%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU737^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.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 09:36:47 AM UTC 2026
% Result : Theorem 36.88s 6.72s
% Output : Refutation 36.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 4789 (1278 equ; 0 cnn)
% Maximal formula atoms : 257 ( 66 avg)
% Number of connectives : 2929 ( 137 ~; 101 |; 829 &; 800 @)
% ( 10 <=>;1052 =>; 0 <=; 0 <~>)
% Maximal formula depth : 264 ( 30 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 457 ( 454 usr; 268 con; 0-4 aty)
% Number of variables : 148 ( 0 ^; 105 !; 43 ?; 148 :)
% 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_305,type,
sP0: $i > $i > $i > $i > $o ).
thf(func_def_307,type,
sP2: $i > $i > $o ).
thf(func_def_308,type,
sP3: $i > $o ).
thf(func_def_309,type,
sP4: $i > $i > $o ).
thf(func_def_310,type,
sP5: $i > $i > $o ).
thf(func_def_311,type,
sP6: $i > $i > $i > $o ).
thf(func_def_316,type,
sP11: $i > $i > $i > $o > $o ).
thf(func_def_320,type,
sK15: $i > $o ).
thf(func_def_321,type,
sK16: $i > $i ).
thf(func_def_322,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_328,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_329,type,
sK24: $i > $o ).
thf(func_def_333,type,
sK28: $i > $o ).
thf(func_def_335,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK55: $i > $i > $o ).
thf(func_def_365,type,
sK60: $i > $i > $o ).
thf(func_def_377,type,
sK72: $i > $o ).
thf(func_def_379,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_380,type,
sK75: ( $i > $o ) > $i ).
thf(func_def_381,type,
sK76: $i > $o ).
thf(func_def_386,type,
sK81: $i > $i > $i ).
thf(func_def_391,type,
sK86: $i > $i > $i > $i > $i ).
thf(func_def_392,type,
sK87: $i > $i > $i > $i > $i ).
thf(func_def_393,type,
sK88: $i > $i > $i > $i > $i ).
thf(func_def_394,type,
sK89: $i > $i > $i > $i > $i ).
thf(func_def_416,type,
sK111: $i > $o ).
thf(func_def_423,type,
sK118: $i > $o ).
thf(func_def_424,type,
sK119: ( $i > $o ) > $i > $i > $i ).
thf(func_def_427,type,
sK122: $i > $i > $i ).
thf(func_def_428,type,
sK123: $i > $i > $i ).
thf(func_def_429,type,
sK124: $i > $i > $i ).
thf(func_def_430,type,
sK125: $i > $i > $i ).
thf(func_def_431,type,
sK126: $i > $i > $i ).
thf(func_def_432,type,
sK127: $i > $i > $i ).
thf(func_def_433,type,
sK128: $i > $i > $i > $i ).
thf(func_def_434,type,
sK129: $i > $i ).
thf(func_def_435,type,
sK130: $i > $i ).
thf(func_def_436,type,
sK131: $i > $i ).
thf(func_def_437,type,
sK132: $i > $i ).
thf(func_def_438,type,
sK133: $i > $i > $i ).
thf(func_def_439,type,
sK134: $i > $i > $i > $i ).
thf(func_def_440,type,
sK135: $i > $i > $i > $i ).
thf(func_def_441,type,
sK136: $i > $i > $i ).
thf(func_def_442,type,
sK137: $i > $i > $i ).
thf(func_def_444,type,
sK139: $i > $i ).
thf(func_def_445,type,
sK140: $i > $i ).
thf(func_def_446,type,
sK141: $i > $i ).
thf(func_def_458,type,
sK153: $i > $o ).
thf(func_def_467,type,
sK162: $i > $o ).
thf(func_def_468,type,
sK163: $i > $o ).
thf(func_def_469,type,
sK164: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_470,type,
sK165: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_473,type,
sK168: $i > $i > $i > $i ).
thf(func_def_474,type,
sK169: $i > $i > $i > $i ).
thf(func_def_496,type,
sK191: $i > $i > $o ).
thf(func_def_505,type,
sK200: $i > $o ).
thf(func_def_508,type,
sK203: $i > $i > $o ).
thf(func_def_526,type,
sK221: ( $i > $o ) > $i > $i ).
thf(func_def_528,type,
sK223: $i > $o ).
thf(func_def_530,type,
sK225: $i > $o ).
thf(func_def_547,type,
sK242: $i > $i > $i > $i > $i ).
thf(func_def_563,type,
sK258: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_564,type,
sK259: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_565,type,
sK260: $i > $o ).
thf(func_def_566,type,
sK261: $i > $o ).
thf(func_def_584,type,
sK279: $i > ( $i > $i ) > $i > $i ).
thf(func_def_586,type,
sK281: $i > $i ).
thf(func_def_595,type,
sK290: $i > $o ).
thf(func_def_601,type,
sK296: $i > $i ).
thf(func_def_608,type,
sK303: $i > $i > $i ).
thf(func_def_611,type,
sK306: $i > $i > $i > $i > $i ).
thf(func_def_656,type,
sK351: $i > ( $i > $o ) > $i ).
thf(func_def_657,type,
sK352: $i > $o ).
thf(func_def_660,type,
sK355: $i > $o ).
thf(func_def_663,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_665,type,
sK360: $i > $o ).
thf(func_def_679,type,
sK374: $i > $i > $i ).
thf(func_def_680,type,
sK375: $i > $i > $i ).
thf(func_def_689,type,
sK384: $i > $i > ( $i > $i ) > $i ).
thf(func_def_690,type,
sK385: $i > $i ).
thf(func_def_697,type,
sK392: $i > $i ).
thf(func_def_701,type,
sK396: $i > $i > $i > $i ).
thf(func_def_702,type,
sK397: $i > $i > $i > $i ).
thf(func_def_710,type,
sK405: ( $i > $o ) > $i ).
thf(func_def_711,type,
sK406: $i > $o ).
thf(func_def_721,type,
sK416: $i > $i > $o ).
thf(func_def_727,type,
sK422: $i > ( $i > $i ) > $i > $i ).
thf(func_def_729,type,
sK424: $i > $i ).
thf(func_def_738,type,
sK433: $i > $o ).
thf(func_def_746,type,
sK441: $i > $i > $i > $i ).
thf(func_def_748,type,
sK443: $i > $o ).
thf(func_def_751,type,
sK446: $i > ( $i > $o ) > $i ).
thf(func_def_753,type,
sK448: $i > $o ).
thf(func_def_755,type,
sK450: ( $i > $o ) > $i > $i ).
thf(func_def_756,type,
sK451: ( $i > $o ) > $i > $i ).
thf(func_def_787,type,
sK482: $i > $i ).
thf(func_def_789,type,
sK484: $i > $i ).
thf(func_def_799,type,
sK494: $i > $i > $i ).
thf(func_def_804,type,
sK499: $i > ( $i > $o ) > $i ).
thf(func_def_805,type,
sK500: $i > $o ).
thf(func_def_816,type,
sK511: $i > $i ).
thf(func_def_828,type,
sK523: $i > $i > $i > $i ).
thf(func_def_835,type,
sK530: $i > $o ).
thf(func_def_844,type,
sK539: ( $i > $o ) > $i > $i ).
thf(func_def_846,type,
sK541: $i > $o ).
thf(func_def_847,type,
sK542: $i > $i > $i ).
thf(func_def_857,type,
sK552: $i > $i ).
thf(func_def_860,type,
sK555: $i > $i > $o ).
thf(func_def_871,type,
sK566: $o > $i > $i > $i ).
thf(func_def_880,type,
sK575: $i > $o ).
thf(func_def_887,type,
sK582: $i > $o ).
thf(func_def_897,type,
sK592: $i > $i > $i ).
thf(func_def_907,type,
sK602: $i > $i > $i > $i > $i ).
thf(func_def_910,type,
sK605: ( $i > $o ) > $i ).
thf(func_def_911,type,
sK606: $i > $o ).
thf(func_def_912,type,
sK607: $i > $i ).
thf(func_def_924,type,
sK619: $i > $i > ( $i > $i ) > $i ).
thf(func_def_925,type,
sK620: $i > $i ).
thf(func_def_954,type,
sK649: $i > $i > $i ).
thf(func_def_957,type,
sK652: $i > $o ).
thf(func_def_964,type,
sK659: $i > $i > $o ).
thf(func_def_977,type,
sK672: $i > $i > $o ).
thf(func_def_979,type,
sK674: $i > $i ).
thf(func_def_980,type,
sK675: $i > $i ).
thf(func_def_981,type,
sK676: $i > ( $i > $i > $o ) > $i ).
thf(func_def_982,type,
sK677: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_983,type,
sK678: $i > ( $i > $i > $o ) > $i ).
thf(func_def_997,type,
sK692: $i > $o ).
thf(func_def_999,type,
sK694: ( $i > $o ) > $i > $i ).
thf(func_def_1000,type,
sK695: ( $i > $o ) > $i > $i ).
thf(func_def_1001,type,
sK696: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1002,type,
sK697: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1006,type,
sK701: $i > $o ).
thf(func_def_1020,type,
sK715: $i > $i ).
thf(func_def_1021,type,
sK716: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1028,type,
sK723: $i > $o ).
thf(func_def_1030,type,
sK725: ( $i > $o ) > $i > $i ).
thf(func_def_1034,type,
sK729: $i > $o ).
thf(func_def_1035,type,
sK730: $i > $o ).
thf(func_def_1036,type,
sK731: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1037,type,
sK732: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1038,type,
sK733: $i > $i ).
thf(func_def_1040,type,
sK735: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1041,type,
sK736: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1045,type,
sK740: $i > $o ).
thf(func_def_1062,type,
sK757: $i > $i > $i ).
thf(func_def_1087,type,
sK782: $i > $o ).
thf(func_def_1090,type,
sK785: $i > $i > $i > $i > $i ).
thf(func_def_1091,type,
sK786: $i > $i > $i > $i > $i ).
thf(func_def_1102,type,
sK797: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1103,type,
sK798: $i > $i ).
thf(func_def_1107,type,
ph802:
!>[X0: $tType] : X0 ).
thf(f7590,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f7589,f3274]) ).
thf(f3274,plain,
( $true
= ( in @ sK666 @ ( powerset @ sK665 ) ) ),
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f2137,plain,
( ( funcGraphProp1 = $true )
& ( setminusIRneg = $true )
& ( setukpairinjR = $true )
& ( foundationAx = $true )
& ( setukpairinjR2 = $true )
& ( upairset2E = $true )
& ( ap2p = $true )
& ( nonemptyImpWitness = $true )
& ( complementT_lem = $true )
& ( setunionE = $true )
& ( ap2apEq2 = $true )
& ( notsubsetI = $true )
& ( emptyinPowerset = $true )
& ( notinemptyset = $true )
& ( binunionIR = $true )
& ( setadjoin__Cong = $true )
& ( singletonsswitch = $true )
& ( omega__Cong = $true )
& ( powersetTI1 = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( symdiffIneg2 = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ( upairset2IR = $true )
& ( emptysetimpfalse = $true )
& ( bs114d = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrI = $true )
& ( exuE2 = $true )
& ( lamp = $true )
& ( exuE3u = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstr__Cong = $true )
& ( kpairiskpair = $true )
& ( setunionAx = $true )
& ( setminusELneg = $true )
& ( ex1I = $true )
& ( setukpairinjL2 = $true )
& ( setoftrueEq = $true )
& ( doubleComplementE1 = $true )
& ( funcextLem = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE2 = $true )
& ( setukpairinjL1 = $true )
& ( eta2 = $true )
& ( setminusEL = $true )
& ( sepSubset = $true )
& ( doubleComplementSub1 = $true )
& ( setunionI = $true )
& ( ap2apEq1 = $true )
& ( subsetI1 = $true )
& ( binintersectSubset3 = $true )
& ( iftrue = $true )
& ( iftrueProp1 = $true )
& ( binintersectTELcontra = $true )
& ( binintersectLsub = $true )
& ( symdiffE = $true )
& ( funcinfuncset = $true )
& ( ksndpairEq = $true )
& ( dpsetconstrERa = $true )
& ( funcGraphProp2 = $true )
& ( binintersectSubset1 = $true )
& ( iffalse = $true )
& ( infuncsetfunc = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( ifSingleton = $true )
& ( binunionRsub = $true )
& ( subsetTI = $true )
& ( contrasubsetT3 = $true )
& ( iftrueProp2 = $true )
& ( iffalseProp2 = $true )
& ( powersetE = $true )
& ( emptysetsubset = $true )
& ( powersetI1 = $true )
& ( funcext2 = $true )
& ( setadjoinIR = $true )
& ( powerset__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyI1 = $true )
& ( binunionT_lem = $true )
& ( contrasubsetT2 = $true )
& ( complementImpComplementIntersect = $true )
& ( singletoninpowerset = $true )
& ( eqbreln = $true )
& ( exuE3e = $true )
& ( binintersectEL = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyset__Cong = $true )
& ( lam2p = $true )
& ( cartprodsndin = $true )
& ( app = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL2 = $true )
& ( iffalseProp1 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( brelnall1 = $true )
& ( subbreln = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg1 = $true )
& ( prop2setI = $true )
& ( upairinpowunion = $true )
& ( ex1E1 = $true )
& ( theeq = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan3 = $true )
& ( funcext = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( setminusT_lem = $true )
& ( ksndsingleton = $true )
& ( notdallE = $true )
& ( kpairp = $true )
& ( secondinupair = $true )
& ( contraSubsetComplement = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem3 = $true )
& ( cartprodpairin = $true )
& ( noeltsimpempty = $true )
& ( binunionIL = $true )
& ( setukpairIL = $true )
& ( emptyI = $true )
& ( funcImageSingleton = $true )
& ( emptyE1 = $true )
& ( ifp = $true )
& ( funcGraphProp3 = $true )
& ( powersetI = $true )
& ( upairequniteq = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( binintersectRsub = $true )
& ( doubleComplementI1 = $true )
& ( dpsetconstrSub = $true )
& ( binintersectI = $true )
& ( complementTnotintersectT = $true )
& ( notequalI1 = $true )
& ( ex1E2 = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjR11 = $true )
& ( in__Cong = $true )
& ( exu__Cong = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( eqimpsubset1 = $true )
& ( complementTI1 = $true )
& ( subsetE = $true )
& ( dpsetconstrEL1 = $true )
& ( symdiffI1 = $true )
& ( replAx = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetAx = $true )
& ( notinsingleton = $true )
& ( setukpairIR = $true )
& ( cartprodmempaircEq = $true )
& ( symdiffI2 = $true )
& ( cartprodsndpairEq = $true )
& ( quantDeMorgan4 = $true )
& ( sepInPowerset = $true )
& ( brelnall2 = $true )
& ( upairsubunion = $true )
& ( nonemptyI = $true )
& ( subsetE2 = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( contrasubsetT = $true )
& ( complementTE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyinunitempty = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( apProp = $true )
& ( beta2 = $true )
& ( cartprodfstpairEq = $true )
& ( contrasubsetT1 = $true )
& ( setadjoinOr = $true )
& ( kpairsurjEq = $true )
& ( funcGraphProp4 = $true )
& ( dsetconstrI = $true )
& ( setminusILneg = $true )
& ( vacuousDall = $true )
& ( powersetsubset = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjR1 = $true )
& ( setextAx = $true )
& ( wellorderingAx = $true )
& ( binintersectTERcontra = $true )
& ( powersetTE1 = $true )
& ( singletonsuniq = $true )
& ( powersetT_lem = $true )
& ( emptysetE = $true )
& ( cartprodpairmemEL = $true )
& ( ( in @ sK664 @ ( powerset @ sK665 ) )
= $true )
& ( $true
= ( in @ sK666 @ ( powerset @ sK665 ) ) )
& ( ( subset @ sK666 @ ( setminus @ sK665 @ sK664 ) )
!= $true )
& ( $true
= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) )
& ( lamProp = $true )
& ( eta1 = $true )
& ( subsetI2 = $true )
& ( binintersectT_lem = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( singletonsubset = $true )
& ( ubforcartprodlem1 = $true )
& ( doubleComplementEq = $true )
& ( cartprodfstin = $true )
& ( singletonprop = $true )
& ( notdexE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( omegaIndAx = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem2 = $true )
& ( prop2set2propI = $true )
& ( doubleComplementSub2 = $true )
& ( eqinunit = $true )
& ( setminusLsub = $true )
& ( setext = $true )
& ( cartprodmempair = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrER = $true )
& ( descr__Cong = $true )
& ( kfstpairEq = $true )
& ( ex1I2 = $true )
& ( kfstsingleton = $true )
& ( disjointsetsI1 = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( subsetTrans = $true )
& ( setminusSubset2 = $true )
& ( beta1 = $true )
& ( cartprodmempair1 = $true )
& ( binunionE = $true )
& ( exuI3 = $true )
& ( powersetE1 = $true )
& ( setunionsingleton = $true )
& ( uniqinunit = $true )
& ( setextT = $true )
& ( setminusERneg = $true )
& ( setminusI = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK664,sK665,sK666])],[f1062,f2136,f2135]) ).
thf(f2135,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
=> ( ( ( in @ sK664 @ ( powerset @ sK665 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK665 ) )
= $true )
& ( $true
!= ( subset @ X2 @ ( setminus @ sK665 @ sK664 ) ) )
& ( ( subset @ sK664 @ ( setminus @ sK665 @ X2 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2136,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ sK665 ) )
= $true )
& ( $true
!= ( subset @ X2 @ ( setminus @ sK665 @ sK664 ) ) )
& ( ( subset @ sK664 @ ( setminus @ sK665 @ X2 ) )
= $true ) )
=> ( ( $true
= ( in @ sK666 @ ( powerset @ sK665 ) ) )
& ( ( subset @ sK666 @ ( setminus @ sK665 @ sK664 ) )
!= $true )
& ( $true
= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1062,plain,
( ( funcGraphProp1 = $true )
& ( setminusIRneg = $true )
& ( setukpairinjR = $true )
& ( foundationAx = $true )
& ( setukpairinjR2 = $true )
& ( upairset2E = $true )
& ( ap2p = $true )
& ( nonemptyImpWitness = $true )
& ( complementT_lem = $true )
& ( setunionE = $true )
& ( ap2apEq2 = $true )
& ( notsubsetI = $true )
& ( emptyinPowerset = $true )
& ( notinemptyset = $true )
& ( binunionIR = $true )
& ( setadjoin__Cong = $true )
& ( singletonsswitch = $true )
& ( omega__Cong = $true )
& ( powersetTI1 = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub = $true )
& ( symdiffIneg2 = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ( upairset2IR = $true )
& ( emptysetimpfalse = $true )
& ( bs114d = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrI = $true )
& ( exuE2 = $true )
& ( lamp = $true )
& ( exuE3u = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset4 = $true )
& ( dsetconstr__Cong = $true )
& ( kpairiskpair = $true )
& ( setunionAx = $true )
& ( setminusELneg = $true )
& ( ex1I = $true )
& ( setukpairinjL2 = $true )
& ( setoftrueEq = $true )
& ( doubleComplementE1 = $true )
& ( funcextLem = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE2 = $true )
& ( setukpairinjL1 = $true )
& ( eta2 = $true )
& ( setminusEL = $true )
& ( sepSubset = $true )
& ( doubleComplementSub1 = $true )
& ( setunionI = $true )
& ( ap2apEq1 = $true )
& ( subsetI1 = $true )
& ( binintersectSubset3 = $true )
& ( iftrue = $true )
& ( iftrueProp1 = $true )
& ( binintersectTELcontra = $true )
& ( binintersectLsub = $true )
& ( symdiffE = $true )
& ( funcinfuncset = $true )
& ( ksndpairEq = $true )
& ( dpsetconstrERa = $true )
& ( funcGraphProp2 = $true )
& ( binintersectSubset1 = $true )
& ( iffalse = $true )
& ( infuncsetfunc = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( ifSingleton = $true )
& ( binunionRsub = $true )
& ( subsetTI = $true )
& ( contrasubsetT3 = $true )
& ( iftrueProp2 = $true )
& ( iffalseProp2 = $true )
& ( powersetE = $true )
& ( emptysetsubset = $true )
& ( powersetI1 = $true )
& ( funcext2 = $true )
& ( setadjoinIR = $true )
& ( powerset__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyI1 = $true )
& ( binunionT_lem = $true )
& ( contrasubsetT2 = $true )
& ( complementImpComplementIntersect = $true )
& ( singletoninpowerset = $true )
& ( eqbreln = $true )
& ( exuE3e = $true )
& ( binintersectEL = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyset__Cong = $true )
& ( lam2p = $true )
& ( cartprodsndin = $true )
& ( app = $true )
& ( emptyInPowerset = $true )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL2 = $true )
& ( iffalseProp1 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( brelnall1 = $true )
& ( subbreln = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg1 = $true )
& ( prop2setI = $true )
& ( upairinpowunion = $true )
& ( ex1E1 = $true )
& ( theeq = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan3 = $true )
& ( funcext = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( setminusT_lem = $true )
& ( ksndsingleton = $true )
& ( notdallE = $true )
& ( kpairp = $true )
& ( secondinupair = $true )
& ( contraSubsetComplement = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem3 = $true )
& ( cartprodpairin = $true )
& ( noeltsimpempty = $true )
& ( binunionIL = $true )
& ( setukpairIL = $true )
& ( emptyI = $true )
& ( funcImageSingleton = $true )
& ( emptyE1 = $true )
& ( ifp = $true )
& ( funcGraphProp3 = $true )
& ( powersetI = $true )
& ( upairequniteq = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( binintersectRsub = $true )
& ( doubleComplementI1 = $true )
& ( dpsetconstrSub = $true )
& ( binintersectI = $true )
& ( complementTnotintersectT = $true )
& ( notequalI1 = $true )
& ( ex1E2 = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjR11 = $true )
& ( in__Cong = $true )
& ( exu__Cong = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( eqimpsubset1 = $true )
& ( complementTI1 = $true )
& ( subsetE = $true )
& ( dpsetconstrEL1 = $true )
& ( symdiffI1 = $true )
& ( replAx = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( powersetAx = $true )
& ( notinsingleton = $true )
& ( setukpairIR = $true )
& ( cartprodmempaircEq = $true )
& ( symdiffI2 = $true )
& ( cartprodsndpairEq = $true )
& ( quantDeMorgan4 = $true )
& ( sepInPowerset = $true )
& ( brelnall2 = $true )
& ( upairsubunion = $true )
& ( nonemptyI = $true )
& ( subsetE2 = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( contrasubsetT = $true )
& ( complementTE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyinunitempty = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( apProp = $true )
& ( beta2 = $true )
& ( cartprodfstpairEq = $true )
& ( contrasubsetT1 = $true )
& ( setadjoinOr = $true )
& ( kpairsurjEq = $true )
& ( funcGraphProp4 = $true )
& ( dsetconstrI = $true )
& ( setminusILneg = $true )
& ( vacuousDall = $true )
& ( powersetsubset = $true )
& ( upairsetIR = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjR1 = $true )
& ( setextAx = $true )
& ( wellorderingAx = $true )
& ( binintersectTERcontra = $true )
& ( powersetTE1 = $true )
& ( singletonsuniq = $true )
& ( powersetT_lem = $true )
& ( emptysetE = $true )
& ( cartprodpairmemEL = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) )
& ( lamProp = $true )
& ( eta1 = $true )
& ( subsetI2 = $true )
& ( binintersectT_lem = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjL = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( singletonsubset = $true )
& ( ubforcartprodlem1 = $true )
& ( doubleComplementEq = $true )
& ( cartprodfstin = $true )
& ( singletonprop = $true )
& ( notdexE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( omegaIndAx = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem2 = $true )
& ( prop2set2propI = $true )
& ( doubleComplementSub2 = $true )
& ( eqinunit = $true )
& ( setminusLsub = $true )
& ( setext = $true )
& ( cartprodmempair = $true )
& ( setunionsingleton2 = $true )
& ( dpsetconstrER = $true )
& ( descr__Cong = $true )
& ( kfstpairEq = $true )
& ( ex1I2 = $true )
& ( kfstsingleton = $true )
& ( disjointsetsI1 = $true )
& ( setukpairinjR12 = $true )
& ( inPowerset = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( subsetTrans = $true )
& ( setminusSubset2 = $true )
& ( beta1 = $true )
& ( cartprodmempair1 = $true )
& ( binunionE = $true )
& ( exuI3 = $true )
& ( powersetE1 = $true )
& ( setunionsingleton = $true )
& ( uniqinunit = $true )
& ( setextT = $true )
& ( setminusERneg = $true )
& ( setminusI = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[status(thm)],[f1061]) ).
thf(f1061,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $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)],[f352]) ).
thf(f352,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ( ( $true
= ( subset @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( subset @ X2 @ ( setminus @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f351]) ).
thf(f351,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
=> ( subset @ X2 @ ( setminus @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f259]) ).
thf(f259,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
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ( subset @ X11 @ ( setminus @ X3 @ X16 ) )
=> ( subset @ X16 @ ( setminus @ X3 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f258]) ).
thf(f258,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
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ( subset @ X11 @ ( setminus @ X3 @ X16 ) )
=> ( subset @ X16 @ ( setminus @ X3 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',complementTcontraSubset) ).
thf(f7589,plain,
( $true
!= ( in @ sK666 @ ( powerset @ sK665 ) ) ),
inference(subsumption_resolution,[status(thm)],[f7579,f3471]) ).
thf(f3471,plain,
complementT_lem = $true,
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f7579,plain,
( ( complementT_lem != $true )
| ( $true
!= ( in @ sK666 @ ( powerset @ sK665 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f7569]) ).
thf(f7569,plain,
( ( $true
!= ( in @ sK666 @ ( powerset @ sK665 ) ) )
| ( complementT_lem != $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f7074,f2546]) ).
thf(f2546,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true )
| ( complementT_lem != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1349]) ).
thf(f1349,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ( ( ( in @ sK150 @ ( powerset @ sK149 ) )
= $true )
& ( ( in @ ( setminus @ sK149 @ sK150 ) @ ( powerset @ sK149 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150])],[f1347,f1348]) ).
thf(f1348,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
= $true )
& ( $true
!= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) )
=> ( ( ( in @ sK150 @ ( powerset @ sK149 ) )
= $true )
& ( ( in @ ( setminus @ sK149 @ sK150 ) @ ( powerset @ sK149 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1347,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
= $true )
& ( $true
!= ( in @ ( setminus @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1346]) ).
thf(f1346,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
| ( complementT_lem != $true ) )
& ( ( complementT_lem = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f668]) ).
thf(f668,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
= $true ) )
<=> ( complementT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f667]) ).
thf(f667,plain,
( complementT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f235]) ).
thf(f235,axiom,
( complementT_lem
= ( ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ( in @ ( setminus @ X3 @ X11 ) @ ( powerset @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',complementT_lem) ).
thf(f7074,plain,
( $true
!= ( in @ ( setminus @ sK665 @ sK666 ) @ ( powerset @ sK665 ) ) ),
inference(subsumption_resolution,[status(thm)],[f7073,f3428]) ).
thf(f3428,plain,
doubleComplementSub1 = $true,
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f7073,plain,
( ( $true
!= ( in @ ( setminus @ sK665 @ sK666 ) @ ( powerset @ sK665 ) ) )
| ( doubleComplementSub1 != $true ) ),
inference(subsumption_resolution,[status(thm)],[f7072,f3272]) ).
thf(f3272,plain,
( $true
= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) ),
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f7072,plain,
( ( $true
!= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) )
| ( $true
!= ( in @ ( setminus @ sK665 @ sK666 ) @ ( powerset @ sK665 ) ) )
| ( doubleComplementSub1 != $true ) ),
inference(subsumption_resolution,[status(thm)],[f7065,f3274]) ).
thf(f7065,plain,
( ( $true
!= ( in @ sK666 @ ( powerset @ sK665 ) ) )
| ( doubleComplementSub1 != $true )
| ( $true
!= ( in @ ( setminus @ sK665 @ sK666 ) @ ( powerset @ sK665 ) ) )
| ( $true
!= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f7059]) ).
thf(f7059,plain,
( ( $true
!= ( in @ sK666 @ ( powerset @ sK665 ) ) )
| ( $true
!= ( subset @ sK664 @ ( setminus @ sK665 @ sK666 ) ) )
| ( doubleComplementSub1 != $true )
| ( $true
!= ( in @ ( setminus @ sK665 @ sK666 ) @ ( powerset @ sK665 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f4274,f3615]) ).
thf(f3615,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) )
= $true )
| ( doubleComplementSub1 != $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2286]) ).
thf(f2286,plain,
( ( ( doubleComplementSub1 = $true )
| ( ( ( subset @ sK761 @ ( setminus @ sK760 @ ( setminus @ sK760 @ sK761 ) ) )
!= $true )
& ( ( in @ sK761 @ ( powerset @ sK760 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( doubleComplementSub1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK760,sK761])],[f2284,f2285]) ).
thf(f2285,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ( ( subset @ sK761 @ ( setminus @ sK760 @ ( setminus @ sK760 @ sK761 ) ) )
!= $true )
& ( ( in @ sK761 @ ( powerset @ sK760 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2284,plain,
( ( ( doubleComplementSub1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) )
= $true )
| ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
| ( doubleComplementSub1 != $true ) ) ),
inference(rectify,[status(thm)],[f2283]) ).
thf(f2283,plain,
( ( ( doubleComplementSub1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( doubleComplementSub1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f841]) ).
thf(f841,plain,
( ( doubleComplementSub1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f462]) ).
thf(f462,plain,
( ( doubleComplementSub1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( $true
= ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f461]) ).
thf(f461,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
= doubleComplementSub1 ),
inference(rectify,[status(thm)],[f250]) ).
thf(f250,axiom,
! [X3: $i,X11: $i] :
( ( ( in @ X11 @ ( powerset @ X3 ) )
=> ( subset @ X11 @ ( setminus @ X3 @ ( setminus @ X3 @ X11 ) ) ) )
= doubleComplementSub1 ),
file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',doubleComplementSub1) ).
thf(f4274,plain,
! [X0: $i] :
( ( ( subset @ sK666 @ ( setminus @ sK665 @ X0 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK665 ) )
!= $true )
| ( $true
!= ( subset @ sK664 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f4273,f3275]) ).
thf(f3275,plain,
( ( in @ sK664 @ ( powerset @ sK665 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f4273,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK664 @ X0 ) )
| ( ( subset @ sK666 @ ( setminus @ sK665 @ X0 ) )
!= $true )
| ( ( in @ sK664 @ ( powerset @ sK665 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK665 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4256,f3394]) ).
thf(f3394,plain,
contrasubsetT2 = $true,
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f4256,plain,
! [X0: $i] :
( ( contrasubsetT2 != $true )
| ( ( subset @ sK666 @ ( setminus @ sK665 @ X0 ) )
!= $true )
| ( ( in @ X0 @ ( powerset @ sK665 ) )
!= $true )
| ( ( in @ sK664 @ ( powerset @ sK665 ) )
!= $true )
| ( $true
!= ( subset @ sK664 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4232]) ).
thf(f4232,plain,
! [X0: $i] :
( ( ( in @ sK664 @ ( powerset @ sK665 ) )
!= $true )
| ( contrasubsetT2 != $true )
| ( $true != $true )
| ( ( in @ X0 @ ( powerset @ sK665 ) )
!= $true )
| ( ( subset @ sK666 @ ( setminus @ sK665 @ X0 ) )
!= $true )
| ( $true
!= ( subset @ sK664 @ X0 ) ) ),
inference(superposition,[status(thm)],[f3844,f2877]) ).
thf(f2877,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( contrasubsetT2 != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( $true
!= ( subset @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1721]) ).
thf(f1721,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT2 != $true ) )
& ( ( contrasubsetT2 = $true )
| ( ( ( subset @ sK399 @ sK400 )
= $true )
& ( $true
= ( in @ sK400 @ ( powerset @ sK398 ) ) )
& ( ( subset @ ( setminus @ sK398 @ sK400 ) @ ( setminus @ sK398 @ sK399 ) )
!= $true )
& ( $true
= ( in @ sK399 @ ( powerset @ sK398 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK398,sK399,sK400])],[f1718,f1720,f1719]) ).
thf(f1719,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) )
& ( $true
!= ( subset @ ( setminus @ X3 @ X5 ) @ ( setminus @ X3 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
=> ( ? [X5: $i] :
( ( $true
= ( subset @ sK399 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ sK398 ) ) )
& ( $true
!= ( subset @ ( setminus @ sK398 @ X5 ) @ ( setminus @ sK398 @ sK399 ) ) ) )
& ( $true
= ( in @ sK399 @ ( powerset @ sK398 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1720,plain,
( ? [X5: $i] :
( ( $true
= ( subset @ sK399 @ X5 ) )
& ( $true
= ( in @ X5 @ ( powerset @ sK398 ) ) )
& ( $true
!= ( subset @ ( setminus @ sK398 @ X5 ) @ ( setminus @ sK398 @ sK399 ) ) ) )
=> ( ( ( subset @ sK399 @ sK400 )
= $true )
& ( $true
= ( in @ sK400 @ ( powerset @ sK398 ) ) )
& ( ( subset @ ( setminus @ sK398 @ sK400 ) @ ( setminus @ sK398 @ sK399 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1718,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT2 != $true ) )
& ( ( contrasubsetT2 = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( $true
= ( in @ X5 @ ( powerset @ X3 ) ) )
& ( $true
!= ( subset @ ( setminus @ X3 @ X5 ) @ ( setminus @ X3 @ X4 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1717]) ).
thf(f1717,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT2 != $true ) )
& ( ( contrasubsetT2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( $true
!= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f950]) ).
thf(f950,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( contrasubsetT2 = $true ) ),
inference(flattening,[status(thm)],[f949]) ).
thf(f949,plain,
( ( contrasubsetT2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) )
| ( $true
!= ( subset @ X1 @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f368]) ).
thf(f368,plain,
( ( contrasubsetT2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( $true
= ( subset @ X1 @ X2 ) )
=> ( $true
= ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f367]) ).
thf(f367,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) ) )
= contrasubsetT2 ),
inference(rectify,[status(thm)],[f246]) ).
thf(f246,axiom,
! [X3: $i,X11: $i] :
( ( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ( subset @ X11 @ X16 )
=> ( subset @ ( setminus @ X3 @ X16 ) @ ( setminus @ X3 @ X11 ) ) ) ) )
= contrasubsetT2 ),
file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',contrasubsetT2) ).
thf(f3844,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( setminus @ sK665 @ sK664 ) )
!= $true )
| ( $true
!= ( subset @ sK666 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f3839,f3236]) ).
thf(f3236,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f2137]) ).
thf(f3839,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( setminus @ sK665 @ sK664 ) )
!= $true )
| ( subsetTrans != $true )
| ( $true
!= ( subset @ sK666 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3836]) ).
thf(f3836,plain,
! [X0: $i] :
( ( subsetTrans != $true )
| ( $true != $true )
| ( $true
!= ( subset @ sK666 @ X0 ) )
| ( ( subset @ X0 @ ( setminus @ sK665 @ sK664 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f3273,f2583]) ).
thf(f2583,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( subsetTrans != $true )
| ( ( subset @ X5 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1390]) ).
thf(f1390,plain,
( ( ( subsetTrans = $true )
| ( ( ( subset @ sK177 @ sK176 )
= $true )
& ( ( subset @ sK175 @ sK177 )
= $true )
& ( ( subset @ sK175 @ sK176 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ( subsetTrans != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176,sK177])],[f1388,f1389]) ).
thf(f1389,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) )
=> ( ( ( subset @ sK177 @ sK176 )
= $true )
& ( ( subset @ sK175 @ sK177 )
= $true )
& ( ( subset @ sK175 @ sK176 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1388,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X3 @ X5 )
!= $true )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ( subsetTrans != $true ) ) ),
inference(rectify,[status(thm)],[f1387]) ).
thf(f1387,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X0 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( subsetTrans != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1082]) ).
thf(f1082,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X0 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f1081]) ).
thf(f1081,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f364]) ).
thf(f364,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
=> ( ( $true
= ( subset @ X2 @ X1 ) )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f363]) ).
thf(f363,plain,
( subsetTrans
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X0 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
( subsetTrans
= ( ! [X3: $i,X5: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',subsetTrans) ).
