%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU612^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 09:35:36 AM UTC 2026
% Result : Theorem 6.46s 2.19s
% Output : Refutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 2828 ( 783 equ; 0 cnn)
% Maximal formula atoms : 131 ( 53 avg)
% Number of connectives : 1652 ( 100 ~; 57 |; 415 &; 413 @)
% ( 5 <=>; 662 =>; 0 <=; 0 <~>)
% Maximal formula depth : 138 ( 24 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 292 ( 289 usr; 138 con; 0-4 aty)
% Number of variables : 142 ( 34 ^; 81 !; 27 ?; 142 :)
% 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_162,type,
sP0: $i > $i > $o > $o ).
thf(func_def_164,type,
sP2: ( $i > $o ) > $o ).
thf(func_def_165,type,
sP3: ( $i > $o ) > $o ).
thf(func_def_167,type,
sP5: $i > $i > $o ).
thf(func_def_170,type,
sP8: ( $i > $o ) > $i > $o ).
thf(func_def_172,type,
sP10: $i > $i > $i > $o ).
thf(func_def_173,type,
sP11: $i > $i > $o ).
thf(func_def_174,type,
sP12: $i > $i > $o ).
thf(func_def_175,type,
sP13: $i > $i > $o ).
thf(func_def_176,type,
sP14: $i > $o ).
thf(func_def_177,type,
sP15: $i > $i > $o ).
thf(func_def_178,type,
sP16: $o > $i > $i > $o ).
thf(func_def_180,type,
sP18: $i > $o ).
thf(func_def_181,type,
sP19: $i > $o ).
thf(func_def_182,type,
sP20: ( $i > $o ) > $o ).
thf(func_def_183,type,
sP21: ( $i > $o ) > $o ).
thf(func_def_184,type,
sP22: $i > $i > $o ).
thf(func_def_187,type,
sP25: $o > $i > $i > $i > $o ).
thf(func_def_188,type,
sP26: $i > $o > $i > $i > $o ).
thf(func_def_189,type,
sP27: $i > ( $i > $o ) > $o ).
thf(func_def_191,type,
sP29: ( $i > $o ) > $i > $o ).
thf(func_def_193,type,
sP31: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_194,type,
sP32: $i > ( $i > $i > $o ) > $o ).
thf(func_def_197,type,
sP35: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_198,type,
sP36: ( $i > $o ) > $i > $o ).
thf(func_def_200,type,
sP38: $i > $o ).
thf(func_def_201,type,
sP39: ( $i > $o ) > $o ).
thf(func_def_202,type,
sP40: ( $i > $o ) > $i > $o ).
thf(func_def_204,type,
sP42: $i > $i > $o > $o ).
thf(func_def_205,type,
sP43: $i > $i > $i > $o ).
thf(func_def_206,type,
sP44: $i > $i > $i > $o ).
thf(func_def_209,type,
sP47: $i > $i > $o ).
thf(func_def_211,type,
sP49: $i > ( $i > $o ) > $o ).
thf(func_def_233,type,
sK71: $i > $i ).
thf(func_def_242,type,
sK80: $i > $i > $i ).
thf(func_def_247,type,
sK85: ( $i > $o ) > $i ).
thf(func_def_248,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK87: $i > $o ).
thf(func_def_250,type,
sK88: ( $i > $o ) > $i ).
thf(func_def_251,type,
sK89: $i > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK90: $i > $o ).
thf(func_def_257,type,
sK95: $i > $o ).
thf(func_def_264,type,
sK102: $i > $o ).
thf(func_def_265,type,
sK103: $i > $o ).
thf(func_def_266,type,
sK104: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_267,type,
sK105: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_272,type,
sK110: $i > $o ).
thf(func_def_275,type,
sK113: $i > $i > $i ).
thf(func_def_279,type,
sK117: $i > $i > $i ).
thf(func_def_292,type,
sK130: $i > $o ).
thf(func_def_293,type,
sK131: ( $i > $o ) > $i > $i ).
thf(func_def_294,type,
sK132: ( $i > $o ) > $i > $i ).
thf(func_def_306,type,
sK144: $i > $o ).
thf(func_def_309,type,
sK147: $i > $i > $i ).
thf(func_def_310,type,
sK148: $i > $i > $i ).
thf(func_def_311,type,
sK149: $i > $i > $i > $i ).
thf(func_def_312,type,
sK150: $i > $i ).
