%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU680^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n023.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 09:36:17 AM UTC 2026
% Result : Theorem 12.95s 3.06s
% Output : Refutation 12.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 3440 ( 918 equ; 0 cnn)
% Maximal formula atoms : 199 ( 73 avg)
% Number of connectives : 2051 ( 73 ~; 51 |; 615 &; 503 @)
% ( 4 <=>; 805 =>; 0 <=; 0 <~>)
% Maximal formula depth : 207 ( 34 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 364 ( 361 usr; 205 con; 0-4 aty)
% Number of variables : 145 ( 24 ^; 90 !; 31 ?; 145 :)
% 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_249,type,
sP2: $i > $i > $i > $o > $o ).
thf(func_def_251,type,
sP4: $i > $i > $o ).
thf(func_def_252,type,
sP5: $i > $o ).
thf(func_def_253,type,
sP6: $i > $i > $o ).
thf(func_def_254,type,
sP7: $i > $i > $o ).
thf(func_def_263,type,
sK16: $i > $i > $i ).
thf(func_def_268,type,
sK21: $i > $o ).
thf(func_def_270,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_271,type,
sK24: $i > $o ).
thf(func_def_272,type,
sK25: $i > $o ).
thf(func_def_273,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_275,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_277,type,
sK30: $i > $o ).
thf(func_def_296,type,
sK49: $i > $o ).
thf(func_def_298,type,
sK51: ( $i > $o ) > $i > $i ).
thf(func_def_299,type,
sK52: $i > $i ).
thf(func_def_321,type,
sK74: $i > $i > $i ).
thf(func_def_324,type,
sK77: $i > $i > $i ).
thf(func_def_331,type,
sK84: $i > $i > $i > $i ).
thf(func_def_332,type,
sK85: $i > $i > $i > $i ).
thf(func_def_349,type,
sK102: $i > $o ).
thf(func_def_364,type,
sK117: $i > $i > $o ).
thf(func_def_373,type,
sK126: ( $i > $o ) > $i ).
thf(func_def_374,type,
sK127: $i > $o ).
thf(func_def_375,type,
sK128: $i > $i ).
thf(func_def_380,type,
sK133: $i > $i ).
thf(func_def_392,type,
sK145: ( $i > $o ) > $i ).
thf(func_def_393,type,
sK146: $i > $o ).
thf(func_def_394,type,
sK147: $i > $i ).
thf(func_def_399,type,
sK152: $i > $i ).
thf(func_def_402,type,
sK155: $i > $i > $o ).
thf(func_def_408,type,
sK161: $i > $i > $o ).
thf(func_def_410,type,
sK163: $i > $i ).
thf(func_def_411,type,
sK164: $i > $i ).
thf(func_def_412,type,
sK165: $i > ( $i > $i > $o ) > $i ).
thf(func_def_413,type,
sK166: $i > ( $i > $i > $o ) > $i ).
thf(func_def_414,type,
sK167: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_419,type,
sK172: $i > $i > $o ).
thf(func_def_421,type,
sK174: $i > $o ).
thf(func_def_438,type,
sK191: $i > $o ).
thf(func_def_441,type,
sK194: $i > ( $i > $o ) > $i ).
thf(func_def_442,type,
sK195: $i > ( $i > $o ) > $i ).
thf(func_def_443,type,
sK196: $i > $o ).
thf(func_def_446,type,
sK199: $i > $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK204: $i > $o ).
thf(func_def_456,type,
sK209: $i > $i ).
thf(func_def_458,type,
sK211: $i > $i ).
thf(func_def_479,type,
sK232: $i > $i > $o ).
thf(func_def_493,type,
sK246: $i > $i ).
thf(func_def_517,type,
sK270: $i > $o ).
thf(func_def_521,type,
sK274: $i > $i ).
thf(func_def_535,type,
sK288: $i > $i > $i ).
thf(func_def_536,type,
sK289: $o > $i > $i > $i ).
thf(func_def_554,type,
sK307: $i > $o ).
thf(func_def_555,type,
sK308: $i > $o ).
thf(func_def_556,type,
sK309: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_557,type,
sK310: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_561,type,
sK314: $i > $o ).
thf(func_def_563,type,
sK316: $i > ( $i > $o ) > $i ).
thf(func_def_572,type,
sK325: $i > $i > $o ).
thf(func_def_582,type,
sK335: $i > $o ).
thf(func_def_584,type,
sK337: $i > $i > ( $i > $i ) > $i ).
thf(func_def_585,type,
sK338: $i > $i ).
thf(func_def_590,type,
sK343: $i > $o ).
thf(func_def_596,type,
sK349: $i > ( $i > $i ) > $i > $i ).
thf(func_def_598,type,
sK351: $i > $i ).
thf(func_def_601,type,
sK354: $i > $o ).
thf(func_def_603,type,
sK356: ( $i > $o ) > $i > $i ).
thf(func_def_605,type,
sK358: $i > $o ).
thf(func_def_607,type,
sK360: ( $i > $o ) > $i > $i ).
thf(func_def_608,type,
sK361: $i > $o ).
thf(func_def_611,type,
sK364: $i > ( $i > $o ) > $i ).
thf(func_def_612,type,
sK365: $i > ( $i > $o ) > $i ).
thf(func_def_619,type,
sK372: $i > $o ).
thf(func_def_634,type,
sK387: $i > $i > $i ).
thf(func_def_650,type,
sK403: $i > $o ).
thf(func_def_652,type,
sK405: ( $i > $o ) > $i ).
thf(func_def_653,type,
sK406: ( $i > $o ) > $i ).
thf(func_def_658,type,
sK411: $i > $o ).
thf(func_def_663,type,
sK416: $i > $i > $i ).
thf(func_def_670,type,
sK423: $i > $o ).
thf(func_def_673,type,
sK426: $i > ( $i > $o ) > $i ).
thf(func_def_677,type,
sK430: $i > $o ).
thf(func_def_690,type,
sK443: $i > $o ).
thf(func_def_691,type,
sK444: $i > $o ).
thf(func_def_692,type,
sK445: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_693,type,
sK446: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_698,type,
sK451: $i > $o ).
thf(func_def_699,type,
sK452: ( $i > $o ) > $i ).
thf(func_def_706,type,
sK459: $i > $i > $o ).
thf(func_def_715,type,
sK468: $i > $o ).
thf(func_def_717,type,
sK470: $i > ( $i > $o ) > $i ).
thf(func_def_722,type,
sK475: $i > $i > $i ).
thf(func_def_725,type,
sK478: $i > $o ).
thf(func_def_730,type,
sK483: $i > $i > $i ).
thf(func_def_731,type,
sK484: $i > $i > $i ).
thf(func_def_732,type,
sK485: $i > $i > $i ).
thf(func_def_733,type,
sK486: $i > $i > $i ).
thf(func_def_734,type,
sK487: $i > $i > $i > $i ).
thf(func_def_735,type,
sK488: $i > $i ).
thf(func_def_736,type,
sK489: $i > $i ).
thf(func_def_737,type,
sK490: $i > $i ).
thf(func_def_738,type,
sK491: $i > $i ).
thf(func_def_739,type,
sK492: $i > $i > $i ).
thf(func_def_740,type,
sK493: $i > $i > $i > $i ).
thf(func_def_741,type,
sK494: $i > $i > $i > $i ).
thf(func_def_742,type,
sK495: $i > $i > $i ).
thf(func_def_743,type,
sK496: $i > $i > $i ).
thf(func_def_745,type,
sK498: $i > $i ).
thf(func_def_746,type,
sK499: $i > $i ).
thf(func_def_747,type,
sK500: $i > $i ).
thf(func_def_748,type,
sK501: $i > $i > $i ).
thf(func_def_762,type,
sK515: $i > $i > $i ).
thf(func_def_765,type,
sK518: $i > $i > $i ).
thf(func_def_766,type,
sK519: $i > $i > $i ).
thf(func_def_781,type,
sK534: $i > $o ).
thf(func_def_782,type,
sK535: $i > $i ).
thf(func_def_800,type,
sK553: $i > $o ).
thf(func_def_801,type,
sK554: ( $i > $o ) > $i > $i ).
thf(func_def_805,type,
sK558: $i > $o ).
thf(func_def_810,type,
sK563: $i > $i > $o ).
thf(func_def_821,type,
ph574:
!>[X0: $tType] : X0 ).
thf(f3177,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3173,f3159]) ).
thf(f3159,plain,
( ( in @ ( sK349 @ sK244 @ sK246 @ sK245 ) @ sK244 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f3158,f2103]) ).
thf(f2103,plain,
lamp = $true,
inference(cnf_transformation,[status(thm)],[f1233]) ).
thf(f1233,plain,
( ( setminusERneg = $true )
& ( singletonsuniq = $true )
& ( cartprodfstin = $true )
& ( powersetI = $true )
& ( nonemptyI = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( kpairiskpair = $true )
& ( subsetemptysetimpeq = $true )
& ( setadjoinSub2 = $true )
& ( bs114d = $true )
& ( binunionIR = $true )
& ( emptyinunitempty = $true )
& ( setminusER = $true )
& ( ubforcartprodlem1 = $true )
& ( setoftrueEq = $true )
& ( in__Cong = $true )
& ( lamProp = $true )
& ( descr__Cong = $true )
& ( kpairp = $true )
& ( setunionI = $true )
& ( exuI3 = $true )
& ( setukpairinjL1 = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( emptysetAx = $true )
& ( eqimpsubset2 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton2 = $true )
& ( emptysetE = $true )
& ( notdallE = $true )
& ( ksndpairEq = $true )
& ( setadjoinOr = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrERa = $true )
& ( vacuousDall = $true )
& ( upairsubunion = $true )
& ( eqinunit = $true )
& ( funcImageSingleton = $true )
& ( exuI2 = $true )
& ( setadjoinAx = $true )
& ( cartprodpairmemEL = $true )
& ( powersetI1 = $true )
& ( dpsetconstrEL1 = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinE = $true )
& ( powersetAx = $true )
& ( setminusSubset1 = $true )
& ( exuE3u = $true )
& ( symdiffI1 = $true )
& ( ex1E1 = $true )
& ( setukpairinjR = $true )
& ( binintersectSubset5 = $true )
& ( ksndsingleton = $true )
& ( exuEu = $true )
& ( setadjoinSub = $true )
& ( binunionEcases = $true )
& ( descrp = $true )
& ( subsetRefl = $true )
& ( setminusILneg = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( binunionLsub = $true )
& ( setukpairinjL = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairin = $true )
& ( infuncsetfunc = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( singletoninpowerset = $true )
& ( cartprodmempair = $true )
& ( setadjoin__Cong = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( setunionE = $true )
& ( upairsetIL = $true )
& ( upairequniteq = $true )
& ( funcinfuncset = $true )
& ( setunionsingleton = $true )
& ( singletonsubset = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairmemER = $true )
& ( binintersectSubset3 = $true )
& ( dpsetconstrER = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairIL = $true )
& ( foundationAx = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( upairsetIR = $true )
& ( nonemptyE1 = $true )
& ( setunionAx = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR11 = $true )
& ( singletonprop = $true )
& ( cartprodsndin = $true )
& ( notequalI2 = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( cartprodmempaircEq = $true )
& ( app = $true )
& ( subsetE = $true )
& ( binintersectRsub = $true )
& ( setukpairinjL2 = $true )
& ( nonemptyI1 = $true )
& ( sepInPowerset = $true )
& ( setukpairinjR1 = $true )
& ( symdiffIneg1 = $true )
& ( subsetTrans = $true )
& ( symdiffIneg2 = $true )
& ( setunionE2 = $true )
& ( setextsub = $true )
& ( kpairsurjEq = $true )
& ( setminusEL = $true )
& ( singletoninpowunion = $true )
& ( ex1I = $true )
& ( cartprodmempair1 = $true )
& ( emptyInPowerset = $true )
& ( notdexE = $true )
& ( setukpairinjR2 = $true )
& ( upairsetE = $true )
& ( powersetE = $true )
& ( ( in
@ ( lam @ sK244 @ sK245
@ ^ [Y0: $i] : ( sK246 @ Y0 ) )
@ ( funcSet @ sK244 @ sK245 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK244 )
!= $true )
| ( ( in @ ( sK246 @ X3 ) @ sK245 )
= $true ) )
& ( binintersectSubset1 = $true )
& ( prop2setI = $true )
& ( omegaIndAx = $true )
& ( omega__Cong = $true )
& ( notequalI1 = $true )
& ( exuI1 = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( symdiffI2 = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodsndpairEq = $true )
& ( wellorderingAx = $true )
& ( noeltsimpempty = $true )
& ( emptysetsubset = $true )
& ( singletonsswitch = $true )
& ( binintersectEL = $true )
& ( setminusSubset2 = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( emptyset__Cong = $true )
& ( emptyI = $true )
& ( upairinpowunion = $true )
& ( powersetsubset = $true )
& ( upairset2IR = $true )
& ( exu__Cong = $true )
& ( setminusI = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( lamp = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( setextAx = $true )
& ( exuE2 = $true )
& ( setminusELneg = $true )
& ( sepSubset = $true )
& ( uniqinunit = $true )
& ( upairset2E = $true )
& ( ex1I2 = $true )
& ( emptyinPowerset = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( dpsetconstrSub = $true )
& ( omegaSAx = $true )
& ( subsetI2 = $true )
& ( symdiffE = $true )
& ( inPowerset = $true )
& ( subset2powerset = $true )
& ( cartprodpairsurjEq = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( notsubsetI = $true )
& ( ap2p = $true )
& ( subsetE2 = $true )
& ( setukpairinjR12 = $true )
& ( binintersectI = $true )
& ( setOfPairsIsBReln = $true )
& ( dsetconstr__Cong = $true )
& ( setminusIRneg = $true )
& ( cartprodfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( kfstpairEq = $true )
& ( apProp = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan4 = $true )
& ( binunionRsub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK244,sK245,sK246])],[f754,f1232]) ).
thf(f1232,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
!= ( in
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( funcSet @ X0 @ X1 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ ( X2 @ X3 ) @ X1 ) ) ) )
=> ( ( ( in
@ ( lam @ sK244 @ sK245
@ ^ [Y0: $i] : ( sK246 @ Y0 ) )
@ ( funcSet @ sK244 @ sK245 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK244 )
!= $true )
| ( ( in @ ( sK246 @ X3 ) @ sK245 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f754,plain,
( ( setminusERneg = $true )
& ( singletonsuniq = $true )
& ( cartprodfstin = $true )
& ( powersetI = $true )
& ( nonemptyI = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( kpairiskpair = $true )
& ( subsetemptysetimpeq = $true )
& ( setadjoinSub2 = $true )
& ( bs114d = $true )
& ( binunionIR = $true )
& ( emptyinunitempty = $true )
& ( setminusER = $true )
& ( ubforcartprodlem1 = $true )
& ( setoftrueEq = $true )
& ( in__Cong = $true )
& ( lamProp = $true )
& ( descr__Cong = $true )
& ( kpairp = $true )
& ( setunionI = $true )
& ( exuI3 = $true )
& ( setukpairinjL1 = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( emptysetAx = $true )
& ( eqimpsubset2 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton2 = $true )
& ( emptysetE = $true )
& ( notdallE = $true )
& ( ksndpairEq = $true )
& ( setadjoinOr = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrERa = $true )
& ( vacuousDall = $true )
& ( upairsubunion = $true )
& ( eqinunit = $true )
& ( funcImageSingleton = $true )
& ( exuI2 = $true )
& ( setadjoinAx = $true )
& ( cartprodpairmemEL = $true )
& ( powersetI1 = $true )
& ( dpsetconstrEL1 = $true )
& ( notinsingleton = $true )
& ( emptyE1 = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinE = $true )
& ( powersetAx = $true )
& ( setminusSubset1 = $true )
& ( exuE3u = $true )
& ( symdiffI1 = $true )
& ( ex1E1 = $true )
& ( setukpairinjR = $true )
& ( binintersectSubset5 = $true )
& ( ksndsingleton = $true )
& ( exuEu = $true )
& ( setadjoinSub = $true )
& ( binunionEcases = $true )
& ( descrp = $true )
& ( subsetRefl = $true )
& ( setminusILneg = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( prop2setE = $true )
& ( dsetconstrEL = $true )
& ( binunionLsub = $true )
& ( setukpairinjL = $true )
& ( powerset__Cong = $true )
& ( binunionE = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairin = $true )
& ( infuncsetfunc = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( singletoninpowerset = $true )
& ( cartprodmempair = $true )
& ( setadjoin__Cong = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( setunionE = $true )
& ( upairsetIL = $true )
& ( upairequniteq = $true )
& ( funcinfuncset = $true )
& ( setunionsingleton = $true )
& ( singletonsubset = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairmemER = $true )
& ( binintersectSubset3 = $true )
& ( dpsetconstrER = $true )
& ( exuE3e = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairIL = $true )
& ( foundationAx = $true )
& ( subPowSU = $true )
& ( setbeta = $true )
& ( upairsetIR = $true )
& ( nonemptyE1 = $true )
& ( setunionAx = $true )
& ( omega0Ax = $true )
& ( dsetconstrER = $true )
& ( setukpairinjR11 = $true )
& ( singletonprop = $true )
& ( cartprodsndin = $true )
& ( notequalI2 = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( cartprodmempaircEq = $true )
& ( app = $true )
& ( subsetE = $true )
& ( binintersectRsub = $true )
& ( setukpairinjL2 = $true )
& ( nonemptyI1 = $true )
& ( sepInPowerset = $true )
& ( setukpairinjR1 = $true )
& ( symdiffIneg1 = $true )
& ( subsetTrans = $true )
& ( symdiffIneg2 = $true )
& ( setunionE2 = $true )
& ( setextsub = $true )
& ( kpairsurjEq = $true )
& ( setminusEL = $true )
& ( singletoninpowunion = $true )
& ( ex1I = $true )
& ( cartprodmempair1 = $true )
& ( emptyInPowerset = $true )
& ( notdexE = $true )
& ( setukpairinjR2 = $true )
& ( upairsetE = $true )
& ( powersetE = $true )
& ? [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
!= ( in
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( funcSet @ X0 @ X1 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ ( X2 @ X3 ) @ X1 ) ) ) )
& ( binintersectSubset1 = $true )
& ( prop2setI = $true )
& ( omegaIndAx = $true )
& ( omega__Cong = $true )
& ( notequalI1 = $true )
& ( exuI1 = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( symdiffI2 = $true )
& ( quantDeMorgan3 = $true )
& ( cartprodsndpairEq = $true )
& ( wellorderingAx = $true )
& ( noeltsimpempty = $true )
& ( emptysetsubset = $true )
& ( singletonsswitch = $true )
& ( binintersectEL = $true )
& ( setminusSubset2 = $true )
& ( setunionsingleton1 = $true )
& ( theprop = $true )
& ( emptyset__Cong = $true )
& ( emptyI = $true )
& ( upairinpowunion = $true )
& ( powersetsubset = $true )
& ( upairset2IR = $true )
& ( exu__Cong = $true )
& ( setminusI = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( lamp = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( setextAx = $true )
& ( exuE2 = $true )
& ( setminusELneg = $true )
& ( sepSubset = $true )
& ( uniqinunit = $true )
& ( upairset2E = $true )
& ( ex1I2 = $true )
& ( emptyinPowerset = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( dpsetconstrSub = $true )
& ( omegaSAx = $true )
& ( subsetI2 = $true )
& ( symdiffE = $true )
& ( inPowerset = $true )
& ( subset2powerset = $true )
& ( cartprodpairsurjEq = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( notsubsetI = $true )
& ( ap2p = $true )
& ( subsetE2 = $true )
& ( setukpairinjR12 = $true )
& ( binintersectI = $true )
& ( setOfPairsIsBReln = $true )
& ( dsetconstr__Cong = $true )
& ( setminusIRneg = $true )
& ( cartprodfstpairEq = $true )
& ( quantDeMorgan2 = $true )
& ( kfstpairEq = $true )
& ( apProp = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan4 = $true )
& ( binunionRsub = $true ) ),
inference(flattening,[status(thm)],[f753]) ).
thf(f753,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ( $true
!= ( in
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( funcSet @ X0 @ X1 ) ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X0 ) )
| ( $true
= ( in @ ( X2 @ X3 ) @ X1 ) ) ) )
& ( 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)],[f293]) ).
thf(f293,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 )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ( $true
= ( in @ ( X2 @ X3 ) @ X1 ) ) )
=> ( $true
= ( in
@ ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ ( funcSet @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f292]) ).
thf(f292,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
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( X2 @ X3 ) @ X1 ) )
=> ( in
@ ( lam @ X0 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) )
@ ( funcSet @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f206]) ).
thf(f206,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
=> ! [X3: $i,X4: $i,X13: $i > $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( X13 @ X1 ) @ X4 ) )
=> ( in
@ ( lam @ X3 @ X4
@ ^ [X1: $i] : ( X13 @ X1 ) )
@ ( funcSet @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f205]) ).
thf(f205,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
=> ! [X3: $i,X4: $i,X13: $i > $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( X13 @ X1 ) @ X4 ) )
=> ( in
@ ( lam @ X3 @ X4
@ ^ [X1: $i] : ( X13 @ X1 ) )
@ ( funcSet @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',lam2p) ).
thf(f3158,plain,
( ( ( in @ ( sK349 @ sK244 @ sK246 @ sK245 ) @ sK244 )
= $true )
| ( lamp != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3156]) ).
thf(f3156,plain,
( ( ( in @ ( sK349 @ sK244 @ sK246 @ sK245 ) @ sK244 )
= $true )
| ( $true != $true )
| ( lamp != $true ) ),
inference(superposition,[status(thm)],[f3038,f2835]) ).
thf(f2835,plain,
! [X2: $i,X0: $i,X1: $i > $i] :
( ( ( func @ X2 @ X0 @ ( lam @ X2 @ X0 @ X1 ) )
= $true )
| ( lamp != $true )
| ( $true
= ( in @ ( sK349 @ X2 @ X1 @ X0 ) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2403]) ).
thf(f2403,plain,
! [X2: $i,X0: $i,X1: $i > $i] :
( ( lamp != $true )
| ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( $true
= ( in @ ( sK349 @ X2 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1409]) ).
thf(f1409,plain,
( ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ( ( $true
= ( in @ ( sK349 @ X2 @ X1 @ X0 ) @ X2 ) )
& ( ( in @ ( X1 @ ( sK349 @ X2 @ X1 @ X0 ) ) @ X0 )
!= $true ) ) )
| ( lamp != $true ) )
& ( ( lamp = $true )
| ( ( $true
!= ( func @ sK352 @ sK350
@ ( lam @ sK352 @ sK350
@ ^ [Y0: $i] : ( sK351 @ Y0 ) ) ) )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK352 ) )
| ( ( in @ ( sK351 @ X7 ) @ sK350 )
= $true ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK349,sK350,sK351,sK352])],[f1406,f1408,f1407]) ).
thf(f1407,plain,
! [X0: $i,X1: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ ( X1 @ X3 ) @ X0 )
!= $true ) )
=> ( ( $true
= ( in @ ( sK349 @ X2 @ X1 @ X0 ) @ X2 ) )
& ( ( in @ ( X1 @ ( sK349 @ X2 @ X1 @ X0 ) ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1408,plain,
( ? [X4: $i,X5: $i > $i,X6: $i] :
( ( ( func @ X6 @ X4
@ ( lam @ X6 @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ ( X5 @ X7 ) @ X4 )
= $true ) ) )
=> ( ( $true
!= ( func @ sK352 @ sK350
@ ( lam @ sK352 @ sK350
@ ^ [Y0: $i] : ( sK351 @ Y0 ) ) ) )
& ! [X7: $i] :
( ( $true
!= ( in @ X7 @ sK352 ) )
| ( ( in @ ( sK351 @ X7 ) @ sK350 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1406,plain,
( ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ ( X1 @ X3 ) @ X0 )
!= $true ) ) )
| ( lamp != $true ) )
& ( ( lamp = $true )
| ? [X4: $i,X5: $i > $i,X6: $i] :
( ( ( func @ X6 @ X4
@ ( lam @ X6 @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ ( X5 @ X7 ) @ X4 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ ( X1 @ X3 ) @ X0 )
!= $true ) ) )
| ( lamp != $true ) )
& ( ( lamp = $true )
| ? [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ ( X1 @ X3 ) @ X0 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f826]) ).
thf(f826,plain,
( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ ( X1 @ X3 ) @ X0 )
!= $true ) ) )
<=> ( lamp = $true ) ),
inference(ennf_transformation,[status(thm)],[f437]) ).
thf(f437,plain,
( ( lamp = $true )
<=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ ( X1 @ X3 ) @ X0 )
= $true ) )
=> ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f436]) ).
thf(f436,plain,
( lamp
= ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( X1 @ X3 ) @ X0 ) )
=> ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f204]) ).
thf(f204,axiom,
( lamp
= ( ! [X4: $i,X13: $i > $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( X13 @ X1 ) @ X4 ) )
=> ( func @ X3 @ X4
@ ( lam @ X3 @ X4
@ ^ [X1: $i] : ( X13 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',lamp) ).
thf(f3038,plain,
( $true
!= ( func @ sK244 @ sK245 @ ( lam @ sK244 @ sK245 @ sK246 ) ) ),
inference(subsumption_resolution,[status(thm)],[f3026,f2181]) ).
thf(f2181,plain,
funcinfuncset = $true,
inference(cnf_transformation,[status(thm)],[f1233]) ).
thf(f3026,plain,
( ( funcinfuncset != $true )
| ( $true
!= ( func @ sK244 @ sK245 @ ( lam @ sK244 @ sK245 @ sK246 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3018]) ).
thf(f3018,plain,
( ( $true
!= ( func @ sK244 @ sK245 @ ( lam @ sK244 @ sK245 @ sK246 ) ) )
| ( $true != $true )
| ( funcinfuncset != $true ) ),
inference(superposition,[status(thm)],[f2849,f2022]) ).
thf(f2022,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
| ( funcinfuncset != $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1176]) ).
thf(f1176,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ( ( ( in @ sK202 @ ( funcSet @ sK201 @ sK200 ) )
!= $true )
& ( $true
= ( func @ sK201 @ sK200 @ sK202 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201,sK202])],[f1174,f1175]) ).
thf(f1175,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( funcSet @ X4 @ X3 ) ) )
& ( ( func @ X4 @ X3 @ X5 )
= $true ) )
=> ( ( ( in @ sK202 @ ( funcSet @ sK201 @ sK200 ) )
!= $true )
& ( $true
= ( func @ sK201 @ sK200 @ sK202 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1174,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( funcSet @ X4 @ X3 ) ) )
& ( ( func @ X4 @ X3 @ X5 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1173]) ).
thf(f1173,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
| ( funcinfuncset != $true ) )
& ( ( funcinfuncset = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
!= $true )
& ( ( func @ X1 @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f755]) ).
thf(f755,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
| ( ( func @ X1 @ X0 @ X2 )
!= $true ) )
<=> ( funcinfuncset = $true ) ),
inference(ennf_transformation,[status(thm)],[f510]) ).
thf(f510,plain,
( ( funcinfuncset = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
= $true )
=> ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f509]) ).
thf(f509,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
=> ( in @ X2 @ ( funcSet @ X1 @ X0 ) ) )
= funcinfuncset ),
inference(rectify,[status(thm)],[f201]) ).
thf(f201,axiom,
! [X4: $i,X3: $i,X13: $i] :
( ( ( func @ X3 @ X4 @ X13 )
=> ( in @ X13 @ ( funcSet @ X3 @ X4 ) ) )
= funcinfuncset ),
file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',funcinfuncset) ).
thf(f2849,plain,
( $true
!= ( in @ ( lam @ sK244 @ sK245 @ sK246 ) @ ( funcSet @ sK244 @ sK245 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2133]) ).
thf(f2133,plain,
( ( in
@ ( lam @ sK244 @ sK245
@ ^ [Y0: $i] : ( sK246 @ Y0 ) )
@ ( funcSet @ sK244 @ sK245 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1233]) ).
thf(f3173,plain,
( ( in @ ( sK349 @ sK244 @ sK246 @ sK245 ) @ sK244 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3164]) ).
thf(f3164,plain,
( ( $true != $true )
| ( ( in @ ( sK349 @ sK244 @ sK246 @ sK245 ) @ sK244 )
!= $true ) ),
inference(superposition,[status(thm)],[f3160,f2132]) ).
thf(f2132,plain,
! [X3: $i] :
( ( ( in @ ( sK246 @ X3 ) @ sK245 )
= $true )
| ( ( in @ X3 @ sK244 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1233]) ).
thf(f3160,plain,
( ( in @ ( sK246 @ ( sK349 @ sK244 @ sK246 @ sK245 ) ) @ sK245 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f3157,f2103]) ).
thf(f3157,plain,
( ( ( in @ ( sK246 @ ( sK349 @ sK244 @ sK246 @ sK245 ) ) @ sK245 )
!= $true )
| ( lamp != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3155]) ).