thf(f3273,plain,
( ( subset @ sK666 @ ( setminus @ sK665 @ sK664 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f2137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU737^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:32:52 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU737^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.29/0.45 % subset X (setminus A Y) -> subset Y (setminus A X)))
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.45 % Source : [Bro08]
% 0.29/0.45 % Names : ZFC239g [Bro08]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 549 ( 257 unt; 291 typ; 257 def)
% 0.29/0.45 % Number of atoms : 1483 ( 383 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 257 ( 5 avg)
% 0.29/0.45 % Number of connectives : 2972 ( 65 ~; 12 |; 44 &;2116 @)
% 0.29/0.45 % ( 14 <=>; 721 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 263 ( 2 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 294 ( 291 usr; 257 con; 0-4 aty)
% 0.29/0.45 % Number of variables : 863 ( 74 ^; 754 !; 35 ?; 863 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : http://mathgate.info/detsetitem.php?id=299
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(in_type,type,
% 0.29/0.45 in: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu_type,type,
% 0.29/0.45 exu: ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu,definition,
% 0.29/0.45 ( exu
% 0.29/0.45 = ( ^ [Xphi: $i > $o] :
% 0.29/0.45 ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx_type,type,
% 0.29/0.45 setextAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx,definition,
% 0.29/0.45 ( setextAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 <=> ( in @ Xx @ B ) )
% 0.29/0.45 => ( A = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset_type,type,
% 0.29/0.45 emptyset: $i ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx_type,type,
% 0.29/0.45 emptysetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx,definition,
% 0.29/0.45 ( emptysetAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin_type,type,
% 0.29/0.45 setadjoin: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx_type,type,
% 0.29/0.45 setadjoinAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx,definition,
% 0.29/0.45 ( setadjoinAx
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 <=> ( ( Xy = Xx )
% 0.29/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powerset_type,type,
% 0.29/0.45 powerset: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx_type,type,
% 0.29/0.45 powersetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx,definition,
% 0.29/0.45 ( powersetAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.45 <=> ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunion_type,type,
% 0.29/0.45 setunion: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx_type,type,
% 0.29/0.45 setunionAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx,definition,
% 0.29/0.45 ( setunionAx
% 0.29/0.45 = ( ! [A: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.45 <=> ? [B: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omega_type,type,
% 0.29/0.45 omega: $i ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax_type,type,
% 0.29/0.45 omega0Ax: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax,definition,
% 0.29/0.45 ( omega0Ax
% 0.29/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx_type,type,
% 0.29/0.45 omegaSAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx,definition,
% 0.29/0.45 ( omegaSAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx_type,type,
% 0.29/0.45 omegaIndAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx,definition,
% 0.29/0.45 ( omegaIndAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( ( in @ emptyset @ A )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( ( in @ Xx @ omega )
% 0.29/0.45 & ( in @ Xx @ A ) )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(replAx_type,type,
% 0.29/0.45 replAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(replAx,definition,
% 0.29/0.45 ( replAx
% 0.29/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 <=> ? [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ A )
% 0.29/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx_type,type,
% 0.29/0.45 foundationAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx,definition,
% 0.29/0.45 ( foundationAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ( ( in @ B @ A )
% 0.29/0.45 & ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx_type,type,
% 0.29/0.45 wellorderingAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx,definition,
% 0.29/0.45 ( wellorderingAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ? [B: $i] :
% 0.29/0.45 ( ! [C: $i] :
% 0.29/0.45 ( ( in @ C @ B )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1_type,type,
% 0.29/0.46 ubforcartprodlem1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,definition,
% 0.29/0.46 ( ubforcartprodlem1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2_type,type,
% 0.29/0.46 ubforcartprodlem2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2,definition,
% 0.29/0.46 ( ubforcartprodlem2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3_type,type,
% 0.29/0.46 ubforcartprodlem3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3,definition,
% 0.29/0.46 ( ubforcartprodlem3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin_type,type,
% 0.29/0.46 cartprodpairin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin,definition,
% 0.29/0.46 ( cartprodpairin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1_type,type,
% 0.29/0.46 cartprodmempair1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1,definition,
% 0.29/0.46 ( cartprodmempair1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 & ( Xu
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair_type,type,
% 0.29/0.46 cartprodmempair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair,definition,
% 0.29/0.46 ( cartprodmempair
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1_type,type,
% 0.29/0.46 setunionsingleton1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,definition,
% 0.29/0.46 ( setunionsingleton1
% 0.29/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2_type,type,
% 0.29/0.46 setunionsingleton2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2,definition,
% 0.29/0.46 ( setunionsingleton2
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton_type,type,
% 0.29/0.46 setunionsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton,definition,
% 0.29/0.46 ( setunionsingleton
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop_type,type,
% 0.29/0.46 singletonprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,definition,
% 0.29/0.46 ( singletonprop
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1_type,type,
% 0.29/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1,definition,
% 0.29/0.46 ( ex1
% 0.29/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1_type,type,
% 0.29/0.46 ex1E1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1,definition,
% 0.29/0.46 ( ex1E1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I_type,type,
% 0.29/0.46 ex1I: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I,definition,
% 0.29/0.46 ( ex1I
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xy = Xx ) ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2_type,type,
% 0.29/0.46 ex1I2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2,definition,
% 0.29/0.46 ( ex1I2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq_type,type,
% 0.29/0.46 singletonsuniq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq,definition,
% 0.29/0.46 ( singletonsuniq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(atmost1p_type,type,
% 0.29/0.46 atmost1p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atleast2p_type,type,
% 0.29/0.46 atleast2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atmost2p_type,type,
% 0.29/0.46 atmost2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetp_type,type,
% 0.29/0.46 upairsetp: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1_type,type,
% 0.29/0.46 setukpairinjL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1,definition,
% 0.29/0.46 ( setukpairinjL1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton_type,type,
% 0.29/0.46 kfstsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton,definition,
% 0.29/0.46 ( kfstsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theprop_type,type,
% 0.29/0.46 theprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theprop,definition,
% 0.29/0.46 ( theprop
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfst_type,type,
% 0.29/0.46 kfst: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq_type,type,
% 0.29/0.46 kfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq,definition,
% 0.29/0.46 ( kfstpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin_type,type,
% 0.29/0.46 cartprodfstin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin,definition,
% 0.29/0.46 ( cartprodfstin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2_type,type,
% 0.29/0.46 setukpairinjL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2,definition,
% 0.29/0.46 ( setukpairinjL2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL_type,type,
% 0.29/0.46 setukpairinjL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL,definition,
% 0.29/0.46 ( setukpairinjL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11_type,type,
% 0.29/0.46 setukpairinjR11: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11,definition,
% 0.29/0.46 ( setukpairinjR11
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12_type,type,
% 0.29/0.46 setukpairinjR12: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12,definition,
% 0.29/0.46 ( setukpairinjR12
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1_type,type,
% 0.29/0.46 setukpairinjR1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1,definition,
% 0.29/0.46 ( setukpairinjR1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xu )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq_type,type,
% 0.29/0.46 upairequniteq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq,definition,
% 0.29/0.46 ( upairequniteq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2_type,type,
% 0.29/0.46 setukpairinjR2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2,definition,
% 0.29/0.46 ( setukpairinjR2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR_type,type,
% 0.29/0.46 setukpairinjR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR,definition,
% 0.29/0.46 ( setukpairinjR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton_type,type,
% 0.29/0.46 ksndsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton,definition,
% 0.29/0.46 ( ksndsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] :
% 0.29/0.46 ( Xu
% 0.29/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksnd_type,type,
% 0.29/0.46 ksnd: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq_type,type,
% 0.29/0.46 ksndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq,definition,
% 0.29/0.46 ( ksndpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq_type,type,
% 0.29/0.46 kpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq,definition,
% 0.29/0.46 ( kpairsurjEq
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin_type,type,
% 0.29/0.46 cartprodsndin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin,definition,
% 0.29/0.46 ( cartprodsndin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL_type,type,
% 0.29/0.46 cartprodpairmemEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL,definition,
% 0.29/0.46 ( cartprodpairmemEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER_type,type,
% 0.29/0.46 cartprodpairmemER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER,definition,
% 0.29/0.46 ( cartprodpairmemER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq_type,type,
% 0.29/0.46 cartprodmempaircEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq,definition,
% 0.29/0.46 ( cartprodmempaircEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq_type,type,
% 0.29/0.46 cartprodfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq,definition,
% 0.29/0.46 ( cartprodfstpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq_type,type,
% 0.29/0.46 cartprodsndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq,definition,
% 0.29/0.46 ( cartprodsndpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq_type,type,
% 0.29/0.46 cartprodpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq,definition,
% 0.29/0.46 ( cartprodpairsurjEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(breln_type,type,
% 0.29/0.46 breln: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(breln,definition,
% 0.29/0.46 ( breln
% 0.29/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstr_type,type,
% 0.29/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI_type,type,
% 0.29/0.46 dpsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI,definition,
% 0.29/0.46 ( dpsetconstrI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub_type,type,
% 0.29/0.46 dpsetconstrSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub,definition,
% 0.29/0.46 ( dpsetconstrSub
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln_type,type,
% 0.29/0.46 setOfPairsIsBReln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln,definition,
% 0.29/0.46 ( setOfPairsIsBReln
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( breln @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa_type,type,
% 0.29/0.46 dpsetconstrERa: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa,definition,
% 0.29/0.46 ( dpsetconstrERa
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1_type,type,
% 0.29/0.46 dpsetconstrEL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1,definition,
% 0.29/0.46 ( dpsetconstrEL1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2_type,type,
% 0.29/0.46 dpsetconstrEL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2,definition,
% 0.29/0.46 ( dpsetconstrEL2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER_type,type,
% 0.29/0.46 dpsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER,definition,
% 0.29/0.46 ( dpsetconstrER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(func_type,type,
% 0.29/0.46 func: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcSet_type,type,
% 0.29/0.46 funcSet: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton_type,type,
% 0.29/0.46 funcImageSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton,definition,
% 0.29/0.46 ( funcImageSingleton
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(apProp_type,type,
% 0.29/0.46 apProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(apProp,definition,
% 0.29/0.46 ( apProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( setunion
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.46 @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap_type,type,
% 0.29/0.46 ap: $i > $i > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(app_type,type,
% 0.29/0.46 app: $o ).
% 0.29/0.46
% 0.29/0.46 thf(app,definition,
% 0.29/0.46 ( app
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc_type,type,
% 0.29/0.46 infuncsetfunc: $o ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc,definition,
% 0.29/0.46 ( infuncsetfunc
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p_type,type,
% 0.29/0.46 ap2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p,definition,
% 0.29/0.46 ( ap2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset_type,type,
% 0.29/0.46 funcinfuncset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset,definition,
% 0.29/0.46 ( funcinfuncset
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp_type,type,
% 0.29/0.46 lamProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp,definition,
% 0.29/0.46 ( lamProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam_type,type,
% 0.29/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(lamp_type,type,
% 0.29/0.46 lamp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamp,definition,
% 0.29/0.46 ( lamp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p_type,type,
% 0.29/0.46 lam2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p,definition,
% 0.29/0.46 ( lam2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1_type,type,
% 0.29/0.46 brelnall1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1,definition,
% 0.29/0.46 ( brelnall1
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2_type,type,
% 0.29/0.46 brelnall2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2,definition,
% 0.29/0.46 ( brelnall2
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2_type,type,
% 0.29/0.46 ex1E2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2,definition,
% 0.29/0.46 ( ex1E2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1_type,type,
% 0.29/0.46 funcGraphProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1,definition,
% 0.29/0.46 ( funcGraphProp1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3_type,type,
% 0.29/0.46 funcGraphProp3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3,definition,
% 0.29/0.46 ( funcGraphProp3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2_type,type,
% 0.29/0.46 funcGraphProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2,definition,
% 0.29/0.46 ( funcGraphProp2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem_type,type,
% 0.29/0.46 funcextLem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem,definition,
% 0.29/0.46 ( funcextLem
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4_type,type,
% 0.29/0.46 funcGraphProp4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4,definition,
% 0.29/0.46 ( funcGraphProp4
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln_type,type,
% 0.29/0.46 subbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln,definition,
% 0.29/0.46 ( subbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln_type,type,
% 0.29/0.46 eqbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln,definition,
% 0.29/0.46 ( eqbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext_type,type,
% 0.29/0.46 funcext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext,definition,
% 0.29/0.46 ( funcext
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2_type,type,
% 0.29/0.46 funcext2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2,definition,
% 0.29/0.46 ( funcext2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1_type,type,
% 0.29/0.46 ap2apEq1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1,definition,
% 0.29/0.46 ( ap2apEq1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2_type,type,
% 0.29/0.46 ap2apEq2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2,definition,
% 0.29/0.46 ( ap2apEq2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta1_type,type,
% 0.29/0.46 beta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta1,definition,
% 0.29/0.46 ( beta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta1_type,type,
% 0.29/0.46 eta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta1,definition,
% 0.29/0.46 ( eta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq_type,type,
% 0.29/0.46 lam2lamEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq,definition,
% 0.29/0.46 ( lam2lamEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 = ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta2_type,type,
% 0.29/0.46 beta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta2,definition,
% 0.29/0.46 ( beta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta2_type,type,
% 0.29/0.46 eta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta2,definition,
% 0.29/0.46 ( eta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1_type,type,
% 0.29/0.46 iffalseProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1,definition,
% 0.29/0.46 ( iffalseProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( in @ Xy
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2_type,type,
% 0.29/0.46 iffalseProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2,definition,
% 0.29/0.46 ( iffalseProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1_type,type,
% 0.29/0.46 iftrueProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1,definition,
% 0.29/0.46 ( iftrueProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2_type,type,
% 0.29/0.46 iftrueProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2,definition,
% 0.29/0.46 ( iftrueProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton_type,type,
% 0.29/0.46 ifSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton,definition,
% 0.29/0.46 ( ifSingleton
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(if_type,type,
% 0.29/0.46 if: $i > $o > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ifp_type,type,
% 0.29/0.46 ifp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifp,definition,
% 0.29/0.46 ( ifp
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theeq_type,type,
% 0.29/0.46 theeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theeq,definition,
% 0.29/0.46 ( theeq
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ X )
% 0.29/0.46 => ( ( setunion @ X )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue_type,type,
% 0.29/0.46 iftrue: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue,definition,
% 0.29/0.46 ( iftrue
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse_type,type,
% 0.29/0.46 iffalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse,definition,
% 0.29/0.46 ( iffalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse_type,type,
% 0.29/0.46 iftrueorfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse,definition,
% 0.29/0.46 ( iftrueorfalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem_type,type,
% 0.29/0.46 binintersectT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem,definition,
% 0.29/0.46 ( binintersectT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem_type,type,
% 0.29/0.46 binunionT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem,definition,
% 0.29/0.46 ( binunionT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem_type,type,
% 0.29/0.46 powersetT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem,definition,
% 0.29/0.46 ( powersetT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem_type,type,
% 0.29/0.46 setminusT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem,definition,
% 0.29/0.46 ( setminusT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem_type,type,
% 0.29/0.46 complementT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem,definition,
% 0.29/0.46 ( complementT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextT_type,type,
% 0.29/0.46 setextT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextT,definition,
% 0.29/0.46 ( setextT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ X ) ) )
% 0.29/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI_type,type,
% 0.29/0.46 subsetTI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI,definition,
% 0.29/0.46 ( subsetTI
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1_type,type,
% 0.29/0.46 powersetTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1,definition,
% 0.29/0.46 ( powersetTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1_type,type,
% 0.29/0.46 powersetTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1,definition,
% 0.29/0.46 ( powersetTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ X @ ( powerset @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1_type,type,
% 0.29/0.46 complementTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1,definition,
% 0.29/0.46 ( complementTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1_type,type,
% 0.29/0.46 complementTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1,definition,
% 0.29/0.46 ( complementTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra_type,type,
% 0.29/0.46 binintersectTELcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra,definition,
% 0.29/0.46 ( binintersectTELcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra_type,type,
% 0.29/0.46 binintersectTERcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra,definition,
% 0.29/0.46 ( binintersectTERcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT_type,type,
% 0.29/0.46 contrasubsetT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT,definition,
% 0.29/0.46 ( contrasubsetT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1_type,type,
% 0.29/0.46 contrasubsetT1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1,definition,
% 0.29/0.46 ( contrasubsetT1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2_type,type,
% 0.29/0.46 contrasubsetT2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2,definition,
% 0.29/0.46 ( contrasubsetT2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3_type,type,
% 0.29/0.46 contrasubsetT3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3,definition,
% 0.29/0.46 ( contrasubsetT3
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1_type,type,
% 0.29/0.46 doubleComplementI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1,definition,
% 0.29/0.46 ( doubleComplementI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1_type,type,
% 0.29/0.46 doubleComplementE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1,definition,
% 0.29/0.46 ( doubleComplementE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1_type,type,
% 0.29/0.46 doubleComplementSub1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1,definition,
% 0.29/0.46 ( doubleComplementSub1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2_type,type,
% 0.29/0.46 doubleComplementSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2,definition,
% 0.29/0.46 ( doubleComplementSub2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq_type,type,
% 0.29/0.46 doubleComplementEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq,definition,
% 0.29/0.46 ( doubleComplementEq
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( X
% 0.29/0.46 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT_type,type,
% 0.29/0.46 complementTnotintersectT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT,definition,
% 0.29/0.46 ( complementTnotintersectT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect_type,type,
% 0.29/0.46 complementImpComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect,definition,
% 0.29/0.46 ( complementImpComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect_type,type,
% 0.29/0.46 complementSubsetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect,definition,
% 0.29/0.46 ( complementSubsetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect_type,type,
% 0.29/0.46 complementInPowersetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect,definition,
% 0.29/0.46 ( complementInPowersetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement_type,type,
% 0.29/0.46 contraSubsetComplement: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement,definition,
% 0.29/0.46 ( contraSubsetComplement
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTcontraSubset,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ( sepSubset
% 0.29/0.46 => ( binunionIL
% 0.29/0.46 => ( upairset2IR
% 0.29/0.46 => ( binunionIR
% 0.29/0.46 => ( binunionEcases
% 0.29/0.46 => ( binunionE
% 0.29/0.46 => ( binunionLsub
% 0.29/0.46 => ( binunionRsub
% 0.29/0.46 => ( binintersectI
% 0.29/0.46 => ( binintersectSubset5
% 0.29/0.46 => ( binintersectEL
% 0.29/0.46 => ( binintersectLsub
% 0.29/0.46 => ( binintersectSubset2
% 0.29/0.46 => ( binintersectSubset3
% 0.29/0.46 => ( binintersectER
% 0.29/0.46 => ( disjointsetsI1
% 0.29/0.46 => ( binintersectRsub
% 0.29/0.46 => ( binintersectSubset4
% 0.29/0.46 => ( binintersectSubset1
% 0.29/0.46 => ( bs114d
% 0.29/0.46 => ( setminusI
% 0.29/0.46 => ( setminusEL
% 0.29/0.46 => ( setminusER
% 0.29/0.46 => ( setminusSubset2
% 0.29/0.46 => ( setminusERneg
% 0.29/0.46 => ( setminusELneg
% 0.29/0.46 => ( setminusILneg
% 0.29/0.46 => ( setminusIRneg
% 0.29/0.46 => ( setminusLsub
% 0.29/0.46 => ( setminusSubset1
% 0.29/0.46 => ( symdiffE
% 0.29/0.46 => ( symdiffI1
% 0.29/0.46 => ( symdiffI2
% 0.29/0.46 => ( symdiffIneg1
% 0.29/0.46 => ( symdiffIneg2
% 0.29/0.46 => ( secondinupair
% 0.29/0.46 => ( setukpairIL
% 0.29/0.46 => ( setukpairIR
% 0.29/0.46 => ( kpairiskpair
% 0.29/0.46 => ( kpairp
% 0.29/0.46 => ( singletonsubset
% 0.29/0.46 => ( singletoninpowerset
% 0.29/0.46 => ( singletoninpowunion
% 0.29/0.46 => ( upairset2E
% 0.29/0.46 => ( upairsubunion
% 0.29/0.46 => ( upairinpowunion
% 0.29/0.46 => ( ubforcartprodlem1
% 0.29/0.46 => ( ubforcartprodlem2
% 0.29/0.46 => ( ubforcartprodlem3
% 0.29/0.46 => ( cartprodpairin
% 0.29/0.46 => ( cartprodmempair1
% 0.29/0.46 => ( cartprodmempair
% 0.29/0.46 => ( setunionE2
% 0.29/0.46 => ( setunionsingleton1
% 0.29/0.46 => ( setunionsingleton2
% 0.29/0.46 => ( setunionsingleton
% 0.29/0.46 => ( singletonprop
% 0.29/0.46 => ( ex1E1
% 0.29/0.46 => ( ex1I
% 0.29/0.46 => ( ex1I2
% 0.29/0.46 => ( singletonsuniq
% 0.29/0.46 => ( setukpairinjL1
% 0.29/0.46 => ( kfstsingleton
% 0.29/0.46 => ( theprop
% 0.29/0.46 => ( kfstpairEq
% 0.29/0.46 => ( cartprodfstin
% 0.29/0.46 => ( setukpairinjL2
% 0.29/0.46 => ( setukpairinjL
% 0.29/0.46 => ( setukpairinjR11
% 0.29/0.46 => ( setukpairinjR12
% 0.29/0.46 => ( setukpairinjR1
% 0.29/0.46 => ( upairequniteq
% 0.29/0.46 => ( setukpairinjR2
% 0.29/0.46 => ( setukpairinjR
% 0.29/0.46 => ( ksndsingleton
% 0.29/0.46 => ( ksndpairEq
% 0.29/0.46 => ( kpairsurjEq
% 0.29/0.46 => ( cartprodsndin
% 0.29/0.46 => ( cartprodpairmemEL
% 0.29/0.46 => ( cartprodpairmemER
% 0.29/0.46 => ( cartprodmempaircEq
% 0.29/0.46 => ( cartprodfstpairEq
% 0.29/0.46 => ( cartprodsndpairEq
% 0.29/0.46 => ( cartprodpairsurjEq
% 0.29/0.46 => ( dpsetconstrI
% 0.29/0.46 => ( dpsetconstrSub
% 0.29/0.46 => ( setOfPairsIsBReln
% 0.29/0.46 => ( dpsetconstrERa
% 0.29/0.46 => ( dpsetconstrEL1
% 0.29/0.46 => ( dpsetconstrEL2
% 0.29/0.46 => ( dpsetconstrER
% 0.29/0.46 => ( funcImageSingleton
% 0.29/0.46 => ( apProp
% 0.29/0.46 => ( app
% 0.29/0.46 => ( infuncsetfunc
% 0.29/0.46 => ( ap2p
% 0.29/0.46 => ( funcinfuncset
% 0.29/0.46 => ( lamProp
% 0.29/0.46 => ( lamp
% 0.29/0.46 => ( lam2p
% 0.29/0.46 => ( brelnall1
% 0.29/0.46 => ( brelnall2
% 0.29/0.46 => ( ex1E2
% 0.29/0.46 => ( funcGraphProp1
% 0.29/0.46 => ( funcGraphProp3
% 0.29/0.46 => ( funcGraphProp2
% 0.29/0.46 => ( funcextLem
% 0.29/0.46 => ( funcGraphProp4
% 0.29/0.46 => ( subbreln
% 0.29/0.46 => ( eqbreln
% 0.29/0.46 => ( funcext
% 0.29/0.46 => ( funcext2
% 0.29/0.46 => ( ap2apEq1
% 0.29/0.46 => ( ap2apEq2
% 0.29/0.46 => ( beta1
% 0.29/0.46 => ( eta1
% 0.29/0.46 => ( lam2lamEq
% 0.29/0.46 => ( beta2
% 0.29/0.46 => ( eta2
% 0.29/0.46 => ( iffalseProp1
% 0.29/0.46 => ( iffalseProp2
% 0.29/0.46 => ( iftrueProp1
% 0.29/0.46 => ( iftrueProp2
% 0.29/0.46 => ( ifSingleton
% 0.29/0.46 => ( ifp
% 0.29/0.46 => ( theeq
% 0.29/0.46 => ( iftrue
% 0.29/0.46 => ( iffalse
% 0.29/0.46 => ( iftrueorfalse
% 0.29/0.46 => ( binintersectT_lem
% 0.29/0.46 => ( binunionT_lem
% 0.29/0.46 => ( powersetT_lem
% 0.29/0.46 => ( setminusT_lem
% 0.29/0.46 => ( complementT_lem
% 0.29/0.46 => ( setextT
% 0.29/0.46 => ( subsetTI
% 0.29/0.46 => ( powersetTI1
% 0.29/0.46 => ( powersetTE1
% 0.29/0.46 => ( complementTI1
% 0.29/0.46 => ( complementTE1
% 0.29/0.46 => ( binintersectTELcontra
% 0.29/0.46 => ( binintersectTERcontra
% 0.29/0.46 => ( contrasubsetT
% 0.29/0.46 => ( contrasubsetT1
% 0.29/0.46 => ( contrasubsetT2
% 0.29/0.46 => ( contrasubsetT3
% 0.29/0.46 => ( doubleComplementI1
% 0.29/0.46 => ( doubleComplementE1
% 0.29/0.46 => ( doubleComplementSub1
% 0.29/0.46 => ( doubleComplementSub2
% 0.29/0.46 => ( doubleComplementEq
% 0.29/0.46 => ( complementTnotintersectT
% 0.29/0.46 => ( complementImpComplementIntersect
% 0.29/0.46 => ( complementSubsetComplementIntersect
% 0.29/0.46 => ( complementInPowersetComplementIntersect
% 0.29/0.46 => ( contraSubsetComplement
% 0.29/0.46 => ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.86/1.51 ---- Embedded in THF ---
% 2.86/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.86/1.51 %%% Generated on Tue Feb 24 12:32:53 EST 2026
% 2.86/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.86/1.51 %%% Logic specification used:
% 2.86/1.51 %%% thf(spec, logic, $$dhol).
% 2.86/1.51
% 2.86/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2DTF23392.p
% See solution above
% 2.86/1.51 ------------------------
% 2.86/1.55 ---- Cleaned THF ---
% 2.86/1.55 thf(in_type,type,
% 2.86/1.55 in: $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(exu_type,type,
% 2.86/1.55 exu: ( $i > $o ) > $o ).
% 2.86/1.55
% 2.86/1.55 thf(exu,definition,
% 2.86/1.55 ( exu
% 2.86/1.55 = ( ^ [Xphi: $i > $o] :
% 2.86/1.55 ? [Xx: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 & ! [Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setextAx_type,type,
% 2.86/1.55 setextAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setextAx,definition,
% 2.86/1.55 ( setextAx
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 <=> ( in @ Xx @ B ) )
% 2.86/1.55 => ( A = B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyset_type,type,
% 2.86/1.55 emptyset: $i ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetAx_type,type,
% 2.86/1.55 emptysetAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetAx,definition,
% 2.86/1.55 ( emptysetAx
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoin_type,type,
% 2.86/1.55 setadjoin: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinAx_type,type,
% 2.86/1.55 setadjoinAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinAx,definition,
% 2.86/1.55 ( setadjoinAx
% 2.86/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.86/1.55 <=> ( ( Xy = Xx )
% 2.86/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powerset_type,type,
% 2.86/1.55 powerset: $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(powersetAx_type,type,
% 2.86/1.55 powersetAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetAx,definition,
% 2.86/1.55 ( powersetAx
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.86/1.55 <=> ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunion_type,type,
% 2.86/1.55 setunion: $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(setunionAx_type,type,
% 2.86/1.55 setunionAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionAx,definition,
% 2.86/1.55 ( setunionAx
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.86/1.55 <=> ? [B: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 & ( in @ B @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(omega_type,type,
% 2.86/1.55 omega: $i ).
% 2.86/1.55
% 2.86/1.55 thf(omega0Ax_type,type,
% 2.86/1.55 omega0Ax: $o ).
% 2.86/1.55
% 2.86/1.55 thf(omega0Ax,definition,
% 2.86/1.55 ( omega0Ax
% 2.86/1.55 = ( in @ emptyset @ omega ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(omegaSAx_type,type,
% 2.86/1.55 omegaSAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(omegaSAx,definition,
% 2.86/1.55 ( omegaSAx
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ omega )
% 2.86/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(omegaIndAx_type,type,
% 2.86/1.55 omegaIndAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(omegaIndAx,definition,
% 2.86/1.55 ( omegaIndAx
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ( ( in @ emptyset @ A )
% 2.86/1.55 & ! [Xx: $i] :
% 2.86/1.55 ( ( ( in @ Xx @ omega )
% 2.86/1.55 & ( in @ Xx @ A ) )
% 2.86/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ omega )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(replAx_type,type,
% 2.86/1.55 replAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(replAx,definition,
% 2.86/1.55 ( replAx
% 2.86/1.55 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( exu
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.86/1.55 => ? [B: $i] :
% 2.86/1.55 ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 <=> ? [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(foundationAx_type,type,
% 2.86/1.55 foundationAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(foundationAx,definition,
% 2.86/1.55 ( foundationAx
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.86/1.55 => ? [B: $i] :
% 2.86/1.55 ( ( in @ B @ A )
% 2.86/1.55 & ~ ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(wellorderingAx_type,type,
% 2.86/1.55 wellorderingAx: $o ).
% 2.86/1.55
% 2.86/1.55 thf(wellorderingAx,definition,
% 2.86/1.55 ( wellorderingAx
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ? [B: $i] :
% 2.86/1.55 ( ! [C: $i] :
% 2.86/1.55 ( ( in @ C @ B )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ C )
% 2.86/1.55 => ( in @ Xx @ A ) ) )
% 2.86/1.55 & ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( ( in @ Xx @ A )
% 2.86/1.55 & ( in @ Xy @ A ) )
% 2.86/1.55 => ( ! [C: $i] :
% 2.86/1.55 ( ( in @ C @ B )
% 2.86/1.55 => ( ( in @ Xx @ C )
% 2.86/1.55 <=> ( in @ Xy @ C ) ) )
% 2.86/1.55 => ( Xx = Xy ) ) )
% 2.86/1.55 & ! [C: $i,D: $i] :
% 2.86/1.55 ( ( ( in @ C @ B )
% 2.86/1.55 & ( in @ D @ B ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ C )
% 2.86/1.55 => ( in @ Xx @ D ) )
% 2.86/1.55 | ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ D )
% 2.86/1.55 => ( in @ Xx @ C ) ) ) )
% 2.86/1.55 & ! [C: $i] :
% 2.86/1.55 ( ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ C )
% 2.86/1.55 => ( in @ Xx @ A ) )
% 2.86/1.55 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.86/1.55 => ? [D: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ D @ B )
% 2.86/1.55 & ( in @ Xx @ C )
% 2.86/1.55 & ~ ? [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ D )
% 2.86/1.55 & ( in @ Xy @ C ) )
% 2.86/1.55 & ! [E: $i] :
% 2.86/1.55 ( ( in @ E @ B )
% 2.86/1.55 => ( ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ E )
% 2.86/1.55 => ( in @ Xy @ D ) )
% 2.86/1.55 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(descr_type,type,
% 2.86/1.55 descr: ( $i > $o ) > $i ).
% 2.86/1.55
% 2.86/1.55 thf(descrp_type,type,
% 2.86/1.55 descrp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(descrp,definition,
% 2.86/1.55 ( descrp
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ( Xphi
% 2.86/1.55 @ ( descr
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstr_type,type,
% 2.86/1.55 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrI_type,type,
% 2.86/1.55 dsetconstrI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrI,definition,
% 2.86/1.55 ( dsetconstrI
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( in @ Xx
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrEL_type,type,
% 2.86/1.55 dsetconstrEL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrEL,definition,
% 2.86/1.55 ( dsetconstrEL
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrER_type,type,
% 2.86/1.55 dsetconstrER: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstrER,definition,
% 2.86/1.55 ( dsetconstrER
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.86/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuE1_type,type,
% 2.86/1.55 exuE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuE1,definition,
% 2.86/1.55 ( exuE1
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 & ! [Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(prop2set_type,type,
% 2.86/1.55 prop2set: $o > $i ).
% 2.86/1.55
% 2.86/1.55 thf(prop2setE_type,type,
% 2.86/1.55 prop2setE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(prop2setE,definition,
% 2.86/1.55 ( prop2setE
% 2.86/1.55 = ( ! [Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.86/1.55 => Xphi ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetE_type,type,
% 2.86/1.55 emptysetE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetE,definition,
% 2.86/1.55 ( emptysetE
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ emptyset )
% 2.86/1.55 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetimpfalse_type,type,
% 2.86/1.55 emptysetimpfalse: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetimpfalse,definition,
% 2.86/1.55 ( emptysetimpfalse
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ emptyset )
% 2.86/1.55 => $false ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notinemptyset_type,type,
% 2.86/1.55 notinemptyset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notinemptyset,definition,
% 2.86/1.55 ( notinemptyset
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuE3e_type,type,
% 2.86/1.55 exuE3e: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuE3e,definition,
% 2.86/1.55 ( exuE3e
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setext_type,type,
% 2.86/1.55 setext: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setext,definition,
% 2.86/1.55 ( setext
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ B ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ A ) )
% 2.86/1.55 => ( A = B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyI_type,type,
% 2.86/1.55 emptyI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyI,definition,
% 2.86/1.55 ( emptyI
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ~ ( in @ Xx @ A )
% 2.86/1.55 => ( A = emptyset ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(noeltsimpempty_type,type,
% 2.86/1.55 noeltsimpempty: $o ).
% 2.86/1.55
% 2.86/1.55 thf(noeltsimpempty,definition,
% 2.86/1.55 ( noeltsimpempty
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ~ ( in @ Xx @ A )
% 2.86/1.55 => ( A = emptyset ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setbeta_type,type,
% 2.86/1.55 setbeta: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setbeta,definition,
% 2.86/1.55 ( setbeta
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.86/1.55 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(nonempty_type,type,
% 2.86/1.55 nonempty: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(nonempty,definition,
% 2.86/1.55 ( nonempty
% 2.86/1.55 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyE1_type,type,
% 2.86/1.55 nonemptyE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyE1,definition,
% 2.86/1.55 ( nonemptyE1
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ( nonempty @ A )
% 2.86/1.55 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyI_type,type,
% 2.86/1.55 nonemptyI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyI,definition,
% 2.86/1.55 ( nonemptyI
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( nonempty
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyI1_type,type,
% 2.86/1.55 nonemptyI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyI1,definition,
% 2.86/1.55 ( nonemptyI1
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.86/1.55 => ( nonempty @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinIL_type,type,
% 2.86/1.55 setadjoinIL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinIL,definition,
% 2.86/1.55 ( setadjoinIL
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyinunitempty_type,type,
% 2.86/1.55 emptyinunitempty: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyinunitempty,definition,
% 2.86/1.55 ( emptyinunitempty
% 2.86/1.55 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinIR_type,type,
% 2.86/1.55 setadjoinIR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinIR,definition,
% 2.86/1.55 ( setadjoinIR
% 2.86/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinE_type,type,
% 2.86/1.55 setadjoinE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinE,definition,
% 2.86/1.55 ( setadjoinE
% 2.86/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.86/1.55 => ! [Xphi: $o] :
% 2.86/1.55 ( ( ( Xy = Xx )
% 2.86/1.55 => Xphi )
% 2.86/1.55 => ( ( ( in @ Xy @ A )
% 2.86/1.55 => Xphi )
% 2.86/1.55 => Xphi ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinOr_type,type,
% 2.86/1.55 setadjoinOr: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinOr,definition,
% 2.86/1.55 ( setadjoinOr
% 2.86/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.86/1.55 => ( ( Xy = Xx )
% 2.86/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setoftrueEq_type,type,
% 2.86/1.55 setoftrueEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setoftrueEq,definition,
% 2.86/1.55 ( setoftrueEq
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : $true )
% 2.86/1.55 = A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetI_type,type,
% 2.86/1.55 powersetI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetI,definition,
% 2.86/1.55 ( powersetI
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ A ) )
% 2.86/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyinPowerset_type,type,
% 2.86/1.55 emptyinPowerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyinPowerset,definition,
% 2.86/1.55 ( emptyinPowerset
% 2.86/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyInPowerset_type,type,
% 2.86/1.55 emptyInPowerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyInPowerset,definition,
% 2.86/1.55 ( emptyInPowerset
% 2.86/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetE_type,type,
% 2.86/1.55 powersetE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetE,definition,
% 2.86/1.55 ( powersetE
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.86/1.55 => ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionI_type,type,
% 2.86/1.55 setunionI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionI,definition,
% 2.86/1.55 ( setunionI
% 2.86/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( ( in @ B @ A )
% 2.86/1.55 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionE_type,type,
% 2.86/1.55 setunionE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionE,definition,
% 2.86/1.55 ( setunionE
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.86/1.55 => ! [Xphi: $o] :
% 2.86/1.55 ( ! [B: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( ( in @ B @ A )
% 2.86/1.55 => Xphi ) )
% 2.86/1.55 => Xphi ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subPowSU_type,type,
% 2.86/1.55 subPowSU: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subPowSU,definition,
% 2.86/1.55 ( subPowSU
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuE2_type,type,
% 2.86/1.55 exuE2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuE2,definition,
% 2.86/1.55 ( exuE2
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ! [Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xy )
% 2.86/1.55 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyImpWitness_type,type,
% 2.86/1.55 nonemptyImpWitness: $o ).
% 2.86/1.55
% 2.86/1.55 thf(nonemptyImpWitness,definition,
% 2.86/1.55 ( nonemptyImpWitness
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ( nonempty @ A )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & $true ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(uniqinunit_type,type,
% 2.86/1.55 uniqinunit: $o ).
% 2.86/1.55
% 2.86/1.55 thf(uniqinunit,definition,
% 2.86/1.55 ( uniqinunit
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notinsingleton_type,type,
% 2.86/1.55 notinsingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notinsingleton,definition,
% 2.86/1.55 ( notinsingleton
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx != Xy )
% 2.86/1.55 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eqinunit_type,type,
% 2.86/1.55 eqinunit: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eqinunit,definition,
% 2.86/1.55 ( eqinunit
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsswitch_type,type,
% 2.86/1.55 singletonsswitch: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsswitch,definition,
% 2.86/1.55 ( singletonsswitch
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.86/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetE_type,type,
% 2.86/1.55 upairsetE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetE,definition,
% 2.86/1.55 ( upairsetE
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.86/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.86/1.55 => ( ( Xz = Xx )
% 2.86/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetIL_type,type,
% 2.86/1.55 upairsetIL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetIL,definition,
% 2.86/1.55 ( upairsetIL
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetIR_type,type,
% 2.86/1.55 upairsetIR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetIR,definition,
% 2.86/1.55 ( upairsetIR
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyE1_type,type,
% 2.86/1.55 emptyE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyE1,definition,
% 2.86/1.55 ( emptyE1
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) )
% 2.86/1.55 => ( ( ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 = emptyset )
% 2.86/1.55 => $false ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(vacuousDall_type,type,
% 2.86/1.55 vacuousDall: $o ).
% 2.86/1.55
% 2.86/1.55 thf(vacuousDall,definition,
% 2.86/1.55 ( vacuousDall
% 2.86/1.55 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ emptyset )
% 2.86/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan1_type,type,
% 2.86/1.55 quantDeMorgan1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan1,definition,
% 2.86/1.55 ( quantDeMorgan1
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ~ ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan2_type,type,
% 2.86/1.55 quantDeMorgan2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan2,definition,
% 2.86/1.55 ( quantDeMorgan2
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ~ ( Xphi @ Xx ) )
% 2.86/1.55 => ~ ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan3_type,type,
% 2.86/1.55 quantDeMorgan3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan3,definition,
% 2.86/1.55 ( quantDeMorgan3
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ~ ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan4_type,type,
% 2.86/1.55 quantDeMorgan4: $o ).