thf(func_def_313,type,
sK151: $i > $i ).
thf(func_def_314,type,
sK152: $i > $i ).
thf(func_def_315,type,
sK153: $i > $i ).
thf(func_def_316,type,
sK154: $i > $i > $i ).
thf(func_def_317,type,
sK155: $i > $i > $i ).
thf(func_def_318,type,
sK156: $i > $i > $i ).
thf(func_def_319,type,
sK157: $i > $i > $i ).
thf(func_def_320,type,
sK158: $i > $i > $i ).
thf(func_def_321,type,
sK159: $i > $i > $i ).
thf(func_def_322,type,
sK160: $i > $i > $i ).
thf(func_def_323,type,
sK161: $i > $i > $i ).
thf(func_def_324,type,
sK162: $i > $i > $i > $i ).
thf(func_def_325,type,
sK163: $i > $i > $i > $i ).
thf(func_def_327,type,
sK165: $i > $i ).
thf(func_def_328,type,
sK166: $o > $i > $i > $i ).
thf(func_def_332,type,
sK170: $i > $o ).
thf(func_def_334,type,
sK172: ( $i > $o ) > $i ).
thf(func_def_335,type,
sK173: $i > $o ).
thf(func_def_344,type,
sK182: $i > $o ).
thf(func_def_350,type,
sK188: $i > $i > $i ).
thf(func_def_353,type,
sK191: $i > $o ).
thf(func_def_363,type,
sK201: $i > $o ).
thf(func_def_368,type,
sK206: $i > $i ).
thf(func_def_369,type,
sK207: $i > $i ).
thf(func_def_380,type,
sK218: $i > ( $i > $o ) > $i ).
thf(func_def_381,type,
sK219: ( $i > $o ) > $i ).
thf(func_def_382,type,
sK220: $i > $o ).
thf(func_def_383,type,
sK221: $i > $o ).
thf(func_def_393,type,
sK231: ( $i > $o ) > $i ).
thf(func_def_394,type,
sK232: ( $i > $o ) > $i ).
thf(func_def_395,type,
sK233: $i > $o ).
thf(func_def_404,type,
sK242: $i > $i ).
thf(func_def_408,type,
sK246: $i > $i > $i ).
thf(func_def_416,type,
sK254: $i > $i > $i ).
thf(func_def_436,type,
sK274: $i > $o ).
thf(func_def_438,type,
sK276: $i > ( $i > $o ) > $i ).
thf(func_def_439,type,
sK277: $i > ( $i > $o ) > $i ).
thf(func_def_444,type,
sK282: $i > $o ).
thf(func_def_445,type,
sK283: ( $i > $o ) > $i > $i ).
thf(func_def_446,type,
sK284: ( $i > $o ) > $i > $i ).
thf(func_def_450,type,
sK288: $i > $o ).
thf(func_def_458,type,
sK296: $i > $i > $o ).
thf(func_def_459,type,
sK297: ( $i > $i > $o ) > $i > $i ).
thf(func_def_460,type,
sK298: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_461,type,
sK299: $i > ( $i > $i > $o ) > $i ).
thf(func_def_462,type,
sK300: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_465,type,
sK303: $i > $i > $i ).
thf(func_def_476,type,
sK314: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_477,type,
sK315: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_480,type,
sK318: $i > $o ).
thf(func_def_481,type,
sK319: $i > $o ).
thf(func_def_483,type,
sK321: $i > $o ).
thf(func_def_484,type,
sK322: ( $i > $o ) > $i > $i ).
thf(func_def_485,type,
sK323: ( $i > $o ) > $i > $i ).
thf(func_def_486,type,
sK324: $i > $o ).
thf(func_def_490,type,
sK328: $i > $i > $i ).
thf(func_def_491,type,
sK329: $i > $i ).
thf(func_def_497,type,
sK335: $i > $o ).
thf(func_def_499,type,
sK337: $i > ( $i > $o ) > $i ).
thf(func_def_500,type,
sK338: ( $i > $o ) > $i ).
thf(func_def_501,type,
sK339: $i > $o ).
thf(func_def_504,type,
sK342: $i > $o ).
thf(func_def_505,type,
sK343: ( $i > $o ) > $i > $i ).
thf(func_def_506,type,
sK344: ( $i > $o ) > $i > $i ).
thf(func_def_514,type,
sK352: $i > $o ).
thf(func_def_517,type,
sK355: $i > $i > $i > $o ).