thf(f3155,plain,
( ( $true != $true )
| ( lamp != $true )
| ( ( in @ ( sK246 @ ( sK349 @ sK244 @ sK246 @ sK245 ) ) @ sK245 )
!= $true ) ),
inference(superposition,[status(thm)],[f3038,f2844]) ).
thf(f2844,plain,
! [X2: $i,X0: $i,X1: $i > $i] :
( ( ( func @ X2 @ X0 @ ( lam @ X2 @ X0 @ X1 ) )
= $true )
| ( lamp != $true )
| ( ( in @ ( X1 @ ( sK349 @ X2 @ X1 @ X0 ) ) @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2402]) ).
thf(f2402,plain,
! [X2: $i,X0: $i,X1: $i > $i] :
( ( ( in @ ( X1 @ ( sK349 @ X2 @ X1 @ X0 ) ) @ X0 )
!= $true )
| ( lamp != $true )
| ( ( func @ X2 @ X0
@ ( lam @ X2 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU680^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n023.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:31:34 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU680^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Functions - Lambda Abstraction
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.29/0.46 % in (lam A B (^ x:i.f x)) (funcSet A B))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC182g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 438 ( 204 unt; 233 typ; 204 def)
% 0.29/0.46 % Number of atoms : 1081 ( 299 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 199 ( 5 avg)
% 0.29/0.46 % Number of connectives : 1967 ( 47 ~; 7 |; 36 &;1388 @)
% 0.29/0.46 % ( 14 <=>; 475 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 206 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 236 ( 233 usr; 200 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 644 ( 77 ^; 531 !; 36 ?; 644 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=238
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 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
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 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 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 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(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 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,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 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE_type,type,
% 0.29/0.47 setunionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE,definition,
% 0.29/0.47 ( setunionE
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ! [B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( ( in @ B @ A )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU_type,type,
% 0.29/0.47 subPowSU: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU,definition,
% 0.29/0.47 ( subPowSU
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2_type,type,
% 0.29/0.47 exuE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2,definition,
% 0.29/0.47 ( exuE2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness_type,type,
% 0.29/0.47 nonemptyImpWitness: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness,definition,
% 0.29/0.47 ( nonemptyImpWitness
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( nonempty @ A )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & $true ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit_type,type,
% 0.29/0.47 uniqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit,definition,
% 0.29/0.47 ( uniqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton_type,type,
% 0.29/0.47 notinsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton,definition,
% 0.29/0.47 ( notinsingleton
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx != Xy )
% 0.29/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit_type,type,
% 0.29/0.47 eqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit,definition,
% 0.29/0.47 ( eqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch_type,type,
% 0.29/0.47 singletonsswitch: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch,definition,
% 0.29/0.47 ( singletonsswitch
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE_type,type,
% 0.29/0.47 upairsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE,definition,
% 0.29/0.47 ( upairsetE
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xx )
% 0.29/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL_type,type,
% 0.29/0.47 upairsetIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL,definition,
% 0.29/0.47 ( upairsetIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR_type,type,
% 0.29/0.47 upairsetIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR,definition,
% 0.29/0.47 ( upairsetIR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1_type,type,
% 0.29/0.47 emptyE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1,definition,
% 0.29/0.47 ( emptyE1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = emptyset )
% 0.29/0.47 => $false ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall_type,type,
% 0.29/0.47 vacuousDall: $o ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall,definition,
% 0.29/0.47 ( vacuousDall
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ emptyset )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1_type,type,
% 0.29/0.47 quantDeMorgan1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1,definition,
% 0.29/0.47 ( quantDeMorgan1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2_type,type,
% 0.29/0.47 quantDeMorgan2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2,definition,
% 0.29/0.47 ( quantDeMorgan2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3_type,type,
% 0.29/0.47 quantDeMorgan3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3,definition,
% 0.29/0.47 ( quantDeMorgan3
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4_type,type,
% 0.29/0.47 quantDeMorgan4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4,definition,
% 0.29/0.47 ( quantDeMorgan4
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI_type,type,
% 0.29/0.47 prop2setI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI,definition,
% 0.29/0.47 ( prop2setI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(set2prop_type,type,
% 0.29/0.47 set2prop: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI_type,type,
% 0.29/0.47 prop2set2propI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI,definition,
% 0.29/0.47 ( prop2set2propI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE_type,type,
% 0.29/0.47 notdexE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE,definition,
% 0.29/0.47 ( notdexE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE_type,type,
% 0.29/0.47 notdallE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE,definition,
% 0.29/0.47 ( notdallE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1_type,type,
% 0.29/0.47 exuI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1,definition,
% 0.29/0.47 ( exuI1
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3_type,type,
% 0.29/0.47 exuI3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3,definition,
% 0.29/0.47 ( exuI3
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2_type,type,
% 0.29/0.47 exuI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2,definition,
% 0.29/0.47 ( exuI2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP_type,type,
% 0.29/0.47 inCongP: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP,definition,
% 0.29/0.47 ( inCongP
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong_type,type,
% 0.29/0.47 in__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong,definition,
% 0.29/0.47 ( in__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u_type,type,
% 0.29/0.47 exuE3u: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u,definition,
% 0.29/0.47 ( exuE3u
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong_type,type,
% 0.29/0.47 exu__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong,definition,
% 0.29/0.47 ( exu__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 <=> ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong_type,type,
% 0.29/0.47 emptyset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong,definition,
% 0.29/0.47 ( emptyset__Cong
% 0.29/0.47 = ( emptyset = emptyset ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong_type,type,
% 0.29/0.47 setadjoin__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong,definition,
% 0.29/0.47 ( setadjoin__Cong
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ! [Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( Xz = Xu )
% 0.29/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong_type,type,
% 0.29/0.47 powerset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong,definition,
% 0.29/0.47 ( powerset__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( powerset @ A )
% 0.29/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong_type,type,
% 0.29/0.47 setunion__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong,definition,
% 0.29/0.47 ( setunion__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( setunion @ A )
% 0.29/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong_type,type,
% 0.29/0.47 omega__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong,definition,
% 0.29/0.47 ( omega__Cong
% 0.29/0.47 = ( omega = omega ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu_type,type,
% 0.29/0.47 exuEu: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu,definition,
% 0.29/0.47 ( exuEu
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong_type,type,
% 0.29/0.47 descr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong,definition,
% 0.29/0.47 ( descr__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.47 => ( ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong_type,type,
% 0.29/0.47 dsetconstr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong,definition,
% 0.29/0.47 ( dsetconstr__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.47 => ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset_type,type,
% 0.29/0.47 subset: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(disjoint_type,type,
% 0.29/0.47 disjoint: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setsmeet_type,type,
% 0.29/0.47 setsmeet: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1_type,type,
% 0.29/0.47 subsetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1,definition,
% 0.29/0.47 ( subsetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2_type,type,
% 0.29/0.47 eqimpsubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2,definition,
% 0.29/0.47 ( eqimpsubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1_type,type,
% 0.29/0.47 eqimpsubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1,definition,
% 0.29/0.47 ( eqimpsubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2_type,type,
% 0.29/0.47 subsetI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2,definition,
% 0.29/0.47 ( subsetI2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset_type,type,
% 0.29/0.47 emptysetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset,definition,
% 0.29/0.47 ( emptysetsubset
% 0.29/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE_type,type,
% 0.29/0.47 subsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE,definition,
% 0.29/0.47 ( subsetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2_type,type,
% 0.29/0.47 subsetE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2,definition,
% 0.29/0.47 ( subsetE2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI_type,type,
% 0.29/0.47 notsubsetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI,definition,
% 0.29/0.47 ( notsubsetI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1_type,type,
% 0.29/0.47 notequalI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1,definition,
% 0.29/0.47 ( notequalI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ~ ( subset @ A @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2_type,type,
% 0.29/0.47 notequalI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2,definition,
% 0.29/0.47 ( notequalI2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl_type,type,
% 0.29/0.47 subsetRefl: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl,definition,
% 0.29/0.47 ( subsetRefl
% 0.29/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans_type,type,
% 0.29/0.47 subsetTrans: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans,definition,
% 0.29/0.47 ( subsetTrans
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ C )
% 0.29/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub_type,type,
% 0.29/0.47 setadjoinSub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub,definition,
% 0.29/0.47 ( setadjoinSub
% 0.29/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2_type,type,
% 0.29/0.47 setadjoinSub2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2,definition,
% 0.29/0.47 ( setadjoinSub2
% 0.29/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset_type,type,
% 0.29/0.47 subset2powerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset,definition,
% 0.29/0.47 ( subset2powerset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub_type,type,
% 0.29/0.47 setextsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub,definition,
% 0.29/0.47 ( setextsub
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq_type,type,
% 0.29/0.47 subsetemptysetimpeq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq,definition,
% 0.29/0.47 ( subsetemptysetimpeq
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( subset @ A @ emptyset )
% 0.29/0.47 => ( A = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1_type,type,
% 0.29/0.47 powersetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1,definition,
% 0.29/0.47 ( powersetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ B @ A )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1_type,type,
% 0.29/0.47 powersetE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1,definition,
% 0.29/0.47 ( powersetE1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset_type,type,
% 0.29/0.47 inPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset,definition,
% 0.29/0.47 ( inPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset_type,type,
% 0.29/0.47 powersetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset,definition,
% 0.29/0.47 ( powersetsubset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset_type,type,
% 0.29/0.47 sepInPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset,definition,
% 0.29/0.47 ( sepInPowerset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( in
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset_type,type,
% 0.29/0.47 sepSubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset,definition,
% 0.29/0.47 ( sepSubset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( subset
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunion_type,type,
% 0.29/0.47 binunion: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL_type,type,
% 0.29/0.47 binunionIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL,definition,
% 0.29/0.47 ( binunionIL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR_type,type,
% 0.29/0.47 upairset2IR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR,definition,
% 0.29/0.47 ( upairset2IR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR_type,type,
% 0.29/0.47 binunionIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR,definition,
% 0.29/0.47 ( binunionIR
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionEcases_type,type,
% 0.29/0.47 binunionEcases: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionEcases,definition,
% 0.29/0.47 ( binunionEcases
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.47 => ( ( ( in @ Xx @ A )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ Xx @ B )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionE_type,type,
% 0.29/0.47 binunionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionE,definition,
% 0.29/0.47 ( binunionE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionLsub_type,type,
% 0.29/0.47 binunionLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionLsub,definition,
% 0.29/0.47 ( binunionLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionRsub_type,type,
% 0.29/0.47 binunionRsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionRsub,definition,
% 0.29/0.47 ( binunionRsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersect_type,type,
% 0.29/0.47 binintersect: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectI_type,type,
% 0.29/0.47 binintersectI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectI,definition,
% 0.29/0.47 ( binintersectI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset5_type,type,
% 0.29/0.47 binintersectSubset5: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset5,definition,
% 0.29/0.47 ( binintersectSubset5
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( subset @ C @ A )
% 0.29/0.47 => ( ( subset @ C @ B )
% 0.29/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectEL_type,type,
% 0.29/0.47 binintersectEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectEL,definition,
% 0.29/0.47 ( binintersectEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectLsub_type,type,
% 0.29/0.47 binintersectLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectLsub,definition,
% 0.29/0.47 ( binintersectLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset2_type,type,
% 0.29/0.47 binintersectSubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset2,definition,
% 0.29/0.47 ( binintersectSubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset3_type,type,
% 0.29/0.47 binintersectSubset3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset3,definition,
% 0.29/0.47 ( binintersectSubset3
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( binintersect @ A @ B )
% 0.29/0.47 = B )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectER_type,type,
% 0.29/0.47 binintersectER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectER,definition,
% 0.29/0.47 ( binintersectER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(disjointsetsI1_type,type,
% 0.29/0.47 disjointsetsI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(disjointsetsI1,definition,
% 0.29/0.47 ( disjointsetsI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( in @ Xx @ B ) )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectRsub_type,type,
% 0.29/0.47 binintersectRsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectRsub,definition,
% 0.29/0.47 ( binintersectRsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset4_type,type,
% 0.29/0.47 binintersectSubset4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset4,definition,
% 0.29/0.47 ( binintersectSubset4
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ B @ A )
% 0.29/0.47 => ( ( binintersect @ A @ B )
% 0.29/0.47 = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset1_type,type,
% 0.29/0.47 binintersectSubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintersectSubset1,definition,
% 0.29/0.47 ( binintersectSubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( binintersect @ A @ B )
% 0.29/0.47 = A )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(bs114d_type,type,
% 0.29/0.47 bs114d: $o ).
% 0.29/0.47
% 0.29/0.47 thf(bs114d,definition,
% 0.29/0.47 ( bs114d
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(regular_type,type,
% 0.29/0.47 regular: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminus_type,type,
% 0.29/0.47 setminus: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setminusI_type,type,
% 0.29/0.47 setminusI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusI,definition,
% 0.29/0.47 ( setminusI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusEL_type,type,
% 0.29/0.47 setminusEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusEL,definition,
% 0.29/0.47 ( setminusEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusER_type,type,
% 0.29/0.47 setminusER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusER,definition,
% 0.29/0.47 ( setminusER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset2_type,type,
% 0.29/0.47 setminusSubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset2,definition,
% 0.29/0.47 ( setminusSubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( setminus @ A @ B )
% 0.29/0.47 = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusERneg_type,type,
% 0.29/0.47 setminusERneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusERneg,definition,
% 0.29/0.47 ( setminusERneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusELneg_type,type,
% 0.29/0.47 setminusELneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusELneg,definition,
% 0.29/0.47 ( setminusELneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusILneg_type,type,
% 0.29/0.47 setminusILneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusILneg,definition,
% 0.29/0.47 ( setminusILneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusIRneg_type,type,
% 0.29/0.47 setminusIRneg: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusIRneg,definition,
% 0.29/0.47 ( setminusIRneg
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusLsub_type,type,
% 0.29/0.47 setminusLsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusLsub,definition,
% 0.29/0.47 ( setminusLsub
% 0.29/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset1_type,type,
% 0.29/0.47 setminusSubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setminusSubset1,definition,
% 0.29/0.47 ( setminusSubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( ( setminus @ A @ B )
% 0.29/0.47 = emptyset )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiff_type,type,
% 0.29/0.47 symdiff: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffE_type,type,
% 0.29/0.47 symdiffE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffE,definition,
% 0.29/0.47 ( symdiffE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI1_type,type,
% 0.29/0.47 symdiffI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI1,definition,
% 0.29/0.47 ( symdiffI1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI2_type,type,
% 0.29/0.47 symdiffI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffI2,definition,
% 0.29/0.47 ( symdiffI2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg1_type,type,
% 0.29/0.47 symdiffIneg1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg1,definition,
% 0.29/0.47 ( symdiffIneg1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg2_type,type,
% 0.29/0.47 symdiffIneg2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(symdiffIneg2,definition,
% 0.29/0.47 ( symdiffIneg2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(iskpair_type,type,
% 0.29/0.47 iskpair: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(secondinupair_type,type,
% 0.29/0.47 secondinupair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(secondinupair,definition,
% 0.29/0.47 ( secondinupair
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIL_type,type,
% 0.29/0.47 setukpairIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIL,definition,
% 0.29/0.47 ( setukpairIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIR_type,type,
% 0.29/0.47 setukpairIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairIR,definition,
% 0.29/0.47 ( setukpairIR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpairiskpair_type,type,
% 0.29/0.47 kpairiskpair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairiskpair,definition,
% 0.29/0.47 ( kpairiskpair
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpair_type,type,
% 0.29/0.47 kpair: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(kpairp_type,type,
% 0.29/0.47 kpairp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairp,definition,
% 0.29/0.47 ( kpairp
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprod_type,type,
% 0.29/0.47 cartprod: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsubset_type,type,
% 0.29/0.47 singletonsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsubset,definition,
% 0.29/0.47 ( singletonsubset
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowerset_type,type,
% 0.29/0.47 singletoninpowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowerset,definition,
% 0.29/0.47 ( singletoninpowerset
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowunion_type,type,
% 0.29/0.47 singletoninpowunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletoninpowunion,definition,
% 0.29/0.47 ( singletoninpowunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2E_type,type,
% 0.29/0.47 upairset2E: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2E,definition,
% 0.29/0.47 ( upairset2E
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xx )
% 0.29/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsubunion_type,type,
% 0.29/0.47 upairsubunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsubunion,definition,
% 0.29/0.47 ( upairsubunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairinpowunion_type,type,
% 0.29/0.47 upairinpowunion: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairinpowunion,definition,
% 0.29/0.47 ( upairinpowunion
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem1_type,type,
% 0.29/0.47 ubforcartprodlem1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem1,definition,
% 0.29/0.47 ( ubforcartprodlem1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem2_type,type,
% 0.29/0.47 ubforcartprodlem2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem2,definition,
% 0.29/0.47 ( ubforcartprodlem2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem3_type,type,
% 0.29/0.47 ubforcartprodlem3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ubforcartprodlem3,definition,
% 0.29/0.47 ( ubforcartprodlem3
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairin_type,type,
% 0.29/0.47 cartprodpairin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairin,definition,
% 0.29/0.47 ( cartprodpairin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair1_type,type,
% 0.29/0.47 cartprodmempair1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair1,definition,
% 0.29/0.47 ( cartprodmempair1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 & ( Xu
% 0.29/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair_type,type,
% 0.29/0.47 cartprodmempair: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempair,definition,
% 0.29/0.47 ( cartprodmempair
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE2_type,type,
% 0.29/0.47 setunionE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE2,definition,
% 0.29/0.47 ( setunionE2
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 => ? [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton1_type,type,
% 0.29/0.47 setunionsingleton1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton1,definition,
% 0.29/0.47 ( setunionsingleton1
% 0.29/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton2_type,type,
% 0.29/0.47 setunionsingleton2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton2,definition,
% 0.29/0.47 ( setunionsingleton2
% 0.29/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton_type,type,
% 0.29/0.47 setunionsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionsingleton,definition,
% 0.29/0.47 ( setunionsingleton
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.47 = Xx ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singleton_type,type,
% 0.29/0.47 singleton: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(singleton,definition,
% 0.29/0.47 ( singleton
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( A
% 0.29/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonprop_type,type,
% 0.29/0.47 singletonprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonprop,definition,
% 0.29/0.47 ( singletonprop
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) )
% 0.29/0.47 => ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1_type,type,
% 0.29/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1,definition,
% 0.29/0.47 ( ex1
% 0.29/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( singleton
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E1_type,type,
% 0.29/0.47 ex1E1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E1,definition,
% 0.29/0.47 ( ex1E1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ( ex1 @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I_type,type,
% 0.29/0.47 ex1I: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I,definition,
% 0.29/0.47 ( ex1I
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xy = Xx ) ) )
% 0.29/0.47 => ( ex1 @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I2_type,type,
% 0.29/0.47 ex1I2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1I2,definition,
% 0.29/0.47 ( ex1I2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) )
% 0.29/0.47 => ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( ex1 @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsuniq_type,type,
% 0.29/0.47 singletonsuniq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsuniq,definition,
% 0.29/0.47 ( singletonsuniq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(atmost1p_type,type,
% 0.29/0.47 atmost1p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(atleast2p_type,type,
% 0.29/0.47 atleast2p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(atmost2p_type,type,
% 0.29/0.47 atmost2p: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetp_type,type,
% 0.29/0.47 upairsetp: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL1_type,type,
% 0.29/0.47 setukpairinjL1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL1,definition,
% 0.29/0.47 ( setukpairinjL1
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kfstsingleton_type,type,
% 0.29/0.47 kfstsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kfstsingleton,definition,
% 0.29/0.47 ( kfstsingleton
% 0.29/0.47 = ( ! [Xu: $i] :
% 0.29/0.47 ( ( iskpair @ Xu )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(theprop_type,type,
% 0.29/0.47 theprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(theprop,definition,
% 0.29/0.47 ( theprop
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( singleton @ X )
% 0.29/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kfst_type,type,
% 0.29/0.47 kfst: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(kfstpairEq_type,type,
% 0.29/0.47 kfstpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kfstpairEq,definition,
% 0.29/0.47 ( kfstpairEq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xx ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstin_type,type,
% 0.29/0.47 cartprodfstin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstin,definition,
% 0.29/0.47 ( cartprodfstin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL2_type,type,
% 0.29/0.47 setukpairinjL2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL2,definition,
% 0.29/0.47 ( setukpairinjL2
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL_type,type,
% 0.29/0.47 setukpairinjL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL,definition,
% 0.29/0.47 ( setukpairinjL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xz @ Xu ) )
% 0.29/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR11_type,type,
% 0.29/0.47 setukpairinjR11: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR11,definition,
% 0.29/0.47 ( setukpairinjR11
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR12_type,type,
% 0.29/0.47 setukpairinjR12: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR12,definition,
% 0.29/0.47 ( setukpairinjR12
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR1_type,type,
% 0.29/0.47 setukpairinjR1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR1,definition,
% 0.29/0.47 ( setukpairinjR1
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xu )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairequniteq_type,type,
% 0.29/0.47 upairequniteq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairequniteq,definition,
% 0.29/0.47 ( upairequniteq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR2_type,type,
% 0.29/0.47 setukpairinjR2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR2,definition,
% 0.29/0.47 ( setukpairinjR2
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR_type,type,
% 0.29/0.47 setukpairinjR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR,definition,
% 0.29/0.47 ( setukpairinjR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xz @ Xu ) )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ksndsingleton_type,type,
% 0.29/0.47 ksndsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ksndsingleton,definition,
% 0.29/0.47 ( ksndsingleton
% 0.29/0.47 = ( ! [Xu: $i] :
% 0.29/0.47 ( ( iskpair @ Xu )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.47 @ ^ [Xx: $i] :
% 0.29/0.47 ( Xu
% 0.29/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ksnd_type,type,
% 0.29/0.47 ksnd: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(ksndpairEq_type,type,
% 0.29/0.47 ksndpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ksndpairEq,definition,
% 0.29/0.47 ( ksndpairEq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xy ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpairsurjEq_type,type,
% 0.29/0.47 kpairsurjEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairsurjEq,definition,
% 0.29/0.47 ( kpairsurjEq
% 0.29/0.47 = ( ! [Xu: $i] :
% 0.29/0.47 ( ( iskpair @ Xu )
% 0.29/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.47 = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndin_type,type,
% 0.29/0.47 cartprodsndin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndin,definition,
% 0.29/0.47 ( cartprodsndin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemEL_type,type,
% 0.29/0.47 cartprodpairmemEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemEL,definition,
% 0.29/0.47 ( cartprodpairmemEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemER_type,type,
% 0.29/0.47 cartprodpairmemER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemER,definition,
% 0.29/0.47 ( cartprodpairmemER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempaircEq_type,type,
% 0.29/0.47 cartprodmempaircEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempaircEq,definition,
% 0.29/0.47 ( cartprodmempaircEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstpairEq_type,type,
% 0.29/0.47 cartprodfstpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstpairEq,definition,
% 0.29/0.47 ( cartprodfstpairEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndpairEq_type,type,
% 0.29/0.47 cartprodsndpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndpairEq,definition,
% 0.29/0.47 ( cartprodsndpairEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairsurjEq_type,type,
% 0.29/0.47 cartprodpairsurjEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairsurjEq,definition,
% 0.29/0.47 ( cartprodpairsurjEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.47 = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln_type,type,
% 0.29/0.47 breln: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln,definition,
% 0.29/0.47 ( breln
% 0.29/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstr_type,type,
% 0.29/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrI_type,type,
% 0.29/0.47 dpsetconstrI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrI,definition,
% 0.29/0.47 ( dpsetconstrI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrSub_type,type,
% 0.29/0.47 dpsetconstrSub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrSub,definition,
% 0.29/0.47 ( dpsetconstrSub
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( subset
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln_type,type,
% 0.29/0.47 setOfPairsIsBReln: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln,definition,
% 0.29/0.47 ( setOfPairsIsBReln
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( breln @ A @ B
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrERa_type,type,
% 0.29/0.47 dpsetconstrERa: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrERa,definition,
% 0.29/0.47 ( dpsetconstrERa
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL1_type,type,
% 0.29/0.47 dpsetconstrEL1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL1,definition,
% 0.29/0.47 ( dpsetconstrEL1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL2_type,type,
% 0.29/0.47 dpsetconstrEL2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL2,definition,
% 0.29/0.47 ( dpsetconstrEL2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrER_type,type,
% 0.29/0.47 dpsetconstrER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrER,definition,
% 0.29/0.47 ( dpsetconstrER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(func_type,type,
% 0.29/0.47 func: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(func,definition,
% 0.29/0.47 ( func
% 0.29/0.47 = ( ^ [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ex1 @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcSet_type,type,
% 0.29/0.47 funcSet: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(funcImageSingleton_type,type,
% 0.29/0.47 funcImageSingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcImageSingleton,definition,
% 0.29/0.47 ( funcImageSingleton
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(apProp_type,type,
% 0.29/0.47 apProp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(apProp,definition,
% 0.29/0.47 ( apProp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in
% 0.29/0.47 @ ( setunion
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.47 @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ap_type,type,
% 0.29/0.47 ap: $i > $i > $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(ap,definition,
% 0.29/0.47 ( ap
% 0.29/0.47 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 0.29/0.47 ( setunion
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(app_type,type,
% 0.29/0.47 app: $o ).
% 0.29/0.47
% 0.29/0.47 thf(app,definition,
% 0.29/0.47 ( app
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(infuncsetfunc_type,type,
% 0.29/0.47 infuncsetfunc: $o ).