% 2.86/1.55
% 2.86/1.55 thf(quantDeMorgan4,definition,
% 2.86/1.55 ( quantDeMorgan4
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ~ ( Xphi @ Xx ) )
% 2.86/1.55 => ~ ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(prop2setI_type,type,
% 2.86/1.55 prop2setI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(prop2setI,definition,
% 2.86/1.55 ( prop2setI
% 2.86/1.55 = ( ! [Xphi: $o] :
% 2.86/1.55 ( Xphi
% 2.86/1.55 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(set2prop_type,type,
% 2.86/1.55 set2prop: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(prop2set2propI_type,type,
% 2.86/1.55 prop2set2propI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(prop2set2propI,definition,
% 2.86/1.55 ( prop2set2propI
% 2.86/1.55 = ( ! [Xphi: $o] :
% 2.86/1.55 ( Xphi
% 2.86/1.55 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notdexE_type,type,
% 2.86/1.55 notdexE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notdexE,definition,
% 2.86/1.55 ( notdexE
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ~ ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notdallE_type,type,
% 2.86/1.55 notdallE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notdallE,definition,
% 2.86/1.55 ( notdallE
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ~ ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuI1_type,type,
% 2.86/1.55 exuI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuI1,definition,
% 2.86/1.55 ( exuI1
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ? [Xx: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 & ! [Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) )
% 2.86/1.55 => ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuI3_type,type,
% 2.86/1.55 exuI3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuI3,definition,
% 2.86/1.55 ( exuI3
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.86/1.55 => ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) )
% 2.86/1.55 => ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuI2_type,type,
% 2.86/1.55 exuI2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuI2,definition,
% 2.86/1.55 ( exuI2
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ? [Xx: $i] :
% 2.86/1.55 ! [Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xy )
% 2.86/1.55 <=> ( Xy = Xx ) )
% 2.86/1.55 => ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(inCongP_type,type,
% 2.86/1.55 inCongP: $o ).
% 2.86/1.55
% 2.86/1.55 thf(inCongP,definition,
% 2.86/1.55 ( inCongP
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(in__Cong_type,type,
% 2.86/1.55 in__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(in__Cong,definition,
% 2.86/1.55 ( in__Cong
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( in @ Xx @ A )
% 2.86/1.55 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuE3u_type,type,
% 2.86/1.55 exuE3u: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuE3u,definition,
% 2.86/1.55 ( exuE3u
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exu__Cong_type,type,
% 2.86/1.55 exu__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exu__Cong,definition,
% 2.86/1.55 ( exu__Cong
% 2.86/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.86/1.55 => ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 <=> ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptyset__Cong_type,type,
% 2.86/1.55 emptyset__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptyset__Cong,definition,
% 2.86/1.55 ( emptyset__Cong
% 2.86/1.55 = ( emptyset = emptyset ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoin__Cong_type,type,
% 2.86/1.55 setadjoin__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoin__Cong,definition,
% 2.86/1.55 ( setadjoin__Cong
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ! [Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( Xz = Xu )
% 2.86/1.55 => ( ( setadjoin @ Xx @ Xz )
% 2.86/1.55 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powerset__Cong_type,type,
% 2.86/1.55 powerset__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powerset__Cong,definition,
% 2.86/1.55 ( powerset__Cong
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ( ( powerset @ A )
% 2.86/1.55 = ( powerset @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunion__Cong_type,type,
% 2.86/1.55 setunion__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunion__Cong,definition,
% 2.86/1.55 ( setunion__Cong
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ( ( setunion @ A )
% 2.86/1.55 = ( setunion @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(omega__Cong_type,type,
% 2.86/1.55 omega__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(omega__Cong,definition,
% 2.86/1.55 ( omega__Cong
% 2.86/1.55 = ( omega = omega ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(exuEu_type,type,
% 2.86/1.55 exuEu: $o ).
% 2.86/1.55
% 2.86/1.55 thf(exuEu,definition,
% 2.86/1.55 ( exuEu
% 2.86/1.55 = ( ! [Xphi: $i > $o] :
% 2.86/1.55 ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(descr__Cong_type,type,
% 2.86/1.55 descr__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(descr__Cong,definition,
% 2.86/1.55 ( descr__Cong
% 2.86/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.86/1.55 => ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ( ( exu
% 2.86/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.86/1.55 => ( ( descr
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 = ( descr
% 2.86/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstr__Cong_type,type,
% 2.86/1.55 dsetconstr__Cong: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dsetconstr__Cong,definition,
% 2.86/1.55 ( dsetconstr__Cong
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( Xx = Xy )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.86/1.55 => ( ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 = ( dsetconstr @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subset_type,type,
% 2.86/1.55 subset: $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(disjoint_type,type,
% 2.86/1.55 disjoint: $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(setsmeet_type,type,
% 2.86/1.55 setsmeet: $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetI1_type,type,
% 2.86/1.55 subsetI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetI1,definition,
% 2.86/1.55 ( subsetI1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ B ) )
% 2.86/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eqimpsubset2_type,type,
% 2.86/1.55 eqimpsubset2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eqimpsubset2,definition,
% 2.86/1.55 ( eqimpsubset2
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eqimpsubset1_type,type,
% 2.86/1.55 eqimpsubset1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eqimpsubset1,definition,
% 2.86/1.55 ( eqimpsubset1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( A = B )
% 2.86/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetI2_type,type,
% 2.86/1.55 subsetI2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetI2,definition,
% 2.86/1.55 ( subsetI2
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ B ) )
% 2.86/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetsubset_type,type,
% 2.86/1.55 emptysetsubset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(emptysetsubset,definition,
% 2.86/1.55 ( emptysetsubset
% 2.86/1.55 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetE_type,type,
% 2.86/1.55 subsetE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetE,definition,
% 2.86/1.55 ( subsetE
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetE2_type,type,
% 2.86/1.55 subsetE2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetE2,definition,
% 2.86/1.55 ( subsetE2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notsubsetI_type,type,
% 2.86/1.55 notsubsetI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notsubsetI,definition,
% 2.86/1.55 ( notsubsetI
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notequalI1_type,type,
% 2.86/1.55 notequalI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notequalI1,definition,
% 2.86/1.55 ( notequalI1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ~ ( subset @ A @ B )
% 2.86/1.55 => ( A != B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(notequalI2_type,type,
% 2.86/1.55 notequalI2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(notequalI2,definition,
% 2.86/1.55 ( notequalI2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ( A != B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetRefl_type,type,
% 2.86/1.55 subsetRefl: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetRefl,definition,
% 2.86/1.55 ( subsetRefl
% 2.86/1.55 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetTrans_type,type,
% 2.86/1.55 subsetTrans: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetTrans,definition,
% 2.86/1.55 ( subsetTrans
% 2.86/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ( subset @ B @ C )
% 2.86/1.55 => ( subset @ A @ C ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinSub_type,type,
% 2.86/1.55 setadjoinSub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinSub,definition,
% 2.86/1.55 ( setadjoinSub
% 2.86/1.55 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinSub2_type,type,
% 2.86/1.55 setadjoinSub2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setadjoinSub2,definition,
% 2.86/1.55 ( setadjoinSub2
% 2.86/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subset2powerset_type,type,
% 2.86/1.55 subset2powerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subset2powerset,definition,
% 2.86/1.55 ( subset2powerset
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setextsub_type,type,
% 2.86/1.55 setextsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setextsub,definition,
% 2.86/1.55 ( setextsub
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ( subset @ B @ A )
% 2.86/1.55 => ( A = B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetemptysetimpeq_type,type,
% 2.86/1.55 subsetemptysetimpeq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetemptysetimpeq,definition,
% 2.86/1.55 ( subsetemptysetimpeq
% 2.86/1.55 = ( ! [A: $i] :
% 2.86/1.55 ( ( subset @ A @ emptyset )
% 2.86/1.55 => ( A = emptyset ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetI1_type,type,
% 2.86/1.55 powersetI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetI1,definition,
% 2.86/1.55 ( powersetI1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ B @ A )
% 2.86/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetE1_type,type,
% 2.86/1.55 powersetE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetE1,definition,
% 2.86/1.55 ( powersetE1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.86/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(inPowerset_type,type,
% 2.86/1.55 inPowerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(inPowerset,definition,
% 2.86/1.55 ( inPowerset
% 2.86/1.55 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetsubset_type,type,
% 2.86/1.55 powersetsubset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetsubset,definition,
% 2.86/1.55 ( powersetsubset
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(sepInPowerset_type,type,
% 2.86/1.55 sepInPowerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(sepInPowerset,definition,
% 2.86/1.55 ( sepInPowerset
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( in
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 @ ( powerset @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(sepSubset_type,type,
% 2.86/1.55 sepSubset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(sepSubset,definition,
% 2.86/1.55 ( sepSubset
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( subset
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunion_type,type,
% 2.86/1.55 binunion: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(binunionIL_type,type,
% 2.86/1.55 binunionIL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionIL,definition,
% 2.86/1.55 ( binunionIL
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairset2IR_type,type,
% 2.86/1.55 upairset2IR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairset2IR,definition,
% 2.86/1.55 ( upairset2IR
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionIR_type,type,
% 2.86/1.55 binunionIR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionIR,definition,
% 2.86/1.55 ( binunionIR
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionEcases_type,type,
% 2.86/1.55 binunionEcases: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionEcases,definition,
% 2.86/1.55 ( binunionEcases
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.86/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.86/1.55 => ( ( ( in @ Xx @ A )
% 2.86/1.55 => Xphi )
% 2.86/1.55 => ( ( ( in @ Xx @ B )
% 2.86/1.55 => Xphi )
% 2.86/1.55 => Xphi ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionE_type,type,
% 2.86/1.55 binunionE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionE,definition,
% 2.86/1.55 ( binunionE
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.86/1.55 => ( ( in @ Xx @ A )
% 2.86/1.55 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionLsub_type,type,
% 2.86/1.55 binunionLsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionLsub,definition,
% 2.86/1.55 ( binunionLsub
% 2.86/1.55 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionRsub_type,type,
% 2.86/1.55 binunionRsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionRsub,definition,
% 2.86/1.55 ( binunionRsub
% 2.86/1.55 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersect_type,type,
% 2.86/1.55 binintersect: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectI_type,type,
% 2.86/1.55 binintersectI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectI,definition,
% 2.86/1.55 ( binintersectI
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset5_type,type,
% 2.86/1.55 binintersectSubset5: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset5,definition,
% 2.86/1.55 ( binintersectSubset5
% 2.86/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.86/1.55 ( ( subset @ C @ A )
% 2.86/1.55 => ( ( subset @ C @ B )
% 2.86/1.55 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectEL_type,type,
% 2.86/1.55 binintersectEL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectEL,definition,
% 2.86/1.55 ( binintersectEL
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectLsub_type,type,
% 2.86/1.55 binintersectLsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectLsub,definition,
% 2.86/1.55 ( binintersectLsub
% 2.86/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset2_type,type,
% 2.86/1.55 binintersectSubset2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset2,definition,
% 2.86/1.55 ( binintersectSubset2
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ( binintersect @ A @ B )
% 2.86/1.55 = A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset3_type,type,
% 2.86/1.55 binintersectSubset3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset3,definition,
% 2.86/1.55 ( binintersectSubset3
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( ( binintersect @ A @ B )
% 2.86/1.55 = B )
% 2.86/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectER_type,type,
% 2.86/1.55 binintersectER: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectER,definition,
% 2.86/1.55 ( binintersectER
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.86/1.55 => ( in @ Xx @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(disjointsetsI1_type,type,
% 2.86/1.55 disjointsetsI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(disjointsetsI1,definition,
% 2.86/1.55 ( disjointsetsI1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ~ ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( in @ Xx @ B ) )
% 2.86/1.55 => ( ( binintersect @ A @ B )
% 2.86/1.55 = emptyset ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectRsub_type,type,
% 2.86/1.55 binintersectRsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectRsub,definition,
% 2.86/1.55 ( binintersectRsub
% 2.86/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset4_type,type,
% 2.86/1.55 binintersectSubset4: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset4,definition,
% 2.86/1.55 ( binintersectSubset4
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ B @ A )
% 2.86/1.55 => ( ( binintersect @ A @ B )
% 2.86/1.55 = B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset1_type,type,
% 2.86/1.55 binintersectSubset1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectSubset1,definition,
% 2.86/1.55 ( binintersectSubset1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( ( binintersect @ A @ B )
% 2.86/1.55 = A )
% 2.86/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(bs114d_type,type,
% 2.86/1.55 bs114d: $o ).
% 2.86/1.55
% 2.86/1.55 thf(bs114d,definition,
% 2.86/1.55 ( bs114d
% 2.86/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.86/1.55 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.86/1.55 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(regular_type,type,
% 2.86/1.55 regular: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminus_type,type,
% 2.86/1.55 setminus: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(setminusI_type,type,
% 2.86/1.55 setminusI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusI,definition,
% 2.86/1.55 ( setminusI
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusEL_type,type,
% 2.86/1.55 setminusEL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusEL,definition,
% 2.86/1.55 ( setminusEL
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusER_type,type,
% 2.86/1.55 setminusER: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusER,definition,
% 2.86/1.55 ( setminusER
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.86/1.55 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusSubset2_type,type,
% 2.86/1.55 setminusSubset2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusSubset2,definition,
% 2.86/1.55 ( setminusSubset2
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( subset @ A @ B )
% 2.86/1.55 => ( ( setminus @ A @ B )
% 2.86/1.55 = emptyset ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusERneg_type,type,
% 2.86/1.55 setminusERneg: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusERneg,definition,
% 2.86/1.55 ( setminusERneg
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.86/1.55 => ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusELneg_type,type,
% 2.86/1.55 setminusELneg: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusELneg,definition,
% 2.86/1.55 ( setminusELneg
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusILneg_type,type,
% 2.86/1.55 setminusILneg: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusILneg,definition,
% 2.86/1.55 ( setminusILneg
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ~ ( in @ Xx @ A )
% 2.86/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusIRneg_type,type,
% 2.86/1.55 setminusIRneg: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusIRneg,definition,
% 2.86/1.55 ( setminusIRneg
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ B )
% 2.86/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusLsub_type,type,
% 2.86/1.55 setminusLsub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusLsub,definition,
% 2.86/1.55 ( setminusLsub
% 2.86/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusSubset1_type,type,
% 2.86/1.55 setminusSubset1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusSubset1,definition,
% 2.86/1.55 ( setminusSubset1
% 2.86/1.55 = ( ! [A: $i,B: $i] :
% 2.86/1.55 ( ( ( setminus @ A @ B )
% 2.86/1.55 = emptyset )
% 2.86/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(symdiff_type,type,
% 2.86/1.55 symdiff: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffE_type,type,
% 2.86/1.55 symdiffE: $o ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffE,definition,
% 2.86/1.55 ( symdiffE
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.86/1.55 => ! [Xphi: $o] :
% 2.86/1.55 ( ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => Xphi ) )
% 2.86/1.55 => ( ( ~ ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ B )
% 2.86/1.55 => Xphi ) )
% 2.86/1.55 => Xphi ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffI1_type,type,
% 2.86/1.55 symdiffI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffI1,definition,
% 2.86/1.55 ( symdiffI1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffI2_type,type,
% 2.86/1.55 symdiffI2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffI2,definition,
% 2.86/1.55 ( symdiffI2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ~ ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ B )
% 2.86/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffIneg1_type,type,
% 2.86/1.55 symdiffIneg1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffIneg1,definition,
% 2.86/1.55 ( symdiffIneg1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ B )
% 2.86/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffIneg2_type,type,
% 2.86/1.55 symdiffIneg2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(symdiffIneg2,definition,
% 2.86/1.55 ( symdiffIneg2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ~ ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ B )
% 2.86/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iskpair_type,type,
% 2.86/1.55 iskpair: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(secondinupair_type,type,
% 2.86/1.55 secondinupair: $o ).
% 2.86/1.55
% 2.86/1.55 thf(secondinupair,definition,
% 2.86/1.55 ( secondinupair
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairIL_type,type,
% 2.86/1.55 setukpairIL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairIL,definition,
% 2.86/1.55 ( setukpairIL
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairIR_type,type,
% 2.86/1.55 setukpairIR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairIR,definition,
% 2.86/1.55 ( setukpairIR
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(kpairiskpair_type,type,
% 2.86/1.55 kpairiskpair: $o ).
% 2.86/1.55
% 2.86/1.55 thf(kpairiskpair,definition,
% 2.86/1.55 ( kpairiskpair
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(kpair_type,type,
% 2.86/1.55 kpair: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(kpairp_type,type,
% 2.86/1.55 kpairp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(kpairp,definition,
% 2.86/1.55 ( kpairp
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprod_type,type,
% 2.86/1.55 cartprod: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsubset_type,type,
% 2.86/1.55 singletonsubset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsubset,definition,
% 2.86/1.55 ( singletonsubset
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(singletoninpowerset_type,type,
% 2.86/1.55 singletoninpowerset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletoninpowerset,definition,
% 2.86/1.55 ( singletoninpowerset
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(singletoninpowunion_type,type,
% 2.86/1.55 singletoninpowunion: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletoninpowunion,definition,
% 2.86/1.55 ( singletoninpowunion
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairset2E_type,type,
% 2.86/1.55 upairset2E: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairset2E,definition,
% 2.86/1.55 ( upairset2E
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.86/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.86/1.55 => ( ( Xz = Xx )
% 2.86/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairsubunion_type,type,
% 2.86/1.55 upairsubunion: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairsubunion,definition,
% 2.86/1.55 ( upairsubunion
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairinpowunion_type,type,
% 2.86/1.55 upairinpowunion: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairinpowunion,definition,
% 2.86/1.55 ( upairinpowunion
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem1_type,type,
% 2.86/1.55 ubforcartprodlem1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem1,definition,
% 2.86/1.55 ( ubforcartprodlem1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem2_type,type,
% 2.86/1.55 ubforcartprodlem2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem2,definition,
% 2.86/1.55 ( ubforcartprodlem2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem3_type,type,
% 2.86/1.55 ubforcartprodlem3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ubforcartprodlem3,definition,
% 2.86/1.55 ( ubforcartprodlem3
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairin_type,type,
% 2.86/1.55 cartprodpairin: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairin,definition,
% 2.86/1.55 ( cartprodpairin
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempair1_type,type,
% 2.86/1.55 cartprodmempair1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempair1,definition,
% 2.86/1.55 ( cartprodmempair1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.86/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ? [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 & ( Xu
% 2.86/1.55 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempair_type,type,
% 2.86/1.55 cartprodmempair: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempair,definition,
% 2.86/1.55 ( cartprodmempair
% 2.86/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.86/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( iskpair @ Xu ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionE2_type,type,
% 2.86/1.55 setunionE2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionE2,definition,
% 2.86/1.55 ( setunionE2
% 2.86/1.55 = ( ! [A: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.86/1.55 => ? [X: $i] :
% 2.86/1.55 ( ( in @ X @ A )
% 2.86/1.55 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton1_type,type,
% 2.86/1.55 setunionsingleton1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton1,definition,
% 2.86/1.55 ( setunionsingleton1
% 2.86/1.55 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton2_type,type,
% 2.86/1.55 setunionsingleton2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton2,definition,
% 2.86/1.55 ( setunionsingleton2
% 2.86/1.55 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton_type,type,
% 2.86/1.55 setunionsingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setunionsingleton,definition,
% 2.86/1.55 ( setunionsingleton
% 2.86/1.55 = ( ! [Xx: $i] :
% 2.86/1.55 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.86/1.55 = Xx ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(singleton_type,type,
% 2.86/1.55 singleton: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletonprop_type,type,
% 2.86/1.55 singletonprop: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletonprop,definition,
% 2.86/1.55 ( singletonprop
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) )
% 2.86/1.55 => ( ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) )
% 2.86/1.55 => ( singleton
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ex1_type,type,
% 2.86/1.55 ex1: $i > ( $i > $o ) > $o ).
% 2.86/1.55
% 2.86/1.55 thf(ex1,definition,
% 2.86/1.55 ( ex1
% 2.86/1.55 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( singleton
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ex1E1_type,type,
% 2.86/1.55 ex1E1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ex1E1,definition,
% 2.86/1.55 ( ex1E1
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ( ex1 @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ex1I_type,type,
% 2.86/1.55 ex1I: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ex1I,definition,
% 2.86/1.55 ( ex1I
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xy = Xx ) ) )
% 2.86/1.55 => ( ex1 @ A
% 2.86/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ex1I2_type,type,
% 2.86/1.55 ex1I2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ex1I2,definition,
% 2.86/1.55 ( ex1I2
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) )
% 2.86/1.55 => ( ? [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 & ( Xphi @ Xx ) )
% 2.86/1.55 => ( ex1 @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsuniq_type,type,
% 2.86/1.55 singletonsuniq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(singletonsuniq,definition,
% 2.86/1.55 ( singletonsuniq
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( ( setadjoin @ Xx @ emptyset )
% 2.86/1.55 = ( setadjoin @ Xy @ emptyset ) )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(atmost1p_type,type,
% 2.86/1.55 atmost1p: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(atleast2p_type,type,
% 2.86/1.55 atleast2p: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(atmost2p_type,type,
% 2.86/1.55 atmost2p: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairsetp_type,type,
% 2.86/1.55 upairsetp: $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL1_type,type,
% 2.86/1.55 setukpairinjL1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL1,definition,
% 2.86/1.55 ( setukpairinjL1
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.86/1.55 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.86/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(kfstsingleton_type,type,
% 2.86/1.55 kfstsingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(kfstsingleton,definition,
% 2.86/1.55 ( kfstsingleton
% 2.86/1.55 = ( ! [Xu: $i] :
% 2.86/1.55 ( ( iskpair @ Xu )
% 2.86/1.55 => ( singleton
% 2.86/1.55 @ ( dsetconstr @ ( setunion @ Xu )
% 2.86/1.55 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(theprop_type,type,
% 2.86/1.55 theprop: $o ).
% 2.86/1.55
% 2.86/1.55 thf(theprop,definition,
% 2.86/1.55 ( theprop
% 2.86/1.55 = ( ! [X: $i] :
% 2.86/1.55 ( ( singleton @ X )
% 2.86/1.55 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(kfst_type,type,
% 2.86/1.55 kfst: $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(kfstpairEq_type,type,
% 2.86/1.55 kfstpairEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(kfstpairEq,definition,
% 2.86/1.55 ( kfstpairEq
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.86/1.55 = Xx ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodfstin_type,type,
% 2.86/1.55 cartprodfstin: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodfstin,definition,
% 2.86/1.55 ( cartprodfstin
% 2.86/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.86/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL2_type,type,
% 2.86/1.55 setukpairinjL2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL2,definition,
% 2.86/1.55 ( setukpairinjL2
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.86/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL_type,type,
% 2.86/1.55 setukpairinjL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjL,definition,
% 2.86/1.55 ( setukpairinjL
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( ( kpair @ Xx @ Xy )
% 2.86/1.55 = ( kpair @ Xz @ Xu ) )
% 2.86/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR11_type,type,
% 2.86/1.55 setukpairinjR11: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR11,definition,
% 2.86/1.55 ( setukpairinjR11
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR12_type,type,
% 2.86/1.55 setukpairinjR12: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR12,definition,
% 2.86/1.55 ( setukpairinjR12
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xx = Xy )
% 2.86/1.55 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR1_type,type,
% 2.86/1.55 setukpairinjR1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR1,definition,
% 2.86/1.55 ( setukpairinjR1
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.86/1.55 => ( ( Xz = Xu )
% 2.86/1.55 => ( Xy = Xu ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(upairequniteq_type,type,
% 2.86/1.55 upairequniteq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(upairequniteq,definition,
% 2.86/1.55 ( upairequniteq
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.86/1.55 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ Xz @ emptyset ) )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR2_type,type,
% 2.86/1.55 setukpairinjR2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR2,definition,
% 2.86/1.55 ( setukpairinjR2
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.86/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.86/1.55 => ( Xy = Xu ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR_type,type,
% 2.86/1.55 setukpairinjR: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setukpairinjR,definition,
% 2.86/1.55 ( setukpairinjR
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.86/1.55 ( ( ( kpair @ Xx @ Xy )
% 2.86/1.55 = ( kpair @ Xz @ Xu ) )
% 2.86/1.55 => ( Xy = Xu ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ksndsingleton_type,type,
% 2.86/1.55 ksndsingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ksndsingleton,definition,
% 2.86/1.55 ( ksndsingleton
% 2.86/1.55 = ( ! [Xu: $i] :
% 2.86/1.55 ( ( iskpair @ Xu )
% 2.86/1.55 => ( singleton
% 2.86/1.55 @ ( dsetconstr @ ( setunion @ Xu )
% 2.86/1.55 @ ^ [Xx: $i] :
% 2.86/1.55 ( Xu
% 2.86/1.55 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ksnd_type,type,
% 2.86/1.55 ksnd: $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(ksndpairEq_type,type,
% 2.86/1.55 ksndpairEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ksndpairEq,definition,
% 2.86/1.55 ( ksndpairEq
% 2.86/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.86/1.55 = Xy ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(kpairsurjEq_type,type,
% 2.86/1.55 kpairsurjEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(kpairsurjEq,definition,
% 2.86/1.55 ( kpairsurjEq
% 2.86/1.55 = ( ! [Xu: $i] :
% 2.86/1.55 ( ( iskpair @ Xu )
% 2.86/1.55 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.86/1.55 = Xu ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodsndin_type,type,
% 2.86/1.55 cartprodsndin: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodsndin,definition,
% 2.86/1.55 ( cartprodsndin
% 2.86/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.86/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairmemEL_type,type,
% 2.86/1.55 cartprodpairmemEL: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairmemEL,definition,
% 2.86/1.55 ( cartprodpairmemEL
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairmemER_type,type,
% 2.86/1.55 cartprodpairmemER: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairmemER,definition,
% 2.86/1.55 ( cartprodpairmemER
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( in @ Xy @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempaircEq_type,type,
% 2.86/1.55 cartprodmempaircEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodmempaircEq,definition,
% 2.86/1.55 ( cartprodmempaircEq
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( kpair @ Xx @ Xy )
% 2.86/1.55 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodfstpairEq_type,type,
% 2.86/1.55 cartprodfstpairEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodfstpairEq,definition,
% 2.86/1.55 ( cartprodfstpairEq
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.86/1.55 = Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodsndpairEq_type,type,
% 2.86/1.55 cartprodsndpairEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodsndpairEq,definition,
% 2.86/1.55 ( cartprodsndpairEq
% 2.86/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.86/1.55 = Xy ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairsurjEq_type,type,
% 2.86/1.55 cartprodpairsurjEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(cartprodpairsurjEq,definition,
% 2.86/1.55 ( cartprodpairsurjEq
% 2.86/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.86/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.86/1.55 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.86/1.55 = Xu ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(breln_type,type,
% 2.86/1.55 breln: $i > $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(breln,definition,
% 2.86/1.55 ( breln
% 2.86/1.55 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstr_type,type,
% 2.86/1.55 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrI_type,type,
% 2.86/1.55 dpsetconstrI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrI,definition,
% 2.86/1.55 ( dpsetconstrI
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( Xphi @ Xx @ Xy )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy )
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrSub_type,type,
% 2.86/1.55 dpsetconstrSub: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrSub,definition,
% 2.86/1.55 ( dpsetconstrSub
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.86/1.55 ( subset
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.86/1.55 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setOfPairsIsBReln_type,type,
% 2.86/1.55 setOfPairsIsBReln: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setOfPairsIsBReln,definition,
% 2.86/1.55 ( setOfPairsIsBReln
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.86/1.55 ( breln @ A @ B
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrERa_type,type,
% 2.86/1.55 dpsetconstrERa: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrERa,definition,
% 2.86/1.55 ( dpsetconstrERa
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.86/1.55 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrEL1_type,type,
% 2.86/1.55 dpsetconstrEL1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrEL1,definition,
% 2.86/1.55 ( dpsetconstrEL1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.86/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrEL2_type,type,
% 2.86/1.55 dpsetconstrEL2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrEL2,definition,
% 2.86/1.55 ( dpsetconstrEL2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.86/1.55 => ( in @ Xy @ B ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrER_type,type,
% 2.86/1.55 dpsetconstrER: $o ).
% 2.86/1.55
% 2.86/1.55 thf(dpsetconstrER,definition,
% 2.86/1.55 ( dpsetconstrER
% 2.86/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.86/1.55 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(func_type,type,
% 2.86/1.55 func: $i > $i > $i > $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcSet_type,type,
% 2.86/1.55 funcSet: $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(funcImageSingleton_type,type,
% 2.86/1.55 funcImageSingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcImageSingleton,definition,
% 2.86/1.55 ( funcImageSingleton
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( singleton
% 2.86/1.55 @ ( dsetconstr @ B
% 2.86/1.55 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(apProp_type,type,
% 2.86/1.55 apProp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(apProp,definition,
% 2.86/1.55 ( apProp
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in
% 2.86/1.55 @ ( setunion
% 2.86/1.55 @ ( dsetconstr @ B
% 2.86/1.55 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.86/1.55 @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ap_type,type,
% 2.86/1.55 ap: $i > $i > $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(app_type,type,
% 2.86/1.55 app: $o ).
% 2.86/1.55
% 2.86/1.55 thf(app,definition,
% 2.86/1.55 ( app
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(infuncsetfunc_type,type,
% 2.86/1.55 infuncsetfunc: $o ).
% 2.86/1.55
% 2.86/1.55 thf(infuncsetfunc,definition,
% 2.86/1.55 ( infuncsetfunc
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ap2p_type,type,
% 2.86/1.55 ap2p: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ap2p,definition,
% 2.86/1.55 ( ap2p
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcinfuncset_type,type,
% 2.86/1.55 funcinfuncset: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcinfuncset,definition,
% 2.86/1.55 ( funcinfuncset
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(lamProp_type,type,
% 2.86/1.55 lamProp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(lamProp,definition,
% 2.86/1.55 ( lamProp
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ( func @ A @ B
% 2.86/1.55 @ ( dpsetconstr @ A @ B
% 2.86/1.55 @ ^ [Xx: $i,Xy: $i] :
% 2.86/1.55 ( ( Xf @ Xx )
% 2.86/1.55 = Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(lam_type,type,
% 2.86/1.55 lam: $i > $i > ( $i > $i ) > $i ).
% 2.86/1.55
% 2.86/1.55 thf(lamp_type,type,
% 2.86/1.55 lamp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(lamp,definition,
% 2.86/1.55 ( lamp
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ( func @ A @ B
% 2.86/1.55 @ ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(lam2p_type,type,
% 2.86/1.55 lam2p: $o ).
% 2.86/1.55
% 2.86/1.55 thf(lam2p,definition,
% 2.86/1.55 ( lam2p
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ( in
% 2.86/1.55 @ ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.86/1.55 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(brelnall1_type,type,
% 2.86/1.55 brelnall1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(brelnall1,definition,
% 2.86/1.55 ( brelnall1
% 2.86/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ R )
% 2.86/1.55 => ! [Xphi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.86/1.55 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ R )
% 2.86/1.55 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(brelnall2_type,type,
% 2.86/1.55 brelnall2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(brelnall2,definition,
% 2.86/1.55 ( brelnall2
% 2.86/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ R )
% 2.86/1.55 => ! [Xphi: $i > $o] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.86/1.55 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ R )
% 2.86/1.55 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ex1E2_type,type,
% 2.86/1.55 ex1E2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ex1E2,definition,
% 2.86/1.55 ( ex1E2
% 2.86/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.86/1.55 ( ( ex1 @ A
% 2.86/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ( Xphi @ Xx )
% 2.86/1.55 => ( ( Xphi @ Xy )
% 2.86/1.55 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp1_type,type,
% 2.86/1.55 funcGraphProp1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp1,definition,
% 2.86/1.55 ( funcGraphProp1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp3_type,type,
% 2.86/1.55 funcGraphProp3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp3,definition,
% 2.86/1.55 ( funcGraphProp3
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp2_type,type,
% 2.86/1.55 funcGraphProp2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp2,definition,
% 2.86/1.55 ( funcGraphProp2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcextLem_type,type,
% 2.86/1.55 funcextLem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcextLem,definition,
% 2.86/1.55 ( funcextLem
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xg: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xg )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp4_type,type,
% 2.86/1.55 funcGraphProp4: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcGraphProp4,definition,
% 2.86/1.55 ( funcGraphProp4
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = Xy ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subbreln_type,type,
% 2.86/1.55 subbreln: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subbreln,definition,
% 2.86/1.55 ( subbreln
% 2.86/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ R )
% 2.86/1.55 => ! [S: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ S )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.86/1.55 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eqbreln_type,type,
% 2.86/1.55 eqbreln: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eqbreln,definition,
% 2.86/1.55 ( eqbreln
% 2.86/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ R )
% 2.86/1.55 => ! [S: $i] :
% 2.86/1.55 ( ( breln @ A @ B @ S )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ B )
% 2.86/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.86/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.86/1.55 => ( R = S ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcext_type,type,
% 2.86/1.55 funcext: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcext,definition,
% 2.86/1.55 ( funcext
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xg: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xg )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.86/1.55 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(funcext2_type,type,
% 2.86/1.55 funcext2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(funcext2,definition,
% 2.86/1.55 ( funcext2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ! [Xg: $i] :
% 2.86/1.55 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.86/1.55 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ap2apEq1_type,type,
% 2.86/1.55 ap2apEq1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ap2apEq1,definition,
% 2.86/1.55 ( ap2apEq1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ap2apEq2_type,type,
% 2.86/1.55 ap2apEq2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ap2apEq2,definition,
% 2.86/1.55 ( ap2apEq2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.86/1.55 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(beta1_type,type,
% 2.86/1.55 beta1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(beta1,definition,
% 2.86/1.55 ( beta1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B
% 2.86/1.55 @ ( lam @ A @ B
% 2.86/1.55 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.86/1.55 @ Xx )
% 2.86/1.55 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eta1_type,type,
% 2.86/1.55 eta1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eta1,definition,
% 2.86/1.55 ( eta1
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( func @ A @ B @ Xf )
% 2.86/1.55 => ( ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.86/1.55 = Xf ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(lam2lamEq_type,type,
% 2.86/1.55 lam2lamEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(lam2lamEq,definition,
% 2.86/1.55 ( lam2lamEq
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ( ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.86/1.55 = ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(beta2_type,type,
% 2.86/1.55 beta2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(beta2,definition,
% 2.86/1.55 ( beta2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.86/1.55 ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( ap @ A @ B
% 2.86/1.55 @ ( lam @ A @ B
% 2.86/1.55 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.86/1.55 @ Xx )
% 2.86/1.55 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(eta2_type,type,
% 2.86/1.55 eta2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(eta2,definition,
% 2.86/1.55 ( eta2
% 2.86/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.86/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.86/1.55 => ( ( lam @ A @ B
% 2.86/1.55 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.86/1.55 = Xf ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iffalseProp1_type,type,
% 2.86/1.55 iffalseProp1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iffalseProp1,definition,
% 2.86/1.55 ( iffalseProp1
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ~ Xphi
% 2.86/1.55 => ( in @ Xy
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xz: $i] :
% 2.86/1.55 ( ( Xphi
% 2.86/1.55 & ( Xz = Xx ) )
% 2.86/1.55 | ( ~ Xphi
% 2.86/1.55 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iffalseProp2_type,type,
% 2.86/1.55 iffalseProp2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iffalseProp2,definition,
% 2.86/1.55 ( iffalseProp2
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ~ Xphi
% 2.86/1.55 => ( ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xz: $i] :
% 2.86/1.55 ( ( Xphi
% 2.86/1.55 & ( Xz = Xx ) )
% 2.86/1.55 | ( ~ Xphi
% 2.86/1.55 & ( Xz = Xy ) ) ) )
% 2.86/1.55 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueProp1_type,type,
% 2.86/1.55 iftrueProp1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueProp1,definition,
% 2.86/1.55 ( iftrueProp1
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( Xphi
% 2.86/1.55 => ( in @ Xx
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xz: $i] :
% 2.86/1.55 ( ( Xphi
% 2.86/1.55 & ( Xz = Xx ) )
% 2.86/1.55 | ( ~ Xphi
% 2.86/1.55 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueProp2_type,type,
% 2.86/1.55 iftrueProp2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueProp2,definition,
% 2.86/1.55 ( iftrueProp2
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( Xphi
% 2.86/1.55 => ( ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xz: $i] :
% 2.86/1.55 ( ( Xphi
% 2.86/1.55 & ( Xz = Xx ) )
% 2.86/1.55 | ( ~ Xphi
% 2.86/1.55 & ( Xz = Xy ) ) ) )
% 2.86/1.55 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(ifSingleton_type,type,
% 2.86/1.55 ifSingleton: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ifSingleton,definition,
% 2.86/1.55 ( ifSingleton
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( singleton
% 2.86/1.55 @ ( dsetconstr @ A
% 2.86/1.55 @ ^ [Xz: $i] :
% 2.86/1.55 ( ( Xphi
% 2.86/1.55 & ( Xz = Xx ) )
% 2.86/1.55 | ( ~ Xphi
% 2.86/1.55 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(if_type,type,
% 2.86/1.55 if: $i > $o > $i > $i > $i ).
% 2.86/1.55
% 2.86/1.55 thf(ifp_type,type,
% 2.86/1.55 ifp: $o ).
% 2.86/1.55
% 2.86/1.55 thf(ifp,definition,
% 2.86/1.55 ( ifp
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(theeq_type,type,
% 2.86/1.55 theeq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(theeq,definition,
% 2.86/1.55 ( theeq
% 2.86/1.55 = ( ! [X: $i] :
% 2.86/1.55 ( ( singleton @ X )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ X )
% 2.86/1.55 => ( ( setunion @ X )
% 2.86/1.55 = Xx ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iftrue_type,type,
% 2.86/1.55 iftrue: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iftrue,definition,
% 2.86/1.55 ( iftrue
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( Xphi
% 2.86/1.55 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.86/1.55 = Xx ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iffalse_type,type,
% 2.86/1.55 iffalse: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iffalse,definition,
% 2.86/1.55 ( iffalse
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( ~ Xphi
% 2.86/1.55 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.86/1.55 = Xy ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueorfalse_type,type,
% 2.86/1.55 iftrueorfalse: $o ).
% 2.86/1.55
% 2.86/1.55 thf(iftrueorfalse,definition,
% 2.86/1.55 ( iftrueorfalse
% 2.86/1.55 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ! [Xy: $i] :
% 2.86/1.55 ( ( in @ Xy @ A )
% 2.86/1.55 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectT_lem_type,type,
% 2.86/1.55 binintersectT_lem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectT_lem,definition,
% 2.86/1.55 ( binintersectT_lem
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binunionT_lem_type,type,
% 2.86/1.55 binunionT_lem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binunionT_lem,definition,
% 2.86/1.55 ( binunionT_lem
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetT_lem_type,type,
% 2.86/1.55 powersetT_lem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetT_lem,definition,
% 2.86/1.55 ( powersetT_lem
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setminusT_lem_type,type,
% 2.86/1.55 setminusT_lem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setminusT_lem,definition,
% 2.86/1.55 ( setminusT_lem
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementT_lem_type,type,
% 2.86/1.55 complementT_lem: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementT_lem,definition,
% 2.86/1.55 ( complementT_lem
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(setextT_type,type,
% 2.86/1.55 setextT: $o ).