thf(func_def_524,type,
sK362: $i > $i ).
thf(func_def_529,type,
sK367: $i > $o ).
thf(func_def_530,type,
sK368: $i > $o ).
thf(func_def_531,type,
sK369: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_532,type,
sK370: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK373: $i > $i > $i ).
thf(func_def_536,type,
sK374: $i > $i > $i ).
thf(func_def_547,type,
sK385: $i > $o ).
thf(func_def_549,type,
sK387: $i > ( $i > $o ) > $i ).
thf(func_def_550,type,
sK388: $i > ( $i > $o ) > $i ).
thf(func_def_554,type,
sK392: $i > $i ).
thf(func_def_559,type,
ph397:
!>[X0: $tType] : X0 ).
thf(f3961,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3959,f1465]) ).
thf(f1465,plain,
( ( in @ sK75 @ sK76 )
= $true ),
inference(cnf_transformation,[status(thm)],[f682]) ).
thf(f682,plain,
( ( eqimpsubset1 = $true )
& ( setminusSubset2 = $true )
& ( replAx = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( subsetTrans = $true )
& ( setextAx = $true )
& ( binunionLsub = $true )
& ( descr__Cong = $true )
& ( exuI3 = $true )
& ( quantDeMorgan4 = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( quantDeMorgan2 = $true )
& ( setminusER = $true )
& ( binunionE = $true )
& ( notdallE = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( setminusEL = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( powersetI1 = $true )
& ( nonemptyE1 = $true )
& ( emptyE1 = $true )
& ( setunionE = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyImpWitness = $true )
& ( ( in @ sK75 @ sK77 )
!= $true )
& ( ( in @ sK75 @ sK76 )
= $true )
& ( $true
!= ( in @ sK75 @ ( symdiff @ sK76 @ sK77 ) ) )
& ( binintersectSubset1 = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( setminusI = $true )
& ( setminusILneg = $true )
& ( upairset2IR = $true )
& ( eqinunit = $true )
& ( exuI2 = $true )
& ( exuI1 = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( eqimpsubset2 = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( emptyinunitempty = $true )
& ( setminusLsub = $true )
& ( noeltsimpempty = $true )
& ( powersetE1 = $true )
& ( setoftrueEq = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( binintersectI = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( nonemptyI1 = $true )
& ( exuE3u = $true )
& ( exuE3e = $true )
& ( notsubsetI = $true )
& ( notequalI1 = $true )
& ( binintersectSubset2 = $true )
& ( emptyset__Cong = $true )
& ( inPowerset = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectEL = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( subset2powerset = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( subsetE2 = $true )
& ( setminusSubset1 = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( setminusELneg = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( binunionRsub = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ( prop2setE = $true )
& ( notinemptyset = $true )
& ( setadjoinSub = $true )
& ( exu__Cong = $true )
& ( setadjoinIL = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( dsetconstr__Cong = $true )
& ( emptyI = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset5 = $true )
& ( disjointsetsI1 = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( setunion__Cong = $true )
& ( singletonsswitch = $true )
& ( subsetI1 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( setbeta = $true )
& ( binintersectLsub = $true )
& ( sepSubset = $true )
& ( descrp = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( setextsub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76,sK77])],[f464,f681]) ).