% 0.29/0.47
% 0.29/0.47 thf(infuncsetfunc,definition,
% 0.29/0.47 ( infuncsetfunc
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ap2p_type,type,
% 0.29/0.47 ap2p: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ap2p,definition,
% 0.29/0.47 ( ap2p
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcinfuncset_type,type,
% 0.29/0.47 funcinfuncset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcinfuncset,definition,
% 0.29/0.47 ( funcinfuncset
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lamProp_type,type,
% 0.29/0.47 lamProp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(lamProp,definition,
% 0.29/0.47 ( lamProp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( func @ A @ B
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lam_type,type,
% 0.29/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(lam,definition,
% 0.29/0.47 ( lam
% 0.29/0.47 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lamp_type,type,
% 0.29/0.47 lamp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(lamp,definition,
% 0.29/0.47 ( lamp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( func @ A @ B
% 0.29/0.47 @ ( lam @ A @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lam2p,conjecture,
% 0.29/0.47 ( setextAx
% 0.29/0.47 => ( emptysetAx
% 0.29/0.47 => ( setadjoinAx
% 0.29/0.47 => ( powersetAx
% 0.29/0.47 => ( setunionAx
% 0.29/0.47 => ( omega0Ax
% 0.29/0.47 => ( omegaSAx
% 0.29/0.47 => ( omegaIndAx
% 0.29/0.47 => ( replAx
% 0.29/0.47 => ( foundationAx
% 0.29/0.47 => ( wellorderingAx
% 0.29/0.47 => ( descrp
% 0.29/0.47 => ( dsetconstrI
% 0.29/0.47 => ( dsetconstrEL
% 0.29/0.47 => ( dsetconstrER
% 0.29/0.47 => ( exuE1
% 0.29/0.47 => ( prop2setE
% 0.29/0.47 => ( emptysetE
% 0.29/0.47 => ( emptysetimpfalse
% 0.29/0.47 => ( notinemptyset
% 0.29/0.47 => ( exuE3e
% 0.29/0.47 => ( setext
% 0.29/0.47 => ( emptyI
% 0.29/0.47 => ( noeltsimpempty
% 0.29/0.47 => ( setbeta
% 0.29/0.47 => ( nonemptyE1
% 0.29/0.47 => ( nonemptyI
% 0.29/0.47 => ( nonemptyI1
% 0.29/0.47 => ( setadjoinIL
% 0.29/0.47 => ( emptyinunitempty
% 0.29/0.47 => ( setadjoinIR
% 0.29/0.47 => ( setadjoinE
% 0.29/0.47 => ( setadjoinOr
% 0.29/0.47 => ( setoftrueEq
% 0.29/0.47 => ( powersetI
% 0.29/0.47 => ( emptyinPowerset
% 0.29/0.47 => ( emptyInPowerset
% 0.29/0.47 => ( powersetE
% 0.29/0.47 => ( setunionI
% 0.29/0.47 => ( setunionE
% 0.29/0.47 => ( subPowSU
% 0.29/0.47 => ( exuE2
% 0.29/0.47 => ( nonemptyImpWitness
% 0.29/0.47 => ( uniqinunit
% 0.29/0.47 => ( notinsingleton
% 0.29/0.47 => ( eqinunit
% 0.29/0.47 => ( singletonsswitch
% 0.29/0.47 => ( upairsetE
% 0.29/0.47 => ( upairsetIL
% 0.29/0.47 => ( upairsetIR
% 0.29/0.47 => ( emptyE1
% 0.29/0.47 => ( vacuousDall
% 0.29/0.47 => ( quantDeMorgan1
% 0.29/0.47 => ( quantDeMorgan2
% 0.29/0.47 => ( quantDeMorgan3
% 0.29/0.47 => ( quantDeMorgan4
% 0.29/0.47 => ( prop2setI
% 0.29/0.47 => ( prop2set2propI
% 0.29/0.47 => ( notdexE
% 0.29/0.47 => ( notdallE
% 0.29/0.47 => ( exuI1
% 0.29/0.47 => ( exuI3
% 0.29/0.47 => ( exuI2
% 0.29/0.47 => ( inCongP
% 0.29/0.47 => ( in__Cong
% 0.29/0.47 => ( exuE3u
% 0.29/0.47 => ( exu__Cong
% 0.29/0.47 => ( emptyset__Cong
% 0.29/0.47 => ( setadjoin__Cong
% 0.29/0.47 => ( powerset__Cong
% 0.29/0.47 => ( setunion__Cong
% 0.29/0.47 => ( omega__Cong
% 0.29/0.47 => ( exuEu
% 0.29/0.47 => ( descr__Cong
% 0.29/0.47 => ( dsetconstr__Cong
% 0.29/0.47 => ( subsetI1
% 0.29/0.47 => ( eqimpsubset2
% 0.29/0.47 => ( eqimpsubset1
% 0.29/0.47 => ( subsetI2
% 0.29/0.47 => ( emptysetsubset
% 0.29/0.47 => ( subsetE
% 0.29/0.47 => ( subsetE2
% 0.29/0.47 => ( notsubsetI
% 0.29/0.47 => ( notequalI1
% 0.29/0.47 => ( notequalI2
% 0.29/0.47 => ( subsetRefl
% 0.29/0.47 => ( subsetTrans
% 0.29/0.47 => ( setadjoinSub
% 0.29/0.47 => ( setadjoinSub2
% 0.29/0.47 => ( subset2powerset
% 0.29/0.47 => ( setextsub
% 0.29/0.47 => ( subsetemptysetimpeq
% 0.29/0.47 => ( powersetI1
% 0.29/0.47 => ( powersetE1
% 0.29/0.47 => ( inPowerset
% 0.29/0.47 => ( powersetsubset
% 0.29/0.47 => ( sepInPowerset
% 0.29/0.47 => ( sepSubset
% 0.29/0.47 => ( binunionIL
% 0.29/0.47 => ( upairset2IR
% 0.29/0.47 => ( binunionIR
% 0.29/0.47 => ( binunionEcases
% 0.29/0.47 => ( binunionE
% 0.29/0.47 => ( binunionLsub
% 0.29/0.47 => ( binunionRsub
% 0.29/0.47 => ( binintersectI
% 0.29/0.47 => ( binintersectSubset5
% 0.29/0.47 => ( binintersectEL
% 0.29/0.47 => ( binintersectLsub
% 0.29/0.47 => ( binintersectSubset2
% 0.29/0.47 => ( binintersectSubset3
% 0.29/0.47 => ( binintersectER
% 0.29/0.47 => ( disjointsetsI1
% 0.29/0.47 => ( binintersectRsub
% 0.29/0.47 => ( binintersectSubset4
% 0.29/0.47 => ( binintersectSubset1
% 0.29/0.47 => ( bs114d
% 0.29/0.47 => ( setminusI
% 0.29/0.47 => ( setminusEL
% 0.29/0.47 => ( setminusER
% 0.29/0.47 => ( setminusSubset2
% 0.29/0.47 => ( setminusERneg
% 0.29/0.47 => ( setminusELneg
% 0.29/0.47 => ( setminusILneg
% 0.29/0.47 => ( setminusIRneg
% 0.29/0.47 => ( setminusLsub
% 0.29/0.47 => ( setminusSubset1
% 0.29/0.47 => ( symdiffE
% 0.29/0.47 => ( symdiffI1
% 0.29/0.47 => ( symdiffI2
% 0.29/0.47 => ( symdiffIneg1
% 0.29/0.47 => ( symdiffIneg2
% 0.29/0.47 => ( secondinupair
% 0.29/0.47 => ( setukpairIL
% 0.29/0.47 => ( setukpairIR
% 0.29/0.47 => ( kpairiskpair
% 0.29/0.47 => ( kpairp
% 0.29/0.47 => ( singletonsubset
% 0.29/0.47 => ( singletoninpowerset
% 0.29/0.47 => ( singletoninpowunion
% 0.29/0.47 => ( upairset2E
% 0.29/0.47 => ( upairsubunion
% 0.29/0.47 => ( upairinpowunion
% 0.29/0.47 => ( ubforcartprodlem1
% 0.29/0.47 => ( ubforcartprodlem2
% 0.29/0.47 => ( ubforcartprodlem3
% 0.29/0.47 => ( cartprodpairin
% 0.29/0.47 => ( cartprodmempair1
% 0.29/0.47 => ( cartprodmempair
% 0.29/0.47 => ( setunionE2
% 0.29/0.47 => ( setunionsingleton1
% 0.29/0.47 => ( setunionsingleton2
% 0.29/0.47 => ( setunionsingleton
% 0.29/0.47 => ( singletonprop
% 0.29/0.47 => ( ex1E1
% 0.29/0.47 => ( ex1I
% 0.29/0.47 => ( ex1I2
% 0.29/0.47 => ( singletonsuniq
% 0.29/0.47 => ( setukpairinjL1
% 0.29/0.47 => ( kfstsingleton
% 0.29/0.47 => ( theprop
% 0.29/0.47 => ( kfstpairEq
% 0.29/0.47 => ( cartprodfstin
% 0.29/0.47 => ( setukpairinjL2
% 0.29/0.47 => ( setukpairinjL
% 0.29/0.47 => ( setukpairinjR11
% 0.29/0.47 => ( setukpairinjR12
% 0.29/0.47 => ( setukpairinjR1
% 0.29/0.47 => ( upairequniteq
% 0.29/0.47 => ( setukpairinjR2
% 0.29/0.47 => ( setukpairinjR
% 0.29/0.47 => ( ksndsingleton
% 0.29/0.47 => ( ksndpairEq
% 0.29/0.47 => ( kpairsurjEq
% 0.29/0.47 => ( cartprodsndin
% 0.29/0.47 => ( cartprodpairmemEL
% 0.29/0.47 => ( cartprodpairmemER
% 0.29/0.47 => ( cartprodmempaircEq
% 0.29/0.47 => ( cartprodfstpairEq
% 0.29/0.47 => ( cartprodsndpairEq
% 0.29/0.47 => ( cartprodpairsurjEq
% 0.29/0.47 => ( dpsetconstrI
% 0.29/0.47 => ( dpsetconstrSub
% 0.29/0.47 => ( setOfPairsIsBReln
% 0.29/0.47 => ( dpsetconstrERa
% 0.29/0.47 => ( dpsetconstrEL1
% 0.29/0.47 => ( dpsetconstrEL2
% 0.29/0.47 => ( dpsetconstrER
% 0.29/0.47 => ( funcImageSingleton
% 0.29/0.47 => ( apProp
% 0.29/0.47 => ( app
% 0.29/0.47 => ( infuncsetfunc
% 0.29/0.47 => ( ap2p
% 0.29/0.47 => ( funcinfuncset
% 0.29/0.47 => ( lamProp
% 0.29/0.47 => ( lamp
% 0.29/0.47 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( in
% 0.29/0.47 @ ( lam @ A @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.41/1.48 ---- Embedded in THF ---
% 2.41/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.41/1.48 %%% Generated on Tue Feb 24 12:31:35 EST 2026
% 2.41/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.41/1.48 %%% Logic specification used:
% 2.41/1.48 %%% thf(spec, logic, $$dhol).
% 2.41/1.48
% 2.41/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2DTF3655.p
% See solution above
% 2.41/1.48 ------------------------
% 2.67/1.52 ---- Cleaned THF ---
% 2.67/1.53 thf(in_type,type,
% 2.67/1.53 in: $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(exu_type,type,
% 2.67/1.53 exu: ( $i > $o ) > $o ).
% 2.67/1.53
% 2.67/1.53 thf(exu,definition,
% 2.67/1.53 ( exu
% 2.67/1.53 = ( ^ [Xphi: $i > $o] :
% 2.67/1.53 ? [Xx: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 & ! [Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setextAx_type,type,
% 2.67/1.53 setextAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setextAx,definition,
% 2.67/1.53 ( setextAx
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 <=> ( in @ Xx @ B ) )
% 2.67/1.53 => ( A = B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyset_type,type,
% 2.67/1.53 emptyset: $i ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetAx_type,type,
% 2.67/1.53 emptysetAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetAx,definition,
% 2.67/1.53 ( emptysetAx
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoin_type,type,
% 2.67/1.53 setadjoin: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinAx_type,type,
% 2.67/1.53 setadjoinAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinAx,definition,
% 2.67/1.53 ( setadjoinAx
% 2.67/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.67/1.53 <=> ( ( Xy = Xx )
% 2.67/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powerset_type,type,
% 2.67/1.53 powerset: $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(powersetAx_type,type,
% 2.67/1.53 powersetAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetAx,definition,
% 2.67/1.53 ( powersetAx
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.67/1.53 <=> ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunion_type,type,
% 2.67/1.53 setunion: $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(setunionAx_type,type,
% 2.67/1.53 setunionAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionAx,definition,
% 2.67/1.53 ( setunionAx
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.67/1.53 <=> ? [B: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(omega_type,type,
% 2.67/1.53 omega: $i ).
% 2.67/1.53
% 2.67/1.53 thf(omega0Ax_type,type,
% 2.67/1.53 omega0Ax: $o ).
% 2.67/1.53
% 2.67/1.53 thf(omega0Ax,definition,
% 2.67/1.53 ( omega0Ax
% 2.67/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(omegaSAx_type,type,
% 2.67/1.53 omegaSAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(omegaSAx,definition,
% 2.67/1.53 ( omegaSAx
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ omega )
% 2.67/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(omegaIndAx_type,type,
% 2.67/1.53 omegaIndAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(omegaIndAx,definition,
% 2.67/1.53 ( omegaIndAx
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ( ( in @ emptyset @ A )
% 2.67/1.53 & ! [Xx: $i] :
% 2.67/1.53 ( ( ( in @ Xx @ omega )
% 2.67/1.53 & ( in @ Xx @ A ) )
% 2.67/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ omega )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(replAx_type,type,
% 2.67/1.53 replAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(replAx,definition,
% 2.67/1.53 ( replAx
% 2.67/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( exu
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.67/1.53 => ? [B: $i] :
% 2.67/1.53 ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 <=> ? [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ A )
% 2.67/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(foundationAx_type,type,
% 2.67/1.53 foundationAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(foundationAx,definition,
% 2.67/1.53 ( foundationAx
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.67/1.53 => ? [B: $i] :
% 2.67/1.53 ( ( in @ B @ A )
% 2.67/1.53 & ~ ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(wellorderingAx_type,type,
% 2.67/1.53 wellorderingAx: $o ).
% 2.67/1.53
% 2.67/1.53 thf(wellorderingAx,definition,
% 2.67/1.53 ( wellorderingAx
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ? [B: $i] :
% 2.67/1.53 ( ! [C: $i] :
% 2.67/1.53 ( ( in @ C @ B )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ C )
% 2.67/1.53 => ( in @ Xx @ A ) ) )
% 2.67/1.53 & ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( ( in @ Xx @ A )
% 2.67/1.53 & ( in @ Xy @ A ) )
% 2.67/1.53 => ( ! [C: $i] :
% 2.67/1.53 ( ( in @ C @ B )
% 2.67/1.53 => ( ( in @ Xx @ C )
% 2.67/1.53 <=> ( in @ Xy @ C ) ) )
% 2.67/1.53 => ( Xx = Xy ) ) )
% 2.67/1.53 & ! [C: $i,D: $i] :
% 2.67/1.53 ( ( ( in @ C @ B )
% 2.67/1.53 & ( in @ D @ B ) )
% 2.67/1.53 => ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ C )
% 2.67/1.53 => ( in @ Xx @ D ) )
% 2.67/1.53 | ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ D )
% 2.67/1.53 => ( in @ Xx @ C ) ) ) )
% 2.67/1.53 & ! [C: $i] :
% 2.67/1.53 ( ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ C )
% 2.67/1.53 => ( in @ Xx @ A ) )
% 2.67/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.67/1.53 => ? [D: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ D @ B )
% 2.67/1.53 & ( in @ Xx @ C )
% 2.67/1.53 & ~ ? [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ D )
% 2.67/1.53 & ( in @ Xy @ C ) )
% 2.67/1.53 & ! [E: $i] :
% 2.67/1.53 ( ( in @ E @ B )
% 2.67/1.53 => ( ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ E )
% 2.67/1.53 => ( in @ Xy @ D ) )
% 2.67/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(descr_type,type,
% 2.67/1.53 descr: ( $i > $o ) > $i ).
% 2.67/1.53
% 2.67/1.53 thf(descrp_type,type,
% 2.67/1.53 descrp: $o ).
% 2.67/1.53
% 2.67/1.53 thf(descrp,definition,
% 2.67/1.53 ( descrp
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ( Xphi
% 2.67/1.53 @ ( descr
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstr_type,type,
% 2.67/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrI_type,type,
% 2.67/1.53 dsetconstrI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrI,definition,
% 2.67/1.53 ( dsetconstrI
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 => ( in @ Xx
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrEL_type,type,
% 2.67/1.53 dsetconstrEL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrEL,definition,
% 2.67/1.53 ( dsetconstrEL
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrER_type,type,
% 2.67/1.53 dsetconstrER: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstrER,definition,
% 2.67/1.53 ( dsetconstrER
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.67/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuE1_type,type,
% 2.67/1.53 exuE1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuE1,definition,
% 2.67/1.53 ( exuE1
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 & ! [Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(prop2set_type,type,
% 2.67/1.53 prop2set: $o > $i ).
% 2.67/1.53
% 2.67/1.53 thf(prop2setE_type,type,
% 2.67/1.53 prop2setE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(prop2setE,definition,
% 2.67/1.53 ( prop2setE
% 2.67/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.67/1.53 => Xphi ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetE_type,type,
% 2.67/1.53 emptysetE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetE,definition,
% 2.67/1.53 ( emptysetE
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ emptyset )
% 2.67/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetimpfalse_type,type,
% 2.67/1.53 emptysetimpfalse: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetimpfalse,definition,
% 2.67/1.53 ( emptysetimpfalse
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ emptyset )
% 2.67/1.53 => $false ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notinemptyset_type,type,
% 2.67/1.53 notinemptyset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notinemptyset,definition,
% 2.67/1.53 ( notinemptyset
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuE3e_type,type,
% 2.67/1.53 exuE3e: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuE3e,definition,
% 2.67/1.53 ( exuE3e
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setext_type,type,
% 2.67/1.53 setext: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setext,definition,
% 2.67/1.53 ( setext
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ B ) )
% 2.67/1.53 => ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ A ) )
% 2.67/1.53 => ( A = B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyI_type,type,
% 2.67/1.53 emptyI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyI,definition,
% 2.67/1.53 ( emptyI
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ~ ( in @ Xx @ A )
% 2.67/1.53 => ( A = emptyset ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(noeltsimpempty_type,type,
% 2.67/1.53 noeltsimpempty: $o ).
% 2.67/1.53
% 2.67/1.53 thf(noeltsimpempty,definition,
% 2.67/1.53 ( noeltsimpempty
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ~ ( in @ Xx @ A )
% 2.67/1.53 => ( A = emptyset ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setbeta_type,type,
% 2.67/1.53 setbeta: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setbeta,definition,
% 2.67/1.53 ( setbeta
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( in @ Xx
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.67/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(nonempty_type,type,
% 2.67/1.53 nonempty: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(nonempty,definition,
% 2.67/1.53 ( nonempty
% 2.67/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyE1_type,type,
% 2.67/1.53 nonemptyE1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyE1,definition,
% 2.67/1.53 ( nonemptyE1
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ( nonempty @ A )
% 2.67/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyI_type,type,
% 2.67/1.53 nonemptyI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyI,definition,
% 2.67/1.53 ( nonemptyI
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 => ( nonempty
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyI1_type,type,
% 2.67/1.53 nonemptyI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyI1,definition,
% 2.67/1.53 ( nonemptyI1
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.67/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinIL_type,type,
% 2.67/1.53 setadjoinIL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinIL,definition,
% 2.67/1.53 ( setadjoinIL
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyinunitempty_type,type,
% 2.67/1.53 emptyinunitempty: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyinunitempty,definition,
% 2.67/1.53 ( emptyinunitempty
% 2.67/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinIR_type,type,
% 2.67/1.53 setadjoinIR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinIR,definition,
% 2.67/1.53 ( setadjoinIR
% 2.67/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ A )
% 2.67/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinE_type,type,
% 2.67/1.53 setadjoinE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinE,definition,
% 2.67/1.53 ( setadjoinE
% 2.67/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.67/1.53 => ! [Xphi: $o] :
% 2.67/1.53 ( ( ( Xy = Xx )
% 2.67/1.53 => Xphi )
% 2.67/1.53 => ( ( ( in @ Xy @ A )
% 2.67/1.53 => Xphi )
% 2.67/1.53 => Xphi ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinOr_type,type,
% 2.67/1.53 setadjoinOr: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinOr,definition,
% 2.67/1.53 ( setadjoinOr
% 2.67/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.67/1.53 => ( ( Xy = Xx )
% 2.67/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setoftrueEq_type,type,
% 2.67/1.53 setoftrueEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setoftrueEq,definition,
% 2.67/1.53 ( setoftrueEq
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : $true )
% 2.67/1.53 = A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powersetI_type,type,
% 2.67/1.53 powersetI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetI,definition,
% 2.67/1.53 ( powersetI
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ A ) )
% 2.67/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyinPowerset_type,type,
% 2.67/1.53 emptyinPowerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyinPowerset,definition,
% 2.67/1.53 ( emptyinPowerset
% 2.67/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyInPowerset_type,type,
% 2.67/1.53 emptyInPowerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyInPowerset,definition,
% 2.67/1.53 ( emptyInPowerset
% 2.67/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powersetE_type,type,
% 2.67/1.53 powersetE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetE,definition,
% 2.67/1.53 ( powersetE
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.67/1.53 => ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionI_type,type,
% 2.67/1.53 setunionI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionI,definition,
% 2.67/1.53 ( setunionI
% 2.67/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( ( in @ B @ A )
% 2.67/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionE_type,type,
% 2.67/1.53 setunionE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionE,definition,
% 2.67/1.53 ( setunionE
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.67/1.53 => ! [Xphi: $o] :
% 2.67/1.53 ( ! [B: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( ( in @ B @ A )
% 2.67/1.53 => Xphi ) )
% 2.67/1.53 => Xphi ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subPowSU_type,type,
% 2.67/1.53 subPowSU: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subPowSU,definition,
% 2.67/1.53 ( subPowSU
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuE2_type,type,
% 2.67/1.53 exuE2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuE2,definition,
% 2.67/1.53 ( exuE2
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ! [Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xy )
% 2.67/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyImpWitness_type,type,
% 2.67/1.53 nonemptyImpWitness: $o ).
% 2.67/1.53
% 2.67/1.53 thf(nonemptyImpWitness,definition,
% 2.67/1.53 ( nonemptyImpWitness
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ( nonempty @ A )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & $true ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(uniqinunit_type,type,
% 2.67/1.53 uniqinunit: $o ).
% 2.67/1.53
% 2.67/1.53 thf(uniqinunit,definition,
% 2.67/1.53 ( uniqinunit
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notinsingleton_type,type,
% 2.67/1.53 notinsingleton: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notinsingleton,definition,
% 2.67/1.53 ( notinsingleton
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx != Xy )
% 2.67/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(eqinunit_type,type,
% 2.67/1.53 eqinunit: $o ).
% 2.67/1.53
% 2.67/1.53 thf(eqinunit,definition,
% 2.67/1.53 ( eqinunit
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsswitch_type,type,
% 2.67/1.53 singletonsswitch: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsswitch,definition,
% 2.67/1.53 ( singletonsswitch
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.67/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetE_type,type,
% 2.67/1.53 upairsetE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetE,definition,
% 2.67/1.53 ( upairsetE
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.67/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.67/1.53 => ( ( Xz = Xx )
% 2.67/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetIL_type,type,
% 2.67/1.53 upairsetIL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetIL,definition,
% 2.67/1.53 ( upairsetIL
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetIR_type,type,
% 2.67/1.53 upairsetIR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetIR,definition,
% 2.67/1.53 ( upairsetIR
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyE1_type,type,
% 2.67/1.53 emptyE1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyE1,definition,
% 2.67/1.53 ( emptyE1
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) )
% 2.67/1.53 => ( ( ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 = emptyset )
% 2.67/1.53 => $false ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(vacuousDall_type,type,
% 2.67/1.53 vacuousDall: $o ).
% 2.67/1.53
% 2.67/1.53 thf(vacuousDall,definition,
% 2.67/1.53 ( vacuousDall
% 2.67/1.53 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ emptyset )
% 2.67/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan1_type,type,
% 2.67/1.53 quantDeMorgan1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan1,definition,
% 2.67/1.53 ( quantDeMorgan1
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ~ ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan2_type,type,
% 2.67/1.53 quantDeMorgan2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan2,definition,
% 2.67/1.53 ( quantDeMorgan2
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ~ ( Xphi @ Xx ) )
% 2.67/1.53 => ~ ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan3_type,type,
% 2.67/1.53 quantDeMorgan3: $o ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan3,definition,
% 2.67/1.53 ( quantDeMorgan3
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ~ ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan4_type,type,
% 2.67/1.53 quantDeMorgan4: $o ).
% 2.67/1.53
% 2.67/1.53 thf(quantDeMorgan4,definition,
% 2.67/1.53 ( quantDeMorgan4
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ~ ( Xphi @ Xx ) )
% 2.67/1.53 => ~ ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(prop2setI_type,type,
% 2.67/1.53 prop2setI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(prop2setI,definition,
% 2.67/1.53 ( prop2setI
% 2.67/1.53 = ( ! [Xphi: $o] :
% 2.67/1.53 ( Xphi
% 2.67/1.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(set2prop_type,type,
% 2.67/1.53 set2prop: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(prop2set2propI_type,type,
% 2.67/1.53 prop2set2propI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(prop2set2propI,definition,
% 2.67/1.53 ( prop2set2propI
% 2.67/1.53 = ( ! [Xphi: $o] :
% 2.67/1.53 ( Xphi
% 2.67/1.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notdexE_type,type,
% 2.67/1.53 notdexE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notdexE,definition,
% 2.67/1.53 ( notdexE
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ~ ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notdallE_type,type,
% 2.67/1.53 notdallE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notdallE,definition,
% 2.67/1.53 ( notdallE
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ~ ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuI1_type,type,
% 2.67/1.53 exuI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuI1,definition,
% 2.67/1.53 ( exuI1
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ? [Xx: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 & ! [Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) )
% 2.67/1.53 => ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuI3_type,type,
% 2.67/1.53 exuI3: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuI3,definition,
% 2.67/1.53 ( exuI3
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.67/1.53 => ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) )
% 2.67/1.53 => ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuI2_type,type,
% 2.67/1.53 exuI2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuI2,definition,
% 2.67/1.53 ( exuI2
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ? [Xx: $i] :
% 2.67/1.53 ! [Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xy )
% 2.67/1.53 <=> ( Xy = Xx ) )
% 2.67/1.53 => ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(inCongP_type,type,
% 2.67/1.53 inCongP: $o ).
% 2.67/1.53
% 2.67/1.53 thf(inCongP,definition,
% 2.67/1.53 ( inCongP
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(in__Cong_type,type,
% 2.67/1.53 in__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(in__Cong,definition,
% 2.67/1.53 ( in__Cong
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( in @ Xx @ A )
% 2.67/1.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuE3u_type,type,
% 2.67/1.53 exuE3u: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuE3u,definition,
% 2.67/1.53 ( exuE3u
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exu__Cong_type,type,
% 2.67/1.53 exu__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exu__Cong,definition,
% 2.67/1.53 ( exu__Cong
% 2.67/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.67/1.53 => ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 <=> ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptyset__Cong_type,type,
% 2.67/1.53 emptyset__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptyset__Cong,definition,
% 2.67/1.53 ( emptyset__Cong
% 2.67/1.53 = ( emptyset = emptyset ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoin__Cong_type,type,
% 2.67/1.53 setadjoin__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoin__Cong,definition,
% 2.67/1.53 ( setadjoin__Cong
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ! [Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( Xz = Xu )
% 2.67/1.53 => ( ( setadjoin @ Xx @ Xz )
% 2.67/1.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powerset__Cong_type,type,
% 2.67/1.53 powerset__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powerset__Cong,definition,
% 2.67/1.53 ( powerset__Cong
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ( ( powerset @ A )
% 2.67/1.53 = ( powerset @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunion__Cong_type,type,
% 2.67/1.53 setunion__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunion__Cong,definition,
% 2.67/1.53 ( setunion__Cong
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ( ( setunion @ A )
% 2.67/1.53 = ( setunion @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(omega__Cong_type,type,
% 2.67/1.53 omega__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(omega__Cong,definition,
% 2.67/1.53 ( omega__Cong
% 2.67/1.53 = ( omega = omega ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(exuEu_type,type,
% 2.67/1.53 exuEu: $o ).