% 2.86/1.55
% 2.86/1.55 thf(setextT,definition,
% 2.86/1.55 ( setextT
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ( in @ Xx @ Y ) ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ Y )
% 2.86/1.55 => ( in @ Xx @ X ) ) )
% 2.86/1.55 => ( X = Y ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(subsetTI_type,type,
% 2.86/1.55 subsetTI: $o ).
% 2.86/1.55
% 2.86/1.55 thf(subsetTI,definition,
% 2.86/1.55 ( subsetTI
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ( in @ Xx @ Y ) ) )
% 2.86/1.55 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetTI1_type,type,
% 2.86/1.55 powersetTI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetTI1,definition,
% 2.86/1.55 ( powersetTI1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ( in @ Xx @ Y ) ) )
% 2.86/1.55 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(powersetTE1_type,type,
% 2.86/1.55 powersetTE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(powersetTE1,definition,
% 2.86/1.55 ( powersetTE1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ X @ ( powerset @ Y ) )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementTI1_type,type,
% 2.86/1.55 complementTI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementTI1,definition,
% 2.86/1.55 ( complementTI1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementTE1_type,type,
% 2.86/1.55 complementTE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementTE1,definition,
% 2.86/1.55 ( complementTE1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.86/1.55 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectTELcontra_type,type,
% 2.86/1.55 binintersectTELcontra: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectTELcontra,definition,
% 2.86/1.55 ( binintersectTELcontra
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ X )
% 2.86/1.55 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectTERcontra_type,type,
% 2.86/1.55 binintersectTERcontra: $o ).
% 2.86/1.55
% 2.86/1.55 thf(binintersectTERcontra,definition,
% 2.86/1.55 ( binintersectTERcontra
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ~ ( in @ Xx @ Y )
% 2.86/1.55 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT_type,type,
% 2.86/1.55 contrasubsetT: $o ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT,definition,
% 2.86/1.55 ( contrasubsetT
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.86/1.55 => ( ( in @ Xx @ Y )
% 2.86/1.55 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT1_type,type,
% 2.86/1.55 contrasubsetT1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT1,definition,
% 2.86/1.55 ( contrasubsetT1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( subset @ X @ Y )
% 2.86/1.55 => ( ~ ( in @ Xx @ Y )
% 2.86/1.55 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT2_type,type,
% 2.86/1.55 contrasubsetT2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT2,definition,
% 2.86/1.55 ( contrasubsetT2
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ( subset @ X @ Y )
% 2.86/1.55 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT3_type,type,
% 2.86/1.55 contrasubsetT3: $o ).
% 2.86/1.55
% 2.86/1.55 thf(contrasubsetT3,definition,
% 2.86/1.55 ( contrasubsetT3
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.86/1.55 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementI1_type,type,
% 2.86/1.55 doubleComplementI1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementI1,definition,
% 2.86/1.55 ( doubleComplementI1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ X )
% 2.86/1.55 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementE1_type,type,
% 2.86/1.55 doubleComplementE1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementE1,definition,
% 2.86/1.55 ( doubleComplementE1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.86/1.55 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementSub1_type,type,
% 2.86/1.55 doubleComplementSub1: $o ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementSub1,definition,
% 2.86/1.55 ( doubleComplementSub1
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementSub2_type,type,
% 2.86/1.55 doubleComplementSub2: $o ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementSub2,definition,
% 2.86/1.55 ( doubleComplementSub2
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementEq_type,type,
% 2.86/1.55 doubleComplementEq: $o ).
% 2.86/1.55
% 2.86/1.55 thf(doubleComplementEq,definition,
% 2.86/1.55 ( doubleComplementEq
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ( X
% 2.86/1.55 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementTnotintersectT_type,type,
% 2.86/1.55 complementTnotintersectT: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementTnotintersectT,definition,
% 2.86/1.55 ( complementTnotintersectT
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.86/1.55 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementImpComplementIntersect_type,type,
% 2.86/1.55 complementImpComplementIntersect: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementImpComplementIntersect,definition,
% 2.86/1.55 ( complementImpComplementIntersect
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.86/1.55 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementSubsetComplementIntersect_type,type,
% 2.86/1.55 complementSubsetComplementIntersect: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementSubsetComplementIntersect,definition,
% 2.86/1.55 ( complementSubsetComplementIntersect
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementInPowersetComplementIntersect_type,type,
% 2.86/1.55 complementInPowersetComplementIntersect: $o ).
% 2.86/1.55
% 2.86/1.55 thf(complementInPowersetComplementIntersect,definition,
% 2.86/1.55 ( complementInPowersetComplementIntersect
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(contraSubsetComplement_type,type,
% 2.86/1.55 contraSubsetComplement: $o ).
% 2.86/1.55
% 2.86/1.55 thf(contraSubsetComplement,definition,
% 2.86/1.55 ( contraSubsetComplement
% 2.86/1.55 = ( ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.86/1.55 => ! [Xx: $i] :
% 2.86/1.55 ( ( in @ Xx @ A )
% 2.86/1.55 => ( ( in @ Xx @ Y )
% 2.86/1.55 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55
% 2.86/1.55 thf(complementTcontraSubset,conjecture,
% 2.86/1.55 ( setextAx
% 2.86/1.55 => ( emptysetAx
% 2.86/1.55 => ( setadjoinAx
% 2.86/1.55 => ( powersetAx
% 2.86/1.55 => ( setunionAx
% 2.86/1.55 => ( omega0Ax
% 2.86/1.55 => ( omegaSAx
% 2.86/1.55 => ( omegaIndAx
% 2.86/1.55 => ( replAx
% 2.86/1.55 => ( foundationAx
% 2.86/1.55 => ( wellorderingAx
% 2.86/1.55 => ( descrp
% 2.86/1.55 => ( dsetconstrI
% 2.86/1.55 => ( dsetconstrEL
% 2.86/1.55 => ( dsetconstrER
% 2.86/1.55 => ( exuE1
% 2.86/1.55 => ( prop2setE
% 2.86/1.55 => ( emptysetE
% 2.86/1.55 => ( emptysetimpfalse
% 2.86/1.55 => ( notinemptyset
% 2.86/1.55 => ( exuE3e
% 2.86/1.55 => ( setext
% 2.86/1.55 => ( emptyI
% 2.86/1.55 => ( noeltsimpempty
% 2.86/1.55 => ( setbeta
% 2.86/1.55 => ( nonemptyE1
% 2.86/1.55 => ( nonemptyI
% 2.86/1.55 => ( nonemptyI1
% 2.86/1.55 => ( setadjoinIL
% 2.86/1.55 => ( emptyinunitempty
% 2.86/1.55 => ( setadjoinIR
% 2.86/1.55 => ( setadjoinE
% 2.86/1.55 => ( setadjoinOr
% 2.86/1.55 => ( setoftrueEq
% 2.86/1.55 => ( powersetI
% 2.86/1.55 => ( emptyinPowerset
% 2.86/1.55 => ( emptyInPowerset
% 2.86/1.55 => ( powersetE
% 2.86/1.55 => ( setunionI
% 2.86/1.55 => ( setunionE
% 2.86/1.55 => ( subPowSU
% 2.86/1.55 => ( exuE2
% 2.86/1.55 => ( nonemptyImpWitness
% 2.86/1.55 => ( uniqinunit
% 2.86/1.55 => ( notinsingleton
% 2.86/1.55 => ( eqinunit
% 2.86/1.55 => ( singletonsswitch
% 2.86/1.55 => ( upairsetE
% 2.86/1.55 => ( upairsetIL
% 2.86/1.55 => ( upairsetIR
% 2.86/1.55 => ( emptyE1
% 2.86/1.55 => ( vacuousDall
% 2.86/1.55 => ( quantDeMorgan1
% 2.86/1.55 => ( quantDeMorgan2
% 2.86/1.55 => ( quantDeMorgan3
% 2.86/1.55 => ( quantDeMorgan4
% 2.86/1.55 => ( prop2setI
% 2.86/1.55 => ( prop2set2propI
% 2.86/1.55 => ( notdexE
% 2.86/1.55 => ( notdallE
% 2.86/1.55 => ( exuI1
% 2.86/1.55 => ( exuI3
% 2.86/1.55 => ( exuI2
% 2.86/1.55 => ( inCongP
% 2.86/1.55 => ( in__Cong
% 2.86/1.55 => ( exuE3u
% 2.86/1.55 => ( exu__Cong
% 2.86/1.55 => ( emptyset__Cong
% 2.86/1.55 => ( setadjoin__Cong
% 2.86/1.55 => ( powerset__Cong
% 2.86/1.55 => ( setunion__Cong
% 2.86/1.55 => ( omega__Cong
% 2.86/1.55 => ( exuEu
% 2.86/1.55 => ( descr__Cong
% 2.86/1.55 => ( dsetconstr__Cong
% 2.86/1.55 => ( subsetI1
% 2.86/1.55 => ( eqimpsubset2
% 2.86/1.55 => ( eqimpsubset1
% 2.86/1.55 => ( subsetI2
% 2.86/1.55 => ( emptysetsubset
% 2.86/1.55 => ( subsetE
% 2.86/1.55 => ( subsetE2
% 2.86/1.55 => ( notsubsetI
% 2.86/1.55 => ( notequalI1
% 2.86/1.55 => ( notequalI2
% 2.86/1.55 => ( subsetRefl
% 2.86/1.55 => ( subsetTrans
% 2.86/1.55 => ( setadjoinSub
% 2.86/1.55 => ( setadjoinSub2
% 2.86/1.55 => ( subset2powerset
% 2.86/1.55 => ( setextsub
% 2.86/1.55 => ( subsetemptysetimpeq
% 2.86/1.55 => ( powersetI1
% 2.86/1.55 => ( powersetE1
% 2.86/1.55 => ( inPowerset
% 2.86/1.55 => ( powersetsubset
% 2.86/1.55 => ( sepInPowerset
% 2.86/1.55 => ( sepSubset
% 2.86/1.55 => ( binunionIL
% 2.86/1.55 => ( upairset2IR
% 2.86/1.55 => ( binunionIR
% 2.86/1.55 => ( binunionEcases
% 2.86/1.55 => ( binunionE
% 2.86/1.55 => ( binunionLsub
% 2.86/1.55 => ( binunionRsub
% 2.86/1.55 => ( binintersectI
% 2.86/1.55 => ( binintersectSubset5
% 2.86/1.55 => ( binintersectEL
% 2.86/1.55 => ( binintersectLsub
% 2.86/1.55 => ( binintersectSubset2
% 2.86/1.55 => ( binintersectSubset3
% 2.86/1.55 => ( binintersectER
% 2.86/1.55 => ( disjointsetsI1
% 2.86/1.55 => ( binintersectRsub
% 2.86/1.55 => ( binintersectSubset4
% 2.86/1.55 => ( binintersectSubset1
% 2.86/1.55 => ( bs114d
% 2.86/1.55 => ( setminusI
% 2.86/1.55 => ( setminusEL
% 2.86/1.55 => ( setminusER
% 2.86/1.55 => ( setminusSubset2
% 2.86/1.55 => ( setminusERneg
% 2.86/1.55 => ( setminusELneg
% 2.86/1.55 => ( setminusILneg
% 2.86/1.55 => ( setminusIRneg
% 2.86/1.55 => ( setminusLsub
% 2.86/1.55 => ( setminusSubset1
% 2.86/1.55 => ( symdiffE
% 2.86/1.55 => ( symdiffI1
% 2.86/1.55 => ( symdiffI2
% 2.86/1.55 => ( symdiffIneg1
% 2.86/1.55 => ( symdiffIneg2
% 2.86/1.55 => ( secondinupair
% 2.86/1.55 => ( setukpairIL
% 2.86/1.55 => ( setukpairIR
% 2.86/1.55 => ( kpairiskpair
% 2.86/1.55 => ( kpairp
% 2.86/1.55 => ( singletonsubset
% 2.86/1.55 => ( singletoninpowerset
% 2.86/1.55 => ( singletoninpowunion
% 2.86/1.55 => ( upairset2E
% 2.86/1.55 => ( upairsubunion
% 2.86/1.55 => ( upairinpowunion
% 2.86/1.55 => ( ubforcartprodlem1
% 2.86/1.55 => ( ubforcartprodlem2
% 2.86/1.55 => ( ubforcartprodlem3
% 2.86/1.55 => ( cartprodpairin
% 2.86/1.55 => ( cartprodmempair1
% 2.86/1.55 => ( cartprodmempair
% 2.86/1.55 => ( setunionE2
% 2.86/1.55 => ( setunionsingleton1
% 2.86/1.55 => ( setunionsingleton2
% 2.86/1.55 => ( setunionsingleton
% 2.86/1.55 => ( singletonprop
% 2.86/1.55 => ( ex1E1
% 2.86/1.55 => ( ex1I
% 2.86/1.55 => ( ex1I2
% 2.86/1.55 => ( singletonsuniq
% 2.86/1.55 => ( setukpairinjL1
% 2.86/1.55 => ( kfstsingleton
% 2.86/1.55 => ( theprop
% 2.86/1.55 => ( kfstpairEq
% 2.86/1.55 => ( cartprodfstin
% 2.86/1.55 => ( setukpairinjL2
% 2.86/1.55 => ( setukpairinjL
% 2.86/1.55 => ( setukpairinjR11
% 2.86/1.55 => ( setukpairinjR12
% 2.86/1.55 => ( setukpairinjR1
% 2.86/1.55 => ( upairequniteq
% 2.86/1.55 => ( setukpairinjR2
% 2.86/1.55 => ( setukpairinjR
% 2.86/1.55 => ( ksndsingleton
% 2.86/1.55 => ( ksndpairEq
% 2.86/1.55 => ( kpairsurjEq
% 2.86/1.55 => ( cartprodsndin
% 2.86/1.55 => ( cartprodpairmemEL
% 2.86/1.55 => ( cartprodpairmemER
% 2.86/1.55 => ( cartprodmempaircEq
% 2.86/1.55 => ( cartprodfstpairEq
% 2.86/1.55 => ( cartprodsndpairEq
% 2.86/1.55 => ( cartprodpairsurjEq
% 2.86/1.55 => ( dpsetconstrI
% 2.86/1.55 => ( dpsetconstrSub
% 2.86/1.55 => ( setOfPairsIsBReln
% 2.86/1.55 => ( dpsetconstrERa
% 2.86/1.55 => ( dpsetconstrEL1
% 2.86/1.55 => ( dpsetconstrEL2
% 2.86/1.55 => ( dpsetconstrER
% 2.86/1.55 => ( funcImageSingleton
% 2.86/1.55 => ( apProp
% 2.86/1.55 => ( app
% 2.86/1.55 => ( infuncsetfunc
% 2.86/1.55 => ( ap2p
% 2.86/1.55 => ( funcinfuncset
% 2.86/1.55 => ( lamProp
% 2.86/1.55 => ( lamp
% 2.86/1.55 => ( lam2p
% 2.86/1.55 => ( brelnall1
% 2.86/1.55 => ( brelnall2
% 2.86/1.55 => ( ex1E2
% 2.86/1.55 => ( funcGraphProp1
% 2.86/1.55 => ( funcGraphProp3
% 2.86/1.55 => ( funcGraphProp2
% 2.86/1.55 => ( funcextLem
% 2.86/1.55 => ( funcGraphProp4
% 2.86/1.55 => ( subbreln
% 2.86/1.55 => ( eqbreln
% 2.86/1.55 => ( funcext
% 2.86/1.55 => ( funcext2
% 2.86/1.55 => ( ap2apEq1
% 2.86/1.55 => ( ap2apEq2
% 2.86/1.55 => ( beta1
% 2.86/1.55 => ( eta1
% 2.86/1.55 => ( lam2lamEq
% 2.86/1.55 => ( beta2
% 2.86/1.55 => ( eta2
% 2.86/1.55 => ( iffalseProp1
% 2.86/1.55 => ( iffalseProp2
% 2.86/1.55 => ( iftrueProp1
% 2.86/1.55 => ( iftrueProp2
% 2.86/1.55 => ( ifSingleton
% 2.86/1.55 => ( ifp
% 2.86/1.55 => ( theeq
% 2.86/1.55 => ( iftrue
% 2.86/1.55 => ( iffalse
% 2.86/1.55 => ( iftrueorfalse
% 2.86/1.55 => ( binintersectT_lem
% 2.86/1.55 => ( binunionT_lem
% 2.86/1.55 => ( powersetT_lem
% 2.86/1.55 => ( setminusT_lem
% 2.86/1.55 => ( complementT_lem
% 2.86/1.55 => ( setextT
% 2.86/1.55 => ( subsetTI
% 2.86/1.55 => ( powersetTI1
% 2.86/1.55 => ( powersetTE1
% 2.86/1.55 => ( complementTI1
% 2.86/1.55 => ( complementTE1
% 2.86/1.55 => ( binintersectTELcontra
% 2.86/1.55 => ( binintersectTERcontra
% 2.86/1.55 => ( contrasubsetT
% 2.86/1.55 => ( contrasubsetT1
% 2.86/1.55 => ( contrasubsetT2
% 2.86/1.55 => ( contrasubsetT3
% 2.86/1.55 => ( doubleComplementI1
% 2.86/1.55 => ( doubleComplementE1
% 2.86/1.55 => ( doubleComplementSub1
% 2.86/1.55 => ( doubleComplementSub2
% 2.86/1.55 => ( doubleComplementEq
% 2.86/1.55 => ( complementTnotintersectT
% 2.86/1.55 => ( complementImpComplementIntersect
% 2.86/1.55 => ( complementSubsetComplementIntersect
% 2.86/1.55 => ( complementInPowersetComplementIntersect
% 2.86/1.55 => ( contraSubsetComplement
% 2.86/1.55 => ! [A: $i,X: $i] :
% 2.86/1.55 ( ( in @ X @ ( powerset @ A ) )
% 2.86/1.55 => ! [Y: $i] :
% 2.86/1.55 ( ( in @ Y @ ( powerset @ A ) )
% 2.86/1.55 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.86/1.55 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.55 ------------------------
% 2.86/1.59 % (23712)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/183Mi)
% 2.86/1.59 % (23717)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_23392 for (2999ds/275Mi)
% 2.86/1.59 % (23713)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_23392 for (2999ds/4Mi)
% 2.86/1.59 % (23718)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/18Mi)
% 2.86/1.59 % (23713)Instruction limit reached!
% 2.86/1.59 % (23713)------------------------------
% 2.86/1.59 % (23713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.59 % (23713)Termination reason: Unknown
% 2.86/1.59 % (23713)Termination phase: shuffling
% 2.86/1.59
% 2.86/1.59 % (23713)Memory used [KB]: 1535
% 2.86/1.59 % (23713)Time elapsed: 0.003 s
% 2.86/1.59 % (23713)Instructions burned: 6 (million)
% 2.86/1.59 % (23713)------------------------------
% 2.86/1.59 % (23713)------------------------------
% 2.86/1.60 % (23714)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_23392 for (2999ds/27Mi)
% 2.86/1.60 % (23715)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/2Mi)
% 2.92/1.60 % (23716)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_23392 for (2999ds/2Mi)
% 2.92/1.60 % (23715)Instruction limit reached!
% 2.92/1.60 % (23715)------------------------------
% 2.92/1.60 % (23715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (23715)Termination reason: Unknown
% 2.92/1.60 % (23715)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (23715)Memory used [KB]: 1407
% 2.92/1.60 % (23715)Time elapsed: 0.004 s
% 2.92/1.60 % (23715)Instructions burned: 3 (million)
% 2.92/1.60 % (23715)------------------------------
% 2.92/1.60 % (23715)------------------------------
% 2.92/1.60 % (23716)Instruction limit reached!
% 2.92/1.60 % (23716)------------------------------
% 2.92/1.60 % (23716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (23716)Termination reason: Unknown
% 2.92/1.60 % (23716)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (23716)Memory used [KB]: 1407
% 2.92/1.60 % (23716)Time elapsed: 0.004 s
% 2.92/1.60 % (23716)Instructions burned: 3 (million)
% 2.92/1.60 % (23716)------------------------------
% 2.92/1.60 % (23716)------------------------------
% 2.92/1.60 % (23718)Instruction limit reached!
% 2.92/1.60 % (23718)------------------------------
% 2.92/1.60 % (23718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (23718)Termination reason: Unknown
% 2.92/1.60 % (23718)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (23718)Memory used [KB]: 1791
% 2.92/1.60 % (23718)Time elapsed: 0.009 s
% 2.92/1.60 % (23718)Instructions burned: 18 (million)
% 2.92/1.60 % (23718)------------------------------
% 2.92/1.60 % (23718)------------------------------
% 2.92/1.60 % (23719)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/3Mi)
% 2.92/1.60 % (23719)Instruction limit reached!
% 2.92/1.60 % (23719)------------------------------
% 2.92/1.60 % (23719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (23719)Termination reason: Unknown
% 2.92/1.60 % (23719)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (23719)Memory used [KB]: 1407
% 2.92/1.60 % (23719)Time elapsed: 0.002 s
% 2.92/1.60 % (23719)Instructions burned: 3 (million)
% 2.92/1.60 % (23719)------------------------------
% 2.92/1.60 % (23719)------------------------------
% 2.92/1.61 % (23722)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_23392 for (2999ds/3Mi)
% 2.92/1.61 % (23722)Instruction limit reached!
% 2.92/1.61 % (23722)------------------------------
% 2.92/1.61 % (23722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (23722)Termination reason: Unknown
% 2.92/1.61 % (23722)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (23722)Memory used [KB]: 1535
% 2.92/1.61 % (23722)Time elapsed: 0.002 s
% 2.92/1.61 % (23722)Instructions burned: 3 (million)
% 2.92/1.61 % (23722)------------------------------
% 2.92/1.61 % (23722)------------------------------
% 2.92/1.61 % (23714)Instruction limit reached!
% 2.92/1.61 % (23714)------------------------------
% 2.92/1.61 % (23714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (23714)Termination reason: Unknown
% 2.92/1.61 % (23714)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (23714)Memory used [KB]: 2046
% 2.92/1.61 % (23714)Time elapsed: 0.017 s
% 2.92/1.61 % (23714)Instructions burned: 28 (million)
% 2.92/1.61 % (23714)------------------------------
% 2.92/1.61 % (23714)------------------------------
% 2.92/1.61 % (23723)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_23392 for (2999ds/1041Mi)
% 2.92/1.62 % (23720)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_23392 for (2999ds/37Mi)
% 2.92/1.62 % (23721)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_23392 for (2999ds/15Mi)
% 2.92/1.62 % (23724)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/7Mi)
% 2.92/1.62 % (23724)Instruction limit reached!
% 2.92/1.62 % (23724)------------------------------
% 2.92/1.62 % (23724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (23724)Termination reason: Unknown
% 2.92/1.62 % (23724)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (23724)Memory used [KB]: 1535
% 2.92/1.62 % (23724)Time elapsed: 0.003 s
% 2.92/1.62 % (23724)Instructions burned: 7 (million)
% 2.92/1.62 % (23724)------------------------------
% 2.92/1.62 % (23724)------------------------------
% 2.92/1.62 % (23721)Instruction limit reached!
% 2.92/1.62 % (23721)------------------------------
% 2.92/1.62 % (23721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (23721)Termination reason: Unknown
% 2.92/1.62 % (23721)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (23721)Memory used [KB]: 1663
% 2.92/1.62 % (23721)Time elapsed: 0.010 s
% 2.92/1.62 % (23721)Instructions burned: 16 (million)
% 2.92/1.62 % (23721)------------------------------
% 2.92/1.62 % (23721)------------------------------
% 2.92/1.63 % (23725)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/16Mi)
% 2.92/1.63 % (23726)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_23392 for (2999ds/3Mi)
% 2.92/1.63 % (23726)Instruction limit reached!
% 2.92/1.63 % (23726)------------------------------
% 2.92/1.63 % (23726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (23726)Termination reason: Unknown
% 2.92/1.63 % (23726)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (23726)Memory used [KB]: 1535
% 2.92/1.63 % (23726)Time elapsed: 0.002 s
% 2.92/1.63 % (23726)Instructions burned: 3 (million)
% 2.92/1.63 % (23726)------------------------------
% 2.92/1.63 % (23726)------------------------------
% 2.92/1.63 % (23720)Instruction limit reached!
% 2.92/1.63 % (23720)------------------------------
% 2.92/1.63 % (23720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (23720)Termination reason: Unknown
% 2.92/1.63 % (23720)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (23720)Memory used [KB]: 2174
% 2.92/1.63 % (23720)Time elapsed: 0.021 s
% 2.92/1.63 % (23720)Instructions burned: 37 (million)
% 2.92/1.63 % (23720)------------------------------
% 2.92/1.63 % (23720)------------------------------
% 2.92/1.64 % (23727)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_23392 for (2999ds/3Mi)
% 2.92/1.64 % (23712)Instruction limit reached!
% 2.92/1.64 % (23712)------------------------------
% 2.92/1.64 % (23712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (23712)Termination reason: Unknown
% 2.92/1.64 % (23712)Termination phase: Saturation
% 2.92/1.64
% 2.92/1.64 % (23712)Memory used [KB]: 7675
% 2.92/1.64 % (23712)Time elapsed: 0.049 s
% 2.92/1.64 % (23712)Instructions burned: 184 (million)
% 2.92/1.64 % (23712)------------------------------
% 2.92/1.64 % (23712)------------------------------
% 2.92/1.64 % (23727)Instruction limit reached!
% 2.92/1.64 % (23727)------------------------------
% 2.92/1.64 % (23727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (23727)Termination reason: Unknown
% 2.92/1.64 % (23727)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (23727)Memory used [KB]: 1535
% 2.92/1.64 % (23727)Time elapsed: 0.003 s
% 2.92/1.64 % (23727)Instructions burned: 5 (million)
% 2.92/1.64 % (23727)------------------------------
% 2.92/1.64 % (23727)------------------------------
% 2.92/1.64 % (23725)Instruction limit reached!
% 2.92/1.64 % (23725)------------------------------
% 2.92/1.64 % (23725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.64 % (23725)Termination reason: Unknown
% 2.92/1.64 % (23725)Termination phase: shuffling
% 2.92/1.64
% 2.92/1.64 % (23725)Memory used [KB]: 1791
% 2.92/1.64 % (23725)Time elapsed: 0.011 s
% 2.92/1.64 % (23725)Instructions burned: 17 (million)
% 2.92/1.64 % (23725)------------------------------
% 2.92/1.64 % (23725)------------------------------
% 2.92/1.64 % (23728)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/7Mi)
% 2.92/1.64 % (23730)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/4Mi)
% 2.92/1.65 % (23728)Instruction limit reached!
% 2.92/1.65 % (23728)------------------------------
% 2.92/1.65 % (23728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (23728)Termination reason: Unknown
% 2.92/1.65 % (23728)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (23728)Memory used [KB]: 1535
% 2.92/1.65 % (23728)Time elapsed: 0.003 s
% 2.92/1.65 % (23728)Instructions burned: 7 (million)
% 2.92/1.65 % (23728)------------------------------
% 2.92/1.65 % (23728)------------------------------
% 2.92/1.65 % (23730)Instruction limit reached!
% 2.92/1.65 % (23730)------------------------------
% 2.92/1.65 % (23730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (23730)Termination reason: Unknown
% 2.92/1.65 % (23730)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (23730)Memory used [KB]: 1535
% 2.92/1.65 % (23730)Time elapsed: 0.003 s
% 2.92/1.65 % (23730)Instructions burned: 7 (million)
% 2.92/1.65 % (23730)------------------------------
% 2.92/1.65 % (23730)------------------------------
% 2.92/1.65 % (23731)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/18Mi)
% 2.92/1.65 % (23729)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/3Mi)
% 2.92/1.65 % (23731)Instruction limit reached!
% 2.92/1.65 % (23731)------------------------------
% 2.92/1.65 % (23731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (23731)Termination reason: Unknown
% 2.92/1.65 % (23731)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (23731)Memory used [KB]: 1791
% 2.92/1.65 % (23731)Time elapsed: 0.006 s
% 2.92/1.65 % (23731)Instructions burned: 18 (million)
% 2.92/1.65 % (23731)------------------------------
% 2.92/1.65 % (23731)------------------------------
% 2.92/1.65 % (23729)Instruction limit reached!
% 2.92/1.65 % (23729)------------------------------
% 2.92/1.65 % (23729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.65 % (23729)Termination reason: Unknown
% 2.92/1.65 % (23729)Termination phase: shuffling
% 2.92/1.65
% 2.92/1.65 % (23729)Memory used [KB]: 1535
% 2.92/1.65 % (23729)Time elapsed: 0.004 s
% 2.92/1.65 % (23729)Instructions burned: 4 (million)
% 2.92/1.65 % (23729)------------------------------
% 2.92/1.65 % (23729)------------------------------
% 2.92/1.65 % (23732)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/710Mi)
% 2.92/1.66 % (23733)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/6Mi)
% 2.92/1.66 % (23734)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_23392 for (2999ds/902Mi)
% 2.92/1.66 % (23733)Instruction limit reached!
% 2.92/1.66 % (23733)------------------------------
% 2.92/1.66 % (23733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.66 % (23733)Termination reason: Unknown
% 2.92/1.66 % (23733)Termination phase: shuffling
% 2.92/1.66
% 2.92/1.66 % (23733)Memory used [KB]: 1663
% 2.92/1.66 % (23733)Time elapsed: 0.004 s
% 2.92/1.66 % (23733)Instructions burned: 7 (million)
% 2.92/1.66 % (23733)------------------------------
% 2.92/1.66 % (23733)------------------------------
% 2.92/1.66 % (23735)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_23392 for (2999ds/21Mi)
% 2.92/1.67 % (23717)Instruction limit reached!
% 2.92/1.67 % (23717)------------------------------
% 2.92/1.67 % (23717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (23717)Termination reason: Unknown
% 2.92/1.67 % (23717)Termination phase: Saturation
% 2.92/1.67
% 2.92/1.67 % (23717)Memory used [KB]: 9594
% 2.92/1.67 % (23717)Time elapsed: 0.081 s
% 2.92/1.67 % (23717)Instructions burned: 278 (million)
% 2.92/1.67 % (23717)------------------------------
% 2.92/1.67 % (23717)------------------------------
% 2.92/1.67 % (23737)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_23392 for (2999ds/6Mi)
% 2.92/1.67 % (23735)Instruction limit reached!
% 2.92/1.67 % (23735)------------------------------
% 2.92/1.67 % (23735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (23735)Termination reason: Unknown
% 2.92/1.67 % (23735)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (23735)Memory used [KB]: 1918
% 2.92/1.67 % (23735)Time elapsed: 0.008 s
% 2.92/1.67 % (23735)Instructions burned: 21 (million)
% 2.92/1.67 % (23735)------------------------------
% 2.92/1.67 % (23735)------------------------------
% 2.92/1.67 % (23737)Instruction limit reached!
% 2.92/1.67 % (23737)------------------------------
% 2.92/1.67 % (23737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (23737)Termination reason: Unknown
% 2.92/1.67 % (23737)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (23737)Memory used [KB]: 1535
% 2.92/1.67 % (23737)Time elapsed: 0.004 s
% 2.92/1.67 % (23737)Instructions burned: 8 (million)
% 2.92/1.67 % (23737)------------------------------
% 2.92/1.67 % (23737)------------------------------
% 2.92/1.67 % (23736)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23392 for (2999ds/5Mi)
% 2.92/1.67 % (23736)Instruction limit reached!
% 2.92/1.67 % (23736)------------------------------
% 2.92/1.67 % (23736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.67 % (23736)Termination reason: Unknown
% 2.92/1.67 % (23736)Termination phase: shuffling
% 2.92/1.67
% 2.92/1.67 % (23736)Memory used [KB]: 1535
% 2.92/1.67 % (23736)Time elapsed: 0.005 s
% 2.92/1.67 % (23736)Instructions burned: 6 (million)
% 2.92/1.67 % (23736)------------------------------
% 2.92/1.67 % (23736)------------------------------
% 2.92/1.68 % (23738)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/377Mi)
% 2.92/1.68 % (23739)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_23392 for (2998ds/779Mi)
% 2.92/1.68 % (23740)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_23392 for (2998ds/19Mi)
% 2.92/1.69 % (23740)Instruction limit reached!
% 2.92/1.69 % (23740)------------------------------
% 2.92/1.69 % (23740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.69 % (23740)Termination reason: Unknown
% 2.92/1.69 % (23740)Termination phase: shuffling
% 2.92/1.69
% 2.92/1.69 % (23740)Memory used [KB]: 1918
% 2.92/1.69 % (23740)Time elapsed: 0.008 s
% 2.92/1.69 % (23740)Instructions burned: 21 (million)
% 2.92/1.69 % (23740)------------------------------
% 2.92/1.69 % (23740)------------------------------
% 2.92/1.69 % (23741)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/879Mi)
% 2.92/1.70 % (23742)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/17Mi)
% 2.92/1.70 % (23742)Instruction limit reached!
% 2.92/1.70 % (23742)------------------------------
% 2.92/1.70 % (23742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.70 % (23742)Termination reason: Unknown
% 2.92/1.70 % (23742)Termination phase: shuffling
% 2.92/1.70
% 2.92/1.70 % (23742)Memory used [KB]: 1791
% 2.92/1.70 % (23742)Time elapsed: 0.006 s
% 2.92/1.70 % (23742)Instructions burned: 17 (million)
% 2.92/1.70 % (23742)------------------------------
% 2.92/1.70 % (23742)------------------------------
% 2.92/1.71 % (23743)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/3Mi)
% 2.92/1.71 % (23743)Instruction limit reached!
% 2.92/1.71 % (23743)------------------------------
% 2.92/1.71 % (23743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.71 % (23743)Termination reason: Unknown
% 2.92/1.71 % (23743)Termination phase: shuffling
% 2.92/1.71
% 2.92/1.71 % (23743)Memory used [KB]: 1535
% 2.92/1.71 % (23743)Time elapsed: 0.003 s
% 2.92/1.71 % (23743)Instructions burned: 5 (million)
% 2.92/1.71 % (23743)------------------------------
% 2.92/1.71 % (23743)------------------------------
% 2.92/1.72 % (23744)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/30Mi)
% 2.92/1.73 % (23744)Instruction limit reached!
% 2.92/1.73 % (23744)------------------------------
% 2.92/1.73 % (23744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.73 % (23744)Termination reason: Unknown
% 2.92/1.73 % (23744)Termination phase: shuffling
% 2.92/1.73
% 2.92/1.73 % (23744)Memory used [KB]: 1918
% 2.92/1.73 % (23744)Time elapsed: 0.009 s
% 2.92/1.73 % (23744)Instructions burned: 30 (million)
% 2.92/1.73 % (23744)------------------------------
% 2.92/1.73 % (23744)------------------------------
% 2.92/1.74 % (23745)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23392 for (2998ds/127Mi)
% 2.92/1.77 % (23745)Instruction limit reached!
% 2.92/1.77 % (23745)------------------------------
% 2.92/1.77 % (23745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.77 % (23745)Termination reason: Unknown
% 2.92/1.77 % (23745)Termination phase: Property scanning
% 2.92/1.77
% 2.92/1.77 % (23745)Memory used [KB]: 2686
% 2.92/1.77 % (23745)Time elapsed: 0.033 s
% 2.92/1.77 % (23745)Instructions burned: 128 (million)
% 2.92/1.77 % (23745)------------------------------
% 2.92/1.77 % (23745)------------------------------
% 2.92/1.78 % (23738)Instruction limit reached!
% 2.92/1.78 % (23738)------------------------------
% 2.92/1.78 % (23738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.78 % (23738)Termination reason: Unknown
% 2.92/1.78 % (23738)Termination phase: Saturation
% 2.92/1.78
% 2.92/1.78 % (23738)Memory used [KB]: 9338
% 2.92/1.78 % (23738)Time elapsed: 0.104 s
% 2.92/1.78 % (23738)Instructions burned: 379 (million)
% 2.92/1.78 % (23738)------------------------------
% 2.92/1.78 % (23738)------------------------------
% 2.92/1.78 % (23746)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23392 for (2997ds/100Mi)
% 2.92/1.79 % (23747)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_23392 for (2997ds/3Mi)
% 2.92/1.79 % (23747)Instruction limit reached!
% 2.92/1.79 % (23747)------------------------------
% 2.92/1.79 % (23747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.79 % (23747)Termination reason: Unknown
% 2.92/1.79 % (23747)Termination phase: shuffling
% 2.92/1.79
% 2.92/1.79 % (23747)Memory used [KB]: 1535
% 2.92/1.79 % (23747)Time elapsed: 0.002 s
% 2.92/1.79 % (23747)Instructions burned: 3 (million)
% 2.92/1.79 % (23747)------------------------------
% 2.92/1.79 % (23747)------------------------------
% 2.92/1.80 % (23748)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_23392 for (2997ds/20Mi)
% 2.92/1.81 % (23748)Instruction limit reached!
% 2.92/1.81 % (23748)------------------------------
% 2.92/1.81 % (23748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (23748)Termination reason: Unknown
% 2.92/1.81 % (23748)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (23748)Memory used [KB]: 1791
% 2.92/1.81 % (23748)Time elapsed: 0.008 s
% 2.92/1.81 % (23748)Instructions burned: 21 (million)
% 2.92/1.81 % (23748)------------------------------
% 2.92/1.81 % (23748)------------------------------
% 2.92/1.81 % (23746)Instruction limit reached!
% 2.92/1.81 % (23746)------------------------------
% 2.92/1.81 % (23746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (23746)Termination reason: Unknown
% 2.92/1.81 % (23746)Termination phase: Function definition elimination
% 2.92/1.81
% 2.92/1.81 % (23746)Memory used [KB]: 2558
% 2.92/1.81 % (23746)Time elapsed: 0.027 s
% 2.92/1.81 % (23746)Instructions burned: 100 (million)
% 2.92/1.81 % (23746)------------------------------
% 2.92/1.81 % (23746)------------------------------
% 2.92/1.82 % (23750)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_23392 for (2997ds/107Mi)
% 2.92/1.83 % (23749)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_23392 for (2997ds/86Mi)
% 2.92/1.84 % (23750)Instruction limit reached!
