true != (breln1 @ X0 @ X2))) | ($true != (breln1 @ X0 @ X1))) | (woz2W != $true))),
% 16.41/4.01 inference(nnf_transformation,[status(thm)],[f1134])).
% 16.41/4.01 thf(f1134,plain,(
% 16.41/4.01 (woz2W = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) = (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))) | ($true != (breln1 @ X0 @ X2))) | ($true != (breln1 @ X0 @ X1)))),
% 16.41/4.01 inference(ennf_transformation,[status(thm)],[f581])).
% 16.41/4.01 thf(f581,plain,(
% 16.41/4.01 (woz2W = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) = (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1)))))),
% 16.41/4.01 inference(fool_elimination,[status(thm)],[f580])).
% 16.41/4.01 thf(f580,plain,(
% 16.41/4.01 (woz2W = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ((breln1invset @ X0 @ (breln1compset @ X0 @ X1 @ X2)) = (breln1compset @ X0 @ (breln1invset @ X0 @ X2) @ (breln1invset @ X0 @ X1))))))),
% 16.41/4.01 inference(rectify,[status(thm)],[f309])).
% 16.41/4.01 thf(f309,axiom,(
% 16.41/4.01 (woz2W = ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ((breln1invset @ X3 @ (breln1compset @ X3 @ X13 @ X15)) = (breln1compset @ X3 @ (breln1invset @ X3 @ X15) @ (breln1invset @ X3 @ X13))))))),
% 16.41/4.01 file('/export/starexec/sandbox2/tmp/tmp.pXmNTb59JY/DTF2THF_18469.p',woz2W)).
% 16.41/4.01 thf(f4869,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4868,f4339])).
% 16.41/4.01 thf(f4868,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982)) | (woz2W != $true)),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4867,f4539])).
% 16.41/4.01 thf(f4867,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK982)) | (woz2W != $true) | ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 inference(subsumption_resolution,[status(thm)],[f4862,f4537])).
% 16.41/4.01 thf(f4862,plain,(
% 16.41/4.01 ($true != (breln1 @ sK979 @ sK980)) | (woz2W != $true) | ($true != (breln1 @ sK979 @ sK982)) | ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ sK980 @ sK982)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 inference(superposition,[status(thm)],[f4538,f3150])).
% 16.41/4.01 thf(f4538,plain,(
% 16.41/4.01 ((binunion @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK981))) @ (breln1invset @ sK979 @ (breln1compset @ sK979 @ (breln1invset @ sK979 @ sK982) @ (breln1invset @ sK979 @ sK980)))) != (breln1compset @ sK979 @ (binunion @ sK980 @ sK981) @ sK982))),
% 16.41/4.01 inference(cnf_transformation,[status(thm)],[f2874])).
% 16.41/4.01 % SZS output end Proof for DTF2THF_18469
% 16.41/4.01 % (18848)------------------------------
% 16.41/4.01 % (18848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.41/4.01 % (18848)Termination reason: Refutation
% 16.41/4.01
% 16.41/4.01 % (18848)Memory used [KB]: 12153
% 16.41/4.01 % (18848)Time elapsed: 0.311 s
% 16.41/4.01 % (18848)Instructions burned: 521 (million)
% 16.41/4.01 % (18848)------------------------------
% 16.41/4.01 % (18848)------------------------------
% 16.41/4.01 % (18669)Success in time 2.324 s
%------------------------------------------------------------------------------