% 2.67/1.53
% 2.67/1.53 thf(exuEu,definition,
% 2.67/1.53 ( exuEu
% 2.67/1.53 = ( ! [Xphi: $i > $o] :
% 2.67/1.53 ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xphi @ Xx )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(descr__Cong_type,type,
% 2.67/1.53 descr__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(descr__Cong,definition,
% 2.67/1.53 ( descr__Cong
% 2.67/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.67/1.53 => ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ( ( exu
% 2.67/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.67/1.53 => ( ( descr
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 = ( descr
% 2.67/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstr__Cong_type,type,
% 2.67/1.53 dsetconstr__Cong: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dsetconstr__Cong,definition,
% 2.67/1.53 ( dsetconstr__Cong
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( Xx = Xy )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.67/1.53 => ( ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 = ( dsetconstr @ B
% 2.67/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subset_type,type,
% 2.67/1.53 subset: $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(disjoint_type,type,
% 2.67/1.53 disjoint: $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(setsmeet_type,type,
% 2.67/1.53 setsmeet: $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetI1_type,type,
% 2.67/1.53 subsetI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetI1,definition,
% 2.67/1.53 ( subsetI1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ B ) )
% 2.67/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(eqimpsubset2_type,type,
% 2.67/1.53 eqimpsubset2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(eqimpsubset2,definition,
% 2.67/1.53 ( eqimpsubset2
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(eqimpsubset1_type,type,
% 2.67/1.53 eqimpsubset1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(eqimpsubset1,definition,
% 2.67/1.53 ( eqimpsubset1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( A = B )
% 2.67/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetI2_type,type,
% 2.67/1.53 subsetI2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetI2,definition,
% 2.67/1.53 ( subsetI2
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ B ) )
% 2.67/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetsubset_type,type,
% 2.67/1.53 emptysetsubset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(emptysetsubset,definition,
% 2.67/1.53 ( emptysetsubset
% 2.67/1.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetE_type,type,
% 2.67/1.53 subsetE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetE,definition,
% 2.67/1.53 ( subsetE
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetE2_type,type,
% 2.67/1.53 subsetE2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetE2,definition,
% 2.67/1.53 ( subsetE2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notsubsetI_type,type,
% 2.67/1.53 notsubsetI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notsubsetI,definition,
% 2.67/1.53 ( notsubsetI
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notequalI1_type,type,
% 2.67/1.53 notequalI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notequalI1,definition,
% 2.67/1.53 ( notequalI1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ~ ( subset @ A @ B )
% 2.67/1.53 => ( A != B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(notequalI2_type,type,
% 2.67/1.53 notequalI2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(notequalI2,definition,
% 2.67/1.53 ( notequalI2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ( A != B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetRefl_type,type,
% 2.67/1.53 subsetRefl: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetRefl,definition,
% 2.67/1.53 ( subsetRefl
% 2.67/1.53 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetTrans_type,type,
% 2.67/1.53 subsetTrans: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetTrans,definition,
% 2.67/1.53 ( subsetTrans
% 2.67/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ( subset @ B @ C )
% 2.67/1.53 => ( subset @ A @ C ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinSub_type,type,
% 2.67/1.53 setadjoinSub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinSub,definition,
% 2.67/1.53 ( setadjoinSub
% 2.67/1.53 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinSub2_type,type,
% 2.67/1.53 setadjoinSub2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setadjoinSub2,definition,
% 2.67/1.53 ( setadjoinSub2
% 2.67/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subset2powerset_type,type,
% 2.67/1.53 subset2powerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subset2powerset,definition,
% 2.67/1.53 ( subset2powerset
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setextsub_type,type,
% 2.67/1.53 setextsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setextsub,definition,
% 2.67/1.53 ( setextsub
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ( subset @ B @ A )
% 2.67/1.53 => ( A = B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(subsetemptysetimpeq_type,type,
% 2.67/1.53 subsetemptysetimpeq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(subsetemptysetimpeq,definition,
% 2.67/1.53 ( subsetemptysetimpeq
% 2.67/1.53 = ( ! [A: $i] :
% 2.67/1.53 ( ( subset @ A @ emptyset )
% 2.67/1.53 => ( A = emptyset ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powersetI1_type,type,
% 2.67/1.53 powersetI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetI1,definition,
% 2.67/1.53 ( powersetI1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ B @ A )
% 2.67/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powersetE1_type,type,
% 2.67/1.53 powersetE1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetE1,definition,
% 2.67/1.53 ( powersetE1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.67/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(inPowerset_type,type,
% 2.67/1.53 inPowerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(inPowerset,definition,
% 2.67/1.53 ( inPowerset
% 2.67/1.53 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(powersetsubset_type,type,
% 2.67/1.53 powersetsubset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(powersetsubset,definition,
% 2.67/1.53 ( powersetsubset
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(sepInPowerset_type,type,
% 2.67/1.53 sepInPowerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(sepInPowerset,definition,
% 2.67/1.53 ( sepInPowerset
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( in
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 @ ( powerset @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(sepSubset_type,type,
% 2.67/1.53 sepSubset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(sepSubset,definition,
% 2.67/1.53 ( sepSubset
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( subset
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunion_type,type,
% 2.67/1.53 binunion: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(binunionIL_type,type,
% 2.67/1.53 binunionIL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionIL,definition,
% 2.67/1.53 ( binunionIL
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairset2IR_type,type,
% 2.67/1.53 upairset2IR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairset2IR,definition,
% 2.67/1.53 ( upairset2IR
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunionIR_type,type,
% 2.67/1.53 binunionIR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionIR,definition,
% 2.67/1.53 ( binunionIR
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunionEcases_type,type,
% 2.67/1.53 binunionEcases: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionEcases,definition,
% 2.67/1.53 ( binunionEcases
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.67/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.67/1.53 => ( ( ( in @ Xx @ A )
% 2.67/1.53 => Xphi )
% 2.67/1.53 => ( ( ( in @ Xx @ B )
% 2.67/1.53 => Xphi )
% 2.67/1.53 => Xphi ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunionE_type,type,
% 2.67/1.53 binunionE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionE,definition,
% 2.67/1.53 ( binunionE
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.67/1.53 => ( ( in @ Xx @ A )
% 2.67/1.53 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunionLsub_type,type,
% 2.67/1.53 binunionLsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionLsub,definition,
% 2.67/1.53 ( binunionLsub
% 2.67/1.53 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binunionRsub_type,type,
% 2.67/1.53 binunionRsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binunionRsub,definition,
% 2.67/1.53 ( binunionRsub
% 2.67/1.53 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersect_type,type,
% 2.67/1.53 binintersect: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectI_type,type,
% 2.67/1.53 binintersectI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectI,definition,
% 2.67/1.53 ( binintersectI
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset5_type,type,
% 2.67/1.53 binintersectSubset5: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset5,definition,
% 2.67/1.53 ( binintersectSubset5
% 2.67/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.67/1.53 ( ( subset @ C @ A )
% 2.67/1.53 => ( ( subset @ C @ B )
% 2.67/1.53 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectEL_type,type,
% 2.67/1.53 binintersectEL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectEL,definition,
% 2.67/1.53 ( binintersectEL
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectLsub_type,type,
% 2.67/1.53 binintersectLsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectLsub,definition,
% 2.67/1.53 ( binintersectLsub
% 2.67/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset2_type,type,
% 2.67/1.53 binintersectSubset2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset2,definition,
% 2.67/1.53 ( binintersectSubset2
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ( binintersect @ A @ B )
% 2.67/1.53 = A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset3_type,type,
% 2.67/1.53 binintersectSubset3: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset3,definition,
% 2.67/1.53 ( binintersectSubset3
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( ( binintersect @ A @ B )
% 2.67/1.53 = B )
% 2.67/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectER_type,type,
% 2.67/1.53 binintersectER: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectER,definition,
% 2.67/1.53 ( binintersectER
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.67/1.53 => ( in @ Xx @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(disjointsetsI1_type,type,
% 2.67/1.53 disjointsetsI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(disjointsetsI1,definition,
% 2.67/1.53 ( disjointsetsI1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ~ ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( in @ Xx @ B ) )
% 2.67/1.53 => ( ( binintersect @ A @ B )
% 2.67/1.53 = emptyset ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectRsub_type,type,
% 2.67/1.53 binintersectRsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectRsub,definition,
% 2.67/1.53 ( binintersectRsub
% 2.67/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset4_type,type,
% 2.67/1.53 binintersectSubset4: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset4,definition,
% 2.67/1.53 ( binintersectSubset4
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ B @ A )
% 2.67/1.53 => ( ( binintersect @ A @ B )
% 2.67/1.53 = B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset1_type,type,
% 2.67/1.53 binintersectSubset1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(binintersectSubset1,definition,
% 2.67/1.53 ( binintersectSubset1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( ( binintersect @ A @ B )
% 2.67/1.53 = A )
% 2.67/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(bs114d_type,type,
% 2.67/1.53 bs114d: $o ).
% 2.67/1.53
% 2.67/1.53 thf(bs114d,definition,
% 2.67/1.53 ( bs114d
% 2.67/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.67/1.53 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.67/1.53 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(regular_type,type,
% 2.67/1.53 regular: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminus_type,type,
% 2.67/1.53 setminus: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(setminusI_type,type,
% 2.67/1.53 setminusI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusI,definition,
% 2.67/1.53 ( setminusI
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusEL_type,type,
% 2.67/1.53 setminusEL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusEL,definition,
% 2.67/1.53 ( setminusEL
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusER_type,type,
% 2.67/1.53 setminusER: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusER,definition,
% 2.67/1.53 ( setminusER
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.67/1.53 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusSubset2_type,type,
% 2.67/1.53 setminusSubset2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusSubset2,definition,
% 2.67/1.53 ( setminusSubset2
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( subset @ A @ B )
% 2.67/1.53 => ( ( setminus @ A @ B )
% 2.67/1.53 = emptyset ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusERneg_type,type,
% 2.67/1.53 setminusERneg: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusERneg,definition,
% 2.67/1.53 ( setminusERneg
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.67/1.53 => ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusELneg_type,type,
% 2.67/1.53 setminusELneg: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusELneg,definition,
% 2.67/1.53 ( setminusELneg
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusILneg_type,type,
% 2.67/1.53 setminusILneg: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusILneg,definition,
% 2.67/1.53 ( setminusILneg
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ~ ( in @ Xx @ A )
% 2.67/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusIRneg_type,type,
% 2.67/1.53 setminusIRneg: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusIRneg,definition,
% 2.67/1.53 ( setminusIRneg
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ B )
% 2.67/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusLsub_type,type,
% 2.67/1.53 setminusLsub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusLsub,definition,
% 2.67/1.53 ( setminusLsub
% 2.67/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setminusSubset1_type,type,
% 2.67/1.53 setminusSubset1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setminusSubset1,definition,
% 2.67/1.53 ( setminusSubset1
% 2.67/1.53 = ( ! [A: $i,B: $i] :
% 2.67/1.53 ( ( ( setminus @ A @ B )
% 2.67/1.53 = emptyset )
% 2.67/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(symdiff_type,type,
% 2.67/1.53 symdiff: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffE_type,type,
% 2.67/1.53 symdiffE: $o ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffE,definition,
% 2.67/1.53 ( symdiffE
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.67/1.53 => ! [Xphi: $o] :
% 2.67/1.53 ( ( ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => Xphi ) )
% 2.67/1.53 => ( ( ~ ( in @ Xx @ A )
% 2.67/1.53 => ( ( in @ Xx @ B )
% 2.67/1.53 => Xphi ) )
% 2.67/1.53 => Xphi ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffI1_type,type,
% 2.67/1.53 symdiffI1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffI1,definition,
% 2.67/1.53 ( symdiffI1
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffI2_type,type,
% 2.67/1.53 symdiffI2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffI2,definition,
% 2.67/1.53 ( symdiffI2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ~ ( in @ Xx @ A )
% 2.67/1.53 => ( ( in @ Xx @ B )
% 2.67/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffIneg1_type,type,
% 2.67/1.53 symdiffIneg1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffIneg1,definition,
% 2.67/1.53 ( symdiffIneg1
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( in @ Xx @ B )
% 2.67/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffIneg2_type,type,
% 2.67/1.53 symdiffIneg2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(symdiffIneg2,definition,
% 2.67/1.53 ( symdiffIneg2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ~ ( in @ Xx @ A )
% 2.67/1.53 => ( ~ ( in @ Xx @ B )
% 2.67/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(iskpair_type,type,
% 2.67/1.53 iskpair: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(secondinupair_type,type,
% 2.67/1.53 secondinupair: $o ).
% 2.67/1.53
% 2.67/1.53 thf(secondinupair,definition,
% 2.67/1.53 ( secondinupair
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairIL_type,type,
% 2.67/1.53 setukpairIL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairIL,definition,
% 2.67/1.53 ( setukpairIL
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairIR_type,type,
% 2.67/1.53 setukpairIR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairIR,definition,
% 2.67/1.53 ( setukpairIR
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(kpairiskpair_type,type,
% 2.67/1.53 kpairiskpair: $o ).
% 2.67/1.53
% 2.67/1.53 thf(kpairiskpair,definition,
% 2.67/1.53 ( kpairiskpair
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(kpair_type,type,
% 2.67/1.53 kpair: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(kpairp_type,type,
% 2.67/1.53 kpairp: $o ).
% 2.67/1.53
% 2.67/1.53 thf(kpairp,definition,
% 2.67/1.53 ( kpairp
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprod_type,type,
% 2.67/1.53 cartprod: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsubset_type,type,
% 2.67/1.53 singletonsubset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsubset,definition,
% 2.67/1.53 ( singletonsubset
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singletoninpowerset_type,type,
% 2.67/1.53 singletoninpowerset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletoninpowerset,definition,
% 2.67/1.53 ( singletoninpowerset
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singletoninpowunion_type,type,
% 2.67/1.53 singletoninpowunion: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletoninpowunion,definition,
% 2.67/1.53 ( singletoninpowunion
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairset2E_type,type,
% 2.67/1.53 upairset2E: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairset2E,definition,
% 2.67/1.53 ( upairset2E
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.67/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.67/1.53 => ( ( Xz = Xx )
% 2.67/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairsubunion_type,type,
% 2.67/1.53 upairsubunion: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairsubunion,definition,
% 2.67/1.53 ( upairsubunion
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairinpowunion_type,type,
% 2.67/1.53 upairinpowunion: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairinpowunion,definition,
% 2.67/1.53 ( upairinpowunion
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem1_type,type,
% 2.67/1.53 ubforcartprodlem1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem1,definition,
% 2.67/1.53 ( ubforcartprodlem1
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem2_type,type,
% 2.67/1.53 ubforcartprodlem2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem2,definition,
% 2.67/1.53 ( ubforcartprodlem2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem3_type,type,
% 2.67/1.53 ubforcartprodlem3: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ubforcartprodlem3,definition,
% 2.67/1.53 ( ubforcartprodlem3
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairin_type,type,
% 2.67/1.53 cartprodpairin: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairin,definition,
% 2.67/1.53 ( cartprodpairin
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempair1_type,type,
% 2.67/1.53 cartprodmempair1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempair1,definition,
% 2.67/1.53 ( cartprodmempair1
% 2.67/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.67/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ? [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 & ( Xu
% 2.67/1.53 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempair_type,type,
% 2.67/1.53 cartprodmempair: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempair,definition,
% 2.67/1.53 ( cartprodmempair
% 2.67/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.67/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( iskpair @ Xu ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionE2_type,type,
% 2.67/1.53 setunionE2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionE2,definition,
% 2.67/1.53 ( setunionE2
% 2.67/1.53 = ( ! [A: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.67/1.53 => ? [X: $i] :
% 2.67/1.53 ( ( in @ X @ A )
% 2.67/1.53 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton1_type,type,
% 2.67/1.53 setunionsingleton1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton1,definition,
% 2.67/1.53 ( setunionsingleton1
% 2.67/1.53 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton2_type,type,
% 2.67/1.53 setunionsingleton2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton2,definition,
% 2.67/1.53 ( setunionsingleton2
% 2.67/1.53 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton_type,type,
% 2.67/1.53 setunionsingleton: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setunionsingleton,definition,
% 2.67/1.53 ( setunionsingleton
% 2.67/1.53 = ( ! [Xx: $i] :
% 2.67/1.53 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.67/1.53 = Xx ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singleton_type,type,
% 2.67/1.53 singleton: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(singleton,definition,
% 2.67/1.53 ( singleton
% 2.67/1.53 = ( ^ [A: $i] :
% 2.67/1.53 ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( A
% 2.67/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singletonprop_type,type,
% 2.67/1.53 singletonprop: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletonprop,definition,
% 2.67/1.53 ( singletonprop
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ A )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) )
% 2.67/1.53 => ( ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) )
% 2.67/1.53 => ( singleton
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ex1_type,type,
% 2.67/1.53 ex1: $i > ( $i > $o ) > $o ).
% 2.67/1.53
% 2.67/1.53 thf(ex1,definition,
% 2.67/1.53 ( ex1
% 2.67/1.53 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( singleton
% 2.67/1.53 @ ( dsetconstr @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ex1E1_type,type,
% 2.67/1.53 ex1E1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ex1E1,definition,
% 2.67/1.53 ( ex1E1
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ( ex1 @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.67/1.53 => ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ex1I_type,type,
% 2.67/1.53 ex1I: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ex1I,definition,
% 2.67/1.53 ( ex1I
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 => ( ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ A )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xy = Xx ) ) )
% 2.67/1.53 => ( ex1 @ A
% 2.67/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ex1I2_type,type,
% 2.67/1.53 ex1I2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ex1I2,definition,
% 2.67/1.53 ( ex1I2
% 2.67/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ A )
% 2.67/1.53 => ( ( Xphi @ Xx )
% 2.67/1.53 => ( ( Xphi @ Xy )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) )
% 2.67/1.53 => ( ? [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 & ( Xphi @ Xx ) )
% 2.67/1.53 => ( ex1 @ A
% 2.67/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsuniq_type,type,
% 2.67/1.53 singletonsuniq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(singletonsuniq,definition,
% 2.67/1.53 ( singletonsuniq
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( ( setadjoin @ Xx @ emptyset )
% 2.67/1.53 = ( setadjoin @ Xy @ emptyset ) )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(atmost1p_type,type,
% 2.67/1.53 atmost1p: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(atleast2p_type,type,
% 2.67/1.53 atleast2p: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(atmost2p_type,type,
% 2.67/1.53 atmost2p: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairsetp_type,type,
% 2.67/1.53 upairsetp: $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL1_type,type,
% 2.67/1.53 setukpairinjL1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL1,definition,
% 2.67/1.53 ( setukpairinjL1
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.67/1.53 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.67/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(kfstsingleton_type,type,
% 2.67/1.53 kfstsingleton: $o ).
% 2.67/1.53
% 2.67/1.53 thf(kfstsingleton,definition,
% 2.67/1.53 ( kfstsingleton
% 2.67/1.53 = ( ! [Xu: $i] :
% 2.67/1.53 ( ( iskpair @ Xu )
% 2.67/1.53 => ( singleton
% 2.67/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.67/1.53 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(theprop_type,type,
% 2.67/1.53 theprop: $o ).
% 2.67/1.53
% 2.67/1.53 thf(theprop,definition,
% 2.67/1.53 ( theprop
% 2.67/1.53 = ( ! [X: $i] :
% 2.67/1.53 ( ( singleton @ X )
% 2.67/1.53 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(kfst_type,type,
% 2.67/1.53 kfst: $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(kfstpairEq_type,type,
% 2.67/1.53 kfstpairEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(kfstpairEq,definition,
% 2.67/1.53 ( kfstpairEq
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.67/1.53 = Xx ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodfstin_type,type,
% 2.67/1.53 cartprodfstin: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodfstin,definition,
% 2.67/1.53 ( cartprodfstin
% 2.67/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.67/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL2_type,type,
% 2.67/1.53 setukpairinjL2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL2,definition,
% 2.67/1.53 ( setukpairinjL2
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.67/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL_type,type,
% 2.67/1.53 setukpairinjL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjL,definition,
% 2.67/1.53 ( setukpairinjL
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.67/1.53 = ( kpair @ Xz @ Xu ) )
% 2.67/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR11_type,type,
% 2.67/1.53 setukpairinjR11: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR11,definition,
% 2.67/1.53 ( setukpairinjR11
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR12_type,type,
% 2.67/1.53 setukpairinjR12: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR12,definition,
% 2.67/1.53 ( setukpairinjR12
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xx = Xy )
% 2.67/1.53 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR1_type,type,
% 2.67/1.53 setukpairinjR1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR1,definition,
% 2.67/1.53 ( setukpairinjR1
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.67/1.53 => ( ( Xz = Xu )
% 2.67/1.53 => ( Xy = Xu ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(upairequniteq_type,type,
% 2.67/1.53 upairequniteq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(upairequniteq,definition,
% 2.67/1.53 ( upairequniteq
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.67/1.53 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ Xz @ emptyset ) )
% 2.67/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR2_type,type,
% 2.67/1.53 setukpairinjR2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR2,definition,
% 2.67/1.53 ( setukpairinjR2
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.67/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.67/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR_type,type,
% 2.67/1.53 setukpairinjR: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setukpairinjR,definition,
% 2.67/1.53 ( setukpairinjR
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.67/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.67/1.53 = ( kpair @ Xz @ Xu ) )
% 2.67/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ksndsingleton_type,type,
% 2.67/1.53 ksndsingleton: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ksndsingleton,definition,
% 2.67/1.53 ( ksndsingleton
% 2.67/1.53 = ( ! [Xu: $i] :
% 2.67/1.53 ( ( iskpair @ Xu )
% 2.67/1.53 => ( singleton
% 2.67/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.67/1.53 @ ^ [Xx: $i] :
% 2.67/1.53 ( Xu
% 2.67/1.53 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ksnd_type,type,
% 2.67/1.53 ksnd: $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(ksndpairEq_type,type,
% 2.67/1.53 ksndpairEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ksndpairEq,definition,
% 2.67/1.53 ( ksndpairEq
% 2.67/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.67/1.53 = Xy ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(kpairsurjEq_type,type,
% 2.67/1.53 kpairsurjEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(kpairsurjEq,definition,
% 2.67/1.53 ( kpairsurjEq
% 2.67/1.53 = ( ! [Xu: $i] :
% 2.67/1.53 ( ( iskpair @ Xu )
% 2.67/1.53 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.67/1.53 = Xu ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodsndin_type,type,
% 2.67/1.53 cartprodsndin: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodsndin,definition,
% 2.67/1.53 ( cartprodsndin
% 2.67/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.67/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairmemEL_type,type,
% 2.67/1.53 cartprodpairmemEL: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairmemEL,definition,
% 2.67/1.53 ( cartprodpairmemEL
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairmemER_type,type,
% 2.67/1.53 cartprodpairmemER: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairmemER,definition,
% 2.67/1.53 ( cartprodpairmemER
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( in @ Xy @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempaircEq_type,type,
% 2.67/1.53 cartprodmempaircEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodmempaircEq,definition,
% 2.67/1.53 ( cartprodmempaircEq
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( kpair @ Xx @ Xy )
% 2.67/1.53 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodfstpairEq_type,type,
% 2.67/1.53 cartprodfstpairEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodfstpairEq,definition,
% 2.67/1.53 ( cartprodfstpairEq
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.67/1.53 = Xx ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodsndpairEq_type,type,
% 2.67/1.53 cartprodsndpairEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodsndpairEq,definition,
% 2.67/1.53 ( cartprodsndpairEq
% 2.67/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.67/1.53 = Xy ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairsurjEq_type,type,
% 2.67/1.53 cartprodpairsurjEq: $o ).
% 2.67/1.53
% 2.67/1.53 thf(cartprodpairsurjEq,definition,
% 2.67/1.53 ( cartprodpairsurjEq
% 2.67/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.67/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.67/1.53 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.67/1.53 = Xu ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(breln_type,type,
% 2.67/1.53 breln: $i > $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(breln,definition,
% 2.67/1.53 ( breln
% 2.67/1.53 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstr_type,type,
% 2.67/1.53 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrI_type,type,
% 2.67/1.53 dpsetconstrI: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrI,definition,
% 2.67/1.53 ( dpsetconstrI
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( Xphi @ Xx @ Xy )
% 2.67/1.53 => ( in @ ( kpair @ Xx @ Xy )
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrSub_type,type,
% 2.67/1.53 dpsetconstrSub: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrSub,definition,
% 2.67/1.53 ( dpsetconstrSub
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.67/1.53 ( subset
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.67/1.53 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(setOfPairsIsBReln_type,type,
% 2.67/1.53 setOfPairsIsBReln: $o ).
% 2.67/1.53
% 2.67/1.53 thf(setOfPairsIsBReln,definition,
% 2.67/1.53 ( setOfPairsIsBReln
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.67/1.53 ( breln @ A @ B
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrERa_type,type,
% 2.67/1.53 dpsetconstrERa: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrERa,definition,
% 2.67/1.53 ( dpsetconstrERa
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ! [Xy: $i] :
% 2.67/1.53 ( ( in @ Xy @ B )
% 2.67/1.53 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.67/1.53 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrEL1_type,type,
% 2.67/1.53 dpsetconstrEL1: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrEL1,definition,
% 2.67/1.53 ( dpsetconstrEL1
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.67/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrEL2_type,type,
% 2.67/1.53 dpsetconstrEL2: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrEL2,definition,
% 2.67/1.53 ( dpsetconstrEL2
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.67/1.53 => ( in @ Xy @ B ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrER_type,type,
% 2.67/1.53 dpsetconstrER: $o ).
% 2.67/1.53
% 2.67/1.53 thf(dpsetconstrER,definition,
% 2.67/1.53 ( dpsetconstrER
% 2.67/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.67/1.53 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(func_type,type,
% 2.67/1.53 func: $i > $i > $i > $o ).
% 2.67/1.53
% 2.67/1.53 thf(func,definition,
% 2.67/1.53 ( func
% 2.67/1.53 = ( ^ [A: $i,B: $i,R: $i] :
% 2.67/1.53 ( ( breln @ A @ B @ R )
% 2.67/1.53 & ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( ex1 @ B
% 2.67/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(funcSet_type,type,
% 2.67/1.53 funcSet: $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(funcImageSingleton_type,type,
% 2.67/1.53 funcImageSingleton: $o ).
% 2.67/1.53
% 2.67/1.53 thf(funcImageSingleton,definition,
% 2.67/1.53 ( funcImageSingleton
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( func @ A @ B @ Xf )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( singleton
% 2.67/1.53 @ ( dsetconstr @ B
% 2.67/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(apProp_type,type,
% 2.67/1.53 apProp: $o ).
% 2.67/1.53
% 2.67/1.53 thf(apProp,definition,
% 2.67/1.53 ( apProp
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( func @ A @ B @ Xf )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in
% 2.67/1.53 @ ( setunion
% 2.67/1.53 @ ( dsetconstr @ B
% 2.67/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.67/1.53 @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ap_type,type,
% 2.67/1.53 ap: $i > $i > $i > $i > $i ).
% 2.67/1.53
% 2.67/1.53 thf(ap,definition,
% 2.67/1.53 ( ap
% 2.67/1.53 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 2.67/1.53 ( setunion
% 2.67/1.53 @ ( dsetconstr @ B
% 2.67/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(app_type,type,
% 2.67/1.53 app: $o ).
% 2.67/1.53
% 2.67/1.53 thf(app,definition,
% 2.67/1.53 ( app
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( func @ A @ B @ Xf )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(infuncsetfunc_type,type,
% 2.67/1.53 infuncsetfunc: $o ).
% 2.67/1.53
% 2.67/1.53 thf(infuncsetfunc,definition,
% 2.67/1.53 ( infuncsetfunc
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.67/1.53 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(ap2p_type,type,
% 2.67/1.53 ap2p: $o ).
% 2.67/1.53
% 2.67/1.53 thf(ap2p,definition,
% 2.67/1.53 ( ap2p
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.67/1.53 => ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(funcinfuncset_type,type,
% 2.67/1.53 funcinfuncset: $o ).
% 2.67/1.53
% 2.67/1.53 thf(funcinfuncset,definition,
% 2.67/1.53 ( funcinfuncset
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.67/1.53 ( ( func @ A @ B @ Xf )
% 2.67/1.53 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(lamProp_type,type,
% 2.67/1.53 lamProp: $o ).
% 2.67/1.53
% 2.67/1.53 thf(lamProp,definition,
% 2.67/1.53 ( lamProp
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.67/1.53 => ( func @ A @ B
% 2.67/1.53 @ ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xf @ Xx )
% 2.67/1.53 = Xy ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(lam_type,type,
% 2.67/1.53 lam: $i > $i > ( $i > $i ) > $i ).
% 2.67/1.53
% 2.67/1.53 thf(lam,definition,
% 2.67/1.53 ( lam
% 2.67/1.53 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 2.67/1.53 ( dpsetconstr @ A @ B
% 2.67/1.53 @ ^ [Xx: $i,Xy: $i] :
% 2.67/1.53 ( ( Xf @ Xx )
% 2.67/1.53 = Xy ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(lamp_type,type,
% 2.67/1.53 lamp: $o ).