% 2.92/1.84 % (23750)------------------------------
% 2.92/1.84 % (23750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.84 % (23750)Termination reason: Unknown
% 2.92/1.84 % (23750)Termination phase: Property scanning
% 2.92/1.84
% 2.92/1.84 % (23750)Memory used [KB]: 2558
% 2.92/1.84 % (23750)Time elapsed: 0.028 s
% 2.92/1.84 % (23750)Instructions burned: 109 (million)
% 2.92/1.84 % (23750)------------------------------
% 2.92/1.84 % (23750)------------------------------
% 2.92/1.85 % (23751)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_23392 for (2997ds/39Mi)
% 2.92/1.86 % (23751)Instruction limit reached!
% 2.92/1.86 % (23751)------------------------------
% 2.92/1.86 % (23751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (23751)Termination reason: Unknown
% 2.92/1.86 % (23751)Termination phase: shuffling
% 2.92/1.86
% 2.92/1.86 % (23751)Memory used [KB]: 2302
% 2.92/1.86 % (23751)Time elapsed: 0.012 s
% 2.92/1.86 % (23751)Instructions burned: 39 (million)
% 2.92/1.86 % (23751)------------------------------
% 2.92/1.86 % (23751)------------------------------
% 2.92/1.87 % (23749)Instruction limit reached!
% 2.92/1.87 % (23749)------------------------------
% 2.92/1.87 % (23749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.87 % (23749)Termination reason: Unknown
% 2.92/1.87 % (23749)Termination phase: Property scanning
% 2.92/1.87
% 2.92/1.87 % (23749)Memory used [KB]: 2558
% 2.92/1.87 % (23749)Time elapsed: 0.045 s
% 2.92/1.87 % (23749)Instructions burned: 87 (million)
% 2.92/1.87 % (23749)------------------------------
% 2.92/1.87 % (23749)------------------------------
% 2.92/1.87 % (23752)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_23392 for (2996ds/448Mi)
% 2.92/1.89 % (23753)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_23392 for (2996ds/46Mi)
% 2.92/1.89 % (23739)Instruction limit reached!
% 2.92/1.89 % (23739)------------------------------
% 2.92/1.89 % (23739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (23739)Termination reason: Unknown
% 2.92/1.89 % (23739)Termination phase: Saturation
% 2.92/1.89
% 2.92/1.89 % (23739)Memory used [KB]: 7547
% 2.92/1.89 % (23739)Time elapsed: 0.213 s
% 2.92/1.89 % (23739)Instructions burned: 781 (million)
% 2.92/1.89 % (23739)------------------------------
% 2.92/1.89 % (23739)------------------------------
% 2.92/1.89 % (23723)Instruction limit reached!
% 2.92/1.89 % (23723)------------------------------
% 2.92/1.89 % (23723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (23723)Termination reason: Unknown
% 2.92/1.89 % (23723)Termination phase: Saturation
% 2.92/1.89
% 2.92/1.89 % (23723)Memory used [KB]: 14839
% 2.92/1.89 % (23723)Time elapsed: 0.284 s
% 2.92/1.89 % (23723)Instructions burned: 1044 (million)
% 2.92/1.89 % (23723)------------------------------
% 2.92/1.89 % (23723)------------------------------
% 2.92/1.90 % (23754)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_23392 for (2996ds/98Mi)
% 2.92/1.90 % (23755)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_23392 for (2996ds/507Mi)
% 2.92/1.91 % (23753)Instruction limit reached!
% 2.92/1.91 % (23753)------------------------------
% 2.92/1.91 % (23753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.91 % (23753)Termination reason: Unknown
% 2.92/1.91 % (23753)Termination phase: Property scanning
% 2.92/1.91
% 2.92/1.91 % (23753)Memory used [KB]: 2430
% 2.92/1.91 % (23753)Time elapsed: 0.023 s
% 2.92/1.91 % (23753)Instructions burned: 47 (million)
% 2.92/1.91 % (23753)------------------------------
% 2.92/1.91 % (23753)------------------------------
% 2.92/1.91 % (23732)Instruction limit reached!
% 2.92/1.91 % (23732)------------------------------
% 2.92/1.91 % (23732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.91 % (23732)Termination reason: Unknown
% 2.92/1.91 % (23732)Termination phase: Saturation
% 2.92/1.91
% 2.92/1.91 % (23732)Memory used [KB]: 10490
% 2.92/1.91 % (23732)Time elapsed: 0.260 s
% 2.92/1.91 % (23732)Instructions burned: 712 (million)
% 2.92/1.91 % (23732)------------------------------
% 2.92/1.91 % (23732)------------------------------
% 2.92/1.92 % (23756)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_23392 for (2996ds/149Mi)
% 2.92/1.92 % (23757)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23392 for (2996ds/39Mi)
% 2.92/1.93 % (23734)Instruction limit reached!
% 2.92/1.93 % (23734)------------------------------
% 2.92/1.93 % (23734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.93 % (23734)Termination reason: Unknown
% 2.92/1.93 % (23734)Termination phase: Saturation
% 2.92/1.93
% 2.92/1.93 % (23734)Memory used [KB]: 12537
% 2.92/1.93 % (23734)Time elapsed: 0.271 s
% 2.92/1.93 % (23734)Instructions burned: 904 (million)
% 2.92/1.93 % (23734)------------------------------
% 2.92/1.93 % (23734)------------------------------
% 2.92/1.93 % (23754)Instruction limit reached!
% 2.92/1.93 % (23754)------------------------------
% 2.92/1.93 % (23754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.93 % (23754)Termination reason: Unknown
% 2.92/1.93 % (23754)Termination phase: Property scanning
% 2.92/1.93
% 2.92/1.93 % (23754)Memory used [KB]: 2430
% 2.92/1.93 % (23754)Time elapsed: 0.028 s
% 2.92/1.93 % (23754)Instructions burned: 98 (million)
% 2.92/1.93 % (23754)------------------------------
% 2.92/1.93 % (23754)------------------------------
% 2.92/1.94 % (23757)Instruction limit reached!
% 2.92/1.94 % (23757)------------------------------
% 2.92/1.94 % (23757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (23757)Termination reason: Unknown
% 2.92/1.94 % (23757)Termination phase: shuffling
% 2.92/1.94
% 2.92/1.94 % (23757)Memory used [KB]: 2302
% 2.92/1.94 % (23757)Time elapsed: 0.013 s
% 2.92/1.94 % (23757)Instructions burned: 40 (million)
% 2.92/1.94 % (23757)------------------------------
% 2.92/1.94 % (23757)------------------------------
% 2.92/1.94 % (23758)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_23392 for (2996ds/6Mi)
% 2.92/1.94 % (23758)Instruction limit reached!
% 2.92/1.94 % (23758)------------------------------
% 2.92/1.94 % (23758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (23758)Termination reason: Unknown
% 2.92/1.94 % (23758)Termination phase: shuffling
% 2.92/1.94
% 2.92/1.94 % (23758)Memory used [KB]: 1535
% 2.92/1.94 % (23758)Time elapsed: 0.003 s
% 2.92/1.94 % (23758)Instructions burned: 7 (million)
% 2.92/1.94 % (23758)------------------------------
% 2.92/1.94 % (23758)------------------------------
% 2.92/1.94 % (23759)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_23392 for (2996ds/1087Mi)
% 2.92/1.95 % (23760)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23392 for (2996ds/47Mi)
% 2.92/1.95 % (23761)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_23392 for (2996ds/44Mi)
% 2.92/1.96 % (23760)Instruction limit reached!
% 2.92/1.96 % (23760)------------------------------
% 2.92/1.96 % (23760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.96 % (23760)Termination reason: Unknown
% 2.92/1.96 % (23760)Termination phase: Property scanning
% 2.92/1.96
% 2.92/1.96 % (23760)Memory used [KB]: 2430
% 2.92/1.96 % (23760)Time elapsed: 0.015 s
% 2.92/1.96 % (23760)Instructions burned: 48 (million)
% 2.92/1.96 % (23760)------------------------------
% 2.92/1.96 % (23760)------------------------------
% 2.92/1.96 % (23756)Instruction limit reached!
% 2.92/1.96 % (23756)------------------------------
% 2.92/1.96 % (23756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.96 % (23756)Termination reason: Unknown
% 2.92/1.96 % (23756)Termination phase: Property scanning
% 2.92/1.96
% 2.92/1.96 % (23756)Memory used [KB]: 3326
% 2.92/1.96 % (23756)Time elapsed: 0.044 s
% 2.92/1.96 % (23756)Instructions burned: 150 (million)
% 2.92/1.96 % (23756)------------------------------
% 2.92/1.96 % (23756)------------------------------
% 2.92/1.96 % (23761)Instruction limit reached!
% 2.92/1.96 % (23761)------------------------------
% 2.92/1.96 % (23761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.96 % (23761)Termination reason: Unknown
% 2.92/1.96 % (23761)Termination phase: Property scanning
% 2.92/1.96
% 2.92/1.96 % (23761)Memory used [KB]: 2430
% 2.92/1.96 % (23761)Time elapsed: 0.014 s
% 2.92/1.96 % (23761)Instructions burned: 46 (million)
% 2.92/1.96 % (23761)------------------------------
% 2.92/1.96 % (23761)------------------------------
% 2.92/1.97 % (23764)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_23392 for (2995ds/31Mi)
% 2.92/1.97 % (23762)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_23392 for (2995ds/432Mi)
% 2.92/1.97 % (23763)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/62Mi)
% 2.92/1.98 % (23764)Instruction limit reached!
% 2.92/1.98 % (23764)------------------------------
% 2.92/1.98 % (23764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (23764)Termination reason: Unknown
% 2.92/1.98 % (23764)Termination phase: shuffling
% 2.92/1.98
% 2.92/1.98 % (23764)Memory used [KB]: 2174
% 2.92/1.98 % (23764)Time elapsed: 0.010 s
% 2.92/1.98 % (23764)Instructions burned: 34 (million)
% 2.92/1.98 % (23764)------------------------------
% 2.92/1.98 % (23764)------------------------------
% 2.92/1.98 % (23741)Instruction limit reached!
% 2.92/1.98 % (23741)------------------------------
% 2.92/1.98 % (23741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.98 % (23741)Termination reason: Unknown
% 2.92/1.98 % (23741)Termination phase: Saturation
% 2.92/1.98
% 2.92/1.98 % (23741)Memory used [KB]: 9722
% 2.92/1.98 % (23741)Time elapsed: 0.312 s
% 2.92/1.98 % (23741)Instructions burned: 881 (million)
% 2.92/1.98 % (23741)------------------------------
% 2.92/1.98 % (23741)------------------------------
% 2.92/1.99 % (23752)Instruction limit reached!
% 2.92/1.99 % (23752)------------------------------
% 2.92/1.99 % (23752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (23752)Termination reason: Unknown
% 2.92/1.99 % (23752)Termination phase: Saturation
% 2.92/1.99
% 2.92/1.99 % (23752)Memory used [KB]: 7419
% 2.92/1.99 % (23752)Time elapsed: 0.114 s
% 2.92/1.99 % (23752)Instructions burned: 450 (million)
% 2.92/1.99 % (23752)------------------------------
% 2.92/1.99 % (23752)------------------------------
% 2.92/1.99 % (23765)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/96Mi)
% 2.92/1.99 % (23763)Instruction limit reached!
% 2.92/1.99 % (23763)------------------------------
% 2.92/1.99 % (23763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.99 % (23763)Termination reason: Unknown
% 2.92/1.99 % (23763)Termination phase: Property scanning
% 2.92/1.99
% 2.92/1.99 % (23763)Memory used [KB]: 2430
% 2.92/1.99 % (23763)Time elapsed: 0.019 s
% 2.92/1.99 % (23763)Instructions burned: 65 (million)
% 2.92/1.99 % (23763)------------------------------
% 2.92/1.99 % (23763)------------------------------
% 2.92/1.99 % (23766)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_23392 for (2995ds/453Mi)
% 2.92/2.00 % (23767)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_23392 for (2995ds/71Mi)
% 2.92/2.00 % (23768)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/83Mi)
% 5.92/2.01 % (23765)Instruction limit reached!
% 5.92/2.01 % (23765)------------------------------
% 5.92/2.01 % (23765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.01 % (23765)Termination reason: Unknown
% 5.92/2.01 % (23765)Termination phase: Property scanning
% 5.92/2.01
% 5.92/2.01 % (23765)Memory used [KB]: 2558
% 5.92/2.01 % (23765)Time elapsed: 0.026 s
% 5.92/2.01 % (23765)Instructions burned: 98 (million)
% 5.92/2.01 % (23765)------------------------------
% 5.92/2.01 % (23765)------------------------------
% 5.92/2.02 % (23768)Instruction limit reached!
% 5.92/2.02 % (23768)------------------------------
% 5.92/2.02 % (23768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.02 % (23768)Termination reason: Unknown
% 5.92/2.02 % (23768)Termination phase: SInE selection
% 5.92/2.02
% 5.92/2.02 % (23768)Memory used [KB]: 2430
% 5.92/2.02 % (23768)Time elapsed: 0.025 s
% 5.92/2.02 % (23768)Instructions burned: 83 (million)
% 5.92/2.02 % (23768)------------------------------
% 5.92/2.02 % (23768)------------------------------
% 5.92/2.02 % (23769)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/11Mi)
% 5.92/2.03 % (23769)Instruction limit reached!
% 5.92/2.03 % (23769)------------------------------
% 5.92/2.03 % (23769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.03 % (23769)Termination reason: Unknown
% 5.92/2.03 % (23769)Termination phase: shuffling
% 5.92/2.03
% 5.92/2.03 % (23769)Memory used [KB]: 1663
% 5.92/2.03 % (23769)Time elapsed: 0.004 s
% 5.92/2.03 % (23769)Instructions burned: 11 (million)
% 5.92/2.03 % (23769)------------------------------
% 5.92/2.03 % (23769)------------------------------
% 5.92/2.03 % (23767)Instruction limit reached!
% 5.92/2.03 % (23767)------------------------------
% 5.92/2.03 % (23767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.03 % (23767)Termination reason: Unknown
% 5.92/2.03 % (23767)Termination phase: Property scanning
% 5.92/2.03
% 5.92/2.03 % (23767)Memory used [KB]: 2430
% 5.92/2.03 % (23767)Time elapsed: 0.035 s
% 5.92/2.03 % (23767)Instructions burned: 73 (million)
% 5.92/2.03 % (23767)------------------------------
% 5.92/2.03 % (23767)------------------------------
% 5.92/2.03 % (23770)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_23392 for (2995ds/41Mi)
% 5.92/2.03 % (23771)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/6Mi)
% 5.92/2.04 % (23771)Instruction limit reached!
% 5.92/2.04 % (23771)------------------------------
% 5.92/2.04 % (23771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.04 % (23771)Termination reason: Unknown
% 5.92/2.04 % (23771)Termination phase: shuffling
% 5.92/2.04
% 5.92/2.04 % (23771)Memory used [KB]: 1535
% 5.92/2.04 % (23771)Time elapsed: 0.003 s
% 5.92/2.04 % (23771)Instructions burned: 7 (million)
% 5.92/2.04 % (23771)------------------------------
% 5.92/2.04 % (23771)------------------------------
% 5.92/2.04 % (23772)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/150Mi)
% 5.92/2.04 % (23770)Instruction limit reached!
% 5.92/2.04 % (23770)------------------------------
% 5.92/2.04 % (23770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.04 % (23770)Termination reason: Unknown
% 5.92/2.04 % (23770)Termination phase: shuffling
% 5.92/2.04
% 5.92/2.04 % (23770)Memory used [KB]: 2302
% 5.92/2.04 % (23770)Time elapsed: 0.013 s
% 5.92/2.04 % (23770)Instructions burned: 42 (million)
% 5.92/2.04 % (23770)------------------------------
% 5.92/2.04 % (23770)------------------------------
% 5.92/2.05 % (23773)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23392 for (2995ds/343Mi)
% 5.92/2.05 % (23755)Instruction limit reached!
% 5.92/2.05 % (23755)------------------------------
% 5.92/2.05 % (23755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.05 % (23755)Termination reason: Unknown
% 5.92/2.05 % (23755)Termination phase: Saturation
% 5.92/2.05
% 5.92/2.05 % (23755)Memory used [KB]: 8059
% 5.92/2.05 % (23755)Time elapsed: 0.148 s
% 5.92/2.05 % (23755)Instructions burned: 509 (million)
% 5.92/2.05 % (23755)------------------------------
% 5.92/2.05 % (23755)------------------------------
% 5.92/2.05 % (23774)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_23392 for (2995ds/109Mi)
% 5.92/2.06 % (23775)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_23392 for (2995ds/253Mi)
% 5.92/2.08 % (23762)Instruction limit reached!
% 5.92/2.08 % (23762)------------------------------
% 5.92/2.08 % (23762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.08 % (23762)Termination reason: Unknown
% 5.92/2.08 % (23762)Termination phase: Saturation
% 5.92/2.08
% 5.92/2.08 % (23762)Memory used [KB]: 2942
% 5.92/2.08 % (23762)Time elapsed: 0.113 s
% 5.92/2.08 % (23762)Instructions burned: 432 (million)
% 5.92/2.08 % (23762)------------------------------
% 5.92/2.08 % (23762)------------------------------
% 5.92/2.08 % (23774)Instruction limit reached!
% 5.92/2.08 % (23774)------------------------------
% 5.92/2.08 % (23774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.08 % (23774)Termination reason: Unknown
% 5.92/2.08 % (23774)Termination phase: Property scanning
% 5.92/2.08
% 5.92/2.08 % (23774)Memory used [KB]: 2558
% 5.92/2.08 % (23774)Time elapsed: 0.032 s
% 5.92/2.08 % (23774)Instructions burned: 110 (million)
% 5.92/2.08 % (23774)------------------------------
% 5.92/2.08 % (23774)------------------------------
% 5.92/2.08 % (23772)Instruction limit reached!
% 5.92/2.08 % (23772)------------------------------
% 5.92/2.08 % (23772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.08 % (23772)Termination reason: Unknown
% 5.92/2.08 % (23772)Termination phase: Function definition elimination
% 5.92/2.08
% 5.92/2.08 % (23772)Memory used [KB]: 4477
% 5.92/2.08 % (23772)Time elapsed: 0.043 s
% 5.92/2.08 % (23772)Instructions burned: 151 (million)
% 5.92/2.08 % (23772)------------------------------
% 5.92/2.08 % (23772)------------------------------
% 5.92/2.09 % (23776)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23392 for (2994ds/140Mi)
% 5.92/2.09 % (23777)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_23392 for (2994ds/614Mi)
% 5.92/2.09 % (23778)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_23392 for (2994ds/202Mi)
% 5.92/2.11 % (23766)Instruction limit reached!
% 5.92/2.11 % (23766)------------------------------
% 5.92/2.11 % (23766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.11 % (23766)Termination reason: Unknown
% 5.92/2.11 % (23766)Termination phase: Saturation
% 5.92/2.11
% 5.92/2.11 % (23766)Memory used [KB]: 7419
% 5.92/2.11 % (23766)Time elapsed: 0.117 s
% 5.92/2.11 % (23766)Instructions burned: 454 (million)
% 5.92/2.11 % (23766)------------------------------
% 5.92/2.11 % (23766)------------------------------
% 6.44/2.12 % (23779)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_23392 for (2994ds/339Mi)
% 6.44/2.13 % (23776)Instruction limit reached!
% 6.44/2.13 % (23776)------------------------------
% 6.44/2.13 % (23776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.13 % (23776)Termination reason: Unknown
% 6.44/2.13 % (23776)Termination phase: Property scanning
% 6.44/2.13
% 6.44/2.13 % (23776)Memory used [KB]: 2686
% 6.44/2.13 % (23776)Time elapsed: 0.037 s
% 6.44/2.13 % (23776)Instructions burned: 141 (million)
% 6.44/2.13 % (23776)------------------------------
% 6.44/2.13 % (23776)------------------------------
% 6.44/2.13 % (23775)Instruction limit reached!
% 6.44/2.13 % (23775)------------------------------
% 6.44/2.13 % (23775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.13 % (23775)Termination reason: Unknown
% 6.44/2.13 % (23775)Termination phase: Saturation
% 6.44/2.13
% 6.44/2.13 % (23775)Memory used [KB]: 9722
% 6.44/2.13 % (23775)Time elapsed: 0.074 s
% 6.44/2.13 % (23775)Instructions burned: 255 (million)
% 6.44/2.13 % (23775)------------------------------
% 6.44/2.13 % (23775)------------------------------
% 6.44/2.14 % (23773)Instruction limit reached!
% 6.44/2.14 % (23773)------------------------------
% 6.44/2.14 % (23773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (23773)Termination reason: Unknown
% 6.44/2.14 % (23773)Termination phase: Saturation
% 6.44/2.14
% 6.44/2.14 % (23773)Memory used [KB]: 8571
% 6.44/2.14 % (23773)Time elapsed: 0.091 s
% 6.44/2.14 % (23773)Instructions burned: 345 (million)
% 6.44/2.14 % (23773)------------------------------
% 6.44/2.14 % (23773)------------------------------
% 6.44/2.14 % (23780)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_23392 for (2994ds/283Mi)
% 6.44/2.14 % (23781)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23392 for (2994ds/134Mi)
% 6.44/2.15 % (23782)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23392 for (2994ds/298Mi)
% 6.44/2.15 % (23778)Instruction limit reached!
% 6.44/2.15 % (23778)------------------------------
% 6.44/2.15 % (23778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.15 % (23778)Termination reason: Unknown
% 6.44/2.15 % (23778)Termination phase: Saturation
% 6.44/2.15
% 6.44/2.15 % (23778)Memory used [KB]: 4733
% 6.44/2.15 % (23778)Time elapsed: 0.058 s
% 6.44/2.15 % (23778)Instructions burned: 204 (million)
% 6.44/2.15 % (23778)------------------------------
% 6.44/2.15 % (23778)------------------------------
% 6.44/2.16 % (23783)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23392 for (2994ds/192Mi)
% 6.44/2.18 % (23781)Instruction limit reached!
% 6.44/2.18 % (23781)------------------------------
% 6.44/2.18 % (23781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (23781)Termination reason: Unknown
% 6.44/2.18 % (23781)Termination phase: Property scanning
% 6.44/2.18
% 6.44/2.18 % (23781)Memory used [KB]: 2686
% 6.44/2.18 % (23781)Time elapsed: 0.035 s
% 6.44/2.18 % (23781)Instructions burned: 135 (million)
% 6.44/2.18 % (23781)------------------------------
% 6.44/2.18 % (23781)------------------------------
% 6.44/2.19 % (23784)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_23392 for (2993ds/258Mi)
% 6.86/2.21 % (23780)Instruction limit reached!
% 6.86/2.21 % (23780)------------------------------
% 6.86/2.21 % (23780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.21 % (23780)Termination reason: Unknown
% 6.86/2.21 % (23780)Termination phase: Saturation
% 6.86/2.21
% 6.86/2.21 % (23780)Memory used [KB]: 7419
% 6.86/2.21 % (23780)Time elapsed: 0.072 s
% 6.86/2.21 % (23780)Instructions burned: 285 (million)
% 6.86/2.21 % (23780)------------------------------
% 6.86/2.21 % (23780)------------------------------
% 6.86/2.21 % (23779)Instruction limit reached!
% 6.86/2.21 % (23779)------------------------------
% 6.86/2.21 % (23779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.21 % (23779)Termination reason: Unknown
% 6.86/2.21 % (23779)Termination phase: Saturation
% 6.86/2.21
% 6.86/2.21 % (23779)Memory used [KB]: 7931
% 6.86/2.21 % (23779)Time elapsed: 0.094 s
% 6.86/2.21 % (23779)Instructions burned: 339 (million)
% 6.86/2.21 % (23779)------------------------------
% 6.86/2.21 % (23779)------------------------------
% 6.86/2.21 % (23783)Instruction limit reached!
% 6.86/2.21 % (23783)------------------------------
% 6.86/2.21 % (23783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.21 % (23783)Termination reason: Unknown
% 6.86/2.21 % (23783)Termination phase: Saturation
% 6.86/2.21
% 6.86/2.21 % (23783)Memory used [KB]: 7675
% 6.86/2.21 % (23783)Time elapsed: 0.051 s
% 6.86/2.21 % (23783)Instructions burned: 193 (million)
% 6.86/2.21 % (23783)------------------------------
% 6.86/2.21 % (23783)------------------------------
% 6.86/2.22 % (23785)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_23392 for (2993ds/90Mi)
% 6.86/2.22 % (23786)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_23392 for (2993ds/231Mi)
% 6.86/2.22 % (23782)Instruction limit reached!
% 6.86/2.22 % (23782)------------------------------
% 6.86/2.22 % (23782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.22 % (23782)Termination reason: Unknown
% 6.86/2.22 % (23782)Termination phase: Saturation
% 6.86/2.22
% 6.86/2.22 % (23782)Memory used [KB]: 7419
% 6.86/2.22 % (23782)Time elapsed: 0.075 s
% 6.86/2.22 % (23782)Instructions burned: 300 (million)
% 6.86/2.22 % (23782)------------------------------
% 6.86/2.22 % (23782)------------------------------
% 6.86/2.22 % (23787)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_23392 for (2993ds/458Mi)
% 6.86/2.23 % (23788)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_23392 for (2993ds/31Mi)
% 6.86/2.24 % (23788)Instruction limit reached!
% 6.86/2.24 % (23788)------------------------------
% 6.86/2.24 % (23788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.24 % (23788)Termination reason: Unknown
% 6.86/2.24 % (23788)Termination phase: shuffling
% 6.86/2.24
% 6.86/2.24 % (23788)Memory used [KB]: 2046
% 6.86/2.24 % (23788)Time elapsed: 0.010 s
% 6.86/2.24 % (23788)Instructions burned: 31 (million)
% 6.86/2.24 % (23788)------------------------------
% 6.86/2.24 % (23788)------------------------------
% 6.86/2.24 % (23785)Instruction limit reached!
% 6.86/2.24 % (23785)------------------------------
% 6.86/2.24 % (23785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.24 % (23785)Termination reason: Unknown
% 6.86/2.24 % (23785)Termination phase: Property scanning
% 6.86/2.24
% 6.86/2.24 % (23785)Memory used [KB]: 2558
% 6.86/2.24 % (23785)Time elapsed: 0.025 s
% 6.86/2.24 % (23785)Instructions burned: 90 (million)
% 6.86/2.24 % (23785)------------------------------
% 6.86/2.24 % (23785)------------------------------
% 6.86/2.25 % (23789)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_23392 for (2993ds/297Mi)
% 6.86/2.25 % (23790)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_23392 for (2993ds/987Mi)
% 6.86/2.26 % (23784)Instruction limit reached!
% 6.86/2.26 % (23784)------------------------------
% 6.86/2.26 % (23784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.26 % (23784)Termination reason: Unknown
% 6.86/2.26 % (23784)Termination phase: Saturation
% 6.86/2.26
% 6.86/2.26 % (23784)Memory used [KB]: 7931
% 6.86/2.26 % (23784)Time elapsed: 0.069 s
% 6.86/2.26 % (23784)Instructions burned: 259 (million)
% 6.86/2.26 % (23784)------------------------------
% 6.86/2.26 % (23784)------------------------------
% 6.86/2.26 % (23791)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_23392 for (2993ds/182Mi)
% 6.86/2.27 % (23777)Instruction limit reached!
% 6.86/2.27 % (23777)------------------------------
% 6.86/2.27 % (23777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.27 % (23777)Termination reason: Unknown
% 6.86/2.27 % (23777)Termination phase: Saturation
% 6.86/2.27
% 6.86/2.27 % (23777)Memory used [KB]: 9850
% 6.86/2.27 % (23777)Time elapsed: 0.180 s
% 6.86/2.27 % (23777)Instructions burned: 614 (million)
% 6.86/2.27 % (23777)------------------------------
% 6.86/2.27 % (23777)------------------------------
% 6.86/2.28 % (23786)Instruction limit reached!
% 6.86/2.28 % (23786)------------------------------
% 6.86/2.28 % (23786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.28 % (23786)Termination reason: Unknown
% 6.86/2.28 % (23786)Termination phase: Saturation
% 6.86/2.28
% 6.86/2.28 % (23786)Memory used [KB]: 8443
% 6.86/2.28 % (23786)Time elapsed: 0.062 s
% 6.86/2.28 % (23786)Instructions burned: 233 (million)
% 6.86/2.28 % (23786)------------------------------
% 6.86/2.28 % (23786)------------------------------
% 6.86/2.28 % (23759)Instruction limit reached!
% 6.86/2.28 % (23759)------------------------------
% 6.86/2.28 % (23759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.28 % (23759)Termination reason: Unknown
% 6.86/2.28 % (23759)Termination phase: Saturation
% 6.86/2.28
% 6.86/2.28 % (23759)Memory used [KB]: 12025
% 6.86/2.28 % (23759)Time elapsed: 0.343 s
% 6.86/2.28 % (23759)Instructions burned: 1087 (million)
% 6.86/2.28 % (23759)------------------------------
% 6.86/2.28 % (23759)------------------------------
% 6.86/2.28 % (23792)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_23392 for (2992ds/182Mi)
% 6.86/2.29 % (23793)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_23392 for (2992ds/154Mi)
% 6.86/2.29 % (23794)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_23392 for (2992ds/79Mi)
% 7.67/2.31 % (23791)Instruction limit reached!
% 7.67/2.31 % (23791)------------------------------
% 7.67/2.31 % (23791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.31 % (23791)Termination reason: Unknown
% 7.67/2.31 % (23791)Termination phase: Saturation
% 7.67/2.31
% 7.67/2.31 % (23791)Memory used [KB]: 7675
% 7.67/2.31 % (23791)Time elapsed: 0.048 s
% 7.67/2.31 % (23791)Instructions burned: 184 (million)
% 7.67/2.31 % (23791)------------------------------
% 7.67/2.31 % (23791)------------------------------
% 7.67/2.31 % (23794)Instruction limit reached!
% 7.67/2.31 % (23794)------------------------------
% 7.67/2.31 % (23794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.31 % (23794)Termination reason: Unknown
% 7.67/2.31 % (23794)Termination phase: Property scanning
% 7.67/2.31
% 7.67/2.31 % (23794)Memory used [KB]: 2558
% 7.67/2.31 % (23794)Time elapsed: 0.022 s
% 7.67/2.31 % (23794)Instructions burned: 81 (million)
% 7.67/2.31 % (23794)------------------------------
% 7.67/2.31 % (23794)------------------------------
% 7.67/2.32 % (23789)Instruction limit reached!
% 7.67/2.32 % (23789)------------------------------
% 7.67/2.32 % (23789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.32 % (23789)Termination reason: Unknown
% 7.67/2.32 % (23789)Termination phase: Saturation
% 7.67/2.32
% 7.67/2.32 % (23789)Memory used [KB]: 7419
% 7.67/2.32 % (23789)Time elapsed: 0.074 s
% 7.67/2.32 % (23789)Instructions burned: 297 (million)
% 7.67/2.32 % (23789)------------------------------
% 7.67/2.32 % (23789)------------------------------
% 7.67/2.32 % (23795)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_23392 for (2992ds/216Mi)
% 7.67/2.32 % (23796)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23392 for (2992ds/114Mi)
% 7.67/2.33 % (23793)Instruction limit reached!
% 7.67/2.33 % (23793)------------------------------
% 7.67/2.33 % (23793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.33 % (23793)Termination reason: Unknown
% 7.67/2.33 % (23793)Termination phase: Saturation
% 7.67/2.33
% 7.67/2.33 % (23793)Memory used [KB]: 7036
% 7.67/2.33 % (23793)Time elapsed: 0.040 s
% 7.67/2.33 % (23793)Instructions burned: 156 (million)
% 7.67/2.33 % (23793)------------------------------
% 7.67/2.33 % (23793)------------------------------
% 7.67/2.33 % (23797)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_23392 for (2992ds/922Mi)
% 7.67/2.33 % (23792)Instruction limit reached!
% 7.67/2.33 % (23792)------------------------------
% 7.67/2.33 % (23792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.33 % (23792)Termination reason: Unknown
% 7.67/2.33 % (23792)Termination phase: Property scanning
% 7.67/2.33
% 7.67/2.33 % (23792)Memory used [KB]: 4221
% 7.67/2.33 % (23792)Time elapsed: 0.051 s
% 7.67/2.33 % (23792)Instructions burned: 183 (million)
% 7.67/2.33 % (23792)------------------------------
% 7.67/2.33 % (23792)------------------------------
% 7.67/2.34 % (23798)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_23392 for (2992ds/182Mi)
% 7.67/2.34 % (23799)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_23392 for (2992ds/164Mi)
% 7.67/2.35 % (23787)Instruction limit reached!
% 7.67/2.35 % (23787)------------------------------
% 7.67/2.35 % (23787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.35 % (23787)Termination reason: Unknown
% 7.67/2.35 % (23787)Termination phase: Saturation
% 7.67/2.35
% 7.67/2.35 % (23787)Memory used [KB]: 9466
% 7.67/2.35 % (23787)Time elapsed: 0.128 s
% 7.67/2.35 % (23787)Instructions burned: 459 (million)
% 7.67/2.35 % (23787)------------------------------
% 7.67/2.35 % (23787)------------------------------
% 7.67/2.35 % (23796)Instruction limit reached!
% 7.67/2.35 % (23796)------------------------------
% 7.67/2.35 % (23796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.35 % (23796)Termination reason: Unknown
% 7.67/2.35 % (23796)Termination phase: Property scanning
% 7.67/2.35
% 7.67/2.35 % (23796)Memory used [KB]: 2686
% 7.67/2.35 % (23796)Time elapsed: 0.031 s
% 7.67/2.35 % (23796)Instructions burned: 116 (million)
% 7.67/2.35 % (23796)------------------------------
% 7.67/2.35 % (23796)------------------------------
% 7.67/2.36 % (23800)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_23392 for (2992ds/50Mi)
% 7.67/2.36 % (23801)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23392 for (2992ds/368Mi)
% 7.67/2.37 % (23800)Instruction limit reached!
% 7.67/2.37 % (23800)------------------------------
% 7.67/2.37 % (23800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.37 % (23800)Termination reason: Unknown
% 7.67/2.37 % (23800)Termination phase: Property scanning
% 7.67/2.37
% 7.67/2.37 % (23800)Memory used [KB]: 2430
% 7.67/2.37 % (23800)Time elapsed: 0.014 s
% 7.67/2.37 % (23800)Instructions burned: 50 (million)
% 7.67/2.37 % (23800)------------------------------
% 7.67/2.37 % (23800)------------------------------
% 7.67/2.37 % (23795)Instruction limit reached!
% 7.67/2.37 % (23795)------------------------------
% 7.67/2.37 % (23795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.37 % (23795)Termination reason: Unknown
% 7.67/2.37 % (23795)Termination phase: Saturation
% 7.67/2.37
% 7.67/2.37 % (23795)Memory used [KB]: 7419
% 7.67/2.37 % (23795)Time elapsed: 0.054 s
% 7.67/2.37 % (23795)Instructions burned: 216 (million)
% 7.67/2.37 % (23795)------------------------------
% 7.67/2.37 % (23795)------------------------------
% 7.67/2.38 % (23802)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_23392 for (2991ds/1021Mi)
% 7.67/2.38 % (23799)Instruction limit reached!
% 7.67/2.38 % (23799)------------------------------
% 7.67/2.38 % (23799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.38 % (23799)Termination reason: Unknown
% 7.67/2.38 % (23799)Termination phase: Property scanning
% 7.67/2.38
% 7.67/2.38 % (23799)Memory used [KB]: 2686
% 7.67/2.38 % (23799)Time elapsed: 0.041 s
% 7.67/2.38 % (23799)Instructions burned: 164 (million)
% 7.67/2.38 % (23799)------------------------------
% 7.67/2.38 % (23799)------------------------------
% 7.67/2.38 % (23798)Instruction limit reached!
% 7.67/2.38 % (23798)------------------------------
% 7.67/2.38 % (23798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.67/2.38 % (23798)Termination reason: Unknown
% 7.67/2.38 % (23798)Termination phase: Saturation
% 7.67/2.38
% 7.67/2.38 % (23798)Memory used [KB]: 7419
% 7.67/2.38 % (23798)Time elapsed: 0.046 s
% 7.67/2.38 % (23798)Instructions burned: 183 (million)
% 7.67/2.38 % (23798)------------------------------
% 7.67/2.38 % (23798)------------------------------
% 7.67/2.38 % (23803)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_23392 for (2991ds/267Mi)
% 7.67/2.39 % (23804)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_23392 for (2991ds/204Mi)
% 7.67/2.39 % (23805)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_23392 for (2991ds/26Mi)
% 8.32/2.40 % (23805)Instruction limit reached!
% 8.32/2.40 % (23805)------------------------------
% 8.32/2.40 % (23805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.40 % (23805)Termination reason: Unknown
% 8.32/2.40 % (23805)Termination phase: shuffling
% 8.32/2.40
% 8.32/2.40 % (23805)Memory used [KB]: 1918
% 8.32/2.40 % (23805)Time elapsed: 0.008 s
% 8.32/2.40 % (23805)Instructions burned: 26 (million)
% 8.32/2.40 % (23805)------------------------------
% 8.32/2.40 % (23805)------------------------------
% 8.32/2.41 % (23806)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_23392 for (2991ds/53Mi)
% 8.32/2.42 % (23806)Instruction limit reached!
% 8.32/2.42 % (23806)------------------------------
% 8.32/2.42 % (23806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.42 % (23806)Termination reason: Unknown
% 8.32/2.42 % (23806)Termination phase: Property scanning
% 8.32/2.42
% 8.32/2.42 % (23806)Memory used [KB]: 2430
% 8.32/2.42 % (23806)Time elapsed: 0.015 s
% 8.32/2.42 % (23806)Instructions burned: 53 (million)
% 8.32/2.42 % (23806)------------------------------
% 8.32/2.42 % (23806)------------------------------
% 8.32/2.43 % (23807)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_23392 for (2991ds/4436Mi)
% 8.32/2.44 % (23804)Instruction limit reached!
% 8.32/2.44 % (23804)------------------------------
% 8.32/2.44 % (23804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.44 % (23804)Termination reason: Unknown
% 8.32/2.44 % (23804)Termination phase: Saturation
% 8.32/2.44
% 8.32/2.44 % (23804)Memory used [KB]: 7291
% 8.32/2.44 % (23804)Time elapsed: 0.052 s
% 8.32/2.44 % (23804)Instructions burned: 205 (million)
% 8.32/2.44 % (23804)------------------------------
% 8.32/2.44 % (23804)------------------------------
% 8.32/2.45 % (23803)Instruction limit reached!