thf(f681,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
=> ( ( ( in @ sK75 @ sK77 )
!= $true )
& ( ( in @ sK75 @ sK76 )
= $true )
& ( $true
!= ( in @ sK75 @ ( symdiff @ sK76 @ sK77 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f464,plain,
( ( eqimpsubset1 = $true )
& ( setminusSubset2 = $true )
& ( replAx = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( subsetTrans = $true )
& ( setextAx = $true )
& ( binunionLsub = $true )
& ( descr__Cong = $true )
& ( exuI3 = $true )
& ( quantDeMorgan4 = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( binunionIL = $true )
& ( binintersectER = $true )
& ( quantDeMorgan2 = $true )
& ( setminusER = $true )
& ( binunionE = $true )
& ( notdallE = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( setminusEL = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( powersetI1 = $true )
& ( nonemptyE1 = $true )
& ( emptyE1 = $true )
& ( setunionE = $true )
& ( omega__Cong = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyImpWitness = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
& ( binintersectSubset1 = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( setminusI = $true )
& ( setminusILneg = $true )
& ( upairset2IR = $true )
& ( eqinunit = $true )
& ( exuI2 = $true )
& ( exuI1 = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( omega0Ax = $true )
& ( eqimpsubset2 = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( emptyinunitempty = $true )
& ( setminusLsub = $true )
& ( noeltsimpempty = $true )
& ( powersetE1 = $true )
& ( setoftrueEq = $true )
& ( exuEu = $true )
& ( symdiffE = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( binintersectI = $true )
& ( subsetE = $true )
& ( subsetRefl = $true )
& ( nonemptyI1 = $true )
& ( exuE3u = $true )
& ( exuE3e = $true )
& ( notsubsetI = $true )
& ( notequalI1 = $true )
& ( binintersectSubset2 = $true )
& ( emptyset__Cong = $true )
& ( inPowerset = $true )
& ( uniqinunit = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectEL = $true )
& ( dsetconstrEL = $true )
& ( upairsetIL = $true )
& ( subset2powerset = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( subsetE2 = $true )
& ( setminusSubset1 = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( setminusELneg = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( binunionRsub = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ( prop2setE = $true )
& ( notinemptyset = $true )
& ( setadjoinSub = $true )
& ( exu__Cong = $true )
& ( setadjoinIL = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( dsetconstr__Cong = $true )
& ( emptyI = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset5 = $true )
& ( disjointsetsI1 = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( setunion__Cong = $true )
& ( singletonsswitch = $true )
& ( subsetI1 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( setbeta = $true )
& ( binintersectLsub = $true )
& ( sepSubset = $true )
& ( descrp = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( setextsub = $true ) ),
inference(flattening,[status(thm)],[f463]) ).
thf(f463,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $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)],[f393]) ).
thf(f393,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f185]) ).
thf(f185,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f184]) ).
thf(f184,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f133]) ).
thf(f133,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
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f132]) ).
thf(f132,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
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',symdiffI1) ).
thf(f3959,plain,
( ( in @ sK75 @ sK76 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3955]) ).
thf(f3955,plain,
( ( ( in @ sK75 @ sK76 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3954,f2612]) ).
thf(f2612,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2329]) ).
thf(f2329,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1892,f1487]) ).
thf(f1487,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f682]) ).
thf(f1892,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( binunionIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1154]) ).
thf(f1154,plain,
( ( ( binunionIL = $true )
| ( ( ( in @ sK310 @ ( binunion @ sK311 @ sK309 ) )
!= $true )
& ( $true
= ( in @ sK310 @ sK311 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( binunionIL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK309,sK310,sK311])],[f1152,f1153]) ).
thf(f1153,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) )
=> ( ( ( in @ sK310 @ ( binunion @ sK311 @ sK309 ) )
!= $true )
& ( $true
= ( in @ sK310 @ sK311 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1152,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( binunion @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true ) )
| ( binunionIL != $true ) ) ),
inference(rectify,[status(thm)],[f1151]) ).
thf(f1151,plain,
( ( ( binunionIL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( binunionIL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f533]) ).
thf(f533,plain,
( ( binunionIL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f310]) ).
thf(f310,plain,
( ( binunionIL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ ( binunion @ X2 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f309]) ).
thf(f309,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( binunionIL
= ( ! [X4: $i,X1: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',binunionIL) ).
thf(f3954,plain,
( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f3952,f1466]) ).
thf(f1466,plain,
( ( in @ sK75 @ sK77 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f682]) ).
thf(f3952,plain,
( ( ( in @ sK75 @ sK77 )
= $true )
| ( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f3949]) ).
thf(f3949,plain,
( ( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true )
| ( ( ~ ( in @ sK75 @ sK77 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f3948]) ).
thf(f3948,plain,
( ( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true )
| ( $true
!= ( ~ ( in @ sK75 @ sK76 )
| ~ ( in @ sK75 @ sK77 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3947]) ).
thf(f3947,plain,
( ( $true
!= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK76 )
| ~ ( in @ Y0 @ sK77 ) )
@ sK75 ) )
| ( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3945]) ).
thf(f3945,plain,
( ( ( in @ sK75 @ ( binunion @ sK76 @ sK77 ) )
!= $true )
| ( $true
!= ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK76 )
| ~ ( in @ Y0 @ sK77 ) )
@ sK75 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2592,f2553]) ).
thf(f2553,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) )
= $true )
| ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2552]) ).
thf(f2552,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2200]) ).
thf(f2200,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1704,f1402]) ).
thf(f1402,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f682]) ).