% 2.67/1.53
% 2.67/1.53 thf(lamp,definition,
% 2.67/1.53 ( lamp
% 2.67/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.67/1.53 => ( func @ A @ B
% 2.67/1.53 @ ( lam @ A @ B
% 2.67/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.67/1.53
% 2.67/1.53 thf(lam2p,conjecture,
% 2.67/1.53 ( setextAx
% 2.67/1.53 => ( emptysetAx
% 2.67/1.53 => ( setadjoinAx
% 2.67/1.53 => ( powersetAx
% 2.67/1.53 => ( setunionAx
% 2.67/1.53 => ( omega0Ax
% 2.67/1.53 => ( omegaSAx
% 2.67/1.53 => ( omegaIndAx
% 2.67/1.53 => ( replAx
% 2.67/1.53 => ( foundationAx
% 2.67/1.53 => ( wellorderingAx
% 2.67/1.53 => ( descrp
% 2.67/1.53 => ( dsetconstrI
% 2.67/1.53 => ( dsetconstrEL
% 2.67/1.53 => ( dsetconstrER
% 2.67/1.53 => ( exuE1
% 2.67/1.53 => ( prop2setE
% 2.67/1.53 => ( emptysetE
% 2.67/1.53 => ( emptysetimpfalse
% 2.67/1.53 => ( notinemptyset
% 2.67/1.53 => ( exuE3e
% 2.67/1.53 => ( setext
% 2.67/1.53 => ( emptyI
% 2.67/1.53 => ( noeltsimpempty
% 2.67/1.53 => ( setbeta
% 2.67/1.53 => ( nonemptyE1
% 2.67/1.53 => ( nonemptyI
% 2.67/1.53 => ( nonemptyI1
% 2.67/1.53 => ( setadjoinIL
% 2.67/1.53 => ( emptyinunitempty
% 2.67/1.53 => ( setadjoinIR
% 2.67/1.53 => ( setadjoinE
% 2.67/1.53 => ( setadjoinOr
% 2.67/1.53 => ( setoftrueEq
% 2.67/1.53 => ( powersetI
% 2.67/1.53 => ( emptyinPowerset
% 2.67/1.53 => ( emptyInPowerset
% 2.67/1.53 => ( powersetE
% 2.67/1.53 => ( setunionI
% 2.67/1.53 => ( setunionE
% 2.67/1.53 => ( subPowSU
% 2.67/1.53 => ( exuE2
% 2.67/1.53 => ( nonemptyImpWitness
% 2.67/1.53 => ( uniqinunit
% 2.67/1.53 => ( notinsingleton
% 2.67/1.53 => ( eqinunit
% 2.67/1.53 => ( singletonsswitch
% 2.67/1.53 => ( upairsetE
% 2.67/1.53 => ( upairsetIL
% 2.67/1.53 => ( upairsetIR
% 2.67/1.53 => ( emptyE1
% 2.67/1.53 => ( vacuousDall
% 2.67/1.53 => ( quantDeMorgan1
% 2.67/1.53 => ( quantDeMorgan2
% 2.67/1.53 => ( quantDeMorgan3
% 2.67/1.53 => ( quantDeMorgan4
% 2.67/1.53 => ( prop2setI
% 2.67/1.53 => ( prop2set2propI
% 2.67/1.53 => ( notdexE
% 2.67/1.53 => ( notdallE
% 2.67/1.53 => ( exuI1
% 2.67/1.53 => ( exuI3
% 2.67/1.53 => ( exuI2
% 2.67/1.53 => ( inCongP
% 2.67/1.53 => ( in__Cong
% 2.67/1.53 => ( exuE3u
% 2.67/1.53 => ( exu__Cong
% 2.67/1.53 => ( emptyset__Cong
% 2.67/1.53 => ( setadjoin__Cong
% 2.67/1.53 => ( powerset__Cong
% 2.67/1.53 => ( setunion__Cong
% 2.67/1.53 => ( omega__Cong
% 2.67/1.53 => ( exuEu
% 2.67/1.53 => ( descr__Cong
% 2.67/1.53 => ( dsetconstr__Cong
% 2.67/1.53 => ( subsetI1
% 2.67/1.53 => ( eqimpsubset2
% 2.67/1.53 => ( eqimpsubset1
% 2.67/1.53 => ( subsetI2
% 2.67/1.53 => ( emptysetsubset
% 2.67/1.53 => ( subsetE
% 2.67/1.53 => ( subsetE2
% 2.67/1.53 => ( notsubsetI
% 2.67/1.53 => ( notequalI1
% 2.67/1.53 => ( notequalI2
% 2.67/1.53 => ( subsetRefl
% 2.67/1.53 => ( subsetTrans
% 2.67/1.53 => ( setadjoinSub
% 2.67/1.53 => ( setadjoinSub2
% 2.67/1.53 => ( subset2powerset
% 2.67/1.53 => ( setextsub
% 2.67/1.53 => ( subsetemptysetimpeq
% 2.67/1.53 => ( powersetI1
% 2.67/1.53 => ( powersetE1
% 2.67/1.53 => ( inPowerset
% 2.67/1.53 => ( powersetsubset
% 2.67/1.53 => ( sepInPowerset
% 2.67/1.53 => ( sepSubset
% 2.67/1.53 => ( binunionIL
% 2.67/1.53 => ( upairset2IR
% 2.67/1.53 => ( binunionIR
% 2.67/1.53 => ( binunionEcases
% 2.67/1.53 => ( binunionE
% 2.67/1.53 => ( binunionLsub
% 2.67/1.53 => ( binunionRsub
% 2.67/1.53 => ( binintersectI
% 2.67/1.53 => ( binintersectSubset5
% 2.67/1.53 => ( binintersectEL
% 2.67/1.53 => ( binintersectLsub
% 2.67/1.53 => ( binintersectSubset2
% 2.67/1.53 => ( binintersectSubset3
% 2.67/1.53 => ( binintersectER
% 2.67/1.53 => ( disjointsetsI1
% 2.67/1.53 => ( binintersectRsub
% 2.67/1.53 => ( binintersectSubset4
% 2.67/1.53 => ( binintersectSubset1
% 2.67/1.53 => ( bs114d
% 2.67/1.53 => ( setminusI
% 2.67/1.53 => ( setminusEL
% 2.67/1.53 => ( setminusER
% 2.67/1.53 => ( setminusSubset2
% 2.67/1.53 => ( setminusERneg
% 2.67/1.53 => ( setminusELneg
% 2.67/1.53 => ( setminusILneg
% 2.67/1.53 => ( setminusIRneg
% 2.67/1.53 => ( setminusLsub
% 2.67/1.53 => ( setminusSubset1
% 2.67/1.53 => ( symdiffE
% 2.67/1.53 => ( symdiffI1
% 2.67/1.53 => ( symdiffI2
% 2.67/1.53 => ( symdiffIneg1
% 2.67/1.53 => ( symdiffIneg2
% 2.67/1.53 => ( secondinupair
% 2.67/1.53 => ( setukpairIL
% 2.67/1.53 => ( setukpairIR
% 2.67/1.53 => ( kpairiskpair
% 2.67/1.53 => ( kpairp
% 2.67/1.53 => ( singletonsubset
% 2.67/1.53 => ( singletoninpowerset
% 2.67/1.53 => ( singletoninpowunion
% 2.67/1.53 => ( upairset2E
% 2.67/1.53 => ( upairsubunion
% 2.67/1.53 => ( upairinpowunion
% 2.67/1.53 => ( ubforcartprodlem1
% 2.67/1.53 => ( ubforcartprodlem2
% 2.67/1.53 => ( ubforcartprodlem3
% 2.67/1.53 => ( cartprodpairin
% 2.67/1.53 => ( cartprodmempair1
% 2.67/1.53 => ( cartprodmempair
% 2.67/1.53 => ( setunionE2
% 2.67/1.53 => ( setunionsingleton1
% 2.67/1.53 => ( setunionsingleton2
% 2.67/1.53 => ( setunionsingleton
% 2.67/1.53 => ( singletonprop
% 2.67/1.53 => ( ex1E1
% 2.67/1.53 => ( ex1I
% 2.67/1.53 => ( ex1I2
% 2.67/1.53 => ( singletonsuniq
% 2.67/1.53 => ( setukpairinjL1
% 2.67/1.53 => ( kfstsingleton
% 2.67/1.53 => ( theprop
% 2.67/1.53 => ( kfstpairEq
% 2.67/1.53 => ( cartprodfstin
% 2.67/1.53 => ( setukpairinjL2
% 2.67/1.53 => ( setukpairinjL
% 2.67/1.53 => ( setukpairinjR11
% 2.67/1.53 => ( setukpairinjR12
% 2.67/1.53 => ( setukpairinjR1
% 2.67/1.53 => ( upairequniteq
% 2.67/1.53 => ( setukpairinjR2
% 2.67/1.53 => ( setukpairinjR
% 2.67/1.53 => ( ksndsingleton
% 2.67/1.53 => ( ksndpairEq
% 2.67/1.53 => ( kpairsurjEq
% 2.67/1.53 => ( cartprodsndin
% 2.67/1.53 => ( cartprodpairmemEL
% 2.67/1.53 => ( cartprodpairmemER
% 2.67/1.53 => ( cartprodmempaircEq
% 2.67/1.53 => ( cartprodfstpairEq
% 2.67/1.53 => ( cartprodsndpairEq
% 2.67/1.53 => ( cartprodpairsurjEq
% 2.67/1.53 => ( dpsetconstrI
% 2.67/1.53 => ( dpsetconstrSub
% 2.67/1.53 => ( setOfPairsIsBReln
% 2.67/1.53 => ( dpsetconstrERa
% 2.67/1.53 => ( dpsetconstrEL1
% 2.67/1.53 => ( dpsetconstrEL2
% 2.67/1.53 => ( dpsetconstrER
% 2.67/1.53 => ( funcImageSingleton
% 2.67/1.53 => ( apProp
% 2.67/1.53 => ( app
% 2.67/1.53 => ( infuncsetfunc
% 2.67/1.53 => ( ap2p
% 2.67/1.53 => ( funcinfuncset
% 2.67/1.53 => ( lamProp
% 2.67/1.53 => ( lamp
% 2.67/1.53 => ! [A: $i,B: $i,Xf: $i > $i] :
% 2.67/1.53 ( ! [Xx: $i] :
% 2.67/1.53 ( ( in @ Xx @ A )
% 2.67/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.67/1.53 => ( in
% 2.67/1.53 @ ( lam @ A @ B
% 2.67/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.67/1.53 @ ( funcSet @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.67/1.53 ------------------------
% 2.67/1.56 % (3878)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_3655 for (2999ds/275Mi)
% 2.67/1.56 % (3874)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_3655 for (2999ds/4Mi)
% 2.67/1.56 % (3874)Instruction limit reached!
% 2.67/1.56 % (3874)------------------------------
% 2.67/1.56 % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.56 % (3874)Termination reason: Unknown
% 2.67/1.56 % (3874)Termination phase: shuffling
% 2.67/1.56
% 2.67/1.56 % (3874)Memory used [KB]: 1407
% 2.67/1.56 % (3874)Time elapsed: 0.003 s
% 2.67/1.56 % (3874)Instructions burned: 6 (million)
% 2.67/1.56 % (3874)------------------------------
% 2.67/1.56 % (3874)------------------------------
% 2.67/1.56 % (3875)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_3655 for (2999ds/27Mi)
% 2.67/1.56 % (3873)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/183Mi)
% 2.67/1.56 % (3876)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/2Mi)
% 2.67/1.56 % (3877)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_3655 for (2999ds/2Mi)
% 2.67/1.57 % (3879)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/18Mi)
% 2.67/1.57 % (3876)Instruction limit reached!
% 2.67/1.57 % (3876)------------------------------
% 2.67/1.57 % (3876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (3876)Termination reason: Unknown
% 2.67/1.57 % (3876)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (3876)Memory used [KB]: 1407
% 2.67/1.57 % (3876)Time elapsed: 0.004 s
% 2.67/1.57 % (3876)Instructions burned: 3 (million)
% 2.67/1.57 % (3876)------------------------------
% 2.67/1.57 % (3876)------------------------------
% 2.67/1.57 % (3877)Instruction limit reached!
% 2.67/1.57 % (3877)------------------------------
% 2.67/1.57 % (3877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (3877)Termination reason: Unknown
% 2.67/1.57 % (3877)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (3877)Memory used [KB]: 1407
% 2.67/1.57 % (3877)Time elapsed: 0.004 s
% 2.67/1.57 % (3877)Instructions burned: 3 (million)
% 2.67/1.57 % (3877)------------------------------
% 2.67/1.57 % (3877)------------------------------
% 2.67/1.57 % (3880)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/3Mi)
% 2.67/1.57 % (3880)Instruction limit reached!
% 2.67/1.57 % (3880)------------------------------
% 2.67/1.57 % (3880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (3880)Termination reason: Unknown
% 2.67/1.57 % (3880)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (3880)Memory used [KB]: 1407
% 2.67/1.57 % (3880)Time elapsed: 0.002 s
% 2.67/1.57 % (3880)Instructions burned: 4 (million)
% 2.67/1.57 % (3880)------------------------------
% 2.67/1.57 % (3880)------------------------------
% 2.67/1.57 % (3875)Instruction limit reached!
% 2.67/1.57 % (3875)------------------------------
% 2.67/1.57 % (3875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.57 % (3875)Termination reason: Unknown
% 2.67/1.57 % (3875)Termination phase: shuffling
% 2.67/1.57
% 2.67/1.57 % (3875)Memory used [KB]: 1918
% 2.67/1.57 % (3875)Time elapsed: 0.015 s
% 2.67/1.57 % (3875)Instructions burned: 28 (million)
% 2.67/1.57 % (3875)------------------------------
% 2.67/1.57 % (3875)------------------------------
% 2.67/1.58 % (3879)Instruction limit reached!
% 2.67/1.58 % (3879)------------------------------
% 2.67/1.58 % (3879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.58 % (3879)Termination reason: Unknown
% 2.67/1.58 % (3879)Termination phase: shuffling
% 2.67/1.58
% 2.67/1.58 % (3879)Memory used [KB]: 1791
% 2.67/1.58 % (3879)Time elapsed: 0.014 s
% 2.67/1.58 % (3879)Instructions burned: 19 (million)
% 2.67/1.58 % (3879)------------------------------
% 2.67/1.58 % (3879)------------------------------
% 2.67/1.58 % (3883)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_3655 for (2999ds/3Mi)
% 2.67/1.58 % (3883)Instruction limit reached!
% 2.67/1.58 % (3883)------------------------------
% 2.67/1.58 % (3883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.58 % (3883)Termination reason: Unknown
% 2.67/1.58 % (3883)Termination phase: shuffling
% 2.67/1.58
% 2.67/1.58 % (3883)Memory used [KB]: 1407
% 2.67/1.58 % (3883)Time elapsed: 0.002 s
% 2.67/1.58 % (3883)Instructions burned: 4 (million)
% 2.67/1.58 % (3883)------------------------------
% 2.67/1.58 % (3883)------------------------------
% 2.67/1.58 % (3882)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_3655 for (2999ds/15Mi)
% 2.67/1.58 % (3881)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_3655 for (2999ds/37Mi)
% 2.67/1.59 % (3884)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_3655 for (2999ds/1041Mi)
% 2.67/1.59 % (3882)Instruction limit reached!
% 2.67/1.59 % (3882)------------------------------
% 2.67/1.59 % (3882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (3882)Termination reason: Unknown
% 2.67/1.59 % (3882)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (3882)Memory used [KB]: 1663
% 2.67/1.59 % (3882)Time elapsed: 0.010 s
% 2.67/1.59 % (3882)Instructions burned: 15 (million)
% 2.67/1.59 % (3882)------------------------------
% 2.67/1.59 % (3882)------------------------------
% 2.67/1.59 % (3886)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/16Mi)
% 2.67/1.59 % (3885)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/7Mi)
% 2.71/1.60 % (3886)Instruction limit reached!
% 2.71/1.60 % (3886)------------------------------
% 2.71/1.60 % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (3886)Termination reason: Unknown
% 2.71/1.60 % (3886)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (3886)Memory used [KB]: 1791
% 2.71/1.60 % (3886)Time elapsed: 0.007 s
% 2.71/1.60 % (3886)Instructions burned: 18 (million)
% 2.71/1.60 % (3886)------------------------------
% 2.71/1.60 % (3886)------------------------------
% 2.71/1.60 % (3885)Instruction limit reached!
% 2.71/1.60 % (3885)------------------------------
% 2.71/1.60 % (3885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (3885)Termination reason: Unknown
% 2.71/1.60 % (3885)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (3885)Memory used [KB]: 1535
% 2.71/1.60 % (3885)Time elapsed: 0.006 s
% 2.71/1.60 % (3885)Instructions burned: 8 (million)
% 2.71/1.60 % (3885)------------------------------
% 2.71/1.60 % (3885)------------------------------
% 2.71/1.60 % (3887)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_3655 for (2999ds/3Mi)
% 2.71/1.60 % (3881)Instruction limit reached!
% 2.71/1.60 % (3881)------------------------------
% 2.71/1.60 % (3881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (3881)Termination reason: Unknown
% 2.71/1.60 % (3881)Termination phase: Property scanning
% 2.71/1.60
% 2.71/1.60 % (3881)Memory used [KB]: 2174
% 2.71/1.60 % (3881)Time elapsed: 0.021 s
% 2.71/1.60 % (3881)Instructions burned: 38 (million)
% 2.71/1.60 % (3881)------------------------------
% 2.71/1.60 % (3881)------------------------------
% 2.71/1.60 % (3887)Instruction limit reached!
% 2.71/1.60 % (3887)------------------------------
% 2.71/1.60 % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.60 % (3887)Termination reason: Unknown
% 2.71/1.60 % (3887)Termination phase: shuffling
% 2.71/1.60
% 2.71/1.60 % (3887)Memory used [KB]: 1407
% 2.71/1.60 % (3887)Time elapsed: 0.002 s
% 2.71/1.60 % (3887)Instructions burned: 4 (million)
% 2.71/1.60 % (3887)------------------------------
% 2.71/1.60 % (3887)------------------------------
% 2.71/1.61 % (3888)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_3655 for (2999ds/3Mi)
% 2.71/1.61 % (3888)Instruction limit reached!
% 2.71/1.61 % (3888)------------------------------
% 2.71/1.61 % (3888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (3888)Termination reason: Unknown
% 2.71/1.61 % (3888)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (3888)Memory used [KB]: 1407
% 2.71/1.61 % (3888)Time elapsed: 0.003 s
% 2.71/1.61 % (3888)Instructions burned: 4 (million)
% 2.71/1.61 % (3888)------------------------------
% 2.71/1.61 % (3888)------------------------------
% 2.71/1.61 % (3891)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/4Mi)
% 2.71/1.61 % (3891)Instruction limit reached!
% 2.71/1.61 % (3891)------------------------------
% 2.71/1.61 % (3891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.61 % (3891)Termination reason: Unknown
% 2.71/1.61 % (3891)Termination phase: shuffling
% 2.71/1.61
% 2.71/1.61 % (3891)Memory used [KB]: 1407
% 2.71/1.61 % (3891)Time elapsed: 0.003 s
% 2.71/1.61 % (3891)Instructions burned: 4 (million)
% 2.71/1.61 % (3891)------------------------------
% 2.71/1.61 % (3891)------------------------------
% 2.71/1.62 % (3889)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/7Mi)
% 2.71/1.62 % (3892)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/18Mi)
% 2.71/1.62 % (3889)Instruction limit reached!
% 2.71/1.62 % (3889)------------------------------
% 2.71/1.62 % (3889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (3889)Termination reason: Unknown
% 2.71/1.62 % (3889)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (3889)Memory used [KB]: 1535
% 2.71/1.62 % (3889)Time elapsed: 0.006 s
% 2.71/1.62 % (3889)Instructions burned: 8 (million)
% 2.71/1.62 % (3889)------------------------------
% 2.71/1.62 % (3889)------------------------------
% 2.71/1.62 % (3890)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/3Mi)
% 2.71/1.62 % (3890)Instruction limit reached!
% 2.71/1.62 % (3890)------------------------------
% 2.71/1.62 % (3890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (3890)Termination reason: Unknown
% 2.71/1.62 % (3890)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (3890)Memory used [KB]: 1407
% 2.71/1.62 % (3890)Time elapsed: 0.004 s
% 2.71/1.62 % (3890)Instructions burned: 4 (million)
% 2.71/1.62 % (3890)------------------------------
% 2.71/1.62 % (3890)------------------------------
% 2.71/1.62 % (3892)Instruction limit reached!
% 2.71/1.62 % (3892)------------------------------
% 2.71/1.62 % (3892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.62 % (3892)Termination reason: Unknown
% 2.71/1.62 % (3892)Termination phase: shuffling
% 2.71/1.62
% 2.71/1.62 % (3892)Memory used [KB]: 1791
% 2.71/1.62 % (3892)Time elapsed: 0.006 s
% 2.71/1.62 % (3892)Instructions burned: 18 (million)
% 2.71/1.62 % (3892)------------------------------
% 2.71/1.62 % (3892)------------------------------
% 2.71/1.62 % (3893)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/710Mi)
% 2.71/1.63 % (3896)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_3655 for (2999ds/21Mi)
% 2.71/1.64 % (3894)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/6Mi)
% 2.71/1.64 % (3896)Instruction limit reached!
% 2.71/1.64 % (3896)------------------------------
% 2.71/1.64 % (3896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.64 % (3896)Termination reason: Unknown
% 2.71/1.64 % (3896)Termination phase: shuffling
% 2.71/1.64
% 2.71/1.64 % (3896)Memory used [KB]: 1791
% 2.71/1.64 % (3896)Time elapsed: 0.007 s
% 2.71/1.64 % (3896)Instructions burned: 22 (million)
% 2.71/1.64 % (3896)------------------------------
% 2.71/1.64 % (3896)------------------------------
% 2.71/1.64 % (3878)Instruction limit reached!
% 2.71/1.64 % (3878)------------------------------
% 2.71/1.64 % (3878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.64 % (3878)Termination reason: Unknown
% 2.71/1.64 % (3878)Termination phase: Saturation
% 2.71/1.64
% 2.71/1.64 % (3878)Memory used [KB]: 8571
% 2.71/1.64 % (3878)Time elapsed: 0.084 s
% 2.71/1.64 % (3878)Instructions burned: 276 (million)
% 2.71/1.64 % (3878)------------------------------
% 2.71/1.64 % (3878)------------------------------
% 2.71/1.64 % (3894)Instruction limit reached!
% 2.71/1.64 % (3894)------------------------------
% 2.71/1.64 % (3894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.64 % (3894)Termination reason: Unknown
% 2.71/1.64 % (3894)Termination phase: shuffling
% 2.71/1.64
% 2.71/1.64 % (3894)Memory used [KB]: 1407
% 2.71/1.64 % (3894)Time elapsed: 0.005 s
% 2.71/1.64 % (3894)Instructions burned: 6 (million)
% 2.71/1.64 % (3894)------------------------------
% 2.71/1.64 % (3894)------------------------------
% 2.71/1.64 % (3895)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_3655 for (2999ds/902Mi)
% 2.71/1.65 % (3873)Instruction limit reached!
% 2.71/1.65 % (3873)------------------------------
% 2.71/1.65 % (3873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.65 % (3873)Termination reason: Unknown
% 2.71/1.65 % (3873)Termination phase: Saturation
% 2.71/1.65
% 2.71/1.65 % (3873)Memory used [KB]: 7419
% 2.71/1.65 % (3873)Time elapsed: 0.082 s
% 2.71/1.65 % (3873)Instructions burned: 183 (million)
% 2.71/1.65 % (3873)------------------------------
% 2.71/1.65 % (3873)------------------------------
% 2.71/1.65 % (3897)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/5Mi)
% 2.71/1.65 % (3898)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_3655 for (2999ds/6Mi)
% 2.71/1.65 % (3897)Instruction limit reached!
% 2.71/1.65 % (3897)------------------------------
% 2.71/1.65 % (3897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.65 % (3897)Termination reason: Unknown
% 2.71/1.65 % (3897)Termination phase: shuffling
% 2.71/1.65
% 2.71/1.65 % (3897)Memory used [KB]: 1407
% 2.71/1.65 % (3897)Time elapsed: 0.003 s
% 2.71/1.65 % (3897)Instructions burned: 6 (million)
% 2.71/1.65 % (3897)------------------------------
% 2.71/1.65 % (3897)------------------------------
% 2.71/1.65 % (3898)Instruction limit reached!
% 2.71/1.65 % (3898)------------------------------
% 2.71/1.65 % (3898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.65 % (3898)Termination reason: Unknown
% 2.71/1.65 % (3898)Termination phase: shuffling
% 2.71/1.65
% 2.71/1.65 % (3898)Memory used [KB]: 1407
% 2.71/1.65 % (3898)Time elapsed: 0.003 s
% 2.71/1.65 % (3898)Instructions burned: 6 (million)
% 2.71/1.65 % (3898)------------------------------
% 2.71/1.65 % (3898)------------------------------
% 2.71/1.66 % (3900)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_3655 for (2998ds/779Mi)
% 2.71/1.66 % (3899)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3655 for (2999ds/377Mi)
% 2.71/1.66 % (3901)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_3655 for (2998ds/19Mi)
% 2.71/1.66 % (3902)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3655 for (2998ds/879Mi)
% 2.71/1.66 % (3901)Instruction limit reached!
% 2.71/1.66 % (3901)------------------------------
% 2.71/1.66 % (3901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.66 % (3901)Termination reason: Unknown
% 2.71/1.66 % (3901)Termination phase: shuffling
% 2.71/1.66
% 2.71/1.66 % (3901)Memory used [KB]: 1791
% 2.71/1.66 % (3901)Time elapsed: 0.007 s
% 2.71/1.66 % (3901)Instructions burned: 21 (million)
% 2.71/1.66 % (3901)------------------------------
% 2.71/1.66 % (3901)------------------------------
% 2.71/1.67 % (3903)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3655 for (2998ds/17Mi)
% 2.71/1.68 % (3903)Instruction limit reached!
% 2.71/1.68 % (3903)------------------------------
% 2.71/1.68 % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.68 % (3903)Termination reason: Unknown
% 2.71/1.68 % (3903)Termination phase: shuffling
% 2.71/1.68
% 2.71/1.68 % (3903)Memory used [KB]: 1791
% 2.71/1.68 % (3903)Time elapsed: 0.006 s
% 2.71/1.68 % (3903)Instructions burned: 18 (million)
% 2.71/1.68 % (3903)------------------------------
% 2.71/1.68 % (3903)------------------------------
% 2.71/1.69 % (3904)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3655 for (2998ds/3Mi)
% 2.71/1.69 % (3904)Instruction limit reached!
% 2.71/1.69 % (3904)------------------------------
% 2.71/1.69 % (3904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.69 % (3904)Termination reason: Unknown
% 2.71/1.69 % (3904)Termination phase: shuffling
% 2.71/1.69
% 2.71/1.69 % (3904)Memory used [KB]: 1407
% 2.71/1.69 % (3904)Time elapsed: 0.003 s
% 2.71/1.69 % (3904)Instructions burned: 6 (million)
% 2.71/1.69 % (3904)------------------------------
% 2.71/1.69 % (3904)------------------------------
% 2.71/1.70 % (3905)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3655 for (2998ds/30Mi)
% 2.71/1.71 % (3905)Instruction limit reached!
% 2.71/1.71 % (3905)------------------------------
% 2.71/1.71 % (3905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.71 % (3905)Termination reason: Unknown
% 2.71/1.71 % (3905)Termination phase: shuffling
% 2.71/1.71
% 2.71/1.71 % (3905)Memory used [KB]: 1918
% 2.71/1.71 % (3905)Time elapsed: 0.009 s
% 2.71/1.71 % (3905)Instructions burned: 30 (million)
% 2.71/1.71 % (3905)------------------------------
% 2.71/1.71 % (3905)------------------------------
% 2.71/1.72 % (3906)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3655 for (2998ds/127Mi)
% 2.71/1.75 % (3906)Instruction limit reached!
% 2.71/1.75 % (3906)------------------------------
% 2.71/1.75 % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.75 % (3906)Termination reason: Unknown
% 2.71/1.75 % (3906)Termination phase: Saturation
% 2.71/1.75
% 2.71/1.75 % (3906)Memory used [KB]: 6908
% 2.71/1.75 % (3906)Time elapsed: 0.034 s
% 2.71/1.75 % (3906)Instructions burned: 128 (million)
% 2.71/1.75 % (3906)------------------------------
% 2.71/1.75 % (3906)------------------------------
% 2.71/1.76 % (3907)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3655 for (2997ds/100Mi)
% 2.71/1.78 % (3899)Instruction limit reached!
% 2.71/1.78 % (3899)------------------------------
% 2.71/1.78 % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.78 % (3899)Termination reason: Unknown
% 2.71/1.78 % (3899)Termination phase: Saturation
% 2.71/1.78
% 2.71/1.78 % (3899)Memory used [KB]: 8443
% 2.71/1.78 % (3899)Time elapsed: 0.123 s
% 2.71/1.78 % (3899)Instructions burned: 379 (million)
% 2.71/1.78 % (3899)------------------------------
% 2.71/1.78 % (3899)------------------------------
% 2.71/1.79 % (3907)Instruction limit reached!
% 2.71/1.79 % (3907)------------------------------
% 2.71/1.79 % (3907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.79 % (3907)Termination reason: Unknown
% 2.71/1.79 % (3907)Termination phase: Saturation
% 2.71/1.79
% 2.71/1.79 % (3907)Memory used [KB]: 6780
% 2.71/1.79 % (3907)Time elapsed: 0.027 s
% 2.71/1.79 % (3907)Instructions burned: 102 (million)
% 2.71/1.79 % (3907)------------------------------
% 2.71/1.79 % (3907)------------------------------
% 2.71/1.79 % (3908)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_3655 for (2997ds/3Mi)
% 2.71/1.79 % (3908)Instruction limit reached!
% 2.71/1.79 % (3908)------------------------------
% 2.71/1.79 % (3908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.79 % (3908)Termination reason: Unknown
% 2.71/1.79 % (3908)Termination phase: shuffling
% 2.71/1.79
% 2.71/1.79 % (3908)Memory used [KB]: 1407
% 2.71/1.79 % (3908)Time elapsed: 0.002 s
% 2.71/1.79 % (3908)Instructions burned: 4 (million)
% 2.71/1.79 % (3908)------------------------------
% 2.71/1.79 % (3908)------------------------------
% 2.71/1.80 % (3909)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_3655 for (2997ds/20Mi)
% 2.71/1.80 % (3910)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_3655 for (2997ds/86Mi)
% 2.71/1.80 % (3909)Instruction limit reached!
% 2.71/1.80 % (3909)------------------------------
% 2.71/1.80 % (3909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.80 % (3909)Termination reason: Unknown
% 2.71/1.80 % (3909)Termination phase: Property scanning
% 2.71/1.80
% 2.71/1.80 % (3909)Memory used [KB]: 1791
% 2.71/1.80 % (3909)Time elapsed: 0.008 s
% 2.71/1.80 % (3909)Instructions burned: 21 (million)
% 2.71/1.80 % (3909)------------------------------
% 2.71/1.80 % (3909)------------------------------
% 2.71/1.81 % (3911)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_3655 for (2997ds/107Mi)
% 2.71/1.82 % (3910)Instruction limit reached!
% 2.71/1.82 % (3910)------------------------------
% 2.71/1.82 % (3910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.82 % (3910)Termination reason: Unknown
% 2.71/1.82 % (3910)Termination phase: Property scanning
% 2.71/1.82
% 2.71/1.82 % (3910)Memory used [KB]: 2174
% 2.71/1.82 % (3910)Time elapsed: 0.025 s
% 2.71/1.82 % (3910)Instructions burned: 87 (million)
% 2.71/1.82 % (3910)------------------------------
% 2.71/1.82 % (3910)------------------------------
% 2.71/1.83 % (3912)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_3655 for (2997ds/39Mi)
% 2.71/1.84 % (3911)Instruction limit reached!