% 8.32/2.45 % (23803)------------------------------
% 8.32/2.45 % (23803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.45 % (23803)Termination reason: Unknown
% 8.32/2.45 % (23803)Termination phase: Saturation
% 8.32/2.45
% 8.32/2.45 % (23803)Memory used [KB]: 7419
% 8.32/2.45 % (23803)Time elapsed: 0.067 s
% 8.32/2.45 % (23803)Instructions burned: 267 (million)
% 8.32/2.45 % (23803)------------------------------
% 8.32/2.45 % (23803)------------------------------
% 8.32/2.45 % (23808)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_23392 for (2991ds/1539Mi)
% 8.32/2.46 % (23809)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_23392 for (2991ds/408Mi)
% 8.32/2.46 % (23801)Instruction limit reached!
% 8.32/2.46 % (23801)------------------------------
% 8.32/2.46 % (23801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.32/2.46 % (23801)Termination reason: Unknown
% 8.32/2.46 % (23801)Termination phase: Saturation
% 8.32/2.46
% 8.32/2.46 % (23801)Memory used [KB]: 9338
% 8.32/2.46 % (23801)Time elapsed: 0.103 s
% 8.32/2.46 % (23801)Instructions burned: 370 (million)
% 8.32/2.46 % (23801)------------------------------
% 8.32/2.46 % (23801)------------------------------
% 8.32/2.47 % (23810)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_23392 for (2991ds/5205Mi)
% 8.60/2.50 % (23790)Instruction limit reached!
% 8.60/2.50 % (23790)------------------------------
% 8.60/2.50 % (23790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.50 % (23790)Termination reason: Unknown
% 8.60/2.50 % (23790)Termination phase: Saturation
% 8.60/2.50
% 8.60/2.50 % (23790)Memory used [KB]: 14456
% 8.60/2.50 % (23790)Time elapsed: 0.252 s
% 8.60/2.50 % (23790)Instructions burned: 988 (million)
% 8.60/2.50 % (23790)------------------------------
% 8.60/2.50 % (23790)------------------------------
% 8.60/2.51 % (23811)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_23392 for (2990ds/1913Mi)
% 8.60/2.58 % (23809)Instruction limit reached!
% 8.60/2.58 % (23809)------------------------------
% 8.60/2.58 % (23809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.58 % (23809)Termination reason: Unknown
% 8.60/2.58 % (23809)Termination phase: Saturation
% 8.60/2.58
% 8.60/2.58 % (23809)Memory used [KB]: 10618
% 8.60/2.58 % (23809)Time elapsed: 0.144 s
% 8.60/2.58 % (23809)Instructions burned: 408 (million)
% 8.60/2.58 % (23809)------------------------------
% 8.60/2.58 % (23809)------------------------------
% 8.60/2.59 % (23812)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_23392 for (2989ds/4350Mi)
% 9.01/2.61 % (23797)Instruction limit reached!
% 9.01/2.61 % (23797)------------------------------
% 9.01/2.61 % (23797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.61 % (23797)Termination reason: Unknown
% 9.01/2.61 % (23797)Termination phase: Saturation
% 9.01/2.61
% 9.01/2.61 % (23797)Memory used [KB]: 11257
% 9.01/2.61 % (23797)Time elapsed: 0.285 s
% 9.01/2.61 % (23797)Instructions burned: 923 (million)
% 9.01/2.61 % (23797)------------------------------
% 9.01/2.61 % (23797)------------------------------
% 9.01/2.62 % (23813)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_23392 for (2989ds/68Mi)
% 9.01/2.64 % (23813)Instruction limit reached!
% 9.01/2.64 % (23813)------------------------------
% 9.01/2.64 % (23813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.64 % (23813)Termination reason: Unknown
% 9.01/2.64 % (23813)Termination phase: Property scanning
% 9.01/2.64
% 9.01/2.64 % (23813)Memory used [KB]: 2430
% 9.01/2.64 % (23813)Time elapsed: 0.020 s
% 9.01/2.64 % (23813)Instructions burned: 69 (million)
% 9.01/2.64 % (23813)------------------------------
% 9.01/2.64 % (23813)------------------------------
% 9.01/2.65 % (23814)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_23392 for (2989ds/358Mi)
% 9.01/2.70 % (23802)Instruction limit reached!
% 9.01/2.70 % (23802)------------------------------
% 9.01/2.70 % (23802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.01/2.70 % (23802)Termination reason: Unknown
% 9.01/2.70 % (23802)Termination phase: Saturation
% 9.01/2.70
% 9.01/2.70 % (23802)Memory used [KB]: 12281
% 9.01/2.70 % (23802)Time elapsed: 0.317 s
% 9.01/2.70 % (23802)Instructions burned: 1023 (million)
% 9.01/2.70 % (23802)------------------------------
% 9.01/2.70 % (23802)------------------------------
% 9.33/2.71 % (23815)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_23392 for (2988ds/31Mi)
% 9.33/2.71 % (23815)Instruction limit reached!
% 9.33/2.71 % (23815)------------------------------
% 9.33/2.71 % (23815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.71 % (23815)Termination reason: Unknown
% 9.33/2.71 % (23815)Termination phase: shuffling
% 9.33/2.71
% 9.33/2.71 % (23815)Memory used [KB]: 2046
% 9.33/2.71 % (23815)Time elapsed: 0.010 s
% 9.33/2.71 % (23815)Instructions burned: 33 (million)
% 9.33/2.71 % (23815)------------------------------
% 9.33/2.71 % (23815)------------------------------
% 9.33/2.72 % (23816)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23392 for (2988ds/279Mi)
% 9.33/2.75 % (23814)Instruction limit reached!
% 9.33/2.75 % (23814)------------------------------
% 9.33/2.75 % (23814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.75 % (23814)Termination reason: Unknown
% 9.33/2.75 % (23814)Termination phase: Saturation
% 9.33/2.75
% 9.33/2.75 % (23814)Memory used [KB]: 8571
% 9.33/2.75 % (23814)Time elapsed: 0.095 s
% 9.33/2.75 % (23814)Instructions burned: 360 (million)
% 9.33/2.75 % (23814)------------------------------
% 9.33/2.75 % (23814)------------------------------
% 9.33/2.76 % (23817)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23392 for (2988ds/258Mi)
% 9.33/2.80 % (23816)Instruction limit reached!
% 9.33/2.80 % (23816)------------------------------
% 9.33/2.80 % (23816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.80 % (23816)Termination reason: Unknown
% 9.33/2.80 % (23816)Termination phase: Saturation
% 9.33/2.80
% 9.33/2.80 % (23816)Memory used [KB]: 7419
% 9.33/2.80 % (23816)Time elapsed: 0.072 s
% 9.33/2.80 % (23816)Instructions burned: 282 (million)
% 9.33/2.80 % (23816)------------------------------
% 9.33/2.80 % (23816)------------------------------
% 9.86/2.81 % (23818)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_23392 for (2987ds/26Mi)
% 9.86/2.81 % (23818)Instruction limit reached!
% 9.86/2.81 % (23818)------------------------------
% 9.86/2.81 % (23818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.81 % (23818)Termination reason: Unknown
% 9.86/2.81 % (23818)Termination phase: shuffling
% 9.86/2.81
% 9.86/2.81 % (23818)Memory used [KB]: 1918
% 9.86/2.81 % (23818)Time elapsed: 0.008 s
% 9.86/2.81 % (23818)Instructions burned: 26 (million)
% 9.86/2.81 % (23818)------------------------------
% 9.86/2.81 % (23818)------------------------------
% 9.86/2.82 % (23819)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_23392 for (2987ds/995Mi)
% 9.86/2.83 % (23817)Instruction limit reached!
% 9.86/2.83 % (23817)------------------------------
% 9.86/2.83 % (23817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.83 % (23817)Termination reason: Unknown
% 9.86/2.83 % (23817)Termination phase: Saturation
% 9.86/2.83
% 9.86/2.83 % (23817)Memory used [KB]: 8443
% 9.86/2.83 % (23817)Time elapsed: 0.070 s
% 9.86/2.83 % (23817)Instructions burned: 259 (million)
% 9.86/2.83 % (23817)------------------------------
% 9.86/2.83 % (23817)------------------------------
% 9.86/2.84 % (23820)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_23392 for (2987ds/373Mi)
% 9.96/2.92 % (23808)Instruction limit reached!
% 9.96/2.92 % (23808)------------------------------
% 9.96/2.92 % (23808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.92 % (23808)Termination reason: Unknown
% 9.96/2.92 % (23808)Termination phase: Saturation
% 9.96/2.92
% 9.96/2.92 % (23808)Memory used [KB]: 10746
% 9.96/2.92 % (23808)Time elapsed: 0.494 s
% 9.96/2.92 % (23808)Instructions burned: 1541 (million)
% 9.96/2.92 % (23808)------------------------------
% 9.96/2.92 % (23808)------------------------------
% 9.96/2.93 % (23821)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_23392 for (2986ds/253Mi)
% 9.96/2.94 % (23820)Instruction limit reached!
% 9.96/2.94 % (23820)------------------------------
% 9.96/2.94 % (23820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.94 % (23820)Termination reason: Unknown
% 9.96/2.94 % (23820)Termination phase: Saturation
% 9.96/2.94
% 9.96/2.94 % (23820)Memory used [KB]: 8827
% 9.96/2.94 % (23820)Time elapsed: 0.104 s
% 9.96/2.94 % (23820)Instructions burned: 375 (million)
% 9.96/2.94 % (23820)------------------------------
% 9.96/2.94 % (23820)------------------------------
% 9.96/2.95 % (23823)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_23392 for (2986ds/832Mi)
% 9.96/3.00 % (23821)Instruction limit reached!
% 9.96/3.00 % (23821)------------------------------
% 9.96/3.00 % (23821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/3.00 % (23821)Termination reason: Unknown
% 9.96/3.00 % (23821)Termination phase: Saturation
% 9.96/3.00
% 9.96/3.00 % (23821)Memory used [KB]: 7419
% 9.96/3.00 % (23821)Time elapsed: 0.064 s
% 9.96/3.00 % (23821)Instructions burned: 254 (million)
% 9.96/3.00 % (23821)------------------------------
% 9.96/3.00 % (23821)------------------------------
% 9.96/3.01 % (23824)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_23392 for (2985ds/668Mi)
% 12.97/3.07 % (23819)Instruction limit reached!
% 12.97/3.07 % (23819)------------------------------
% 12.97/3.07 % (23819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.07 % (23819)Termination reason: Unknown
% 12.97/3.07 % (23819)Termination phase: Saturation
% 12.97/3.07
% 12.97/3.07 % (23819)Memory used [KB]: 14200
% 12.97/3.07 % (23819)Time elapsed: 0.254 s
% 12.97/3.07 % (23819)Instructions burned: 997 (million)
% 12.97/3.07 % (23819)------------------------------
% 12.97/3.07 % (23819)------------------------------
% 12.97/3.08 % (23825)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_23392 for (2984ds/40Mi)
% 12.97/3.10 % (23825)Instruction limit reached!
% 12.97/3.10 % (23825)------------------------------
% 12.97/3.10 % (23825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.10 % (23825)Termination reason: Unknown
% 12.97/3.10 % (23825)Termination phase: shuffling
% 12.97/3.10
% 12.97/3.10 % (23825)Memory used [KB]: 2302
% 12.97/3.10 % (23825)Time elapsed: 0.013 s
% 12.97/3.10 % (23825)Instructions burned: 42 (million)
% 12.97/3.10 % (23825)------------------------------
% 12.97/3.10 % (23825)------------------------------
% 12.97/3.10 % (23811)Instruction limit reached!
% 12.97/3.10 % (23811)------------------------------
% 12.97/3.10 % (23811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.10 % (23811)Termination reason: Unknown
% 12.97/3.10 % (23811)Termination phase: Saturation
% 12.97/3.10
% 12.97/3.10 % (23811)Memory used [KB]: 5884
% 12.97/3.10 % (23811)Time elapsed: 0.610 s
% 12.97/3.10 % (23811)Instructions burned: 1913 (million)
% 12.97/3.10 % (23811)------------------------------
% 12.97/3.10 % (23811)------------------------------
% 12.97/3.11 % (23826)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_23392 for (2984ds/294Mi)
% 12.97/3.11 % (23827)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_23392 for (2984ds/187Mi)
% 13.54/3.16 % (23827)Instruction limit reached!
% 13.54/3.16 % (23827)------------------------------
% 13.54/3.16 % (23827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.54/3.16 % (23827)Termination reason: Unknown
% 13.54/3.16 % (23827)Termination phase: Saturation
% 13.54/3.16
% 13.54/3.16 % (23827)Memory used [KB]: 7675
% 13.54/3.16 % (23827)Time elapsed: 0.050 s
% 13.54/3.16 % (23827)Instructions burned: 190 (million)
% 13.54/3.16 % (23827)------------------------------
% 13.54/3.16 % (23827)------------------------------
% 13.54/3.17 % (23828)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23392 for (2984ds/371Mi)
% 13.54/3.18 % (23824)Instruction limit reached!
% 13.54/3.18 % (23824)------------------------------
% 13.54/3.18 % (23824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.54/3.18 % (23824)Termination reason: Unknown
% 13.54/3.18 % (23824)Termination phase: Saturation
% 13.54/3.18
% 13.54/3.18 % (23824)Memory used [KB]: 18677
% 13.54/3.18 % (23824)Time elapsed: 0.174 s
% 13.54/3.18 % (23824)Instructions burned: 671 (million)
% 13.54/3.18 % (23824)------------------------------
% 13.54/3.18 % (23824)------------------------------
% 13.54/3.18 % (23826)Instruction limit reached!
% 13.54/3.18 % (23826)------------------------------
% 13.54/3.18 % (23826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.54/3.18 % (23826)Termination reason: Unknown
% 13.54/3.18 % (23826)Termination phase: Saturation
% 13.54/3.18
% 13.54/3.18 % (23826)Memory used [KB]: 7419
% 13.54/3.18 % (23826)Time elapsed: 0.075 s
% 13.54/3.18 % (23826)Instructions burned: 297 (million)
% 13.54/3.18 % (23826)------------------------------
% 13.54/3.18 % (23826)------------------------------
% 13.54/3.19 % (23829)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23392 for (2983ds/1827Mi)
% 13.54/3.19 % (23830)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_23392 for (2983ds/70Mi)
% 14.17/3.20 % (23823)Instruction limit reached!
% 14.17/3.20 % (23823)------------------------------
% 14.17/3.20 % (23823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.20 % (23823)Termination reason: Unknown
% 14.17/3.20 % (23823)Termination phase: Saturation
% 14.17/3.20
% 14.17/3.20 % (23823)Memory used [KB]: 11129
% 14.17/3.20 % (23823)Time elapsed: 0.255 s
% 14.17/3.20 % (23823)Instructions burned: 834 (million)
% 14.17/3.20 % (23823)------------------------------
% 14.17/3.20 % (23823)------------------------------
% 14.17/3.21 % (23830)Instruction limit reached!
% 14.17/3.21 % (23830)------------------------------
% 14.17/3.21 % (23830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.21 % (23830)Termination reason: Unknown
% 14.17/3.21 % (23830)Termination phase: Property scanning
% 14.17/3.21
% 14.17/3.21 % (23830)Memory used [KB]: 2430
% 14.17/3.21 % (23830)Time elapsed: 0.019 s
% 14.17/3.21 % (23830)Instructions burned: 70 (million)
% 14.17/3.21 % (23830)------------------------------
% 14.17/3.21 % (23830)------------------------------
% 14.17/3.21 % (23831)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_23392 for (2983ds/316Mi)
% 14.17/3.22 % (23832)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_23392 for (2983ds/932Mi)
% 14.17/3.27 % (23828)Instruction limit reached!
% 14.17/3.27 % (23828)------------------------------
% 14.17/3.27 % (23828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.27 % (23828)Termination reason: Unknown
% 14.17/3.27 % (23828)Termination phase: Saturation
% 14.17/3.27
% 14.17/3.27 % (23828)Memory used [KB]: 9338
% 14.17/3.27 % (23828)Time elapsed: 0.101 s
% 14.17/3.27 % (23828)Instructions burned: 371 (million)
% 14.17/3.27 % (23828)------------------------------
% 14.17/3.27 % (23828)------------------------------
% 14.17/3.28 % (23833)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_23392 for (2982ds/4714Mi)
% 14.17/3.29 % (23831)Instruction limit reached!
% 14.17/3.29 % (23831)------------------------------
% 14.17/3.29 % (23831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.29 % (23831)Termination reason: Unknown
% 14.17/3.29 % (23831)Termination phase: Saturation
% 14.17/3.29
% 14.17/3.29 % (23831)Memory used [KB]: 7419
% 14.17/3.29 % (23831)Time elapsed: 0.079 s
% 14.17/3.29 % (23831)Instructions burned: 316 (million)
% 14.17/3.29 % (23831)------------------------------
% 14.17/3.29 % (23831)------------------------------
% 14.72/3.30 % (23834)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_23392 for (2982ds/8250Mi)
% 15.02/3.45 % (23832)Instruction limit reached!
% 15.02/3.45 % (23832)------------------------------
% 15.02/3.45 % (23832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.45 % (23832)Termination reason: Unknown
% 15.02/3.45 % (23832)Termination phase: Saturation
% 15.02/3.45
% 15.02/3.45 % (23832)Memory used [KB]: 16119
% 15.02/3.45 % (23832)Time elapsed: 0.238 s
% 15.02/3.45 % (23832)Instructions burned: 932 (million)
% 15.02/3.45 % (23832)------------------------------
% 15.02/3.45 % (23832)------------------------------
% 15.02/3.47 % (23835)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_23392 for (2981ds/770Mi)
% 15.87/3.68 % (23835)Instruction limit reached!
% 15.87/3.68 % (23835)------------------------------
% 15.87/3.68 % (23835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.87/3.68 % (23835)Termination reason: Unknown
% 15.87/3.68 % (23835)Termination phase: Saturation
% 15.87/3.68
% 15.87/3.68 % (23835)Memory used [KB]: 7547
% 15.87/3.68 % (23835)Time elapsed: 0.217 s
% 15.87/3.68 % (23835)Instructions burned: 770 (million)
% 15.87/3.68 % (23835)------------------------------
% 15.87/3.68 % (23835)------------------------------
% 15.87/3.69 % (23836)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23392 for (2978ds/794Mi)
% 16.40/3.72 % (23829)Instruction limit reached!
% 16.40/3.72 % (23829)------------------------------
% 16.40/3.72 % (23829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.72 % (23829)Termination reason: Unknown
% 16.40/3.72 % (23829)Termination phase: Saturation
% 16.40/3.72
% 16.40/3.72 % (23829)Memory used [KB]: 19957
% 16.40/3.72 % (23829)Time elapsed: 0.532 s
% 16.40/3.72 % (23829)Instructions burned: 1829 (million)
% 16.40/3.72 % (23829)------------------------------
% 16.40/3.72 % (23829)------------------------------
% 16.40/3.73 % (23837)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23392 for (2978ds/464Mi)
% 16.40/3.77 % (23810)Instruction limit reached!
% 16.40/3.77 % (23810)------------------------------
% 16.40/3.77 % (23810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.77 % (23810)Termination reason: Unknown
% 16.40/3.77 % (23810)Termination phase: Saturation
% 16.40/3.77
% 16.40/3.77 % (23810)Memory used [KB]: 15351
% 16.40/3.77 % (23810)Time elapsed: 1.325 s
% 16.40/3.77 % (23810)Instructions burned: 5207 (million)
% 16.40/3.77 % (23810)------------------------------
% 16.40/3.77 % (23810)------------------------------
% 16.40/3.79 % (23838)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_23392 for (2977ds/1376Mi)
% 17.22/3.83 % (23807)Instruction limit reached!
% 17.22/3.83 % (23807)------------------------------
% 17.22/3.83 % (23807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.22/3.83 % (23807)Termination reason: Unknown
% 17.22/3.83 % (23807)Termination phase: Saturation
% 17.22/3.83
% 17.22/3.83 % (23807)Memory used [KB]: 17270
% 17.22/3.83 % (23807)Time elapsed: 1.420 s
% 17.22/3.83 % (23807)Instructions burned: 4436 (million)
% 17.22/3.83 % (23807)------------------------------
% 17.22/3.83 % (23807)------------------------------
% 17.22/3.84 % (23839)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23392 for (2977ds/906Mi)
% 17.22/3.86 % (23837)Instruction limit reached!
% 17.22/3.86 % (23837)------------------------------
% 17.22/3.86 % (23837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.22/3.86 % (23837)Termination reason: Unknown
% 17.22/3.86 % (23837)Termination phase: Saturation
% 17.22/3.86
% 17.22/3.86 % (23837)Memory used [KB]: 9466
% 17.22/3.86 % (23837)Time elapsed: 0.131 s
% 17.22/3.86 % (23837)Instructions burned: 465 (million)
% 17.22/3.86 % (23837)------------------------------
% 17.22/3.86 % (23837)------------------------------
% 17.22/3.87 % (23840)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_23392 for (2977ds/434Mi)
% 17.51/3.93 % (23836)Instruction limit reached!
% 17.51/3.93 % (23836)------------------------------
% 17.51/3.93 % (23836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.93 % (23836)Termination reason: Unknown
% 17.51/3.93 % (23836)Termination phase: Saturation
% 17.51/3.93
% 17.51/3.93 % (23836)Memory used [KB]: 5628
% 17.51/3.93 % (23836)Time elapsed: 0.236 s
% 17.51/3.93 % (23836)Instructions burned: 794 (million)
% 17.51/3.93 % (23836)------------------------------
% 17.51/3.93 % (23836)------------------------------
% 17.51/3.93 % (23812)Instruction limit reached!
% 17.51/3.93 % (23812)------------------------------
% 17.51/3.93 % (23812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.93 % (23812)Termination reason: Unknown
% 17.51/3.93 % (23812)Termination phase: Saturation
% 17.51/3.93
% 17.51/3.93 % (23812)Memory used [KB]: 13560
% 17.51/3.93 % (23812)Time elapsed: 1.339 s
% 17.51/3.93 % (23812)Instructions burned: 4350 (million)
% 17.51/3.93 % (23812)------------------------------
% 17.51/3.93 % (23812)------------------------------
% 17.51/3.94 % (23841)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_23392 for (2976ds/865Mi)
% 17.51/3.94 % (23842)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_23392 for (2976ds/593Mi)
% 17.51/4.00 % (23840)Instruction limit reached!
% 17.51/4.00 % (23840)------------------------------
% 17.51/4.00 % (23840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/4.00 % (23840)Termination reason: Unknown
% 17.51/4.00 % (23840)Termination phase: Saturation
% 17.51/4.00
% 17.51/4.00 % (23840)Memory used [KB]: 10490
% 17.51/4.00 % (23840)Time elapsed: 0.150 s
% 17.51/4.00 % (23840)Instructions burned: 435 (million)
% 17.51/4.00 % (23840)------------------------------
% 17.51/4.00 % (23840)------------------------------
% 17.51/4.01 % (23843)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23392 for (2975ds/443Mi)
% 20.02/4.09 % (23842)Instruction limit reached!
% 20.02/4.09 % (23842)------------------------------
% 20.02/4.09 % (23842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.09 % (23842)Termination reason: Unknown
% 20.02/4.09 % (23842)Termination phase: Saturation
% 20.02/4.09
% 20.02/4.09 % (23842)Memory used [KB]: 7547
% 20.02/4.09 % (23842)Time elapsed: 0.150 s
% 20.02/4.09 % (23842)Instructions burned: 594 (million)
% 20.02/4.09 % (23842)------------------------------
% 20.02/4.09 % (23842)------------------------------
% 20.02/4.10 % (23844)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_23392 for (2974ds/594Mi)
% 20.02/4.12 % (23839)Instruction limit reached!
% 20.02/4.12 % (23839)------------------------------
% 20.02/4.12 % (23839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.12 % (23839)Termination reason: Unknown
% 20.02/4.12 % (23839)Termination phase: Saturation
% 20.02/4.12
% 20.02/4.12 % (23839)Memory used [KB]: 10746
% 20.02/4.12 % (23839)Time elapsed: 0.283 s
% 20.02/4.12 % (23839)Instructions burned: 908 (million)
% 20.02/4.12 % (23839)------------------------------
% 20.02/4.12 % (23839)------------------------------
% 20.60/4.13 % (23843)Instruction limit reached!
% 20.60/4.13 % (23843)------------------------------
% 20.60/4.13 % (23843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.60/4.13 % (23843)Termination reason: Unknown
% 20.60/4.13 % (23843)Termination phase: Saturation
% 20.60/4.13
% 20.60/4.13 % (23843)Memory used [KB]: 9466
% 20.60/4.13 % (23843)Time elapsed: 0.125 s
% 20.60/4.13 % (23843)Instructions burned: 445 (million)
% 20.60/4.13 % (23843)------------------------------
% 20.60/4.13 % (23843)------------------------------
% 20.60/4.13 % (23845)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_23392 for (2974ds/327Mi)
% 20.60/4.13 % (23838)Instruction limit reached!
% 20.60/4.13 % (23838)------------------------------
% 20.60/4.13 % (23838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.60/4.13 % (23838)Termination reason: Unknown
% 20.60/4.13 % (23838)Termination phase: Saturation
% 20.60/4.13
% 20.60/4.13 % (23838)Memory used [KB]: 9594
% 20.60/4.13 % (23838)Time elapsed: 0.351 s
% 20.60/4.13 % (23838)Instructions burned: 1377 (million)
% 20.60/4.13 % (23838)------------------------------
% 20.60/4.13 % (23838)------------------------------
% 20.60/4.14 % (23846)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_23392 for (2974ds/5411Mi)
% 20.60/4.14 % (23847)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_23392 for (2974ds/1762Mi)
% 20.60/4.19 % (23841)Instruction limit reached!
% 20.60/4.19 % (23841)------------------------------
% 20.60/4.19 % (23841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.60/4.19 % (23841)Termination reason: Unknown
% 20.60/4.19 % (23841)Termination phase: Saturation
% 20.60/4.19
% 20.60/4.19 % (23841)Memory used [KB]: 9850
% 20.60/4.19 % (23841)Time elapsed: 0.255 s
% 20.60/4.19 % (23841)Instructions burned: 868 (million)
% 20.60/4.19 % (23841)------------------------------
% 20.60/4.19 % (23841)------------------------------
% 20.97/4.20 % (23848)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_23392 for (2973ds/96Mi)
% 20.97/4.22 % (23848)Instruction limit reached!
% 20.97/4.22 % (23848)------------------------------
% 20.97/4.22 % (23848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.22 % (23848)Termination reason: Unknown
% 20.97/4.22 % (23848)Termination phase: Property scanning
% 20.97/4.22
% 20.97/4.22 % (23848)Memory used [KB]: 2430
% 20.97/4.22 % (23848)Time elapsed: 0.026 s
% 20.97/4.22 % (23848)Instructions burned: 99 (million)
% 20.97/4.22 % (23848)------------------------------
% 20.97/4.22 % (23848)------------------------------
% 20.97/4.23 % (23845)Instruction limit reached!
% 20.97/4.23 % (23845)------------------------------
% 20.97/4.23 % (23845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.23 % (23845)Termination reason: Unknown
% 20.97/4.23 % (23845)Termination phase: Saturation
% 20.97/4.23
% 20.97/4.23 % (23845)Memory used [KB]: 11257
% 20.97/4.23 % (23845)Time elapsed: 0.099 s
% 20.97/4.23 % (23845)Instructions burned: 328 (million)
% 20.97/4.23 % (23845)------------------------------
% 20.97/4.23 % (23845)------------------------------
% 20.97/4.23 % (23849)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_23392 for (2973ds/503Mi)
% 20.97/4.24 % (23850)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_23392 for (2973ds/90Mi)
% 20.97/4.27 % (23850)Instruction limit reached!
% 20.97/4.27 % (23850)------------------------------
% 20.97/4.27 % (23850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.27 % (23850)Termination reason: Unknown
% 20.97/4.27 % (23850)Termination phase: Property scanning
% 20.97/4.27
% 20.97/4.27 % (23850)Memory used [KB]: 2558
% 20.97/4.27 % (23850)Time elapsed: 0.026 s
% 20.97/4.27 % (23850)Instructions burned: 93 (million)
% 20.97/4.27 % (23850)------------------------------
% 20.97/4.27 % (23850)------------------------------
% 20.97/4.27 % (23844)Instruction limit reached!
% 20.97/4.27 % (23844)------------------------------
% 20.97/4.27 % (23844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.27 % (23844)Termination reason: Unknown
% 20.97/4.27 % (23844)Termination phase: Saturation
% 20.97/4.27
% 20.97/4.27 % (23844)Memory used [KB]: 9466
% 20.97/4.27 % (23844)Time elapsed: 0.173 s
% 20.97/4.27 % (23844)Instructions burned: 595 (million)
% 20.97/4.27 % (23844)------------------------------
% 20.97/4.27 % (23844)------------------------------
% 20.97/4.27 % (23851)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23392 for (2972ds/593Mi)
% 20.97/4.28 % (23852)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_23392 for (2972ds/1512Mi)
% 21.53/4.38 % (23849)Instruction limit reached!
% 21.53/4.38 % (23849)------------------------------
% 21.53/4.38 % (23849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.53/4.38 % (23849)Termination reason: Unknown
% 21.53/4.38 % (23849)Termination phase: Saturation
% 21.53/4.38
% 21.53/4.38 % (23849)Memory used [KB]: 9722
% 21.53/4.38 % (23849)Time elapsed: 0.143 s
% 21.53/4.38 % (23849)Instructions burned: 503 (million)
% 21.53/4.38 % (23849)------------------------------
% 21.53/4.38 % (23849)------------------------------
% 21.53/4.39 % (23853)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_23392 for (2971ds/569Mi)
% 21.89/4.44 % (23851)Instruction limit reached!
% 21.89/4.44 % (23851)------------------------------
% 21.89/4.44 % (23851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.89/4.44 % (23851)Termination reason: Unknown
% 21.89/4.44 % (23851)Termination phase: Saturation
% 21.89/4.44
% 21.89/4.44 % (23851)Memory used [KB]: 9850
% 21.89/4.44 % (23851)Time elapsed: 0.170 s
% 21.89/4.44 % (23851)Instructions burned: 593 (million)
% 21.89/4.44 % (23851)------------------------------
% 21.89/4.44 % (23851)------------------------------
% 21.89/4.45 % (23854)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_23392 for (2971ds/501Mi)
% 21.89/4.47 % (23833)Instruction limit reached!
% 21.89/4.47 % (23833)------------------------------
% 21.89/4.47 % (23833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.89/4.47 % (23833)Termination reason: Unknown
% 21.89/4.47 % (23833)Termination phase: Saturation
% 21.89/4.47
% 21.89/4.47 % (23833)Memory used [KB]: 7547
% 21.89/4.47 % (23833)Time elapsed: 1.195 s
% 21.89/4.47 % (23833)Instructions burned: 4715 (million)
% 21.89/4.47 % (23833)------------------------------
% 21.89/4.47 % (23833)------------------------------
% 21.89/4.48 % (23855)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_23392 for (2970ds/562Mi)
% 22.25/4.53 % (23853)Instruction limit reached!
% 22.25/4.53 % (23853)------------------------------
% 22.25/4.53 % (23853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.25/4.53 % (23853)Termination reason: Unknown
% 22.25/4.53 % (23853)Termination phase: Saturation
% 22.25/4.53
% 22.25/4.53 % (23853)Memory used [KB]: 11385
% 22.25/4.53 % (23853)Time elapsed: 0.144 s
% 22.25/4.53 % (23853)Instructions burned: 569 (million)
% 22.25/4.53 % (23853)------------------------------
% 22.25/4.53 % (23853)------------------------------
% 22.25/4.54 % (23856)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23392 for (2970ds/406Mi)
% 22.25/4.57 % (23847)Instruction limit reached!
% 22.25/4.57 % (23847)------------------------------
% 22.25/4.57 % (23847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.25/4.57 % (23847)Termination reason: Unknown
% 22.25/4.57 % (23847)Termination phase: Saturation
% 22.25/4.57
% 22.25/4.57 % (23847)Memory used [KB]: 22387
% 22.25/4.57 % (23847)Time elapsed: 0.431 s
% 22.25/4.57 % (23847)Instructions burned: 1765 (million)
% 22.25/4.57 % (23847)------------------------------
% 22.25/4.57 % (23847)------------------------------
% 22.25/4.59 % (23857)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_23392 for (2969ds/582Mi)
% 22.95/4.60 % (23854)Instruction limit reached!
% 22.95/4.60 % (23854)------------------------------
% 22.95/4.60 % (23854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.95/4.60 % (23854)Termination reason: Unknown
% 22.95/4.60 % (23854)Termination phase: Saturation
% 22.95/4.60
% 22.95/4.60 % (23854)Memory used [KB]: 10106
% 22.95/4.60 % (23854)Time elapsed: 0.150 s
% 22.95/4.60 % (23854)Instructions burned: 501 (million)
% 22.95/4.60 % (23854)------------------------------
% 22.95/4.60 % (23854)------------------------------
% 22.95/4.61 % (23858)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_23392 for (2969ds/456Mi)
% 22.95/4.64 % (23855)Instruction limit reached!
% 22.95/4.64 % (23855)------------------------------
% 22.95/4.64 % (23855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.95/4.64 % (23855)Termination reason: Unknown
% 22.95/4.64 % (23855)Termination phase: Saturation
% 22.95/4.64
% 22.95/4.64 % (23855)Memory used [KB]: 8315
% 22.95/4.64 % (23855)Time elapsed: 0.156 s
% 22.95/4.64 % (23855)Instructions burned: 565 (million)
% 22.95/4.64 % (23855)------------------------------
% 22.95/4.64 % (23855)------------------------------
% 22.95/4.65 % (23859)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_23392 for (2969ds/393Mi)
% 22.95/4.65 % (23856)Instruction limit reached!
% 22.95/4.65 % (23856)------------------------------
% 22.95/4.65 % (23856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.95/4.65 % (23856)Termination reason: Unknown
% 22.95/4.65 % (23856)Termination phase: Saturation
% 22.95/4.65
% 22.95/4.65 % (23856)Memory used [KB]: 7675
% 22.95/4.65 % (23856)Time elapsed: 0.112 s
% 22.95/4.65 % (23856)Instructions burned: 406 (million)
% 22.95/4.65 % (23856)------------------------------
% 22.95/4.65 % (23856)------------------------------
% 22.95/4.66 % (23860)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_23392 for (2969ds/1335Mi)
% 23.49/4.74 % (23858)Instruction limit reached!
% 23.49/4.74 % (23858)------------------------------
% 23.49/4.74 % (23858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.74 % (23858)Termination reason: Unknown
% 23.49/4.74 % (23858)Termination phase: Saturation
% 23.49/4.74
% 23.49/4.74 % (23858)Memory used [KB]: 9466
% 23.49/4.74 % (23858)Time elapsed: 0.129 s
% 23.49/4.74 % (23858)Instructions burned: 459 (million)
% 23.49/4.74 % (23858)------------------------------
% 23.49/4.74 % (23858)------------------------------
% 23.49/4.74 % (23859)Instruction limit reached!
% 23.49/4.74 % (23859)------------------------------
% 23.49/4.74 % (23859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.74 % (23859)Termination reason: Unknown
% 23.49/4.74 % (23859)Termination phase: Saturation
% 23.49/4.74
% 23.49/4.74 % (23859)Memory used [KB]: 9466
% 23.49/4.74 % (23859)Time elapsed: 0.100 s
% 23.49/4.74 % (23859)Instructions burned: 393 (million)
% 23.49/4.74 % (23859)------------------------------
% 23.49/4.74 % (23859)------------------------------
% 23.49/4.75 % (23861)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_23392 for (2968ds/3373Mi)
% 23.49/4.75 % (23862)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_23392 for (2968ds/474Mi)
% 23.49/4.76 % (23852)Instruction limit reached!
% 23.49/4.76 % (23852)------------------------------
% 23.49/4.76 % (23852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.76 % (23852)Termination reason: Unknown
% 23.49/4.76 % (23852)Termination phase: Saturation
% 23.49/4.76
% 23.49/4.76 % (23852)Memory used [KB]: 12537
% 23.49/4.76 % (23852)Time elapsed: 0.480 s
% 23.49/4.76 % (23852)Instructions burned: 1512 (million)
% 23.49/4.76 % (23852)------------------------------
% 23.49/4.76 % (23852)------------------------------
% 23.49/4.77 % (23857)Instruction limit reached!
% 23.49/4.77 % (23857)------------------------------
% 23.49/4.77 % (23857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.77 % (23857)Termination reason: Unknown
% 23.49/4.77 % (23857)Termination phase: Saturation
% 23.49/4.77
% 23.49/4.77 % (23857)Memory used [KB]: 10362
% 23.49/4.77 % (23857)Time elapsed: 0.181 s
% 23.49/4.77 % (23857)Instructions burned: 583 (million)
% 23.49/4.77 % (23857)------------------------------
% 23.49/4.77 % (23857)------------------------------
% 23.49/4.77 % (23863)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23392 for (2968ds/157Mi)
% 23.49/4.78 % (23864)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_23392 for (2967ds/590Mi)
% 24.52/4.81 % (23863)Instruction limit reached!
% 24.52/4.81 % (23863)------------------------------
% 24.52/4.81 % (23863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.81 % (23863)Termination reason: Unknown
% 24.52/4.81 % (23863)Termination phase: Saturation
% 24.52/4.81
% 24.52/4.81 % (23863)Memory used [KB]: 7036
% 24.52/4.81 % (23863)Time elapsed: 0.040 s
% 24.52/4.81 % (23863)Instructions burned: 158 (million)
% 24.52/4.81 % (23863)------------------------------
% 24.52/4.81 % (23863)------------------------------
% 24.52/4.82 % (23865)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_23392 for (2967ds/104Mi)
% 24.52/4.84 % (23865)Instruction limit reached!
% 24.52/4.84 % (23865)------------------------------
% 24.52/4.84 % (23865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.84 % (23865)Termination reason: Unknown
% 24.52/4.84 % (23865)Termination phase: Function definition elimination
% 24.52/4.84
% 24.52/4.84 % (23865)Memory used [KB]: 2558
% 24.52/4.84 % (23865)Time elapsed: 0.029 s
% 24.52/4.84 % (23865)Instructions burned: 106 (million)
% 24.52/4.84 % (23865)------------------------------
% 24.52/4.84 % (23865)------------------------------
% 24.52/4.85 % (23866)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_23392 for (2967ds/414Mi)
% 24.52/4.87 % (23862)Instruction limit reached!
% 24.52/4.87 % (23862)------------------------------
% 24.52/4.87 % (23862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.87 % (23862)Termination reason: Unknown
% 24.52/4.87 % (23862)Termination phase: Saturation
% 24.52/4.87
% 24.52/4.87 % (23862)Memory used [KB]: 7419
% 24.52/4.87 % (23862)Time elapsed: 0.121 s
% 24.52/4.87 % (23862)Instructions burned: 477 (million)
% 24.52/4.87 % (23862)------------------------------
% 24.52/4.87 % (23862)------------------------------
% 24.52/4.88 % (23867)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_23392 for (2966ds/715Mi)
% 24.83/4.94 % (23864)Instruction limit reached!
% 24.83/4.94 % (23864)------------------------------
% 24.83/4.94 % (23864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.83/4.94 % (23864)Termination reason: Unknown
% 24.83/4.94 % (23864)Termination phase: Saturation
% 24.83/4.94
% 24.83/4.94 % (23864)Memory used [KB]: 8699
% 24.83/4.94 % (23864)Time elapsed: 0.168 s
% 24.83/4.94 % (23864)Instructions burned: 590 (million)
% 24.83/4.94 % (23864)------------------------------
% 24.83/4.94 % (23864)------------------------------
% 24.83/4.95 % (23868)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_23392 for (2966ds/961Mi)
% 24.83/4.96 % (23866)Instruction limit reached!
% 24.83/4.96 % (23866)------------------------------
% 24.83/4.96 % (23866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.83/4.96 % (23866)Termination reason: Unknown
% 24.83/4.96 % (23866)Termination phase: Saturation
% 24.83/4.96
% 24.83/4.96 % (23866)Memory used [KB]: 7419
% 24.83/4.96 % (23866)Time elapsed: 0.103 s
% 24.83/4.96 % (23866)Instructions burned: 415 (million)
% 24.83/4.96 % (23866)------------------------------
% 24.83/4.96 % (23866)------------------------------
% 24.83/4.97 % (23869)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_23392 for (2966ds/1213Mi)
% 27.04/5.06 % (23860)Instruction limit reached!
% 27.04/5.06 % (23860)------------------------------
% 27.04/5.06 % (23860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.06 % (23860)Termination reason: Unknown
% 27.04/5.06 % (23860)Termination phase: Saturation
% 27.04/5.06
% 27.04/5.06 % (23860)Memory used [KB]: 9978
% 27.04/5.06 % (23860)Time elapsed: 0.401 s
% 27.04/5.06 % (23860)Instructions burned: 1335 (million)
% 27.04/5.06 % (23860)------------------------------
% 27.04/5.06 % (23860)------------------------------
% 27.04/5.07 % (23870)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_23392 for (2964ds/1979Mi)
% 27.04/5.10 % (23867)Instruction limit reached!
% 27.04/5.10 % (23867)------------------------------
% 27.04/5.10 % (23867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.10 % (23867)Termination reason: Unknown
% 27.04/5.10 % (23867)Termination phase: Saturation
% 27.04/5.10
% 27.04/5.10 % (23867)Memory used [KB]: 5245
% 27.04/5.10 % (23867)Time elapsed: 0.213 s
% 27.04/5.10 % (23867)Instructions burned: 716 (million)
% 27.04/5.10 % (23867)------------------------------
% 27.04/5.10 % (23867)------------------------------
% 27.04/5.11 % (23871)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_23392 for (2964ds/481Mi)
% 28.04/5.23 % (23871)Instruction limit reached!
% 28.04/5.23 % (23871)------------------------------
% 28.04/5.23 % (23871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.04/5.23 % (23871)Termination reason: Unknown
% 28.04/5.23 % (23871)Termination phase: Saturation
% 28.04/5.23
% 28.04/5.23 % (23871)Memory used [KB]: 7419
% 28.04/5.23 % (23871)Time elapsed: 0.121 s
% 28.04/5.23 % (23871)Instructions burned: 482 (million)
% 28.04/5.23 % (23871)------------------------------
% 28.04/5.23 % (23871)------------------------------
% 28.04/5.24 % (23872)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_23392 for (2963ds/783Mi)
% 28.04/5.24 % (23868)Instruction limit reached!
% 28.04/5.24 % (23868)------------------------------
% 28.04/5.24 % (23868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.04/5.24 % (23868)Termination reason: Unknown
% 28.04/5.24 % (23868)Termination phase: Saturation
% 28.04/5.24
% 28.04/5.24 % (23868)Memory used [KB]: 10106
% 28.04/5.24 % (23868)Time elapsed: 0.291 s
% 28.04/5.24 % (23868)Instructions burned: 964 (million)
% 28.04/5.24 % (23868)------------------------------
% 28.04/5.24 % (23868)------------------------------
% 28.04/5.25 % (23873)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_23392 for (2963ds/432Mi)
% 28.62/5.34 % (23869)Instruction limit reached!
% 28.62/5.34 % (23869)------------------------------
% 28.62/5.34 % (23869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.34 % (23869)Termination reason: Unknown
% 28.62/5.34 % (23869)Termination phase: Saturation
% 28.62/5.34
% 28.62/5.34 % (23869)Memory used [KB]: 14072
% 28.62/5.34 % (23869)Time elapsed: 0.379 s
% 28.62/5.34 % (23869)Instructions burned: 1213 (million)
% 28.62/5.34 % (23869)------------------------------
% 28.62/5.34 % (23869)------------------------------
% 28.62/5.35 % (23874)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_23392 for (2962ds/1670Mi)
% 28.62/5.37 % (23873)Instruction limit reached!
% 28.62/5.37 % (23873)------------------------------
% 28.62/5.37 % (23873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.37 % (23873)Termination reason: Unknown
% 28.62/5.37 % (23873)Termination phase: Saturation
% 28.62/5.37
% 28.62/5.37 % (23873)Memory used [KB]: 9466
% 28.62/5.37 % (23873)Time elapsed: 0.121 s
% 28.62/5.37 % (23873)Instructions burned: 432 (million)
% 28.62/5.37 % (23873)------------------------------
% 28.62/5.37 % (23873)------------------------------
% 28.62/5.38 % (23875)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_23392 for (2961ds/90Mi)
% 29.12/5.41 % (23875)Instruction limit reached!
% 29.12/5.41 % (23875)------------------------------
% 29.12/5.41 % (23875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.12/5.41 % (23875)Termination reason: Unknown
% 29.12/5.41 % (23875)Termination phase: Property scanning
% 29.12/5.41
% 29.12/5.41 % (23875)Memory used [KB]: 2558
% 29.12/5.41 % (23875)Time elapsed: 0.026 s
% 29.12/5.41 % (23875)Instructions burned: 93 (million)
% 29.12/5.41 % (23875)------------------------------
% 29.12/5.41 % (23875)------------------------------
% 29.12/5.42 % (23876)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23392 for (2961ds/346Mi)
% 29.12/5.48 % (23872)Instruction limit reached!
% 29.12/5.48 % (23872)------------------------------
% 29.12/5.48 % (23872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.12/5.48 % (23872)Termination reason: Unknown
% 29.12/5.48 % (23872)Termination phase: Saturation
% 29.12/5.48
% 29.12/5.48 % (23872)Memory used [KB]: 11257
% 29.12/5.48 % (23872)Time elapsed: 0.243 s
% 29.12/5.48 % (23872)Instructions burned: 785 (million)
% 29.12/5.48 % (23872)------------------------------
% 29.12/5.48 % (23872)------------------------------
% 29.12/5.49 % (23877)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_23392 for (2960ds/401Mi)
% 29.71/5.50 % (23876)Instruction limit reached!
% 29.71/5.50 % (23876)------------------------------
% 29.71/5.50 % (23876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.71/5.50 % (23876)Termination reason: Unknown
% 29.71/5.50 % (23876)Termination phase: Saturation
% 29.71/5.50
% 29.71/5.50 % (23876)Memory used [KB]: 7419
% 29.71/5.50 % (23876)Time elapsed: 0.087 s
% 29.71/5.50 % (23876)Instructions burned: 349 (million)
% 29.71/5.50 % (23876)------------------------------
% 29.71/5.50 % (23876)------------------------------
% 29.71/5.51 % (23878)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_23392 for (2960ds/6454Mi)
% 29.71/5.59 % (23877)Instruction limit reached!
% 29.71/5.59 % (23877)------------------------------
% 29.71/5.59 % (23877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.71/5.59 % (23877)Termination reason: Unknown
% 29.71/5.59 % (23877)Termination phase: Saturation
% 29.71/5.59
% 29.71/5.59 % (23877)Memory used [KB]: 7419
% 29.71/5.59 % (23877)Time elapsed: 0.103 s
% 29.71/5.59 % (23877)Instructions burned: 402 (million)
% 29.71/5.59 % (23877)------------------------------
% 29.71/5.59 % (23877)------------------------------
% 30.21/5.60 % (23879)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_23392 for (2959ds/283Mi)
% 30.21/5.67 % (23870)Instruction limit reached!
% 30.21/5.67 % (23870)------------------------------
% 30.21/5.67 % (23870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.21/5.67 % (23870)Termination reason: Unknown
% 30.21/5.67 % (23870)Termination phase: Saturation
% 30.21/5.67
% 30.21/5.67 % (23870)Memory used [KB]: 10490
% 30.21/5.67 % (23870)Time elapsed: 0.602 s
% 30.21/5.67 % (23870)Instructions burned: 1979 (million)
% 30.21/5.67 % (23870)------------------------------
% 30.21/5.67 % (23870)------------------------------
% 30.21/5.67 % (23879)Instruction limit reached!
% 30.21/5.67 % (23879)------------------------------
% 30.21/5.67 % (23879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.21/5.67 % (23879)Termination reason: Unknown
% 30.21/5.67 % (23879)Termination phase: Saturation
% 30.21/5.67
% 30.21/5.67 % (23879)Memory used [KB]: 8443
% 30.21/5.67 % (23879)Time elapsed: 0.075 s
% 30.21/5.67 % (23879)Instructions burned: 284 (million)
% 30.21/5.67 % (23879)------------------------------
% 30.21/5.67 % (23879)------------------------------
% 30.21/5.68 % (23880)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_23392 for (2958ds/865Mi)
% 30.21/5.68 % (23881)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_23392 for (2958ds/4528Mi)
% 31.21/5.78 % (23874)Instruction limit reached!
% 31.21/5.78 % (23874)------------------------------
% 31.21/5.78 % (23874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.21/5.78 % (23874)Termination reason: Unknown
% 31.21/5.78 % (23874)Termination phase: Saturation
% 31.21/5.78
% 31.21/5.78 % (23874)Memory used [KB]: 16119
% 31.21/5.78 % (23874)Time elapsed: 0.432 s
% 31.21/5.78 % (23874)Instructions burned: 1672 (million)
% 31.21/5.78 % (23874)------------------------------
% 31.21/5.78 % (23874)------------------------------
% 31.21/5.79 % (23861)Instruction limit reached!
% 31.21/5.79 % (23861)------------------------------
% 31.21/5.79 % (23861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.21/5.79 % (23861)Termination reason: Unknown
% 31.21/5.79 % (23861)Termination phase: Saturation
% 31.21/5.79
% 31.21/5.79 % (23861)Memory used [KB]: 12409
% 31.21/5.79 % (23861)Time elapsed: 1.037 s
% 31.21/5.79 % (23861)Instructions burned: 3374 (million)
% 31.21/5.79 % (23861)------------------------------
% 31.21/5.79 % (23861)------------------------------
% 31.21/5.80 % (23882)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_23392 for (2957ds/1001Mi)
% 31.21/5.80 % (23883)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_23392 for (2957ds/102Mi)
% 31.95/5.82 % (23883)Instruction limit reached!
% 31.95/5.82 % (23883)------------------------------
% 31.95/5.82 % (23883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.82 % (23883)Termination reason: Unknown
% 31.95/5.82 % (23883)Termination phase: Function definition elimination
% 31.95/5.82
% 31.95/5.82 % (23883)Memory used [KB]: 2558
% 31.95/5.82 % (23883)Time elapsed: 0.028 s
% 31.95/5.82 % (23883)Instructions burned: 104 (million)
% 31.95/5.82 % (23883)------------------------------
% 31.95/5.82 % (23883)------------------------------
% 31.95/5.83 % (23884)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_23392 for (2957ds/952Mi)
% 31.95/5.84 % (23881)Refutation not found, incomplete strategy
% 31.95/5.84 % (23881)------------------------------
% 31.95/5.84 % (23881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.84 % (23881)Termination reason: Refutation not found, incomplete strategy
% 31.95/5.84
% 31.95/5.84
% 31.95/5.84 % (23881)Memory used [KB]: 2942
% 31.95/5.84 % (23881)Time elapsed: 0.159 s
% 31.95/5.84 % (23881)Instructions burned: 599 (million)
% 31.95/5.84 % (23881)------------------------------
% 31.95/5.84 % (23881)------------------------------
% 31.95/5.85 % (23846)Instruction limit reached!
% 31.95/5.85 % (23846)------------------------------
% 31.95/5.85 % (23846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.85 % (23846)Termination reason: Unknown
% 31.95/5.85 % (23846)Termination phase: Saturation
% 31.95/5.85
% 31.95/5.85 % (23846)Memory used [KB]: 16502
% 31.95/5.85 % (23846)Time elapsed: 1.707 s
% 31.95/5.85 % (23846)Instructions burned: 5411 (million)
% 31.95/5.85 % (23846)------------------------------
% 31.95/5.85 % (23846)------------------------------
% 31.95/5.85 % (23885)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_23392 for (2957ds/578Mi)
% 31.95/5.86 % (23886)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_23392 for (2957ds/643Mi)
% 32.33/5.93 % (23880)Instruction limit reached!
% 32.33/5.93 % (23880)------------------------------
% 32.33/5.93 % (23880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/5.93 % (23880)Termination reason: Unknown
% 32.33/5.93 % (23880)Termination phase: Saturation
% 32.33/5.93
% 32.33/5.93 % (23880)Memory used [KB]: 8315
% 32.33/5.93 % (23880)Time elapsed: 0.251 s
% 32.33/5.93 % (23880)Instructions burned: 865 (million)
% 32.33/5.93 % (23880)------------------------------
% 32.33/5.93 % (23880)------------------------------
% 32.33/5.94 % (23887)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_23392 for (2956ds/865Mi)
% 32.33/5.95 % (23834)Instruction limit reached!
% 32.33/5.95 % (23834)------------------------------
% 32.33/5.95 % (23834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/5.95 % (23834)Termination reason: Unknown
% 32.33/5.95 % (23834)Termination phase: Saturation
% 32.33/5.95
% 32.33/5.95 % (23834)Memory used [KB]: 25202
% 32.33/5.95 % (23834)Time elapsed: 2.655 s
% 32.33/5.95 % (23834)Instructions burned: 8251 (million)
% 32.33/5.95 % (23834)------------------------------
% 32.33/5.95 % (23834)------------------------------
% 32.33/5.96 % (23888)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_23392 for (2956ds/1174Mi)
% 32.33/5.99 % (23885)Instruction limit reached!
% 32.33/5.99 % (23885)------------------------------
% 32.33/5.99 % (23885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/5.99 % (23885)Termination reason: Unknown
% 32.33/5.99 % (23885)Termination phase: Saturation
% 32.33/5.99
% 32.33/5.99 % (23885)Memory used [KB]: 9850
% 32.33/5.99 % (23885)Time elapsed: 0.136 s
% 32.33/5.99 % (23885)Instructions burned: 579 (million)
% 32.33/5.99 % (23885)------------------------------
% 32.33/5.99 % (23885)------------------------------
% 32.33/6.00 % (23889)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_23392 for (2955ds/644Mi)
% 32.33/6.02 % (23886)Instruction limit reached!
% 32.33/6.02 % (23886)------------------------------
% 32.33/6.02 % (23886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/6.02 % (23886)Termination reason: Unknown
% 32.33/6.02 % (23886)Termination phase: Saturation
% 32.33/6.02
% 32.33/6.02 % (23886)Memory used [KB]: 12153
% 32.33/6.02 % (23886)Time elapsed: 0.163 s
% 32.33/6.02 % (23886)Instructions burned: 643 (million)
% 32.33/6.02 % (23886)------------------------------
% 32.33/6.02 % (23886)------------------------------
% 34.09/6.03 % (23890)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_23392 for (2955ds/1201Mi)
% 34.09/6.10 % (23882)Instruction limit reached!
% 34.09/6.10 % (23882)------------------------------
% 34.09/6.10 % (23882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.10 % (23882)Termination reason: Unknown
% 34.09/6.10 % (23882)Termination phase: Saturation
% 34.09/6.10
% 34.09/6.10 % (23882)Memory used [KB]: 11513
% 34.09/6.10 % (23882)Time elapsed: 0.304 s
% 34.09/6.10 % (23882)Instructions burned: 1002 (million)
% 34.09/6.10 % (23882)------------------------------
% 34.09/6.10 % (23882)------------------------------
% 34.09/6.11 % (23891)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_23392 for (2954ds/1046Mi)
% 34.09/6.12 % (23884)Instruction limit reached!
% 34.09/6.12 % (23884)------------------------------
% 34.09/6.12 % (23884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.09/6.12 % (23884)Termination reason: Unknown
% 34.09/6.12 % (23884)Termination phase: Saturation
% 34.09/6.12
% 34.09/6.12 % (23884)Memory used [KB]: 10234
% 34.09/6.12 % (23884)Time elapsed: 0.285 s
% 34.09/6.12 % (23884)Instructions burned: 953 (million)
% 34.09/6.12 % (23884)------------------------------
% 34.09/6.12 % (23884)------------------------------
% 34.68/6.13 % (23892)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_23392 for (2954ds/222Mi)
% 34.68/6.17 % (23887)Instruction limit reached!
% 34.68/6.17 % (23887)------------------------------
% 34.68/6.17 % (23887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.17 % (23887)Termination reason: Unknown
% 34.68/6.17 % (23887)Termination phase: Saturation
% 34.68/6.17
% 34.68/6.17 % (23887)Memory used [KB]: 7675
% 34.68/6.17 % (23887)Time elapsed: 0.234 s
% 34.68/6.17 % (23887)Instructions burned: 866 (million)
% 34.68/6.17 % (23887)------------------------------
% 34.68/6.17 % (23887)------------------------------
% 34.68/6.18 % (23889)Instruction limit reached!
% 34.68/6.18 % (23889)------------------------------
% 34.68/6.18 % (23889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.18 % (23889)Termination reason: Unknown
% 34.68/6.18 % (23889)Termination phase: Saturation
% 34.68/6.18
% 34.68/6.18 % (23889)Memory used [KB]: 8059
% 34.68/6.18 % (23889)Time elapsed: 0.186 s
% 34.68/6.18 % (23889)Instructions burned: 645 (million)
% 34.68/6.18 % (23889)------------------------------
% 34.68/6.18 % (23889)------------------------------
% 34.68/6.18 % (23893)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_23392 for (2953ds/68Mi)
% 34.68/6.18 % (23892)Instruction limit reached!
% 34.68/6.18 % (23892)------------------------------
% 34.68/6.18 % (23892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.68/6.18 % (23892)Termination reason: Unknown
% 34.68/6.18 % (23892)Termination phase: Saturation
% 34.68/6.18
% 34.68/6.18 % (23892)Memory used [KB]: 7419
% 34.68/6.18 % (23892)Time elapsed: 0.057 s
% 34.68/6.18 % (23892)Instructions burned: 225 (million)
% 34.68/6.18 % (23892)------------------------------
% 34.68/6.18 % (23892)------------------------------
% 34.68/6.19 % (23894)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=454:si=on:rtra=on_0 on DTF2THF_23392 for (2953ds/454Mi)
% 34.68/6.19 % (23895)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_23392 for (2953ds/360Mi)
% 34.99/6.20 % (23893)Instruction limit reached!
% 34.99/6.20 % (23893)------------------------------
% 34.99/6.20 % (23893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.99/6.20 % (23893)Termination reason: Unknown
% 34.99/6.20 % (23893)Termination phase: Property scanning
% 34.99/6.20
% 34.99/6.20 % (23893)Memory used [KB]: 2430
% 34.99/6.20 % (23893)Time elapsed: 0.019 s
% 34.99/6.20 % (23893)Instructions burned: 69 (million)
% 34.99/6.20 % (23893)------------------------------
% 34.99/6.20 % (23893)------------------------------
% 34.99/6.21 % (23896)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23392 for (2953ds/157Mi)
% 34.99/6.25 % (23896)Instruction limit reached!
% 34.99/6.25 % (23896)------------------------------
% 34.99/6.25 % (23896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.99/6.25 % (23896)Termination reason: Unknown
% 34.99/6.25 % (23896)Termination phase: Saturation
% 34.99/6.25
% 34.99/6.25 % (23896)Memory used [KB]: 7036
% 34.99/6.25 % (23896)Time elapsed: 0.040 s
% 34.99/6.25 % (23896)Instructions burned: 159 (million)
% 34.99/6.25 % (23896)------------------------------
% 34.99/6.25 % (23896)------------------------------
% 34.99/6.26 % (23897)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_23392 for (2953ds/5061Mi)
% 34.99/6.28 % (23895)Instruction limit reached!
% 34.99/6.28 % (23895)------------------------------
% 34.99/6.28 % (23895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.99/6.28 % (23895)Termination reason: Unknown
% 34.99/6.28 % (23895)Termination phase: Saturation
% 34.99/6.28
% 34.99/6.28 % (23895)Memory used [KB]: 7419
% 34.99/6.28 % (23895)Time elapsed: 0.090 s
% 34.99/6.28 % (23895)Instructions burned: 360 (million)
% 34.99/6.28 % (23895)------------------------------
% 34.99/6.28 % (23895)------------------------------
% 34.99/6.29 % (23898)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_23392 for (2952ds/2401Mi)
% 35.38/6.30 % (23894)Instruction limit reached!
% 35.38/6.30 % (23894)------------------------------
% 35.38/6.30 % (23894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.38/6.30 % (23894)Termination reason: Unknown
% 35.38/6.30 % (23894)Termination phase: Saturation
% 35.38/6.30
% 35.38/6.30 % (23894)Memory used [KB]: 11897
% 35.38/6.30 % (23894)Time elapsed: 0.115 s
% 35.38/6.30 % (23894)Instructions burned: 457 (million)
% 35.38/6.30 % (23894)------------------------------
% 35.38/6.30 % (23894)------------------------------
% 35.38/6.31 % (23899)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_23392 for (2952ds/5798Mi)
% 35.38/6.32 % (23888)Instruction limit reached!
% 35.38/6.32 % (23888)------------------------------
% 35.38/6.32 % (23888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.38/6.32 % (23888)Termination reason: Unknown
% 35.38/6.32 % (23888)Termination phase: Saturation
% 35.38/6.32
% 35.38/6.32 % (23888)Memory used [KB]: 9850
% 35.38/6.32 % (23888)Time elapsed: 0.356 s
% 35.38/6.32 % (23888)Instructions burned: 1174 (million)
% 35.38/6.32 % (23888)------------------------------
% 35.38/6.32 % (23888)------------------------------
% 35.38/6.33 % (23900)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23392 for (2952ds/346Mi)
% 35.38/6.37 % (23891)Instruction limit reached!
% 35.38/6.37 % (23891)------------------------------
% 35.38/6.37 % (23891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.38/6.37 % (23891)Termination reason: Unknown
% 35.38/6.37 % (23891)Termination phase: Saturation
% 35.38/6.37
% 35.38/6.37 % (23891)Memory used [KB]: 7547
% 35.38/6.37 % (23891)Time elapsed: 0.264 s
% 35.38/6.37 % (23891)Instructions burned: 1048 (million)
% 35.38/6.37 % (23891)------------------------------
% 35.38/6.37 % (23891)------------------------------
% 35.38/6.37 % (23890)Instruction limit reached!
% 35.38/6.37 % (23890)------------------------------
% 35.38/6.37 % (23890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.38/6.37 % (23890)Termination reason: Unknown
% 35.38/6.37 % (23890)Termination phase: Saturation
% 35.38/6.37
% 35.38/6.37 % (23890)Memory used [KB]: 10874
% 35.38/6.37 % (23890)Time elapsed: 0.365 s
% 35.38/6.37 % (23890)Instructions burned: 1203 (million)
% 35.38/6.37 % (23890)------------------------------
% 35.38/6.37 % (23890)------------------------------
% 35.38/6.38 % (23901)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_23392 for (2951ds/1321Mi)
% 35.38/6.38 % (23902)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_23392 for (2951ds/1312Mi)
% 36.26/6.42 % (23900)Instruction limit reached!
% 36.26/6.42 % (23900)------------------------------
% 36.26/6.42 % (23900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.26/6.42 % (23900)Termination reason: Unknown
% 36.26/6.42 % (23900)Termination phase: Saturation
% 36.26/6.42
% 36.26/6.42 % (23900)Memory used [KB]: 7419
% 36.26/6.42 % (23900)Time elapsed: 0.087 s
% 36.26/6.42 % (23900)Instructions burned: 348 (million)
% 36.26/6.42 % (23900)------------------------------
% 36.26/6.42 % (23900)------------------------------
% 36.26/6.42 % (23903)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_23392 for (2951ds/672Mi)
% 36.56/6.63 % (23903)Instruction limit reached!
% 36.56/6.63 % (23903)------------------------------
% 36.56/6.63 % (23903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.56/6.63 % (23903)Termination reason: Unknown
% 36.56/6.63 % (23903)Termination phase: Saturation
% 36.56/6.63
% 36.56/6.63 % (23903)Memory used [KB]: 10618
% 36.56/6.63 % (23903)Time elapsed: 0.205 s
% 36.56/6.63 % (23903)Instructions burned: 674 (million)
% 36.56/6.63 % (23903)------------------------------
% 36.56/6.63 % (23903)------------------------------
% 36.56/6.64 % (23904)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_23392 for (2949ds/1897Mi)
% 36.88/6.71 % (23902)Instruction limit reached!
% 36.88/6.71 % (23902)------------------------------
% 36.88/6.71 % (23902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.88/6.71 % (23902)Termination reason: Unknown
% 36.88/6.71 % (23902)Termination phase: Saturation
% 36.88/6.71
% 36.88/6.71 % (23902)Memory used [KB]: 14967
% 36.88/6.71 % (23902)Time elapsed: 0.331 s
% 36.88/6.71 % (23902)Instructions burned: 1313 (million)
% 36.88/6.71 % (23902)------------------------------
% 36.88/6.71 % (23902)------------------------------
% 36.88/6.72 % (23901)First to succeed.
% 36.88/6.72 % (23905)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_23392 for (2948ds/1202Mi)
% 36.88/6.72 % (23901)Refutation found. Thanks to Tanya!
% 36.88/6.72 % SZS status Theorem for DTF2THF_23392
% 36.88/6.72 % SZS output start Proof for DTF2THF_23392
% 36.88/6.72 thf(func_def_0, type, in: $i > $i > $o).
% 36.88/6.72 thf(func_def_1, type, exu: ($i > $o) > $o).
% 36.88/6.72 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 36.88/6.72 thf(func_def_8, type, powerset: $i > $i).
% 36.88/6.72 thf(func_def_10, type, setunion: $i > $i).
% 36.88/6.72 thf(func_def_19, type, descr: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_26, type, prop2set: $o > $i).
% 36.88/6.72 thf(func_def_36, type, nonempty: $i > $o).
% 36.88/6.72 thf(func_def_69, type, set2prop: $i > $o).
% 36.88/6.72 thf(func_def_88, type, subset: $i > $i > $o).
% 36.88/6.72 thf(func_def_89, type, disjoint: $i > $i > $o).
% 36.88/6.72 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 36.88/6.72 thf(func_def_114, type, binunion: $i > $i > $i).
% 36.88/6.72 thf(func_def_122, type, binintersect: $i > $i > $i).
% 36.88/6.72 thf(func_def_135, type, regular: $i > $o).
% 36.88/6.72 thf(func_def_136, type, setminus: $i > $i > $i).
% 36.88/6.72 thf(func_def_147, type, symdiff: $i > $i > $i).
% 36.88/6.72 thf(func_def_153, type, iskpair: $i > $o).
% 36.88/6.72 thf(func_def_158, type, kpair: $i > $i > $i).
% 36.88/6.72 thf(func_def_160, type, cartprod: $i > $i > $i).
% 36.88/6.72 thf(func_def_177, type, singleton: $i > $o).
% 36.88/6.72 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 36.88/6.72 thf(func_def_184, type, atmost1p: $i > $o).
% 36.88/6.72 thf(func_def_185, type, atleast2p: $i > $o).
% 36.88/6.72 thf(func_def_186, type, atmost2p: $i > $o).
% 36.88/6.72 thf(func_def_187, type, upairsetp: $i > $o).
% 36.88/6.72 thf(func_def_191, type, kfst: $i > $i).
% 36.88/6.72 thf(func_def_203, type, ksnd: $i > $i).
% 36.88/6.72 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 36.88/6.72 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 36.88/6.72 thf(func_def_222, type, func: $i > $i > $i > $o).
% 36.88/6.72 thf(func_def_223, type, funcSet: $i > $i > $i).
% 36.88/6.72 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 36.88/6.72 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 36.88/6.72 thf(func_def_305, type, sP0: $i > $i > $i > $i > $o).
% 36.88/6.72 thf(func_def_307, type, sP2: $i > $i > $o).
% 36.88/6.72 thf(func_def_308, type, sP3: $i > $o).
% 36.88/6.72 thf(func_def_309, type, sP4: $i > $i > $o).
% 36.88/6.72 thf(func_def_310, type, sP5: $i > $i > $o).
% 36.88/6.72 thf(func_def_311, type, sP6: $i > $i > $i > $o).
% 36.88/6.72 thf(func_def_316, type, sP11: $i > $i > $i > $o > $o).
% 36.88/6.72 thf(func_def_320, type, sK15: $i > $o).
% 36.88/6.72 thf(func_def_321, type, sK16: $i > $i).
% 36.88/6.72 thf(func_def_322, type, sK17: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_328, type, sK23: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_329, type, sK24: $i > $o).
% 36.88/6.72 thf(func_def_333, type, sK28: $i > $o).
% 36.88/6.72 thf(func_def_335, type, sK30: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_360, type, sK55: $i > $i > $o).
% 36.88/6.72 thf(func_def_365, type, sK60: $i > $i > $o).
% 36.88/6.72 thf(func_def_377, type, sK72: $i > $o).
% 36.88/6.72 thf(func_def_379, type, sK74: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_380, type, sK75: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_381, type, sK76: $i > $o).
% 36.88/6.72 thf(func_def_386, type, sK81: $i > $i > $i).
% 36.88/6.72 thf(func_def_391, type, sK86: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_392, type, sK87: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_393, type, sK88: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_394, type, sK89: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_416, type, sK111: $i > $o).
% 36.88/6.72 thf(func_def_423, type, sK118: $i > $o).
% 36.88/6.72 thf(func_def_424, type, sK119: ($i > $o) > $i > $i > $i).
% 36.88/6.72 thf(func_def_427, type, sK122: $i > $i > $i).
% 36.88/6.72 thf(func_def_428, type, sK123: $i > $i > $i).
% 36.88/6.72 thf(func_def_429, type, sK124: $i > $i > $i).
% 36.88/6.72 thf(func_def_430, type, sK125: $i > $i > $i).
% 36.88/6.72 thf(func_def_431, type, sK126: $i > $i > $i).
% 36.88/6.72 thf(func_def_432, type, sK127: $i > $i > $i).
% 36.88/6.72 thf(func_def_433, type, sK128: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_434, type, sK129: $i > $i).
% 36.88/6.72 thf(func_def_435, type, sK130: $i > $i).
% 36.88/6.72 thf(func_def_436, type, sK131: $i > $i).
% 36.88/6.72 thf(func_def_437, type, sK132: $i > $i).
% 36.88/6.72 thf(func_def_438, type, sK133: $i > $i > $i).
% 36.88/6.72 thf(func_def_439, type, sK134: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_440, type, sK135: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_441, type, sK136: $i > $i > $i).
% 36.88/6.72 thf(func_def_442, type, sK137: $i > $i > $i).
% 36.88/6.72 thf(func_def_444, type, sK139: $i > $i).
% 36.88/6.72 thf(func_def_445, type, sK140: $i > $i).
% 36.88/6.72 thf(func_def_446, type, sK141: $i > $i).
% 36.88/6.72 thf(func_def_458, type, sK153: $i > $o).
% 36.88/6.72 thf(func_def_467, type, sK162: $i > $o).
% 36.88/6.72 thf(func_def_468, type, sK163: $i > $o).
% 36.88/6.72 thf(func_def_469, type, sK164: ($i > $o) > ($i > $o) > $i > $i > $i).
% 36.88/6.72 thf(func_def_470, type, sK165: ($i > $o) > ($i > $o) > $i > $i > $i).
% 36.88/6.72 thf(func_def_473, type, sK168: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_474, type, sK169: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_496, type, sK191: $i > $i > $o).
% 36.88/6.72 thf(func_def_505, type, sK200: $i > $o).
% 36.88/6.72 thf(func_def_508, type, sK203: $i > $i > $o).
% 36.88/6.72 thf(func_def_526, type, sK221: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_528, type, sK223: $i > $o).
% 36.88/6.72 thf(func_def_530, type, sK225: $i > $o).
% 36.88/6.72 thf(func_def_547, type, sK242: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_563, type, sK258: ($i > $o) > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_564, type, sK259: ($i > $o) > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_565, type, sK260: $i > $o).
% 36.88/6.72 thf(func_def_566, type, sK261: $i > $o).
% 36.88/6.72 thf(func_def_584, type, sK279: $i > ($i > $i) > $i > $i).
% 36.88/6.72 thf(func_def_586, type, sK281: $i > $i).
% 36.88/6.72 thf(func_def_595, type, sK290: $i > $o).
% 36.88/6.72 thf(func_def_601, type, sK296: $i > $i).
% 36.88/6.72 thf(func_def_608, type, sK303: $i > $i > $i).
% 36.88/6.72 thf(func_def_611, type, sK306: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_656, type, sK351: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_657, type, sK352: $i > $o).
% 36.88/6.72 thf(func_def_660, type, sK355: $i > $o).
% 36.88/6.72 thf(func_def_663, type, sK358: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_665, type, sK360: $i > $o).
% 36.88/6.72 thf(func_def_679, type, sK374: $i > $i > $i).
% 36.88/6.72 thf(func_def_680, type, sK375: $i > $i > $i).
% 36.88/6.72 thf(func_def_689, type, sK384: $i > $i > ($i > $i) > $i).
% 36.88/6.72 thf(func_def_690, type, sK385: $i > $i).
% 36.88/6.72 thf(func_def_697, type, sK392: $i > $i).
% 36.88/6.72 thf(func_def_701, type, sK396: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_702, type, sK397: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_710, type, sK405: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_711, type, sK406: $i > $o).
% 36.88/6.72 thf(func_def_721, type, sK416: $i > $i > $o).
% 36.88/6.72 thf(func_def_727, type, sK422: $i > ($i > $i) > $i > $i).
% 36.88/6.72 thf(func_def_729, type, sK424: $i > $i).
% 36.88/6.72 thf(func_def_738, type, sK433: $i > $o).
% 36.88/6.72 thf(func_def_746, type, sK441: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_748, type, sK443: $i > $o).
% 36.88/6.72 thf(func_def_751, type, sK446: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_753, type, sK448: $i > $o).
% 36.88/6.72 thf(func_def_755, type, sK450: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_756, type, sK451: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_787, type, sK482: $i > $i).
% 36.88/6.72 thf(func_def_789, type, sK484: $i > $i).
% 36.88/6.72 thf(func_def_799, type, sK494: $i > $i > $i).
% 36.88/6.72 thf(func_def_804, type, sK499: $i > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_805, type, sK500: $i > $o).
% 36.88/6.72 thf(func_def_816, type, sK511: $i > $i).
% 36.88/6.72 thf(func_def_828, type, sK523: $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_835, type, sK530: $i > $o).
% 36.88/6.72 thf(func_def_844, type, sK539: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_846, type, sK541: $i > $o).
% 36.88/6.72 thf(func_def_847, type, sK542: $i > $i > $i).
% 36.88/6.72 thf(func_def_857, type, sK552: $i > $i).
% 36.88/6.72 thf(func_def_860, type, sK555: $i > $i > $o).
% 36.88/6.72 thf(func_def_871, type, sK566: $o > $i > $i > $i).
% 36.88/6.72 thf(func_def_880, type, sK575: $i > $o).
% 36.88/6.72 thf(func_def_887, type, sK582: $i > $o).
% 36.88/6.72 thf(func_def_897, type, sK592: $i > $i > $i).
% 36.88/6.72 thf(func_def_907, type, sK602: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_910, type, sK605: ($i > $o) > $i).
% 36.88/6.72 thf(func_def_911, type, sK606: $i > $o).
% 36.88/6.72 thf(func_def_912, type, sK607: $i > $i).
% 36.88/6.72 thf(func_def_924, type, sK619: $i > $i > ($i > $i) > $i).
% 36.88/6.72 thf(func_def_925, type, sK620: $i > $i).
% 36.88/6.72 thf(func_def_954, type, sK649: $i > $i > $i).
% 36.88/6.72 thf(func_def_957, type, sK652: $i > $o).
% 36.88/6.72 thf(func_def_964, type, sK659: $i > $i > $o).
% 36.88/6.72 thf(func_def_977, type, sK672: $i > $i > $o).
% 36.88/6.72 thf(func_def_979, type, sK674: $i > $i).
% 36.88/6.72 thf(func_def_980, type, sK675: $i > $i).
% 36.88/6.72 thf(func_def_981, type, sK676: $i > ($i > $i > $o) > $i).
% 36.88/6.72 thf(func_def_982, type, sK677: $i > $i > ($i > $i > $o) > $i).
% 36.88/6.72 thf(func_def_983, type, sK678: $i > ($i > $i > $o) > $i).
% 36.88/6.72 thf(func_def_997, type, sK692: $i > $o).