% 2.71/1.84 % (3911)------------------------------
% 2.71/1.84 % (3911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.84 % (3911)Termination reason: Unknown
% 2.71/1.84 % (3911)Termination phase: Property scanning
% 2.71/1.84
% 2.71/1.84 % (3911)Memory used [KB]: 2174
% 2.71/1.84 % (3911)Time elapsed: 0.029 s
% 2.71/1.84 % (3911)Instructions burned: 109 (million)
% 2.71/1.84 % (3911)------------------------------
% 2.71/1.84 % (3911)------------------------------
% 2.71/1.85 % (3912)Instruction limit reached!
% 2.71/1.85 % (3912)------------------------------
% 2.71/1.85 % (3912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.85 % (3912)Termination reason: Unknown
% 2.71/1.85 % (3912)Termination phase: Property scanning
% 2.71/1.85
% 2.71/1.85 % (3912)Memory used [KB]: 2174
% 2.71/1.85 % (3912)Time elapsed: 0.013 s
% 2.71/1.85 % (3912)Instructions burned: 40 (million)
% 2.71/1.85 % (3912)------------------------------
% 2.71/1.85 % (3912)------------------------------
% 2.71/1.85 % (3913)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_3655 for (2996ds/448Mi)
% 2.71/1.86 % (3914)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_3655 for (2996ds/46Mi)
% 2.71/1.86 % (3893)Instruction limit reached!
% 2.71/1.86 % (3893)------------------------------
% 2.71/1.86 % (3893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.86 % (3893)Termination reason: Unknown
% 2.71/1.86 % (3893)Termination phase: Saturation
% 2.71/1.86
% 2.71/1.86 % (3893)Memory used [KB]: 9594
% 2.71/1.86 % (3893)Time elapsed: 0.238 s
% 2.71/1.86 % (3893)Instructions burned: 712 (million)
% 2.71/1.86 % (3893)------------------------------
% 2.71/1.86 % (3893)------------------------------
% 2.71/1.86 % (3900)Instruction limit reached!
% 2.71/1.86 % (3900)------------------------------
% 2.71/1.86 % (3900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.86 % (3900)Termination reason: Unknown
% 2.71/1.86 % (3900)Termination phase: Saturation
% 2.71/1.86
% 2.71/1.86 % (3900)Memory used [KB]: 7291
% 2.71/1.86 % (3900)Time elapsed: 0.207 s
% 2.71/1.86 % (3900)Instructions burned: 781 (million)
% 2.71/1.86 % (3900)------------------------------
% 2.71/1.86 % (3900)------------------------------
% 2.71/1.87 % (3914)Instruction limit reached!
% 2.71/1.87 % (3914)------------------------------
% 2.71/1.87 % (3914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.87 % (3914)Termination reason: Unknown
% 2.71/1.87 % (3914)Termination phase: Property scanning
% 2.71/1.87
% 2.71/1.87 % (3914)Memory used [KB]: 1918
% 2.71/1.87 % (3914)Time elapsed: 0.014 s
% 2.71/1.87 % (3914)Instructions burned: 46 (million)
% 2.71/1.87 % (3914)------------------------------
% 2.71/1.87 % (3914)------------------------------
% 2.71/1.87 % (3884)Instruction limit reached!
% 2.71/1.87 % (3884)------------------------------
% 2.71/1.87 % (3884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.87 % (3884)Termination reason: Unknown
% 2.71/1.87 % (3884)Termination phase: Saturation
% 2.71/1.87
% 2.71/1.87 % (3884)Memory used [KB]: 11513
% 2.71/1.87 % (3884)Time elapsed: 0.283 s
% 2.71/1.87 % (3884)Instructions burned: 1041 (million)
% 2.71/1.87 % (3884)------------------------------
% 2.71/1.87 % (3884)------------------------------
% 2.71/1.87 % (3916)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_3655 for (2996ds/507Mi)
% 2.71/1.88 % (3915)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_3655 for (2996ds/98Mi)
% 2.71/1.88 % (3917)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_3655 for (2996ds/149Mi)
% 2.71/1.88 % (3918)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3655 for (2996ds/39Mi)
% 2.71/1.89 % (3918)Instruction limit reached!
% 2.71/1.89 % (3918)------------------------------
% 2.71/1.89 % (3918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.89 % (3918)Termination reason: Unknown
% 2.71/1.89 % (3918)Termination phase: Property scanning
% 2.71/1.89
% 2.71/1.89 % (3918)Memory used [KB]: 2046
% 2.71/1.89 % (3918)Time elapsed: 0.013 s
% 2.71/1.89 % (3918)Instructions burned: 42 (million)
% 2.71/1.89 % (3918)------------------------------
% 2.71/1.89 % (3918)------------------------------
% 2.71/1.90 % (3919)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_3655 for (2996ds/6Mi)
% 2.71/1.91 % (3919)Instruction limit reached!
% 2.71/1.91 % (3919)------------------------------
% 2.71/1.91 % (3919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.91 % (3919)Termination reason: Unknown
% 2.71/1.91 % (3919)Termination phase: shuffling
% 2.71/1.91
% 2.71/1.91 % (3919)Memory used [KB]: 1535
% 2.71/1.91 % (3919)Time elapsed: 0.004 s
% 2.71/1.91 % (3919)Instructions burned: 7 (million)
% 2.71/1.91 % (3919)------------------------------
% 2.71/1.91 % (3919)------------------------------
% 2.71/1.91 % (3920)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_3655 for (2996ds/1087Mi)
% 2.71/1.92 % (3917)Instruction limit reached!
% 2.71/1.92 % (3917)------------------------------
% 2.71/1.92 % (3917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.92 % (3917)Termination reason: Unknown
% 2.71/1.92 % (3917)Termination phase: Saturation
% 2.71/1.92
% 2.71/1.92 % (3917)Memory used [KB]: 7419
% 2.71/1.92 % (3917)Time elapsed: 0.044 s
% 2.71/1.92 % (3917)Instructions burned: 149 (million)
% 2.71/1.92 % (3917)------------------------------
% 2.71/1.92 % (3917)------------------------------
% 2.71/1.93 % (3915)Instruction limit reached!
% 2.71/1.93 % (3915)------------------------------
% 2.71/1.93 % (3915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.93 % (3915)Termination reason: Unknown
% 2.71/1.93 % (3915)Termination phase: Property scanning
% 2.71/1.93
% 2.71/1.93 % (3915)Memory used [KB]: 2302
% 2.71/1.93 % (3915)Time elapsed: 0.049 s
% 2.71/1.93 % (3915)Instructions burned: 100 (million)
% 2.71/1.93 % (3915)------------------------------
% 2.71/1.93 % (3915)------------------------------
% 2.71/1.93 % (3902)Instruction limit reached!
% 2.71/1.93 % (3902)------------------------------
% 2.71/1.93 % (3902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.93 % (3902)Termination reason: Unknown
% 2.71/1.93 % (3902)Termination phase: Saturation
% 2.71/1.93
% 2.71/1.93 % (3902)Memory used [KB]: 8571
% 2.71/1.93 % (3902)Time elapsed: 0.294 s
% 2.71/1.93 % (3902)Instructions burned: 879 (million)
% 2.71/1.93 % (3902)------------------------------
% 2.71/1.93 % (3902)------------------------------
% 2.71/1.93 % (3921)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3655 for (2996ds/47Mi)
% 2.71/1.94 % (3923)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_3655 for (2996ds/432Mi)
% 2.71/1.94 % (3922)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_3655 for (2996ds/44Mi)
% 2.71/1.95 % (3921)Instruction limit reached!
% 2.71/1.95 % (3921)------------------------------
% 2.71/1.95 % (3921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.95 % (3921)Termination reason: Unknown
% 2.71/1.95 % (3921)Termination phase: Property scanning
% 2.71/1.95
% 2.71/1.95 % (3921)Memory used [KB]: 2046
% 2.71/1.95 % (3921)Time elapsed: 0.016 s
% 2.71/1.95 % (3921)Instructions burned: 50 (million)
% 2.71/1.95 % (3921)------------------------------
% 2.71/1.95 % (3921)------------------------------
% 2.71/1.96 % (3924)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/62Mi)
% 2.71/1.96 % (3913)Instruction limit reached!
% 2.71/1.96 % (3913)------------------------------
% 2.71/1.96 % (3913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.96 % (3913)Termination reason: Unknown
% 2.71/1.96 % (3913)Termination phase: Saturation
% 2.71/1.96
% 2.71/1.96 % (3913)Memory used [KB]: 6908
% 2.71/1.96 % (3913)Time elapsed: 0.112 s
% 2.71/1.96 % (3913)Instructions burned: 452 (million)
% 2.71/1.96 % (3913)------------------------------
% 2.71/1.96 % (3913)------------------------------
% 2.71/1.97 % (3922)Instruction limit reached!
% 2.71/1.97 % (3922)------------------------------
% 2.71/1.97 % (3922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.97 % (3922)Termination reason: Unknown
% 2.71/1.97 % (3922)Termination phase: Property scanning
% 2.71/1.97
% 2.71/1.97 % (3922)Memory used [KB]: 2174
% 2.71/1.97 % (3922)Time elapsed: 0.024 s
% 2.71/1.97 % (3922)Instructions burned: 45 (million)
% 2.71/1.97 % (3922)------------------------------
% 2.71/1.97 % (3922)------------------------------
% 2.71/1.97 % (3895)Instruction limit reached!
% 2.71/1.97 % (3895)------------------------------
% 2.71/1.97 % (3895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.97 % (3895)Termination reason: Unknown
% 2.71/1.97 % (3895)Termination phase: Saturation
% 2.71/1.97
% 2.71/1.97 % (3895)Memory used [KB]: 10618
% 2.71/1.97 % (3895)Time elapsed: 0.331 s
% 2.71/1.97 % (3895)Instructions burned: 902 (million)
% 2.71/1.97 % (3895)------------------------------
% 2.71/1.97 % (3895)------------------------------
% 2.71/1.97 % (3925)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_3655 for (2995ds/31Mi)
% 2.71/1.97 % (3924)Instruction limit reached!
% 2.71/1.97 % (3924)------------------------------
% 2.71/1.97 % (3924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.97 % (3924)Termination reason: Unknown
% 2.71/1.97 % (3924)Termination phase: Property scanning
% 2.71/1.97
% 2.71/1.97 % (3924)Memory used [KB]: 2174
% 2.71/1.97 % (3924)Time elapsed: 0.018 s
% 2.71/1.97 % (3924)Instructions burned: 62 (million)
% 2.71/1.97 % (3924)------------------------------
% 2.71/1.97 % (3924)------------------------------
% 2.71/1.98 % (3925)Instruction limit reached!
% 2.71/1.98 % (3925)------------------------------
% 2.71/1.98 % (3925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.98 % (3925)Termination reason: Unknown
% 2.71/1.98 % (3925)Termination phase: shuffling
% 2.71/1.98
% 2.71/1.98 % (3925)Memory used [KB]: 1918
% 2.71/1.98 % (3925)Time elapsed: 0.010 s
% 2.71/1.98 % (3925)Instructions burned: 32 (million)
% 2.71/1.98 % (3925)------------------------------
% 2.71/1.98 % (3925)------------------------------
% 2.71/1.98 % (3927)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_3655 for (2995ds/453Mi)
% 2.71/1.98 % (3926)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/96Mi)
% 2.71/1.98 % (3928)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_3655 for (2995ds/71Mi)
% 2.71/1.99 % (3929)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/83Mi)
% 2.71/2.00 % (3928)Instruction limit reached!
% 2.71/2.00 % (3928)------------------------------
% 2.71/2.00 % (3928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.00 % (3928)Termination reason: Unknown
% 2.71/2.00 % (3928)Termination phase: Function definition elimination
% 2.71/2.01
% 2.71/2.01 % (3928)Memory used [KB]: 2046
% 2.71/2.01 % (3928)Time elapsed: 0.022 s
% 2.71/2.01 % (3928)Instructions burned: 73 (million)
% 2.71/2.01 % (3928)------------------------------
% 2.71/2.01 % (3928)------------------------------
% 2.71/2.01 % (3929)Instruction limit reached!
% 2.71/2.01 % (3929)------------------------------
% 2.71/2.01 % (3929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.01 % (3929)Termination reason: Unknown
% 2.71/2.01 % (3929)Termination phase: Property scanning
% 2.71/2.01
% 2.71/2.01 % (3929)Memory used [KB]: 2046
% 2.71/2.01 % (3929)Time elapsed: 0.022 s
% 2.71/2.01 % (3929)Instructions burned: 84 (million)
% 2.71/2.01 % (3929)------------------------------
% 2.71/2.01 % (3929)------------------------------
% 2.71/2.01 % (3926)Instruction limit reached!
% 2.71/2.01 % (3926)------------------------------
% 2.71/2.01 % (3926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/2.01 % (3926)Termination reason: Unknown
% 2.71/2.01 % (3926)Termination phase: Property scanning
% 2.71/2.01
% 2.71/2.01 % (3926)Memory used [KB]: 2174
% 2.71/2.01 % (3926)Time elapsed: 0.029 s
% 2.71/2.01 % (3926)Instructions burned: 96 (million)
% 2.71/2.01 % (3926)------------------------------
% 2.71/2.01 % (3926)------------------------------
% 5.89/2.02 % (3930)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/11Mi)
% 5.89/2.02 % (3930)Instruction limit reached!
% 5.89/2.02 % (3930)------------------------------
% 5.89/2.02 % (3930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.02 % (3931)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_3655 for (2995ds/41Mi)
% 5.89/2.02 % (3930)Termination reason: Unknown
% 5.89/2.02 % (3930)Termination phase: shuffling
% 5.89/2.02
% 5.89/2.02 % (3930)Memory used [KB]: 1535
% 5.89/2.02 % (3930)Time elapsed: 0.005 s
% 5.89/2.02 % (3930)Instructions burned: 11 (million)
% 5.89/2.02 % (3930)------------------------------
% 5.89/2.02 % (3930)------------------------------
% 5.89/2.02 % (3932)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/6Mi)
% 5.89/2.02 % (3932)Instruction limit reached!
% 5.89/2.02 % (3932)------------------------------
% 5.89/2.02 % (3932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.02 % (3932)Termination reason: Unknown
% 5.89/2.02 % (3932)Termination phase: shuffling
% 5.89/2.02
% 5.89/2.02 % (3932)Memory used [KB]: 1407
% 5.89/2.02 % (3932)Time elapsed: 0.003 s
% 5.89/2.02 % (3932)Instructions burned: 7 (million)
% 5.89/2.02 % (3932)------------------------------
% 5.89/2.02 % (3932)------------------------------
% 5.89/2.03 % (3933)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/150Mi)
% 5.89/2.03 % (3931)Instruction limit reached!
% 5.89/2.03 % (3931)------------------------------
% 5.89/2.03 % (3931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.03 % (3931)Termination reason: Unknown
% 5.89/2.03 % (3931)Termination phase: Property scanning
% 5.89/2.03
% 5.89/2.03 % (3931)Memory used [KB]: 2046
% 5.89/2.03 % (3931)Time elapsed: 0.012 s
% 5.89/2.03 % (3931)Instructions burned: 41 (million)
% 5.89/2.03 % (3931)------------------------------
% 5.89/2.03 % (3931)------------------------------
% 5.89/2.03 % (3934)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3655 for (2995ds/343Mi)
% 5.89/2.04 % (3916)Instruction limit reached!
% 5.89/2.04 % (3916)------------------------------
% 5.89/2.04 % (3916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.04 % (3916)Termination reason: Unknown
% 5.89/2.04 % (3916)Termination phase: Saturation
% 5.89/2.04
% 5.89/2.04 % (3916)Memory used [KB]: 7547
% 5.89/2.04 % (3916)Time elapsed: 0.165 s
% 5.89/2.04 % (3916)Instructions burned: 510 (million)
% 5.89/2.04 % (3916)------------------------------
% 5.89/2.04 % (3916)------------------------------
% 5.89/2.04 % (3935)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_3655 for (2995ds/109Mi)
% 5.89/2.05 % (3936)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_3655 for (2994ds/253Mi)
% 5.89/2.05 % (3923)Instruction limit reached!
% 5.89/2.05 % (3923)------------------------------
% 5.89/2.05 % (3923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.05 % (3923)Termination reason: Unknown
% 5.89/2.05 % (3923)Termination phase: Saturation
% 5.89/2.05
% 5.89/2.05 % (3923)Memory used [KB]: 3326
% 5.89/2.05 % (3923)Time elapsed: 0.110 s
% 5.89/2.05 % (3923)Instructions burned: 434 (million)
% 5.89/2.05 % (3923)------------------------------
% 5.89/2.05 % (3923)------------------------------
% 5.89/2.06 % (3937)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3655 for (2994ds/140Mi)
% 5.89/2.07 % (3935)Instruction limit reached!
% 5.89/2.07 % (3935)------------------------------
% 5.89/2.07 % (3935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.07 % (3935)Termination reason: Unknown
% 5.89/2.07 % (3935)Termination phase: Property scanning
% 5.89/2.07
% 5.89/2.07 % (3935)Memory used [KB]: 2302
% 5.89/2.07 % (3935)Time elapsed: 0.030 s
% 5.89/2.07 % (3935)Instructions burned: 110 (million)
% 5.89/2.07 % (3935)------------------------------
% 5.89/2.07 % (3935)------------------------------
% 5.89/2.07 % (3933)Instruction limit reached!
% 5.89/2.07 % (3933)------------------------------
% 5.89/2.07 % (3933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.07 % (3933)Termination reason: Unknown
% 5.89/2.07 % (3933)Termination phase: Saturation
% 5.89/2.07
% 5.89/2.07 % (3933)Memory used [KB]: 8187
% 5.89/2.07 % (3933)Time elapsed: 0.047 s
% 5.89/2.07 % (3933)Instructions burned: 151 (million)
% 5.89/2.07 % (3933)------------------------------
% 5.89/2.07 % (3933)------------------------------
% 5.89/2.08 % (3938)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_3655 for (2994ds/614Mi)
% 5.89/2.08 % (3939)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_3655 for (2994ds/202Mi)
% 5.89/2.10 % (3927)Instruction limit reached!
% 5.89/2.10 % (3927)------------------------------
% 5.89/2.10 % (3927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.10 % (3927)Termination reason: Unknown
% 5.89/2.10 % (3927)Termination phase: Saturation
% 5.89/2.10
% 5.89/2.10 % (3927)Memory used [KB]: 7036
% 5.89/2.10 % (3927)Time elapsed: 0.116 s
% 5.89/2.10 % (3927)Instructions burned: 456 (million)
% 5.89/2.10 % (3927)------------------------------
% 5.89/2.10 % (3927)------------------------------
% 5.89/2.10 % (3937)Instruction limit reached!
% 5.89/2.10 % (3937)------------------------------
% 5.89/2.10 % (3937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.89/2.10 % (3937)Termination reason: Unknown
% 5.89/2.10 % (3937)Termination phase: Saturation
% 5.89/2.10
% 5.89/2.10 % (3937)Memory used [KB]: 6908
% 5.89/2.10 % (3937)Time elapsed: 0.039 s
% 5.89/2.10 % (3937)Instructions burned: 142 (million)
% 5.89/2.10 % (3937)------------------------------
% 5.89/2.10 % (3937)------------------------------
% 5.89/2.11 % (3940)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_3655 for (2994ds/339Mi)
% 5.89/2.11 % (3941)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_3655 for (2994ds/283Mi)
% 6.39/2.12 % (3936)Instruction limit reached!
% 6.39/2.12 % (3936)------------------------------
% 6.39/2.12 % (3936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.12 % (3936)Termination reason: Unknown
% 6.39/2.12 % (3936)Termination phase: Saturation
% 6.39/2.12
% 6.39/2.12 % (3936)Memory used [KB]: 8699
% 6.39/2.12 % (3936)Time elapsed: 0.078 s
% 6.39/2.12 % (3936)Instructions burned: 255 (million)
% 6.39/2.12 % (3936)------------------------------
% 6.39/2.12 % (3936)------------------------------
% 6.39/2.13 % (3942)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3655 for (2994ds/134Mi)
% 6.39/2.13 % (3934)Instruction limit reached!
% 6.39/2.13 % (3934)------------------------------
% 6.39/2.13 % (3934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.13 % (3934)Termination reason: Unknown
% 6.39/2.13 % (3934)Termination phase: Saturation
% 6.39/2.13
% 6.39/2.13 % (3934)Memory used [KB]: 8187
% 6.39/2.13 % (3934)Time elapsed: 0.104 s
% 6.39/2.13 % (3934)Instructions burned: 345 (million)
% 6.39/2.13 % (3934)------------------------------
% 6.39/2.13 % (3934)------------------------------
% 6.39/2.14 % (3939)Instruction limit reached!
% 6.39/2.14 % (3939)------------------------------
% 6.39/2.14 % (3939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (3939)Termination reason: Unknown
% 6.39/2.14 % (3939)Termination phase: Saturation
% 6.39/2.14
% 6.39/2.14 % (3939)Memory used [KB]: 4733
% 6.39/2.14 % (3939)Time elapsed: 0.061 s
% 6.39/2.14 % (3939)Instructions burned: 204 (million)
% 6.39/2.14 % (3939)------------------------------
% 6.39/2.14 % (3939)------------------------------
% 6.39/2.14 % (3943)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3655 for (2993ds/298Mi)
% 6.39/2.15 % (3944)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3655 for (2993ds/192Mi)
% 6.39/2.17 % (3942)Instruction limit reached!
% 6.39/2.17 % (3942)------------------------------
% 6.39/2.17 % (3942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.17 % (3942)Termination reason: Unknown
% 6.39/2.17 % (3942)Termination phase: Saturation
% 6.39/2.17
% 6.39/2.17 % (3942)Memory used [KB]: 7036
% 6.39/2.17 % (3942)Time elapsed: 0.037 s
% 6.39/2.17 % (3942)Instructions burned: 137 (million)
% 6.39/2.17 % (3942)------------------------------
% 6.39/2.17 % (3942)------------------------------
% 6.39/2.18 % (3945)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_3655 for (2993ds/258Mi)
% 6.39/2.18 % (3941)Instruction limit reached!
% 6.39/2.18 % (3941)------------------------------
% 6.39/2.18 % (3941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.18 % (3941)Termination reason: Unknown
% 6.39/2.18 % (3941)Termination phase: Saturation
% 6.39/2.18
% 6.39/2.18 % (3941)Memory used [KB]: 7036
% 6.39/2.18 % (3941)Time elapsed: 0.072 s
% 6.39/2.18 % (3941)Instructions burned: 284 (million)
% 6.39/2.18 % (3941)------------------------------
% 6.39/2.18 % (3941)------------------------------
% 6.39/2.19 % (3946)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_3655 for (2993ds/90Mi)
% 6.87/2.20 % (3940)Instruction limit reached!
% 6.87/2.20 % (3940)------------------------------
% 6.87/2.20 % (3940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.20 % (3940)Termination reason: Unknown
% 6.87/2.20 % (3940)Termination phase: Saturation
% 6.87/2.20
% 6.87/2.20 % (3940)Memory used [KB]: 7803
% 6.87/2.20 % (3940)Time elapsed: 0.098 s
% 6.87/2.20 % (3940)Instructions burned: 341 (million)
% 6.87/2.20 % (3940)------------------------------
% 6.87/2.20 % (3940)------------------------------
% 6.87/2.21 % (3944)Instruction limit reached!
% 6.87/2.21 % (3944)------------------------------
% 6.87/2.21 % (3944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.21 % (3944)Termination reason: Unknown
% 6.87/2.21 % (3944)Termination phase: Saturation
% 6.87/2.21
% 6.87/2.21 % (3944)Memory used [KB]: 7419
% 6.87/2.21 % (3944)Time elapsed: 0.053 s
% 6.87/2.21 % (3944)Instructions burned: 194 (million)
% 6.87/2.21 % (3944)------------------------------
% 6.87/2.21 % (3944)------------------------------
% 6.87/2.21 % (3947)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_3655 for (2993ds/231Mi)
% 6.87/2.21 % (3946)Instruction limit reached!
% 6.87/2.21 % (3946)------------------------------
% 6.87/2.21 % (3946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.21 % (3946)Termination reason: Unknown
% 6.87/2.21 % (3946)Termination phase: Twee Goal Transformation
% 6.87/2.21
% 6.87/2.21 % (3946)Memory used [KB]: 2558
% 6.87/2.21 % (3946)Time elapsed: 0.026 s
% 6.87/2.21 % (3946)Instructions burned: 91 (million)
% 6.87/2.21 % (3946)------------------------------
% 6.87/2.21 % (3946)------------------------------
% 6.87/2.21 % (3948)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_3655 for (2993ds/458Mi)
% 6.87/2.22 % (3949)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_3655 for (2993ds/31Mi)
% 6.87/2.22 % (3943)Instruction limit reached!
% 6.87/2.22 % (3943)------------------------------
% 6.87/2.22 % (3943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.22 % (3943)Termination reason: Unknown
% 6.87/2.22 % (3943)Termination phase: Saturation
% 6.87/2.22
% 6.87/2.22 % (3943)Memory used [KB]: 6908
% 6.87/2.22 % (3943)Time elapsed: 0.081 s
% 6.87/2.22 % (3943)Instructions burned: 298 (million)
% 6.87/2.22 % (3943)------------------------------
% 6.87/2.22 % (3943)------------------------------
% 6.87/2.23 % (3949)Instruction limit reached!
% 6.87/2.23 % (3949)------------------------------
% 6.87/2.23 % (3949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.23 % (3949)Termination reason: Unknown
% 6.87/2.23 % (3949)Termination phase: Property scanning
% 6.87/2.23
% 6.87/2.23 % (3949)Memory used [KB]: 2046
% 6.87/2.23 % (3949)Time elapsed: 0.010 s
% 6.87/2.23 % (3949)Instructions burned: 34 (million)
% 6.87/2.23 % (3949)------------------------------
% 6.87/2.23 % (3949)------------------------------
% 6.87/2.23 % (3950)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_3655 for (2993ds/297Mi)
% 6.87/2.24 % (3951)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_3655 for (2993ds/987Mi)
% 6.87/2.25 % (3945)Instruction limit reached!
% 6.87/2.25 % (3945)------------------------------
% 6.87/2.25 % (3945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.25 % (3945)Termination reason: Unknown
% 6.87/2.25 % (3945)Termination phase: Saturation
% 6.87/2.25
% 6.87/2.25 % (3945)Memory used [KB]: 7803
% 6.87/2.25 % (3945)Time elapsed: 0.072 s
% 6.87/2.25 % (3945)Instructions burned: 260 (million)
% 6.87/2.25 % (3945)------------------------------
% 6.87/2.25 % (3945)------------------------------
% 6.87/2.26 % (3952)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_3655 for (2992ds/182Mi)
% 6.87/2.26 % (3938)Instruction limit reached!
% 6.87/2.26 % (3938)------------------------------
% 6.87/2.26 % (3938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.26 % (3938)Termination reason: Unknown
% 6.87/2.26 % (3938)Termination phase: Saturation
% 6.87/2.26
% 6.87/2.26 % (3938)Memory used [KB]: 8827
% 6.87/2.26 % (3938)Time elapsed: 0.184 s
% 6.87/2.26 % (3938)Instructions burned: 614 (million)
% 6.87/2.26 % (3938)------------------------------
% 6.87/2.26 % (3938)------------------------------
% 6.87/2.26 % (3920)Instruction limit reached!
% 6.87/2.26 % (3920)------------------------------
% 6.87/2.26 % (3920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.26 % (3920)Termination reason: Unknown
% 6.87/2.26 % (3920)Termination phase: Saturation
% 6.87/2.26
% 6.87/2.26 % (3920)Memory used [KB]: 10874
% 6.87/2.26 % (3920)Time elapsed: 0.347 s
% 6.87/2.26 % (3920)Instructions burned: 1087 (million)
% 6.87/2.26 % (3920)------------------------------
% 6.87/2.26 % (3920)------------------------------
% 6.87/2.27 % (3953)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_3655 for (2992ds/182Mi)
% 6.87/2.27 % (3954)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_3655 for (2992ds/154Mi)
% 6.87/2.28 % (3947)Instruction limit reached!
% 6.87/2.28 % (3947)------------------------------
% 6.87/2.28 % (3947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.87/2.28 % (3947)Termination reason: Unknown
% 6.87/2.28 % (3947)Termination phase: Saturation
% 6.87/2.28
% 6.87/2.28 % (3947)Memory used [KB]: 12281
% 6.87/2.28 % (3947)Time elapsed: 0.066 s
% 6.87/2.28 % (3947)Instructions burned: 232 (million)
% 6.87/2.28 % (3947)------------------------------
% 6.87/2.28 % (3947)------------------------------
% 6.87/2.29 % (3955)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_3655 for (2992ds/79Mi)
% 7.60/2.31 % (3952)Instruction limit reached!