% 36.88/6.72 thf(func_def_999, type, sK694: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_1000, type, sK695: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_1001, type, sK696: ($i > $o) > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1002, type, sK697: ($i > $o) > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1006, type, sK701: $i > $o).
% 36.88/6.72 thf(func_def_1020, type, sK715: $i > $i).
% 36.88/6.72 thf(func_def_1021, type, sK716: ($i > $i) > $i > $i > $i).
% 36.88/6.72 thf(func_def_1028, type, sK723: $i > $o).
% 36.88/6.72 thf(func_def_1030, type, sK725: ($i > $o) > $i > $i).
% 36.88/6.72 thf(func_def_1034, type, sK729: $i > $o).
% 36.88/6.72 thf(func_def_1035, type, sK730: $i > $o).
% 36.88/6.72 thf(func_def_1036, type, sK731: ($i > $o) > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_1037, type, sK732: ($i > $o) > ($i > $o) > $i).
% 36.88/6.72 thf(func_def_1038, type, sK733: $i > $i).
% 36.88/6.72 thf(func_def_1040, type, sK735: ($i > $o) > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1041, type, sK736: ($i > $o) > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1045, type, sK740: $i > $o).
% 36.88/6.72 thf(func_def_1062, type, sK757: $i > $i > $i).
% 36.88/6.72 thf(func_def_1087, type, sK782: $i > $o).
% 36.88/6.72 thf(func_def_1090, type, sK785: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1091, type, sK786: $i > $i > $i > $i > $i).
% 36.88/6.72 thf(func_def_1102, type, sK797: $i > $i > ($i > $i) > $i).
% 36.88/6.72 thf(func_def_1103, type, sK798: $i > $i).
% 36.88/6.72 thf(func_def_1107, type, ph802: !>[X0: $tType]:(X0)).
% 36.88/6.72 thf(f7590,plain,(
% 36.88/6.72 $false),
% 36.88/6.72 inference(subsumption_resolution,[status(thm)],[f7589,f3274])).
% 36.88/6.72 thf(f3274,plain,(
% 36.88/6.72 ($true = (in @ sK666 @ (powerset @ sK665)))),
% 36.88/6.72 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.72 thf(f2137,plain,(
% 36.88/6.72 (funcGraphProp1 = $true) & (setminusIRneg = $true) & (setukpairinjR = $true) & (foundationAx = $true) & (setukpairinjR2 = $true) & (upairset2E = $true) & (ap2p = $true) & (nonemptyImpWitness = $true) & (complementT_lem = $true) & (setunionE = $true) & (ap2apEq2 = $true) & (notsubsetI = $true) & (emptyinPowerset = $true) & (notinemptyset = $true) & (binunionIR = $true) & (setadjoin__Cong = $true) & (singletonsswitch = $true) & (omega__Cong = $true) & (powersetTI1 = $true) & (binintersectSubset2 = $true) & (setadjoinSub = $true) & (symdiffIneg2 = $true) & (notequalI2 = $true) & (exuI2 = $true) & (upairset2IR = $true) & (emptysetimpfalse = $true) & (bs114d = $true) & (lam2lamEq = $true) & (dpsetconstrI = $true) & (exuE2 = $true) & (lamp = $true) & (exuE3u = $true) & (setadjoinSub2 = $true) & (upairsetE = $true) & (singletoninpowunion = $true) & (binintersectSubset4 = $true) & (dsetconstr__Cong = $true) & (kpairiskpair = $true) & (setunionAx = $true) & (setminusELneg = $true) & (ex1I = $true) & (setukpairinjL2 = $true) & (setoftrueEq = $true) & (doubleComplementE1 = $true) & (funcextLem = $true) & (quantDeMorgan2 = $true) & (setunionE2 = $true) & (setukpairinjL1 = $true) & (eta2 = $true) & (setminusEL = $true) & (sepSubset = $true) & (doubleComplementSub1 = $true) & (setunionI = $true) & (ap2apEq1 = $true) & (subsetI1 = $true) & (binintersectSubset3 = $true) & (iftrue = $true) & (iftrueProp1 = $true) & (binintersectTELcontra = $true) & (binintersectLsub = $true) & (symdiffE = $true) & (funcinfuncset = $true) & (ksndpairEq = $true) & (dpsetconstrERa = $true) & (funcGraphProp2 = $true) & (binintersectSubset1 = $true) & (iffalse = $true) & (infuncsetfunc = $true) & (binunionEcases = $true) & (binintersectER = $true) & (ifSingleton = $true) & (binunionRsub = $true) & (subsetTI = $true) & (contrasubsetT3 = $true) & (iftrueProp2 = $true) & (iffalseProp2 = $true) & (powersetE = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (funcext2 = $true) & (setadjoinIR = $true) & (powerset__Cong = $true) & (setOfPairsIsBReln = $true) & (nonemptyI1 = $true) & (binunionT_lem = $true) & (contrasubsetT2 = $true) & (complementImpComplementIntersect = $true) & (singletoninpowerset = $true) & (eqbreln = $true) & (exuE3e = $true) & (binintersectEL = $true) & (cartprodpairsurjEq = $true) & (emptyset__Cong = $true) & (lam2p = $true) & (cartprodsndin = $true) & (app = $true) & (emptyInPowerset = $true) & (dsetconstrEL = $true) & (nonemptyE1 = $true) & (dpsetconstrEL2 = $true) & (iffalseProp1 = $true) & (setadjoinAx = $true) & (exuI1 = $true) & (brelnall1 = $true) & (subbreln = $true) & (setunion__Cong = $true) & (symdiffIneg1 = $true) & (prop2setI = $true) & (upairinpowunion = $true) & (ex1E1 = $true) & (theeq = $true) & (omega0Ax = $true) & (quantDeMorgan1 = $true) & (exuEu = $true) & (quantDeMorgan3 = $true) & (funcext = $true) & (descrp = $true) & (omegaSAx = $true) & (setminusT_lem = $true) & (ksndsingleton = $true) & (notdallE = $true) & (kpairp = $true) & (secondinupair = $true) & (contraSubsetComplement = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem3 = $true) & (cartprodpairin = $true) & (noeltsimpempty = $true) & (binunionIL = $true) & (setukpairIL = $true) & (emptyI = $true) & (funcImageSingleton = $true) & (emptyE1 = $true) & (ifp = $true) & (funcGraphProp3 = $true) & (powersetI = $true) & (upairequniteq = $true) & (setminusER = $true) & (subsetRefl = $true) & (binintersectRsub = $true) & (doubleComplementI1 = $true) & (dpsetconstrSub = $true) & (binintersectI = $true) & (complementTnotintersectT = $true) & (notequalI1 = $true) & (ex1E2 = $true) & (iftrueorfalse = $true) & (setukpairinjR11 = $true) & (in__Cong = $true) & (exu__Cong = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (eqimpsubset1 = $true) & (complementTI1 = $true) & (subsetE = $true) & (dpsetconstrEL1 = $true) & (symdiffI1 = $true) & (replAx = $true) & (complementInPowersetComplementIntersect = $true) & (powersetAx = $true) & (notinsingleton = $true) & (setukpairIR = $true) & (cartprodmempaircEq = $true) & (symdiffI2 = $true) & (cartprodsndpairEq = $true) & (quantDeMorgan4 = $true) & (sepInPowerset = $true) & (brelnall2 = $true) & (upairsubunion = $true) & (nonemptyI = $true) & (subsetE2 = $true) & (setextsub = $true) & (exuE1 = $true) & (contrasubsetT = $true) & (complementTE1 = $true) & (subsetemptysetimpeq = $true) & (emptyinunitempty = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (inCongP = $true) & (apProp = $true) & (beta2 = $true) & (cartprodfstpairEq = $true) & (contrasubsetT1 = $true) & (setadjoinOr = $true) & (kpairsurjEq = $true) & (funcGraphProp4 = $true) & (dsetconstrI = $true) & (setminusILneg = $true) & (vacuousDall = $true) & (powersetsubset = $true) & (upairsetIR = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (setminusSubset1 = $true) & (setukpairinjR1 = $true) & (setextAx = $true) & (wellorderingAx = $true) & (binintersectTERcontra = $true) & (powersetTE1 = $true) & (singletonsuniq = $true) & (powersetT_lem = $true) & (emptysetE = $true) & (cartprodpairmemEL = $true) & (((in @ sK664 @ (powerset @ sK665)) = $true) & (($true = (in @ sK666 @ (powerset @ sK665))) & ((subset @ sK666 @ (setminus @ sK665 @ sK664)) != $true) & ($true = (subset @ sK664 @ (setminus @ sK665 @ sK666))))) & (lamProp = $true) & (eta1 = $true) & (subsetI2 = $true) & (binintersectT_lem = $true) & (binintersectSubset5 = $true) & (setukpairinjL = $true) & (subPowSU = $true) & (setbeta = $true) & (singletonsubset = $true) & (ubforcartprodlem1 = $true) & (doubleComplementEq = $true) & (cartprodfstin = $true) & (singletonprop = $true) & (notdexE = $true) & (complementSubsetComplementIntersect = $true) & (omegaIndAx = $true) & (upairsetIL = $true) & (ubforcartprodlem2 = $true) & (prop2set2propI = $true) & (doubleComplementSub2 = $true) & (eqinunit = $true) & (setminusLsub = $true) & (setext = $true) & (cartprodmempair = $true) & (setunionsingleton2 = $true) & (dpsetconstrER = $true) & (descr__Cong = $true) & (kfstpairEq = $true) & (ex1I2 = $true) & (kfstsingleton = $true) & (disjointsetsI1 = $true) & (setukpairinjR12 = $true) & (inPowerset = $true) & (setunionsingleton1 = $true) & (theprop = $true) & (subsetTrans = $true) & (setminusSubset2 = $true) & (beta1 = $true) & (cartprodmempair1 = $true) & (binunionE = $true) & (exuI3 = $true) & (powersetE1 = $true) & (setunionsingleton = $true) & (uniqinunit = $true) & (setextT = $true) & (setminusERneg = $true) & (setminusI = $true) & (cartprodpairmemER = $true) & (setadjoinIL = $true)),
% 36.88/6.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK664,sK665,sK666])],[f1062,f2136,f2135])).
% 36.88/6.72 thf(f2135,plain,(
% 36.88/6.72 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ($true = (subset @ X0 @ (setminus @ X1 @ X2))))) => (((in @ sK664 @ (powerset @ sK665)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ sK665)) = $true) & ($true != (subset @ X2 @ (setminus @ sK665 @ sK664))) & ((subset @ sK664 @ (setminus @ sK665 @ X2)) = $true)))),
% 36.88/6.72 introduced(definition,[],[choice_axiom])).
% 36.88/6.72 thf(f2136,plain,(
% 36.88/6.72 ? [X2 : $i] : (((in @ X2 @ (powerset @ sK665)) = $true) & ($true != (subset @ X2 @ (setminus @ sK665 @ sK664))) & ((subset @ sK664 @ (setminus @ sK665 @ X2)) = $true)) => (($true = (in @ sK666 @ (powerset @ sK665))) & ((subset @ sK666 @ (setminus @ sK665 @ sK664)) != $true) & ($true = (subset @ sK664 @ (setminus @ sK665 @ sK666))))),
% 36.88/6.72 introduced(definition,[],[choice_axiom])).
% 36.88/6.72 thf(f1062,plain,(
% 36.88/6.72 (funcGraphProp1 = $true) & (setminusIRneg = $true) & (setukpairinjR = $true) & (foundationAx = $true) & (setukpairinjR2 = $true) & (upairset2E = $true) & (ap2p = $true) & (nonemptyImpWitness = $true) & (complementT_lem = $true) & (setunionE = $true) & (ap2apEq2 = $true) & (notsubsetI = $true) & (emptyinPowerset = $true) & (notinemptyset = $true) & (binunionIR = $true) & (setadjoin__Cong = $true) & (singletonsswitch = $true) & (omega__Cong = $true) & (powersetTI1 = $true) & (binintersectSubset2 = $true) & (setadjoinSub = $true) & (symdiffIneg2 = $true) & (notequalI2 = $true) & (exuI2 = $true) & (upairset2IR = $true) & (emptysetimpfalse = $true) & (bs114d = $true) & (lam2lamEq = $true) & (dpsetconstrI = $true) & (exuE2 = $true) & (lamp = $true) & (exuE3u = $true) & (setadjoinSub2 = $true) & (upairsetE = $true) & (singletoninpowunion = $true) & (binintersectSubset4 = $true) & (dsetconstr__Cong = $true) & (kpairiskpair = $true) & (setunionAx = $true) & (setminusELneg = $true) & (ex1I = $true) & (setukpairinjL2 = $true) & (setoftrueEq = $true) & (doubleComplementE1 = $true) & (funcextLem = $true) & (quantDeMorgan2 = $true) & (setunionE2 = $true) & (setukpairinjL1 = $true) & (eta2 = $true) & (setminusEL = $true) & (sepSubset = $true) & (doubleComplementSub1 = $true) & (setunionI = $true) & (ap2apEq1 = $true) & (subsetI1 = $true) & (binintersectSubset3 = $true) & (iftrue = $true) & (iftrueProp1 = $true) & (binintersectTELcontra = $true) & (binintersectLsub = $true) & (symdiffE = $true) & (funcinfuncset = $true) & (ksndpairEq = $true) & (dpsetconstrERa = $true) & (funcGraphProp2 = $true) & (binintersectSubset1 = $true) & (iffalse = $true) & (infuncsetfunc = $true) & (binunionEcases = $true) & (binintersectER = $true) & (ifSingleton = $true) & (binunionRsub = $true) & (subsetTI = $true) & (contrasubsetT3 = $true) & (iftrueProp2 = $true) & (iffalseProp2 = $true) & (powersetE = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (funcext2 = $true) & (setadjoinIR = $true) & (powerset__Cong = $true) & (setOfPairsIsBReln = $true) & (nonemptyI1 = $true) & (binunionT_lem = $true) & (contrasubsetT2 = $true) & (complementImpComplementIntersect = $true) & (singletoninpowerset = $true) & (eqbreln = $true) & (exuE3e = $true) & (binintersectEL = $true) & (cartprodpairsurjEq = $true) & (emptyset__Cong = $true) & (lam2p = $true) & (cartprodsndin = $true) & (app = $true) & (emptyInPowerset = $true) & (dsetconstrEL = $true) & (nonemptyE1 = $true) & (dpsetconstrEL2 = $true) & (iffalseProp1 = $true) & (setadjoinAx = $true) & (exuI1 = $true) & (brelnall1 = $true) & (subbreln = $true) & (setunion__Cong = $true) & (symdiffIneg1 = $true) & (prop2setI = $true) & (upairinpowunion = $true) & (ex1E1 = $true) & (theeq = $true) & (omega0Ax = $true) & (quantDeMorgan1 = $true) & (exuEu = $true) & (quantDeMorgan3 = $true) & (funcext = $true) & (descrp = $true) & (omegaSAx = $true) & (setminusT_lem = $true) & (ksndsingleton = $true) & (notdallE = $true) & (kpairp = $true) & (secondinupair = $true) & (contraSubsetComplement = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem3 = $true) & (cartprodpairin = $true) & (noeltsimpempty = $true) & (binunionIL = $true) & (setukpairIL = $true) & (emptyI = $true) & (funcImageSingleton = $true) & (emptyE1 = $true) & (ifp = $true) & (funcGraphProp3 = $true) & (powersetI = $true) & (upairequniteq = $true) & (setminusER = $true) & (subsetRefl = $true) & (binintersectRsub = $true) & (doubleComplementI1 = $true) & (dpsetconstrSub = $true) & (binintersectI = $true) & (complementTnotintersectT = $true) & (notequalI1 = $true) & (ex1E2 = $true) & (iftrueorfalse = $true) & (setukpairinjR11 = $true) & (in__Cong = $true) & (exu__Cong = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (eqimpsubset1 = $true) & (complementTI1 = $true) & (subsetE = $true) & (dpsetconstrEL1 = $true) & (symdiffI1 = $true) & (replAx = $true) & (complementInPowersetComplementIntersect = $true) & (powersetAx = $true) & (notinsingleton = $true) & (setukpairIR = $true) & (cartprodmempaircEq = $true) & (symdiffI2 = $true) & (cartprodsndpairEq = $true) & (quantDeMorgan4 = $true) & (sepInPowerset = $true) & (brelnall2 = $true) & (upairsubunion = $true) & (nonemptyI = $true) & (subsetE2 = $true) & (setextsub = $true) & (exuE1 = $true) & (contrasubsetT = $true) & (complementTE1 = $true) & (subsetemptysetimpeq = $true) & (emptyinunitempty = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (inCongP = $true) & (apProp = $true) & (beta2 = $true) & (cartprodfstpairEq = $true) & (contrasubsetT1 = $true) & (setadjoinOr = $true) & (kpairsurjEq = $true) & (funcGraphProp4 = $true) & (dsetconstrI = $true) & (setminusILneg = $true) & (vacuousDall = $true) & (powersetsubset = $true) & (upairsetIR = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (setminusSubset1 = $true) & (setukpairinjR1 = $true) & (setextAx = $true) & (wellorderingAx = $true) & (binintersectTERcontra = $true) & (powersetTE1 = $true) & (singletonsuniq = $true) & (powersetT_lem = $true) & (emptysetE = $true) & (cartprodpairmemEL = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ($true = (subset @ X0 @ (setminus @ X1 @ X2))))) & (lamProp = $true) & (eta1 = $true) & (subsetI2 = $true) & (binintersectT_lem = $true) & (binintersectSubset5 = $true) & (setukpairinjL = $true) & (subPowSU = $true) & (setbeta = $true) & (singletonsubset = $true) & (ubforcartprodlem1 = $true) & (doubleComplementEq = $true) & (cartprodfstin = $true) & (singletonprop = $true) & (notdexE = $true) & (complementSubsetComplementIntersect = $true) & (omegaIndAx = $true) & (upairsetIL = $true) & (ubforcartprodlem2 = $true) & (prop2set2propI = $true) & (doubleComplementSub2 = $true) & (eqinunit = $true) & (setminusLsub = $true) & (setext = $true) & (cartprodmempair = $true) & (setunionsingleton2 = $true) & (dpsetconstrER = $true) & (descr__Cong = $true) & (kfstpairEq = $true) & (ex1I2 = $true) & (kfstsingleton = $true) & (disjointsetsI1 = $true) & (setukpairinjR12 = $true) & (inPowerset = $true) & (setunionsingleton1 = $true) & (theprop = $true) & (subsetTrans = $true) & (setminusSubset2 = $true) & (beta1 = $true) & (cartprodmempair1 = $true) & (binunionE = $true) & (exuI3 = $true) & (powersetE1 = $true) & (setunionsingleton = $true) & (uniqinunit = $true) & (setextT = $true) & (setminusERneg = $true) & (setminusI = $true) & (cartprodpairmemER = $true) & (setadjoinIL = $true)),
% 36.88/6.72 inference(flattening,[status(thm)],[f1061])).
% 36.88/6.72 thf(f1061,plain,(
% 36.88/6.72 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ X2 @ (setminus @ X1 @ X0)) != $true) & ($true = (subset @ X0 @ (setminus @ X1 @ X2)))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 36.88/6.72 inference(ennf_transformation,[status(thm)],[f352])).
% 36.88/6.72 thf(f352,plain,(
% 36.88/6.72 ~((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) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => (($true = (subset @ X0 @ (setminus @ X1 @ X2))) => ((subset @ X2 @ (setminus @ X1 @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.88/6.72 inference(fool_elimination,[status(thm)],[f351])).
% 36.88/6.72 thf(f351,plain,(
% 36.88/6.72 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ (setminus @ X1 @ X2)) => (subset @ X2 @ (setminus @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.88/6.73 inference(rectify,[status(thm)],[f259])).
% 36.88/6.73 thf(f259,negated_conjecture,(
% 36.88/6.73 ~(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 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ((subset @ X11 @ (setminus @ X3 @ X16)) => (subset @ X16 @ (setminus @ X3 @ X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.88/6.73 inference(negated_conjecture,[status(cth)],[f258])).
% 36.88/6.73 thf(f258,conjecture,(
% 36.88/6.73 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 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ((subset @ X11 @ (setminus @ X3 @ X16)) => (subset @ X16 @ (setminus @ X3 @ X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 36.88/6.73 file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',complementTcontraSubset)).
% 36.88/6.73 thf(f7589,plain,(
% 36.88/6.73 ($true != (in @ sK666 @ (powerset @ sK665)))),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f7579,f3471])).
% 36.88/6.73 thf(f3471,plain,(
% 36.88/6.73 (complementT_lem = $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f7579,plain,(
% 36.88/6.73 (complementT_lem != $true) | ($true != (in @ sK666 @ (powerset @ sK665)))),
% 36.88/6.73 inference(trivial_inequality_removal,[status(thm)],[f7569])).
% 36.88/6.73 thf(f7569,plain,(
% 36.88/6.73 ($true != (in @ sK666 @ (powerset @ sK665))) | (complementT_lem != $true) | ($true != $true)),
% 36.88/6.73 inference(superposition,[status(thm)],[f7074,f2546])).
% 36.88/6.73 thf(f2546,plain,(
% 36.88/6.73 ( ! [X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true) | (complementT_lem != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f1349])).
% 36.88/6.73 thf(f1349,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | (((in @ sK150 @ (powerset @ sK149)) = $true) & ((in @ (setminus @ sK149 @ sK150) @ (powerset @ sK149)) != $true)))),
% 36.88/6.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150])],[f1347,f1348])).
% 36.88/6.73 thf(f1348,plain,(
% 36.88/6.73 ? [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) = $true) & ($true != (in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) => (((in @ sK150 @ (powerset @ sK149)) = $true) & ((in @ (setminus @ sK149 @ sK150) @ (powerset @ sK149)) != $true))),
% 36.88/6.73 introduced(definition,[],[choice_axiom])).
% 36.88/6.73 thf(f1347,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (((in @ X3 @ (powerset @ X2)) = $true) & ($true != (in @ (setminus @ X2 @ X3) @ (powerset @ X2)))))),
% 36.88/6.73 inference(rectify,[status(thm)],[f1346])).
% 36.88/6.73 thf(f1346,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)))),
% 36.88/6.73 inference(nnf_transformation,[status(thm)],[f1005])).
% 36.88/6.73 thf(f1005,plain,(
% 36.88/6.73 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) <=> (complementT_lem = $true)),
% 36.88/6.73 inference(ennf_transformation,[status(thm)],[f668])).
% 36.88/6.73 thf(f668,plain,(
% 36.88/6.73 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) = $true)) <=> (complementT_lem = $true)),
% 36.88/6.73 inference(fool_elimination,[status(thm)],[f667])).
% 36.88/6.73 thf(f667,plain,(
% 36.88/6.73 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 36.88/6.73 inference(rectify,[status(thm)],[f235])).
% 36.88/6.73 thf(f235,axiom,(
% 36.88/6.73 (complementT_lem = ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => (in @ (setminus @ X3 @ X11) @ (powerset @ X3))))),
% 36.88/6.73 file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',complementT_lem)).
% 36.88/6.73 thf(f7074,plain,(
% 36.88/6.73 ($true != (in @ (setminus @ sK665 @ sK666) @ (powerset @ sK665)))),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f7073,f3428])).
% 36.88/6.73 thf(f3428,plain,(
% 36.88/6.73 (doubleComplementSub1 = $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f7073,plain,(
% 36.88/6.73 ($true != (in @ (setminus @ sK665 @ sK666) @ (powerset @ sK665))) | (doubleComplementSub1 != $true)),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f7072,f3272])).
% 36.88/6.73 thf(f3272,plain,(
% 36.88/6.73 ($true = (subset @ sK664 @ (setminus @ sK665 @ sK666)))),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f7072,plain,(
% 36.88/6.73 ($true != (subset @ sK664 @ (setminus @ sK665 @ sK666))) | ($true != (in @ (setminus @ sK665 @ sK666) @ (powerset @ sK665))) | (doubleComplementSub1 != $true)),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f7065,f3274])).
% 36.88/6.73 thf(f7065,plain,(
% 36.88/6.73 ($true != (in @ sK666 @ (powerset @ sK665))) | (doubleComplementSub1 != $true) | ($true != (in @ (setminus @ sK665 @ sK666) @ (powerset @ sK665))) | ($true != (subset @ sK664 @ (setminus @ sK665 @ sK666)))),
% 36.88/6.73 inference(trivial_inequality_removal,[status(thm)],[f7059])).
% 36.88/6.73 thf(f7059,plain,(
% 36.88/6.73 ($true != (in @ sK666 @ (powerset @ sK665))) | ($true != (subset @ sK664 @ (setminus @ sK665 @ sK666))) | (doubleComplementSub1 != $true) | ($true != (in @ (setminus @ sK665 @ sK666) @ (powerset @ sK665))) | ($true != $true)),
% 36.88/6.73 inference(superposition,[status(thm)],[f4274,f3615])).
% 36.88/6.73 thf(f3615,plain,(
% 36.88/6.73 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ (setminus @ X2 @ (setminus @ X2 @ X3))) = $true) | (doubleComplementSub1 != $true) | ((in @ X3 @ (powerset @ X2)) != $true)) )),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2286])).
% 36.88/6.73 thf(f2286,plain,(
% 36.88/6.73 ((doubleComplementSub1 = $true) | (((subset @ sK761 @ (setminus @ sK760 @ (setminus @ sK760 @ sK761))) != $true) & ((in @ sK761 @ (powerset @ sK760)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ (setminus @ X2 @ (setminus @ X2 @ X3))) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (doubleComplementSub1 != $true))),
% 36.88/6.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK760,sK761])],[f2284,f2285])).
% 36.88/6.73 thf(f2285,plain,(
% 36.88/6.73 ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (((subset @ sK761 @ (setminus @ sK760 @ (setminus @ sK760 @ sK761))) != $true) & ((in @ sK761 @ (powerset @ sK760)) = $true))),
% 36.88/6.73 introduced(definition,[],[choice_axiom])).
% 36.88/6.73 thf(f2284,plain,(
% 36.88/6.73 ((doubleComplementSub1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ (setminus @ X2 @ (setminus @ X2 @ X3))) = $true) | ((in @ X3 @ (powerset @ X2)) != $true)) | (doubleComplementSub1 != $true))),
% 36.88/6.73 inference(rectify,[status(thm)],[f2283])).
% 36.88/6.73 thf(f2283,plain,(
% 36.88/6.73 ((doubleComplementSub1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (doubleComplementSub1 != $true))),
% 36.88/6.73 inference(nnf_transformation,[status(thm)],[f841])).
% 36.88/6.73 thf(f841,plain,(
% 36.88/6.73 (doubleComplementSub1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 36.88/6.73 inference(ennf_transformation,[status(thm)],[f462])).
% 36.88/6.73 thf(f462,plain,(
% 36.88/6.73 (doubleComplementSub1 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ($true = (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))))),
% 36.88/6.73 inference(fool_elimination,[status(thm)],[f461])).
% 36.88/6.73 thf(f461,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = doubleComplementSub1)),
% 36.88/6.73 inference(rectify,[status(thm)],[f250])).
% 36.88/6.73 thf(f250,axiom,(
% 36.88/6.73 (! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => (subset @ X11 @ (setminus @ X3 @ (setminus @ X3 @ X11)))) = doubleComplementSub1)),
% 36.88/6.73 file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',doubleComplementSub1)).
% 36.88/6.73 thf(f4274,plain,(
% 36.88/6.73 ( ! [X0 : $i] : (((subset @ sK666 @ (setminus @ sK665 @ X0)) != $true) | ((in @ X0 @ (powerset @ sK665)) != $true) | ($true != (subset @ sK664 @ X0))) )),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f4273,f3275])).
% 36.88/6.73 thf(f3275,plain,(
% 36.88/6.73 ((in @ sK664 @ (powerset @ sK665)) = $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f4273,plain,(
% 36.88/6.73 ( ! [X0 : $i] : (($true != (subset @ sK664 @ X0)) | ((subset @ sK666 @ (setminus @ sK665 @ X0)) != $true) | ((in @ sK664 @ (powerset @ sK665)) != $true) | ((in @ X0 @ (powerset @ sK665)) != $true)) )),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f4256,f3394])).
% 36.88/6.73 thf(f3394,plain,(
% 36.88/6.73 (contrasubsetT2 = $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f4256,plain,(
% 36.88/6.73 ( ! [X0 : $i] : ((contrasubsetT2 != $true) | ((subset @ sK666 @ (setminus @ sK665 @ X0)) != $true) | ((in @ X0 @ (powerset @ sK665)) != $true) | ((in @ sK664 @ (powerset @ sK665)) != $true) | ($true != (subset @ sK664 @ X0))) )),
% 36.88/6.73 inference(trivial_inequality_removal,[status(thm)],[f4232])).
% 36.88/6.73 thf(f4232,plain,(
% 36.88/6.73 ( ! [X0 : $i] : (((in @ sK664 @ (powerset @ sK665)) != $true) | (contrasubsetT2 != $true) | ($true != $true) | ((in @ X0 @ (powerset @ sK665)) != $true) | ((subset @ sK666 @ (setminus @ sK665 @ X0)) != $true) | ($true != (subset @ sK664 @ X0))) )),
% 36.88/6.73 inference(superposition,[status(thm)],[f3844,f2877])).
% 36.88/6.73 thf(f2877,plain,(
% 36.88/6.73 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) | ((in @ X2 @ (powerset @ X0)) != $true) | (contrasubsetT2 != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ($true != (subset @ X1 @ X2))) )),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f1721])).
% 36.88/6.73 thf(f1721,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT2 != $true)) & ((contrasubsetT2 = $true) | ((((subset @ sK399 @ sK400) = $true) & ($true = (in @ sK400 @ (powerset @ sK398))) & ((subset @ (setminus @ sK398 @ sK400) @ (setminus @ sK398 @ sK399)) != $true)) & ($true = (in @ sK399 @ (powerset @ sK398)))))),
% 36.88/6.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK398,sK399,sK400])],[f1718,f1720,f1719])).
% 36.88/6.73 thf(f1719,plain,(
% 36.88/6.73 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((subset @ X4 @ X5) = $true) & ($true = (in @ X5 @ (powerset @ X3))) & ($true != (subset @ (setminus @ X3 @ X5) @ (setminus @ X3 @ X4)))) & ((in @ X4 @ (powerset @ X3)) = $true)) => (? [X5 : $i] : (($true = (subset @ sK399 @ X5)) & ($true = (in @ X5 @ (powerset @ sK398))) & ($true != (subset @ (setminus @ sK398 @ X5) @ (setminus @ sK398 @ sK399)))) & ($true = (in @ sK399 @ (powerset @ sK398))))),
% 36.88/6.73 introduced(definition,[],[choice_axiom])).
% 36.88/6.73 thf(f1720,plain,(
% 36.88/6.73 ? [X5 : $i] : (($true = (subset @ sK399 @ X5)) & ($true = (in @ X5 @ (powerset @ sK398))) & ($true != (subset @ (setminus @ sK398 @ X5) @ (setminus @ sK398 @ sK399)))) => (((subset @ sK399 @ sK400) = $true) & ($true = (in @ sK400 @ (powerset @ sK398))) & ((subset @ (setminus @ sK398 @ sK400) @ (setminus @ sK398 @ sK399)) != $true))),
% 36.88/6.73 introduced(definition,[],[choice_axiom])).
% 36.88/6.73 thf(f1718,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT2 != $true)) & ((contrasubsetT2 = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((subset @ X4 @ X5) = $true) & ($true = (in @ X5 @ (powerset @ X3))) & ($true != (subset @ (setminus @ X3 @ X5) @ (setminus @ X3 @ X4)))) & ((in @ X4 @ (powerset @ X3)) = $true)))),
% 36.88/6.73 inference(rectify,[status(thm)],[f1717])).
% 36.88/6.73 thf(f1717,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (contrasubsetT2 != $true)) & ((contrasubsetT2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (subset @ X1 @ X2)) & ((in @ X2 @ (powerset @ X0)) = $true) & ($true != (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 36.88/6.73 inference(nnf_transformation,[status(thm)],[f950])).
% 36.88/6.73 thf(f950,plain,(
% 36.88/6.73 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (subset @ X1 @ X2)) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (contrasubsetT2 = $true)),
% 36.88/6.73 inference(flattening,[status(thm)],[f949])).
% 36.88/6.73 thf(f949,plain,(
% 36.88/6.73 (contrasubsetT2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))) | ($true != (subset @ X1 @ X2))) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 36.88/6.73 inference(ennf_transformation,[status(thm)],[f368])).
% 36.88/6.73 thf(f368,plain,(
% 36.88/6.73 (contrasubsetT2 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (($true = (subset @ X1 @ X2)) => ($true = (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))))),
% 36.88/6.73 inference(fool_elimination,[status(thm)],[f367])).
% 36.88/6.73 thf(f367,plain,(
% 36.88/6.73 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ X2) => (subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1))))) = contrasubsetT2)),
% 36.88/6.73 inference(rectify,[status(thm)],[f246])).
% 36.88/6.73 thf(f246,axiom,(
% 36.88/6.73 (! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ((subset @ X11 @ X16) => (subset @ (setminus @ X3 @ X16) @ (setminus @ X3 @ X11))))) = contrasubsetT2)),
% 36.88/6.73 file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',contrasubsetT2)).
% 36.88/6.73 thf(f3844,plain,(
% 36.88/6.73 ( ! [X0 : $i] : (((subset @ X0 @ (setminus @ sK665 @ sK664)) != $true) | ($true != (subset @ sK666 @ X0))) )),
% 36.88/6.73 inference(subsumption_resolution,[status(thm)],[f3839,f3236])).
% 36.88/6.73 thf(f3236,plain,(
% 36.88/6.73 (subsetTrans = $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 thf(f3839,plain,(
% 36.88/6.73 ( ! [X0 : $i] : (((subset @ X0 @ (setminus @ sK665 @ sK664)) != $true) | (subsetTrans != $true) | ($true != (subset @ sK666 @ X0))) )),
% 36.88/6.73 inference(trivial_inequality_removal,[status(thm)],[f3836])).
% 36.88/6.73 thf(f3836,plain,(
% 36.88/6.73 ( ! [X0 : $i] : ((subsetTrans != $true) | ($true != $true) | ($true != (subset @ sK666 @ X0)) | ((subset @ X0 @ (setminus @ sK665 @ sK664)) != $true)) )),
% 36.88/6.73 inference(superposition,[status(thm)],[f3273,f2583])).
% 36.88/6.73 thf(f2583,plain,(
% 36.88/6.73 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X4) = $true) | ((subset @ X3 @ X5) != $true) | (subsetTrans != $true) | ((subset @ X5 @ X4) != $true)) )),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f1390])).
% 36.88/6.73 thf(f1390,plain,(
% 36.88/6.73 ((subsetTrans = $true) | (((subset @ sK177 @ sK176) = $true) & ((subset @ sK175 @ sK177) = $true) & ((subset @ sK175 @ sK176) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) != $true) | ((subset @ X3 @ X5) != $true) | ((subset @ X3 @ X4) = $true)) | (subsetTrans != $true))),
% 36.88/6.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176,sK177])],[f1388,f1389])).
% 36.88/6.73 thf(f1389,plain,(
% 36.88/6.73 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X0 @ X2) = $true) & ((subset @ X0 @ X1) != $true)) => (((subset @ sK177 @ sK176) = $true) & ((subset @ sK175 @ sK177) = $true) & ((subset @ sK175 @ sK176) != $true))),
% 36.88/6.73 introduced(definition,[],[choice_axiom])).
% 36.88/6.73 thf(f1388,plain,(
% 36.88/6.73 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X0 @ X2) = $true) & ((subset @ X0 @ X1) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) != $true) | ((subset @ X3 @ X5) != $true) | ((subset @ X3 @ X4) = $true)) | (subsetTrans != $true))),
% 36.88/6.73 inference(rectify,[status(thm)],[f1387])).
% 36.88/6.73 thf(f1387,plain,(
% 36.88/6.73 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X0 @ X2) = $true) & ((subset @ X0 @ X1) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ X1)) | ((subset @ X0 @ X2) != $true) | ((subset @ X0 @ X1) = $true)) | (subsetTrans != $true))),
% 36.88/6.73 inference(nnf_transformation,[status(thm)],[f1082])).
% 36.88/6.73 thf(f1082,plain,(
% 36.88/6.73 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ X1)) | ((subset @ X0 @ X2) != $true) | ((subset @ X0 @ X1) = $true))),
% 36.88/6.73 inference(flattening,[status(thm)],[f1081])).
% 36.88/6.73 thf(f1081,plain,(
% 36.88/6.73 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X1) = $true) | ($true != (subset @ X2 @ X1))) | ((subset @ X0 @ X2) != $true))),
% 36.88/6.73 inference(ennf_transformation,[status(thm)],[f364])).
% 36.88/6.73 thf(f364,plain,(
% 36.88/6.73 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) = $true) => (($true = (subset @ X2 @ X1)) => ((subset @ X0 @ X1) = $true)))),
% 36.88/6.73 inference(fool_elimination,[status(thm)],[f363])).
% 36.88/6.73 thf(f363,plain,(
% 36.88/6.73 (subsetTrans = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((subset @ X2 @ X1) => (subset @ X0 @ X1))))),
% 36.88/6.73 inference(rectify,[status(thm)],[f89])).
% 36.88/6.73 thf(f89,axiom,(
% 36.88/6.73 (subsetTrans = ! [X3 : $i,X5 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))))),
% 36.88/6.73 file('/export/starexec/sandbox/tmp/tmp.N41KBN15dc/DTF2THF_23392.p',subsetTrans)).
% 36.88/6.73 thf(f3273,plain,(
% 36.88/6.73 ((subset @ sK666 @ (setminus @ sK665 @ sK664)) != $true)),
% 36.88/6.73 inference(cnf_transformation,[status(thm)],[f2137])).
% 36.88/6.73 % SZS output end Proof for DTF2THF_23392
% 36.88/6.73 % (23901)------------------------------
% 36.88/6.73 % (23901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.88/6.73 % (23901)Termination reason: Refutation
% 36.88/6.73
% 36.88/6.73 % (23901)Memory used [KB]: 8187
% 36.88/6.73 % (23901)Time elapsed: 0.343 s
% 36.88/6.73 % (23901)Instructions burned: 1121 (million)
% 36.88/6.73 % (23901)------------------------------
% 36.88/6.73 % (23901)------------------------------
% 36.88/6.73 % (23711)Success in time 5.168 s
%------------------------------------------------------------------------------