% 7.60/2.31 % (3952)------------------------------
% 7.60/2.31 % (3952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (3952)Termination reason: Unknown
% 7.60/2.31 % (3952)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (3952)Memory used [KB]: 7419
% 7.60/2.31 % (3952)Time elapsed: 0.050 s
% 7.60/2.31 % (3952)Instructions burned: 183 (million)
% 7.60/2.31 % (3952)------------------------------
% 7.60/2.31 % (3952)------------------------------
% 7.60/2.31 % (3955)Instruction limit reached!
% 7.60/2.31 % (3955)------------------------------
% 7.60/2.31 % (3955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (3955)Termination reason: Unknown
% 7.60/2.31 % (3955)Termination phase: Property scanning
% 7.60/2.31
% 7.60/2.31 % (3955)Memory used [KB]: 2174
% 7.60/2.31 % (3955)Time elapsed: 0.022 s
% 7.60/2.31 % (3955)Instructions burned: 81 (million)
% 7.60/2.31 % (3955)------------------------------
% 7.60/2.31 % (3955)------------------------------
% 7.60/2.31 % (3954)Instruction limit reached!
% 7.60/2.31 % (3954)------------------------------
% 7.60/2.31 % (3954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (3954)Termination reason: Unknown
% 7.60/2.31 % (3954)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (3954)Memory used [KB]: 6908
% 7.60/2.31 % (3954)Time elapsed: 0.040 s
% 7.60/2.31 % (3954)Instructions burned: 155 (million)
% 7.60/2.31 % (3954)------------------------------
% 7.60/2.31 % (3954)------------------------------
% 7.60/2.31 % (3950)Instruction limit reached!
% 7.60/2.31 % (3950)------------------------------
% 7.60/2.31 % (3950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (3950)Termination reason: Unknown
% 7.60/2.31 % (3950)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (3950)Memory used [KB]: 7036
% 7.60/2.31 % (3950)Time elapsed: 0.081 s
% 7.60/2.31 % (3950)Instructions burned: 297 (million)
% 7.60/2.31 % (3950)------------------------------
% 7.60/2.31 % (3950)------------------------------
% 7.60/2.32 % (3957)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3655 for (2992ds/114Mi)
% 7.60/2.32 % (3958)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_3655 for (2992ds/922Mi)
% 7.60/2.32 % (3953)Instruction limit reached!
% 7.60/2.32 % (3953)------------------------------
% 7.60/2.32 % (3953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.32 % (3953)Termination reason: Unknown
% 7.60/2.32 % (3953)Termination phase: Saturation
% 7.60/2.32
% 7.60/2.32 % (3953)Memory used [KB]: 10234
% 7.60/2.32 % (3953)Time elapsed: 0.055 s
% 7.60/2.32 % (3953)Instructions burned: 184 (million)
% 7.60/2.32 % (3953)------------------------------
% 7.60/2.32 % (3953)------------------------------
% 7.60/2.32 % (3959)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_3655 for (2992ds/182Mi)
% 7.60/2.33 % (3956)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_3655 for (2992ds/216Mi)
% 7.60/2.33 % (3960)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_3655 for (2992ds/164Mi)
% 7.60/2.35 % (3948)Instruction limit reached!
% 7.60/2.35 % (3948)------------------------------
% 7.60/2.35 % (3948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.35 % (3948)Termination reason: Unknown
% 7.60/2.35 % (3948)Termination phase: Saturation
% 7.60/2.35
% 7.60/2.35 % (3948)Memory used [KB]: 8571
% 7.60/2.35 % (3948)Time elapsed: 0.133 s
% 7.60/2.35 % (3948)Instructions burned: 459 (million)
% 7.60/2.35 % (3948)------------------------------
% 7.60/2.35 % (3948)------------------------------
% 7.60/2.35 % (3957)Instruction limit reached!
% 7.60/2.35 % (3957)------------------------------
% 7.60/2.35 % (3957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.35 % (3957)Termination reason: Unknown
% 7.60/2.35 % (3957)Termination phase: Saturation
% 7.60/2.35
% 7.60/2.35 % (3957)Memory used [KB]: 6908
% 7.60/2.35 % (3957)Time elapsed: 0.032 s
% 7.60/2.35 % (3957)Instructions burned: 117 (million)
% 7.60/2.35 % (3957)------------------------------
% 7.60/2.35 % (3957)------------------------------
% 7.60/2.36 % (3961)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_3655 for (2991ds/50Mi)
% 7.60/2.36 % (3962)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3655 for (2991ds/368Mi)
% 7.60/2.37 % (3961)Instruction limit reached!
% 7.60/2.37 % (3961)------------------------------
% 7.60/2.37 % (3961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (3961)Termination reason: Unknown
% 7.60/2.37 % (3961)Termination phase: Property scanning
% 7.60/2.37
% 7.60/2.37 % (3961)Memory used [KB]: 2046
% 7.60/2.37 % (3961)Time elapsed: 0.015 s
% 7.60/2.37 % (3961)Instructions burned: 51 (million)
% 7.60/2.37 % (3961)------------------------------
% 7.60/2.37 % (3961)------------------------------
% 7.60/2.37 % (3959)Instruction limit reached!
% 7.60/2.37 % (3959)------------------------------
% 7.60/2.37 % (3959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (3959)Termination reason: Unknown
% 7.60/2.37 % (3959)Termination phase: Saturation
% 7.60/2.37
% 7.60/2.37 % (3959)Memory used [KB]: 6908
% 7.60/2.37 % (3959)Time elapsed: 0.049 s
% 7.60/2.37 % (3959)Instructions burned: 184 (million)
% 7.60/2.37 % (3959)------------------------------
% 7.60/2.37 % (3959)------------------------------
% 7.60/2.38 % (3960)Instruction limit reached!
% 7.60/2.38 % (3960)------------------------------
% 7.60/2.38 % (3960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.38 % (3960)Termination reason: Unknown
% 7.60/2.38 % (3960)Termination phase: Saturation
% 7.60/2.38
% 7.60/2.38 % (3960)Memory used [KB]: 2558
% 7.60/2.38 % (3960)Time elapsed: 0.045 s
% 7.60/2.38 % (3960)Instructions burned: 167 (million)
% 7.60/2.38 % (3960)------------------------------
% 7.60/2.38 % (3960)------------------------------
% 7.60/2.38 % (3963)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_3655 for (2991ds/1021Mi)
% 7.60/2.38 % (3964)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_3655 for (2991ds/267Mi)
% 7.60/2.39 % (3965)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_3655 for (2991ds/204Mi)
% 8.21/2.40 % (3956)Instruction limit reached!
% 8.21/2.40 % (3956)------------------------------
% 8.21/2.40 % (3956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.40 % (3956)Termination reason: Unknown
% 8.21/2.40 % (3956)Termination phase: Saturation
% 8.21/2.40
% 8.21/2.40 % (3956)Memory used [KB]: 6908
% 8.21/2.40 % (3956)Time elapsed: 0.077 s
% 8.21/2.40 % (3956)Instructions burned: 219 (million)
% 8.21/2.40 % (3956)------------------------------
% 8.21/2.40 % (3956)------------------------------
% 8.21/2.41 % (3966)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_3655 for (2991ds/26Mi)
% 8.21/2.42 % (3966)Instruction limit reached!
% 8.21/2.42 % (3966)------------------------------
% 8.21/2.42 % (3966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.42 % (3966)Termination reason: Unknown
% 8.21/2.42 % (3966)Termination phase: shuffling
% 8.21/2.42
% 8.21/2.42 % (3966)Memory used [KB]: 1918
% 8.21/2.42 % (3966)Time elapsed: 0.009 s
% 8.21/2.42 % (3966)Instructions burned: 28 (million)
% 8.21/2.42 % (3966)------------------------------
% 8.21/2.42 % (3966)------------------------------
% 8.21/2.43 % (3967)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_3655 for (2991ds/53Mi)
% 8.21/2.44 % (3965)Instruction limit reached!
% 8.21/2.44 % (3965)------------------------------
% 8.21/2.44 % (3965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.44 % (3965)Termination reason: Unknown
% 8.21/2.44 % (3965)Termination phase: Saturation
% 8.21/2.44
% 8.21/2.44 % (3965)Memory used [KB]: 7419
% 8.21/2.44 % (3965)Time elapsed: 0.055 s
% 8.21/2.44 % (3965)Instructions burned: 204 (million)
% 8.21/2.44 % (3965)------------------------------
% 8.21/2.44 % (3965)------------------------------
% 8.21/2.44 % (3967)Instruction limit reached!
% 8.21/2.44 % (3967)------------------------------
% 8.21/2.44 % (3967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.44 % (3967)Termination reason: Unknown
% 8.21/2.44 % (3967)Termination phase: shuffling
% 8.21/2.44
% 8.21/2.44 % (3967)Memory used [KB]: 2174
% 8.21/2.44 % (3967)Time elapsed: 0.016 s
% 8.21/2.44 % (3967)Instructions burned: 53 (million)
% 8.21/2.44 % (3967)------------------------------
% 8.21/2.44 % (3967)------------------------------
% 8.21/2.45 % (3964)Instruction limit reached!
% 8.21/2.45 % (3964)------------------------------
% 8.21/2.45 % (3964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.45 % (3964)Termination reason: Unknown
% 8.21/2.45 % (3964)Termination phase: Saturation
% 8.21/2.45
% 8.21/2.45 % (3964)Memory used [KB]: 6908
% 8.21/2.45 % (3964)Time elapsed: 0.069 s
% 8.21/2.45 % (3964)Instructions burned: 270 (million)
% 8.21/2.45 % (3964)------------------------------
% 8.21/2.45 % (3964)------------------------------
% 8.21/2.45 % (3968)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_3655 for (2991ds/4436Mi)
% 8.21/2.45 % (3969)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_3655 for (2990ds/1539Mi)
% 8.21/2.46 % (3970)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_3655 for (2990ds/408Mi)
% 8.21/2.47 % (3962)Instruction limit reached!
% 8.21/2.47 % (3962)------------------------------
% 8.21/2.47 % (3962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.47 % (3962)Termination reason: Unknown
% 8.21/2.47 % (3962)Termination phase: Saturation
% 8.21/2.47
% 8.21/2.47 % (3962)Memory used [KB]: 8443
% 8.21/2.47 % (3962)Time elapsed: 0.110 s
% 8.21/2.47 % (3962)Instructions burned: 369 (million)
% 8.21/2.47 % (3962)------------------------------
% 8.21/2.47 % (3962)------------------------------
% 8.21/2.48 % (3971)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_3655 for (2990ds/5205Mi)
% 8.21/2.49 % (3951)Instruction limit reached!
% 8.21/2.49 % (3951)------------------------------
% 8.21/2.49 % (3951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.49 % (3951)Termination reason: Unknown
% 8.21/2.49 % (3951)Termination phase: Saturation
% 8.21/2.49
% 8.21/2.49 % (3951)Memory used [KB]: 11385
% 8.21/2.49 % (3951)Time elapsed: 0.247 s
% 8.21/2.49 % (3951)Instructions burned: 989 (million)
% 8.21/2.49 % (3951)------------------------------
% 8.21/2.49 % (3951)------------------------------
% 8.86/2.50 % (3972)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_3655 for (2990ds/1913Mi)
% 8.86/2.59 % (3970)Instruction limit reached!
% 8.86/2.59 % (3970)------------------------------
% 8.86/2.59 % (3970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.86/2.59 % (3970)Termination reason: Unknown
% 8.86/2.59 % (3970)Termination phase: Saturation
% 8.86/2.59
% 8.86/2.59 % (3970)Memory used [KB]: 9850
% 8.86/2.59 % (3970)Time elapsed: 0.127 s
% 8.86/2.59 % (3970)Instructions burned: 408 (million)
% 8.86/2.59 % (3970)------------------------------
% 8.86/2.59 % (3970)------------------------------
% 8.86/2.60 % (3973)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_3655 for (2989ds/4350Mi)
% 9.00/2.61 % (3958)Instruction limit reached!
% 9.00/2.61 % (3958)------------------------------
% 9.00/2.61 % (3958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.61 % (3958)Termination reason: Unknown
% 9.00/2.61 % (3958)Termination phase: Saturation
% 9.00/2.61
% 9.00/2.61 % (3958)Memory used [KB]: 10106
% 9.00/2.61 % (3958)Time elapsed: 0.290 s
% 9.00/2.61 % (3958)Instructions burned: 924 (million)
% 9.00/2.61 % (3958)------------------------------
% 9.00/2.61 % (3958)------------------------------
% 9.00/2.62 % (3974)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_3655 for (2989ds/68Mi)
% 9.00/2.64 % (3974)Instruction limit reached!
% 9.00/2.64 % (3974)------------------------------
% 9.00/2.64 % (3974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.64 % (3974)Termination reason: Unknown
% 9.00/2.64 % (3974)Termination phase: Property scanning
% 9.00/2.64
% 9.00/2.64 % (3974)Memory used [KB]: 2174
% 9.00/2.64 % (3974)Time elapsed: 0.020 s
% 9.00/2.64 % (3974)Instructions burned: 70 (million)
% 9.00/2.64 % (3974)------------------------------
% 9.00/2.64 % (3974)------------------------------
% 9.00/2.65 % (3975)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_3655 for (2988ds/358Mi)
% 9.33/2.70 % (3963)Instruction limit reached!
% 9.33/2.70 % (3963)------------------------------
% 9.33/2.70 % (3963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.70 % (3963)Termination reason: Unknown
% 9.33/2.70 % (3963)Termination phase: Saturation
% 9.33/2.70
% 9.33/2.70 % (3963)Memory used [KB]: 10874
% 9.33/2.70 % (3963)Time elapsed: 0.321 s
% 9.33/2.70 % (3963)Instructions burned: 1022 (million)
% 9.33/2.70 % (3963)------------------------------
% 9.33/2.70 % (3963)------------------------------
% 9.33/2.71 % (3976)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_3655 for (2988ds/31Mi)
% 9.33/2.72 % (3976)Instruction limit reached!
% 9.33/2.72 % (3976)------------------------------
% 9.33/2.72 % (3976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.72 % (3976)Termination reason: Unknown
% 9.33/2.72 % (3976)Termination phase: Property scanning
% 9.33/2.72
% 9.33/2.72 % (3976)Memory used [KB]: 1918
% 9.33/2.72 % (3976)Time elapsed: 0.011 s
% 9.33/2.72 % (3976)Instructions burned: 34 (million)
% 9.33/2.72 % (3976)------------------------------
% 9.33/2.72 % (3976)------------------------------
% 9.33/2.73 % (3977)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3655 for (2988ds/279Mi)
% 9.33/2.75 % (3975)Instruction limit reached!
% 9.33/2.75 % (3975)------------------------------
% 9.33/2.75 % (3975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.75 % (3975)Termination reason: Unknown
% 9.33/2.75 % (3975)Termination phase: Saturation
% 9.33/2.75
% 9.33/2.75 % (3975)Memory used [KB]: 8059
% 9.33/2.75 % (3975)Time elapsed: 0.101 s
% 9.33/2.75 % (3975)Instructions burned: 358 (million)
% 9.33/2.75 % (3975)------------------------------
% 9.33/2.75 % (3975)------------------------------
% 9.33/2.76 % (3978)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3655 for (2987ds/258Mi)
% 9.80/2.80 % (3977)Instruction limit reached!
% 9.80/2.80 % (3977)------------------------------
% 9.80/2.80 % (3977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.80 % (3977)Termination reason: Unknown
% 9.80/2.80 % (3977)Termination phase: Saturation
% 9.80/2.80
% 9.80/2.80 % (3977)Memory used [KB]: 7036
% 9.80/2.80 % (3977)Time elapsed: 0.072 s
% 9.80/2.80 % (3977)Instructions burned: 279 (million)
% 9.80/2.80 % (3977)------------------------------
% 9.80/2.80 % (3977)------------------------------
% 9.80/2.81 % (3979)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_3655 for (2987ds/26Mi)
% 9.80/2.82 % (3979)Instruction limit reached!
% 9.80/2.82 % (3979)------------------------------
% 9.80/2.82 % (3979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.82 % (3979)Termination reason: Unknown
% 9.80/2.82 % (3979)Termination phase: shuffling
% 9.80/2.82
% 9.80/2.82 % (3979)Memory used [KB]: 1918
% 9.80/2.82 % (3979)Time elapsed: 0.008 s
% 9.80/2.82 % (3979)Instructions burned: 26 (million)
% 9.80/2.82 % (3979)------------------------------
% 9.80/2.82 % (3979)------------------------------
% 9.80/2.83 % (3980)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_3655 for (2987ds/995Mi)
% 9.80/2.83 % (3978)Instruction limit reached!
% 9.80/2.83 % (3978)------------------------------
% 9.80/2.83 % (3978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.83 % (3978)Termination reason: Unknown
% 9.80/2.83 % (3978)Termination phase: Saturation
% 9.80/2.83
% 9.80/2.83 % (3978)Memory used [KB]: 8315
% 9.80/2.83 % (3978)Time elapsed: 0.073 s
% 9.80/2.83 % (3978)Instructions burned: 259 (million)
% 9.80/2.83 % (3978)------------------------------
% 9.80/2.83 % (3978)------------------------------
% 9.80/2.84 % (3981)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_3655 for (2987ds/373Mi)
% 9.98/2.92 % (3969)Instruction limit reached!
% 9.98/2.92 % (3969)------------------------------
% 9.98/2.92 % (3969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.92 % (3969)Termination reason: Unknown
% 9.98/2.92 % (3969)Termination phase: Saturation
% 9.98/2.92
% 9.98/2.92 % (3969)Memory used [KB]: 8955
% 9.98/2.92 % (3969)Time elapsed: 0.468 s
% 9.98/2.92 % (3969)Instructions burned: 1539 (million)
% 9.98/2.92 % (3969)------------------------------
% 9.98/2.92 % (3969)------------------------------
% 9.98/2.93 % (3982)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_3655 for (2986ds/253Mi)
% 9.98/2.95 % (3981)Instruction limit reached!
% 9.98/2.95 % (3981)------------------------------
% 9.98/2.95 % (3981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.95 % (3981)Termination reason: Unknown
% 9.98/2.95 % (3981)Termination phase: Saturation
% 9.98/2.95
% 9.98/2.95 % (3981)Memory used [KB]: 8187
% 9.98/2.95 % (3981)Time elapsed: 0.109 s
% 9.98/2.95 % (3981)Instructions burned: 373 (million)
% 9.98/2.95 % (3981)------------------------------
% 9.98/2.95 % (3981)------------------------------
% 9.98/2.95 % (3983)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_3655 for (2985ds/832Mi)
% 9.98/2.99 % (3982)Instruction limit reached!
% 9.98/2.99 % (3982)------------------------------
% 9.98/2.99 % (3982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.99 % (3982)Termination reason: Unknown
% 9.98/2.99 % (3982)Termination phase: Saturation
% 9.98/2.99
% 9.98/2.99 % (3982)Memory used [KB]: 7164
% 9.98/2.99 % (3982)Time elapsed: 0.065 s
% 9.98/2.99 % (3982)Instructions burned: 255 (million)
% 9.98/2.99 % (3982)------------------------------
% 9.98/2.99 % (3982)------------------------------
% 12.95/3.02 % (3984)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_3655 for (2985ds/668Mi)
% 12.95/3.05 % (3983)First to succeed.
% 12.95/3.06 % (3983)Refutation found. Thanks to Tanya!
% 12.95/3.06 % SZS status Theorem for DTF2THF_3655
% 12.95/3.06 % SZS output start Proof for DTF2THF_3655
% 12.95/3.06 thf(func_def_0, type, in: $i > $i > $o).
% 12.95/3.06 thf(func_def_1, type, exu: ($i > $o) > $o).
% 12.95/3.06 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 12.95/3.06 thf(func_def_8, type, powerset: $i > $i).
% 12.95/3.06 thf(func_def_10, type, setunion: $i > $i).
% 12.95/3.06 thf(func_def_19, type, descr: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_26, type, prop2set: $o > $i).
% 12.95/3.06 thf(func_def_36, type, nonempty: $i > $o).
% 12.95/3.06 thf(func_def_69, type, set2prop: $i > $o).
% 12.95/3.06 thf(func_def_88, type, subset: $i > $i > $o).
% 12.95/3.06 thf(func_def_89, type, disjoint: $i > $i > $o).
% 12.95/3.06 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 12.95/3.06 thf(func_def_114, type, binunion: $i > $i > $i).
% 12.95/3.06 thf(func_def_122, type, binintersect: $i > $i > $i).
% 12.95/3.06 thf(func_def_135, type, regular: $i > $o).
% 12.95/3.06 thf(func_def_136, type, setminus: $i > $i > $i).
% 12.95/3.06 thf(func_def_147, type, symdiff: $i > $i > $i).
% 12.95/3.06 thf(func_def_153, type, iskpair: $i > $o).
% 12.95/3.06 thf(func_def_158, type, kpair: $i > $i > $i).
% 12.95/3.06 thf(func_def_160, type, cartprod: $i > $i > $i).
% 12.95/3.06 thf(func_def_177, type, singleton: $i > $o).
% 12.95/3.06 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 12.95/3.06 thf(func_def_184, type, atmost1p: $i > $o).
% 12.95/3.06 thf(func_def_185, type, atleast2p: $i > $o).
% 12.95/3.06 thf(func_def_186, type, atmost2p: $i > $o).
% 12.95/3.06 thf(func_def_187, type, upairsetp: $i > $o).
% 12.95/3.06 thf(func_def_191, type, kfst: $i > $i).
% 12.95/3.06 thf(func_def_203, type, ksnd: $i > $i).
% 12.95/3.06 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 12.95/3.06 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 12.95/3.06 thf(func_def_222, type, func: $i > $i > $i > $o).
% 12.95/3.06 thf(func_def_223, type, funcSet: $i > $i > $i).
% 12.95/3.06 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 12.95/3.06 thf(func_def_249, type, sP2: $i > $i > $i > $o > $o).
% 12.95/3.06 thf(func_def_251, type, sP4: $i > $i > $o).
% 12.95/3.06 thf(func_def_252, type, sP5: $i > $o).
% 12.95/3.06 thf(func_def_253, type, sP6: $i > $i > $o).
% 12.95/3.06 thf(func_def_254, type, sP7: $i > $i > $o).
% 12.95/3.06 thf(func_def_263, type, sK16: $i > $i > $i).
% 12.95/3.06 thf(func_def_268, type, sK21: $i > $o).
% 12.95/3.06 thf(func_def_270, type, sK23: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_271, type, sK24: $i > $o).
% 12.95/3.06 thf(func_def_272, type, sK25: $i > $o).
% 12.95/3.06 thf(func_def_273, type, sK26: ($i > $o) > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_274, type, sK27: ($i > $o) > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_275, type, sK28: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_277, type, sK30: $i > $o).
% 12.95/3.06 thf(func_def_296, type, sK49: $i > $o).
% 12.95/3.06 thf(func_def_298, type, sK51: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_299, type, sK52: $i > $i).
% 12.95/3.06 thf(func_def_321, type, sK74: $i > $i > $i).
% 12.95/3.06 thf(func_def_324, type, sK77: $i > $i > $i).
% 12.95/3.06 thf(func_def_331, type, sK84: $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_332, type, sK85: $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_349, type, sK102: $i > $o).
% 12.95/3.06 thf(func_def_364, type, sK117: $i > $i > $o).
% 12.95/3.06 thf(func_def_373, type, sK126: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_374, type, sK127: $i > $o).
% 12.95/3.06 thf(func_def_375, type, sK128: $i > $i).
% 12.95/3.06 thf(func_def_380, type, sK133: $i > $i).
% 12.95/3.06 thf(func_def_392, type, sK145: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_393, type, sK146: $i > $o).
% 12.95/3.06 thf(func_def_394, type, sK147: $i > $i).
% 12.95/3.06 thf(func_def_399, type, sK152: $i > $i).
% 12.95/3.06 thf(func_def_402, type, sK155: $i > $i > $o).
% 12.95/3.06 thf(func_def_408, type, sK161: $i > $i > $o).
% 12.95/3.06 thf(func_def_410, type, sK163: $i > $i).
% 12.95/3.06 thf(func_def_411, type, sK164: $i > $i).
% 12.95/3.06 thf(func_def_412, type, sK165: $i > ($i > $i > $o) > $i).
% 12.95/3.06 thf(func_def_413, type, sK166: $i > ($i > $i > $o) > $i).
% 12.95/3.06 thf(func_def_414, type, sK167: $i > $i > ($i > $i > $o) > $i).
% 12.95/3.06 thf(func_def_419, type, sK172: $i > $i > $o).
% 12.95/3.06 thf(func_def_421, type, sK174: $i > $o).
% 12.95/3.06 thf(func_def_438, type, sK191: $i > $o).
% 12.95/3.06 thf(func_def_441, type, sK194: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_442, type, sK195: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_443, type, sK196: $i > $o).
% 12.95/3.06 thf(func_def_446, type, sK199: $i > $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_451, type, sK204: $i > $o).
% 12.95/3.06 thf(func_def_456, type, sK209: $i > $i).
% 12.95/3.06 thf(func_def_458, type, sK211: $i > $i).
% 12.95/3.06 thf(func_def_479, type, sK232: $i > $i > $o).
% 12.95/3.06 thf(func_def_493, type, sK246: $i > $i).
% 12.95/3.06 thf(func_def_517, type, sK270: $i > $o).
% 12.95/3.06 thf(func_def_521, type, sK274: $i > $i).
% 12.95/3.06 thf(func_def_535, type, sK288: $i > $i > $i).
% 12.95/3.06 thf(func_def_536, type, sK289: $o > $i > $i > $i).
% 12.95/3.06 thf(func_def_554, type, sK307: $i > $o).
% 12.95/3.06 thf(func_def_555, type, sK308: $i > $o).
% 12.95/3.06 thf(func_def_556, type, sK309: ($i > $o) > ($i > $o) > $i > $i > $i).
% 12.95/3.06 thf(func_def_557, type, sK310: ($i > $o) > ($i > $o) > $i > $i > $i).
% 12.95/3.06 thf(func_def_561, type, sK314: $i > $o).
% 12.95/3.06 thf(func_def_563, type, sK316: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_572, type, sK325: $i > $i > $o).
% 12.95/3.06 thf(func_def_582, type, sK335: $i > $o).
% 12.95/3.06 thf(func_def_584, type, sK337: $i > $i > ($i > $i) > $i).
% 12.95/3.06 thf(func_def_585, type, sK338: $i > $i).
% 12.95/3.06 thf(func_def_590, type, sK343: $i > $o).
% 12.95/3.06 thf(func_def_596, type, sK349: $i > ($i > $i) > $i > $i).
% 12.95/3.06 thf(func_def_598, type, sK351: $i > $i).
% 12.95/3.06 thf(func_def_601, type, sK354: $i > $o).
% 12.95/3.06 thf(func_def_603, type, sK356: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_605, type, sK358: $i > $o).
% 12.95/3.06 thf(func_def_607, type, sK360: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_608, type, sK361: $i > $o).
% 12.95/3.06 thf(func_def_611, type, sK364: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_612, type, sK365: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_619, type, sK372: $i > $o).
% 12.95/3.06 thf(func_def_634, type, sK387: $i > $i > $i).
% 12.95/3.06 thf(func_def_650, type, sK403: $i > $o).
% 12.95/3.06 thf(func_def_652, type, sK405: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_653, type, sK406: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_658, type, sK411: $i > $o).
% 12.95/3.06 thf(func_def_663, type, sK416: $i > $i > $i).
% 12.95/3.06 thf(func_def_670, type, sK423: $i > $o).
% 12.95/3.06 thf(func_def_673, type, sK426: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_677, type, sK430: $i > $o).
% 12.95/3.06 thf(func_def_690, type, sK443: $i > $o).
% 12.95/3.06 thf(func_def_691, type, sK444: $i > $o).
% 12.95/3.06 thf(func_def_692, type, sK445: ($i > $o) > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_693, type, sK446: ($i > $o) > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_698, type, sK451: $i > $o).
% 12.95/3.06 thf(func_def_699, type, sK452: ($i > $o) > $i).
% 12.95/3.06 thf(func_def_706, type, sK459: $i > $i > $o).
% 12.95/3.06 thf(func_def_715, type, sK468: $i > $o).
% 12.95/3.06 thf(func_def_717, type, sK470: $i > ($i > $o) > $i).
% 12.95/3.06 thf(func_def_722, type, sK475: $i > $i > $i).
% 12.95/3.06 thf(func_def_725, type, sK478: $i > $o).
% 12.95/3.06 thf(func_def_730, type, sK483: $i > $i > $i).
% 12.95/3.06 thf(func_def_731, type, sK484: $i > $i > $i).
% 12.95/3.06 thf(func_def_732, type, sK485: $i > $i > $i).
% 12.95/3.06 thf(func_def_733, type, sK486: $i > $i > $i).
% 12.95/3.06 thf(func_def_734, type, sK487: $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_735, type, sK488: $i > $i).
% 12.95/3.06 thf(func_def_736, type, sK489: $i > $i).
% 12.95/3.06 thf(func_def_737, type, sK490: $i > $i).
% 12.95/3.06 thf(func_def_738, type, sK491: $i > $i).
% 12.95/3.06 thf(func_def_739, type, sK492: $i > $i > $i).
% 12.95/3.06 thf(func_def_740, type, sK493: $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_741, type, sK494: $i > $i > $i > $i).
% 12.95/3.06 thf(func_def_742, type, sK495: $i > $i > $i).
% 12.95/3.06 thf(func_def_743, type, sK496: $i > $i > $i).
% 12.95/3.06 thf(func_def_745, type, sK498: $i > $i).
% 12.95/3.06 thf(func_def_746, type, sK499: $i > $i).
% 12.95/3.06 thf(func_def_747, type, sK500: $i > $i).
% 12.95/3.06 thf(func_def_748, type, sK501: $i > $i > $i).
% 12.95/3.06 thf(func_def_762, type, sK515: $i > $i > $i).
% 12.95/3.06 thf(func_def_765, type, sK518: $i > $i > $i).
% 12.95/3.06 thf(func_def_766, type, sK519: $i > $i > $i).
% 12.95/3.06 thf(func_def_781, type, sK534: $i > $o).
% 12.95/3.06 thf(func_def_782, type, sK535: $i > $i).
% 12.95/3.06 thf(func_def_800, type, sK553: $i > $o).
% 12.95/3.06 thf(func_def_801, type, sK554: ($i > $o) > $i > $i).
% 12.95/3.06 thf(func_def_805, type, sK558: $i > $o).
% 12.95/3.06 thf(func_def_810, type, sK563: $i > $i > $o).
% 12.95/3.06 thf(func_def_821, type, ph574: !>[X0: $tType]:(X0)).
% 12.95/3.06 thf(f3177,plain,(
% 12.95/3.06 $false),
% 12.95/3.06 inference(subsumption_resolution,[status(thm)],[f3173,f3159])).
% 12.95/3.06 thf(f3159,plain,(
% 12.95/3.06 ((in @ (sK349 @ sK244 @ sK246 @ sK245) @ sK244) = $true)),
% 12.95/3.06 inference(subsumption_resolution,[status(thm)],[f3158,f2103])).
% 12.95/3.06 thf(f2103,plain,(
% 12.95/3.06 (lamp = $true)),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1233])).
% 12.95/3.06 thf(f1233,plain,(
% 12.95/3.06 (setminusERneg = $true) & (singletonsuniq = $true) & (cartprodfstin = $true) & (powersetI = $true) & (nonemptyI = $true) & (secondinupair = $true) & (nonemptyImpWitness = $true) & (kpairiskpair = $true) & (subsetemptysetimpeq = $true) & (setadjoinSub2 = $true) & (bs114d = $true) & (binunionIR = $true) & (emptyinunitempty = $true) & (setminusER = $true) & (ubforcartprodlem1 = $true) & (setoftrueEq = $true) & (in__Cong = $true) & (lamProp = $true) & (descr__Cong = $true) & (kpairp = $true) & (setunionI = $true) & (exuI3 = $true) & (setukpairinjL1 = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (emptysetAx = $true) & (eqimpsubset2 = $true) & (setminusLsub = $true) & (setunionsingleton2 = $true) & (emptysetE = $true) & (notdallE = $true) & (ksndpairEq = $true) & (setadjoinOr = $true) & (disjointsetsI1 = $true) & (dpsetconstrERa = $true) & (vacuousDall = $true) & (upairsubunion = $true) & (eqinunit = $true) & (funcImageSingleton = $true) & (exuI2 = $true) & (setadjoinAx = $true) & (cartprodpairmemEL = $true) & (powersetI1 = $true) & (dpsetconstrEL1 = $true) & (notinsingleton = $true) & (emptyE1 = $true) & (ubforcartprodlem2 = $true) & (setadjoinE = $true) & (powersetAx = $true) & (setminusSubset1 = $true) & (exuE3u = $true) & (symdiffI1 = $true) & (ex1E1 = $true) & (setukpairinjR = $true) & (binintersectSubset5 = $true) & (ksndsingleton = $true) & (exuEu = $true) & (setadjoinSub = $true) & (binunionEcases = $true) & (descrp = $true) & (subsetRefl = $true) & (setminusILneg = $true) & (powersetE1 = $true) & (subsetI1 = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (binunionLsub = $true) & (setukpairinjL = $true) & (powerset__Cong = $true) & (binunionE = $true) & (dpsetconstrEL2 = $true) & (cartprodpairin = $true) & (infuncsetfunc = $true) & (prop2set2propI = $true) & (dsetconstrI = $true) & (singletoninpowerset = $true) & (cartprodmempair = $true) & (setadjoin__Cong = $true) & (binunionIL = $true) & (binintersectER = $true) & (setunionE = $true) & (upairsetIL = $true) & (upairequniteq = $true) & (funcinfuncset = $true) & (setunionsingleton = $true) & (singletonsubset = $true) & (dpsetconstrI = $true) & (cartprodpairmemER = $true) & (binintersectSubset3 = $true) & (dpsetconstrER = $true) & (exuE3e = $true) & (quantDeMorgan1 = $true) & (setukpairIL = $true) & (foundationAx = $true) & (subPowSU = $true) & (setbeta = $true) & (upairsetIR = $true) & (nonemptyE1 = $true) & (setunionAx = $true) & (omega0Ax = $true) & (dsetconstrER = $true) & (setukpairinjR11 = $true) & (singletonprop = $true) & (cartprodsndin = $true) & (notequalI2 = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (cartprodmempaircEq = $true) & (app = $true) & (subsetE = $true) & (binintersectRsub = $true) & (setukpairinjL2 = $true) & (nonemptyI1 = $true) & (sepInPowerset = $true) & (setukpairinjR1 = $true) & (symdiffIneg1 = $true) & (subsetTrans = $true) & (symdiffIneg2 = $true) & (setunionE2 = $true) & (setextsub = $true) & (kpairsurjEq = $true) & (setminusEL = $true) & (singletoninpowunion = $true) & (ex1I = $true) & (cartprodmempair1 = $true) & (emptyInPowerset = $true) & (notdexE = $true) & (setukpairinjR2 = $true) & (upairsetE = $true) & (powersetE = $true) & (((in @ (lam @ sK244 @ sK245 @ (^[Y0 : $i]: (sK246 @ Y0))) @ (funcSet @ sK244 @ sK245)) != $true) & ! [X3 : $i] : (((in @ X3 @ sK244) != $true) | ((in @ (sK246 @ X3) @ sK245) = $true))) & (binintersectSubset1 = $true) & (prop2setI = $true) & (omegaIndAx = $true) & (omega__Cong = $true) & (notequalI1 = $true) & (exuI1 = $true) & (inCongP = $true) & (notinemptyset = $true) & (symdiffI2 = $true) & (quantDeMorgan3 = $true) & (cartprodsndpairEq = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (emptysetsubset = $true) & (singletonsswitch = $true) & (binintersectEL = $true) & (setminusSubset2 = $true) & (setunionsingleton1 = $true) & (theprop = $true) & (emptyset__Cong = $true) & (emptyI = $true) & (upairinpowunion = $true) & (powersetsubset = $true) & (upairset2IR = $true) & (exu__Cong = $true) & (setminusI = $true) & (setadjoinIL = $true) & (setunion__Cong = $true) & (lamp = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (setextAx = $true) & (exuE2 = $true) & (setminusELneg = $true) & (sepSubset = $true) & (uniqinunit = $true) & (upairset2E = $true) & (ex1I2 = $true) & (emptyinPowerset = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (dpsetconstrSub = $true) & (omegaSAx = $true) & (subsetI2 = $true) & (symdiffE = $true) & (inPowerset = $true) & (subset2powerset = $true) & (cartprodpairsurjEq = $true) & (exuE1 = $true) & (setext = $true) & (notsubsetI = $true) & (ap2p = $true) & (subsetE2 = $true) & (setukpairinjR12 = $true) & (binintersectI = $true) & (setOfPairsIsBReln = $true) & (dsetconstr__Cong = $true) & (setminusIRneg = $true) & (cartprodfstpairEq = $true) & (quantDeMorgan2 = $true) & (kfstpairEq = $true) & (apProp = $true) & (kfstsingleton = $true) & (quantDeMorgan4 = $true) & (binunionRsub = $true)),
% 12.95/3.06 inference(skolemisation,[status(esa),new_symbols(skolem,[sK244,sK245,sK246])],[f754,f1232])).
% 12.95/3.06 thf(f1232,plain,(
% 12.95/3.06 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (($true != (in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (in @ (X2 @ X3) @ X1)))) => (((in @ (lam @ sK244 @ sK245 @ (^[Y0 : $i]: (sK246 @ Y0))) @ (funcSet @ sK244 @ sK245)) != $true) & ! [X3 : $i] : (((in @ X3 @ sK244) != $true) | ((in @ (sK246 @ X3) @ sK245) = $true)))),
% 12.95/3.06 introduced(definition,[],[choice_axiom])).
% 12.95/3.06 thf(f754,plain,(
% 12.95/3.06 (setminusERneg = $true) & (singletonsuniq = $true) & (cartprodfstin = $true) & (powersetI = $true) & (nonemptyI = $true) & (secondinupair = $true) & (nonemptyImpWitness = $true) & (kpairiskpair = $true) & (subsetemptysetimpeq = $true) & (setadjoinSub2 = $true) & (bs114d = $true) & (binunionIR = $true) & (emptyinunitempty = $true) & (setminusER = $true) & (ubforcartprodlem1 = $true) & (setoftrueEq = $true) & (in__Cong = $true) & (lamProp = $true) & (descr__Cong = $true) & (kpairp = $true) & (setunionI = $true) & (exuI3 = $true) & (setukpairinjL1 = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (emptysetAx = $true) & (eqimpsubset2 = $true) & (setminusLsub = $true) & (setunionsingleton2 = $true) & (emptysetE = $true) & (notdallE = $true) & (ksndpairEq = $true) & (setadjoinOr = $true) & (disjointsetsI1 = $true) & (dpsetconstrERa = $true) & (vacuousDall = $true) & (upairsubunion = $true) & (eqinunit = $true) & (funcImageSingleton = $true) & (exuI2 = $true) & (setadjoinAx = $true) & (cartprodpairmemEL = $true) & (powersetI1 = $true) & (dpsetconstrEL1 = $true) & (notinsingleton = $true) & (emptyE1 = $true) & (ubforcartprodlem2 = $true) & (setadjoinE = $true) & (powersetAx = $true) & (setminusSubset1 = $true) & (exuE3u = $true) & (symdiffI1 = $true) & (ex1E1 = $true) & (setukpairinjR = $true) & (binintersectSubset5 = $true) & (ksndsingleton = $true) & (exuEu = $true) & (setadjoinSub = $true) & (binunionEcases = $true) & (descrp = $true) & (subsetRefl = $true) & (setminusILneg = $true) & (powersetE1 = $true) & (subsetI1 = $true) & (prop2setE = $true) & (dsetconstrEL = $true) & (binunionLsub = $true) & (setukpairinjL = $true) & (powerset__Cong = $true) & (binunionE = $true) & (dpsetconstrEL2 = $true) & (cartprodpairin = $true) & (infuncsetfunc = $true) & (prop2set2propI = $true) & (dsetconstrI = $true) & (singletoninpowerset = $true) & (cartprodmempair = $true) & (setadjoin__Cong = $true) & (binunionIL = $true) & (binintersectER = $true) & (setunionE = $true) & (upairsetIL = $true) & (upairequniteq = $true) & (funcinfuncset = $true) & (setunionsingleton = $true) & (singletonsubset = $true) & (dpsetconstrI = $true) & (cartprodpairmemER = $true) & (binintersectSubset3 = $true) & (dpsetconstrER = $true) & (exuE3e = $true) & (quantDeMorgan1 = $true) & (setukpairIL = $true) & (foundationAx = $true) & (subPowSU = $true) & (setbeta = $true) & (upairsetIR = $true) & (nonemptyE1 = $true) & (setunionAx = $true) & (omega0Ax = $true) & (dsetconstrER = $true) & (setukpairinjR11 = $true) & (singletonprop = $true) & (cartprodsndin = $true) & (notequalI2 = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (cartprodmempaircEq = $true) & (app = $true) & (subsetE = $true) & (binintersectRsub = $true) & (setukpairinjL2 = $true) & (nonemptyI1 = $true) & (sepInPowerset = $true) & (setukpairinjR1 = $true) & (symdiffIneg1 = $true) & (subsetTrans = $true) & (symdiffIneg2 = $true) & (setunionE2 = $true) & (setextsub = $true) & (kpairsurjEq = $true) & (setminusEL = $true) & (singletoninpowunion = $true) & (ex1I = $true) & (cartprodmempair1 = $true) & (emptyInPowerset = $true) & (notdexE = $true) & (setukpairinjR2 = $true) & (upairsetE = $true) & (powersetE = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i] : (($true != (in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (in @ (X2 @ X3) @ X1)))) & (binintersectSubset1 = $true) & (prop2setI = $true) & (omegaIndAx = $true) & (omega__Cong = $true) & (notequalI1 = $true) & (exuI1 = $true) & (inCongP = $true) & (notinemptyset = $true) & (symdiffI2 = $true) & (quantDeMorgan3 = $true) & (cartprodsndpairEq = $true) & (wellorderingAx = $true) & (noeltsimpempty = $true) & (emptysetsubset = $true) & (singletonsswitch = $true) & (binintersectEL = $true) & (setminusSubset2 = $true) & (setunionsingleton1 = $true) & (theprop = $true) & (emptyset__Cong = $true) & (emptyI = $true) & (upairinpowunion = $true) & (powersetsubset = $true) & (upairset2IR = $true) & (exu__Cong = $true) & (setminusI = $true) & (setadjoinIL = $true) & (setunion__Cong = $true) & (lamp = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (setextAx = $true) & (exuE2 = $true) & (setminusELneg = $true) & (sepSubset = $true) & (uniqinunit = $true) & (upairset2E = $true) & (ex1I2 = $true) & (emptyinPowerset = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (dpsetconstrSub = $true) & (omegaSAx = $true) & (subsetI2 = $true) & (symdiffE = $true) & (inPowerset = $true) & (subset2powerset = $true) & (cartprodpairsurjEq = $true) & (exuE1 = $true) & (setext = $true) & (notsubsetI = $true) & (ap2p = $true) & (subsetE2 = $true) & (setukpairinjR12 = $true) & (binintersectI = $true) & (setOfPairsIsBReln = $true) & (dsetconstr__Cong = $true) & (setminusIRneg = $true) & (cartprodfstpairEq = $true) & (quantDeMorgan2 = $true) & (kfstpairEq = $true) & (apProp = $true) & (kfstsingleton = $true) & (quantDeMorgan4 = $true) & (binunionRsub = $true)),
% 12.95/3.06 inference(flattening,[status(thm)],[f753])).
% 12.95/3.06 thf(f753,plain,(
% 12.95/3.06 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i > $i] : (($true != (in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) & ! [X3 : $i] : (($true != (in @ X3 @ X0)) | ($true = (in @ (X2 @ X3) @ X1)))) & (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)),
% 12.95/3.06 inference(ennf_transformation,[status(thm)],[f293])).
% 12.95/3.06 thf(f293,plain,(
% 12.95/3.06 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (in @ (X2 @ X3) @ X1))) => ($true = (in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 12.95/3.06 inference(fool_elimination,[status(thm)],[f292])).
% 12.95/3.06 thf(f292,plain,(
% 12.95/3.06 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X4 : $i] : (X2 @ X4))) @ (funcSet @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 12.95/3.06 inference(rectify,[status(thm)],[f206])).
% 12.95/3.06 thf(f206,negated_conjecture,(
% 12.95/3.06 ~(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 => ! [X3 : $i,X4 : $i,X13 : $i > $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (in @ (lam @ X3 @ X4 @ (^[X1 : $i] : (X13 @ X1))) @ (funcSet @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 12.95/3.06 inference(negated_conjecture,[status(cth)],[f205])).
% 12.95/3.06 thf(f205,conjecture,(
% 12.95/3.06 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 => ! [X3 : $i,X4 : $i,X13 : $i > $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (in @ (lam @ X3 @ X4 @ (^[X1 : $i] : (X13 @ X1))) @ (funcSet @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 12.95/3.06 file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',lam2p)).
% 12.95/3.06 thf(f3158,plain,(
% 12.95/3.06 ((in @ (sK349 @ sK244 @ sK246 @ sK245) @ sK244) = $true) | (lamp != $true)),
% 12.95/3.06 inference(trivial_inequality_removal,[status(thm)],[f3156])).
% 12.95/3.06 thf(f3156,plain,(
% 12.95/3.06 ((in @ (sK349 @ sK244 @ sK246 @ sK245) @ sK244) = $true) | ($true != $true) | (lamp != $true)),
% 12.95/3.06 inference(superposition,[status(thm)],[f3038,f2835])).
% 12.95/3.06 thf(f2835,plain,(
% 12.95/3.06 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ X1)) = $true) | (lamp != $true) | ($true = (in @ (sK349 @ X2 @ X1 @ X0) @ X2))) )),
% 12.95/3.06 inference(beta_eta_normalization,[status(thm)],[f2403])).
% 12.95/3.06 thf(f2403,plain,(
% 12.95/3.06 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : ((lamp != $true) | ((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ($true = (in @ (sK349 @ X2 @ X1 @ X0) @ X2))) )),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1409])).
% 12.95/3.06 thf(f1409,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | (($true = (in @ (sK349 @ X2 @ X1 @ X0) @ X2)) & ((in @ (X1 @ (sK349 @ X2 @ X1 @ X0)) @ X0) != $true))) | (lamp != $true)) & ((lamp = $true) | (($true != (func @ sK352 @ sK350 @ (lam @ sK352 @ sK350 @ (^[Y0 : $i]: (sK351 @ Y0))))) & ! [X7 : $i] : (($true != (in @ X7 @ sK352)) | ((in @ (sK351 @ X7) @ sK350) = $true))))),
% 12.95/3.06 inference(skolemisation,[status(esa),new_symbols(skolem,[sK349,sK350,sK351,sK352])],[f1406,f1408,f1407])).
% 12.95/3.06 thf(f1407,plain,(
% 12.95/3.06 ! [X0 : $i,X1 : $i > $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ (X1 @ X3) @ X0) != $true)) => (($true = (in @ (sK349 @ X2 @ X1 @ X0) @ X2)) & ((in @ (X1 @ (sK349 @ X2 @ X1 @ X0)) @ X0) != $true)))),
% 12.95/3.06 introduced(definition,[],[choice_axiom])).
% 12.95/3.06 thf(f1408,plain,(
% 12.95/3.06 ? [X4 : $i,X5 : $i > $i,X6 : $i] : (((func @ X6 @ X4 @ (lam @ X6 @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) & ! [X7 : $i] : (((in @ X7 @ X6) != $true) | ((in @ (X5 @ X7) @ X4) = $true))) => (($true != (func @ sK352 @ sK350 @ (lam @ sK352 @ sK350 @ (^[Y0 : $i]: (sK351 @ Y0))))) & ! [X7 : $i] : (($true != (in @ X7 @ sK352)) | ((in @ (sK351 @ X7) @ sK350) = $true)))),
% 12.95/3.06 introduced(definition,[],[choice_axiom])).
% 12.95/3.06 thf(f1406,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ (X1 @ X3) @ X0) != $true))) | (lamp != $true)) & ((lamp = $true) | ? [X4 : $i,X5 : $i > $i,X6 : $i] : (((func @ X6 @ X4 @ (lam @ X6 @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) != $true) & ! [X7 : $i] : (((in @ X7 @ X6) != $true) | ((in @ (X5 @ X7) @ X4) = $true))))),
% 12.95/3.06 inference(rectify,[status(thm)],[f1405])).
% 12.95/3.06 thf(f1405,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ (X1 @ X3) @ X0) != $true))) | (lamp != $true)) & ((lamp = $true) | ? [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ((in @ (X1 @ X3) @ X0) = $true))))),
% 12.95/3.06 inference(nnf_transformation,[status(thm)],[f826])).
% 12.95/3.06 thf(f826,plain,(
% 12.95/3.06 ! [X0 : $i,X1 : $i > $i,X2 : $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ((in @ (X1 @ X3) @ X0) != $true))) <=> (lamp = $true)),
% 12.95/3.06 inference(ennf_transformation,[status(thm)],[f437])).
% 12.95/3.06 thf(f437,plain,(
% 12.95/3.06 (lamp = $true) <=> ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2) = $true) => ((in @ (X1 @ X3) @ X0) = $true)) => ((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))),
% 12.95/3.06 inference(fool_elimination,[status(thm)],[f436])).
% 12.95/3.06 thf(f436,plain,(
% 12.95/3.06 (lamp = ! [X0 : $i,X1 : $i > $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[X4 : $i] : (X1 @ X4))))))),
% 12.95/3.06 inference(rectify,[status(thm)],[f204])).
% 12.95/3.06 thf(f204,axiom,(
% 12.95/3.06 (lamp = ! [X4 : $i,X13 : $i > $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (func @ X3 @ X4 @ (lam @ X3 @ X4 @ (^[X1 : $i] : (X13 @ X1))))))),
% 12.95/3.06 file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',lamp)).
% 12.95/3.06 thf(f3038,plain,(
% 12.95/3.06 ($true != (func @ sK244 @ sK245 @ (lam @ sK244 @ sK245 @ sK246)))),
% 12.95/3.06 inference(subsumption_resolution,[status(thm)],[f3026,f2181])).
% 12.95/3.06 thf(f2181,plain,(
% 12.95/3.06 (funcinfuncset = $true)),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1233])).
% 12.95/3.06 thf(f3026,plain,(
% 12.95/3.06 (funcinfuncset != $true) | ($true != (func @ sK244 @ sK245 @ (lam @ sK244 @ sK245 @ sK246)))),
% 12.95/3.06 inference(trivial_inequality_removal,[status(thm)],[f3018])).
% 12.95/3.06 thf(f3018,plain,(
% 12.95/3.06 ($true != (func @ sK244 @ sK245 @ (lam @ sK244 @ sK245 @ sK246))) | ($true != $true) | (funcinfuncset != $true)),
% 12.95/3.06 inference(superposition,[status(thm)],[f2849,f2022])).
% 12.95/3.06 thf(f2022,plain,(
% 12.95/3.06 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) | (funcinfuncset != $true) | ((func @ X1 @ X0 @ X2) != $true)) )),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1176])).
% 12.95/3.06 thf(f1176,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) | ((func @ X1 @ X0 @ X2) != $true)) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | (((in @ sK202 @ (funcSet @ sK201 @ sK200)) != $true) & ($true = (func @ sK201 @ sK200 @ sK202))))),
% 12.95/3.06 inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201,sK202])],[f1174,f1175])).
% 12.95/3.06 thf(f1175,plain,(
% 12.95/3.06 ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (funcSet @ X4 @ X3))) & ((func @ X4 @ X3 @ X5) = $true)) => (((in @ sK202 @ (funcSet @ sK201 @ sK200)) != $true) & ($true = (func @ sK201 @ sK200 @ sK202)))),
% 12.95/3.06 introduced(definition,[],[choice_axiom])).
% 12.95/3.06 thf(f1174,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) | ((func @ X1 @ X0 @ X2) != $true)) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (funcSet @ X4 @ X3))) & ((func @ X4 @ X3 @ X5) = $true)))),
% 12.95/3.06 inference(rectify,[status(thm)],[f1173])).
% 12.95/3.06 thf(f1173,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) | ((func @ X1 @ X0 @ X2) != $true)) | (funcinfuncset != $true)) & ((funcinfuncset = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) & ((func @ X1 @ X0 @ X2) = $true)))),
% 12.95/3.06 inference(nnf_transformation,[status(thm)],[f755])).
% 12.95/3.06 thf(f755,plain,(
% 12.95/3.06 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) | ((func @ X1 @ X0 @ X2) != $true)) <=> (funcinfuncset = $true)),
% 12.95/3.06 inference(ennf_transformation,[status(thm)],[f510])).
% 12.95/3.06 thf(f510,plain,(
% 12.95/3.06 (funcinfuncset = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X1 @ X0 @ X2) = $true) => ((in @ X2 @ (funcSet @ X1 @ X0)) = $true))),
% 12.95/3.06 inference(fool_elimination,[status(thm)],[f509])).
% 12.95/3.06 thf(f509,plain,(
% 12.95/3.06 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => (in @ X2 @ (funcSet @ X1 @ X0))) = funcinfuncset)),
% 12.95/3.06 inference(rectify,[status(thm)],[f201])).
% 12.95/3.06 thf(f201,axiom,(
% 12.95/3.06 (! [X4 : $i,X3 : $i,X13 : $i] : ((func @ X3 @ X4 @ X13) => (in @ X13 @ (funcSet @ X3 @ X4))) = funcinfuncset)),
% 12.95/3.06 file('/export/starexec/sandbox2/tmp/tmp.G81oJ3DIf9/DTF2THF_3655.p',funcinfuncset)).
% 12.95/3.06 thf(f2849,plain,(
% 12.95/3.06 ($true != (in @ (lam @ sK244 @ sK245 @ sK246) @ (funcSet @ sK244 @ sK245)))),
% 12.95/3.06 inference(beta_eta_normalization,[status(thm)],[f2133])).
% 12.95/3.06 thf(f2133,plain,(
% 12.95/3.06 ((in @ (lam @ sK244 @ sK245 @ (^[Y0 : $i]: (sK246 @ Y0))) @ (funcSet @ sK244 @ sK245)) != $true)),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1233])).
% 12.95/3.06 thf(f3173,plain,(
% 12.95/3.06 ((in @ (sK349 @ sK244 @ sK246 @ sK245) @ sK244) != $true)),
% 12.95/3.06 inference(trivial_inequality_removal,[status(thm)],[f3164])).
% 12.95/3.06 thf(f3164,plain,(
% 12.95/3.06 ($true != $true) | ((in @ (sK349 @ sK244 @ sK246 @ sK245) @ sK244) != $true)),
% 12.95/3.06 inference(superposition,[status(thm)],[f3160,f2132])).
% 12.95/3.06 thf(f2132,plain,(
% 12.95/3.06 ( ! [X3 : $i] : (((in @ (sK246 @ X3) @ sK245) = $true) | ((in @ X3 @ sK244) != $true)) )),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1233])).
% 12.95/3.06 thf(f3160,plain,(
% 12.95/3.06 ((in @ (sK246 @ (sK349 @ sK244 @ sK246 @ sK245)) @ sK245) != $true)),
% 12.95/3.06 inference(subsumption_resolution,[status(thm)],[f3157,f2103])).
% 12.95/3.06 thf(f3157,plain,(
% 12.95/3.06 ((in @ (sK246 @ (sK349 @ sK244 @ sK246 @ sK245)) @ sK245) != $true) | (lamp != $true)),
% 12.95/3.06 inference(trivial_inequality_removal,[status(thm)],[f3155])).
% 12.95/3.06 thf(f3155,plain,(
% 12.95/3.06 ($true != $true) | (lamp != $true) | ((in @ (sK246 @ (sK349 @ sK244 @ sK246 @ sK245)) @ sK245) != $true)),
% 12.95/3.06 inference(superposition,[status(thm)],[f3038,f2844])).
% 12.95/3.06 thf(f2844,plain,(
% 12.95/3.06 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (((func @ X2 @ X0 @ (lam @ X2 @ X0 @ X1)) = $true) | (lamp != $true) | ((in @ (X1 @ (sK349 @ X2 @ X1 @ X0)) @ X0) != $true)) )),
% 12.95/3.06 inference(beta_eta_normalization,[status(thm)],[f2402])).
% 12.95/3.06 thf(f2402,plain,(
% 12.95/3.06 ( ! [X2 : $i,X0 : $i,X1 : $i > $i] : (((in @ (X1 @ (sK349 @ X2 @ X1 @ X0)) @ X0) != $true) | (lamp != $true) | ((func @ X2 @ X0 @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)) )),
% 12.95/3.06 inference(cnf_transformation,[status(thm)],[f1409])).
% 12.95/3.06 % SZS output end Proof for DTF2THF_3655
% 12.95/3.06 % (3983)------------------------------
% 12.95/3.06 % (3983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.95/3.06 % (3983)Termination reason: Refutation
% 12.95/3.06
% 12.95/3.06 % (3983)Memory used [KB]: 9210
% 12.95/3.06 % (3983)Time elapsed: 0.100 s
% 12.95/3.06 % (3983)Instructions burned: 318 (million)
% 12.95/3.06 % (3983)------------------------------
% 12.95/3.06 % (3983)------------------------------
% 12.95/3.06 % (3872)Success in time 1.522 s
%------------------------------------------------------------------------------