thf(f1704,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[status(thm)],[f930]) ).
thf(f930,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ( ( ( in @ sK200 @ sK199 )
= $true )
& ( ( in @ sK200
@ ( dsetconstr @ sK199
@ ^ [Y0: $i] : ( sK201 @ Y0 ) ) )
!= $true )
& ( ( sK201 @ sK200 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199,sK200,sK201])],[f928,f929]) ).
thf(f929,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ X3 )
= $true )
& ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
= ( X5 @ X4 ) ) )
=> ( ( ( in @ sK200 @ sK199 )
= $true )
& ( ( in @ sK200
@ ( dsetconstr @ sK199
@ ^ [Y0: $i] : ( sK201 @ Y0 ) ) )
!= $true )
& ( ( sK201 @ sK200 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f928,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X4 @ X3 )
= $true )
& ( $true
!= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
= ( X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f927]) ).
thf(f927,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) )
& ( ( dsetconstrI = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f556]) ).
thf(f556,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f555]) ).
thf(f555,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f277]) ).
thf(f277,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( X2 @ X1 )
= $true )
=> ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) )
<=> ( dsetconstrI = $true ) ),
inference(fool_elimination,[status(thm)],[f276]) ).
thf(f276,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X3: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',dsetconstrI) ).
thf(f2592,plain,
( ( in @ sK75
@ ( dsetconstr @ ( binunion @ sK76 @ sK77 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK76 )
| ~ ( in @ Y0 @ sK77 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f2072]) ).
thf(f2072,plain,
( ( in @ sK75
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) )
@ sK76
@ sK77 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1464,f1794]) ).
thf(f1794,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
thf(f306,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y0 )
| ~ ( in @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f305]) ).
thf(f305,plain,
( symdiff
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X1 )
| ~ ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,axiom,
( symdiff
= ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( binunion @ X3 @ X4 )
@ ^ [X1: $i] :
( ~ ( in @ X1 @ X4 )
| ~ ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',symdiff) ).
thf(f1464,plain,
( $true
!= ( in @ sK75 @ ( symdiff @ sK76 @ sK77 ) ) ),
inference(cnf_transformation,[status(thm)],[f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU612^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n004.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 12:28:41 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU612^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> in x (symdiff A B))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC114g [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.44 v9.1.0, 0.50 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.44 v7.3.0, 0.33 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 280 ( 131 unt; 148 typ; 131 def)
% 0.18/0.38 % Number of atoms : 698 ( 188 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 131 ( 5 avg)
% 0.18/0.38 % Number of connectives : 1124 ( 44 ~; 7 |; 28 &; 719 @)
% 0.18/0.38 % ( 14 <=>; 312 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 137 ( 2 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 151 ( 148 usr; 132 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 380 ( 33 ^; 318 !; 29 ?; 380 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=490
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(exu_type,type,
% 0.18/0.38 exu: ( $i > $o ) > $o ).
% 0.18/0.38
% 0.18/0.38 thf(exu,definition,
% 0.18/0.38 ( exu
% 0.18/0.38 = ( ^ [Xphi: $i > $o] :
% 0.18/0.38 ? [Xx: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 & ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setextAx_type,type,
% 0.18/0.38 setextAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setextAx,definition,
% 0.18/0.38 ( setextAx
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 <=> ( in @ Xx @ B ) )
% 0.18/0.38 => ( A = B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyset_type,type,
% 0.18/0.38 emptyset: $i ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetAx_type,type,
% 0.18/0.38 emptysetAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetAx,definition,
% 0.18/0.38 ( emptysetAx
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoin_type,type,
% 0.18/0.38 setadjoin: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinAx_type,type,
% 0.18/0.38 setadjoinAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinAx,definition,
% 0.18/0.38 ( setadjoinAx
% 0.18/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.38 <=> ( ( Xy = Xx )
% 0.18/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powerset_type,type,
% 0.18/0.38 powerset: $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(powersetAx_type,type,
% 0.18/0.38 powersetAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetAx,definition,
% 0.18/0.38 ( powersetAx
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.38 <=> ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setunion_type,type,
% 0.18/0.38 setunion: $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(setunionAx_type,type,
% 0.18/0.38 setunionAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setunionAx,definition,
% 0.18/0.38 ( setunionAx
% 0.18/0.38 = ( ! [A: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.38 <=> ? [B: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omega_type,type,
% 0.18/0.38 omega: $i ).
% 0.18/0.38
% 0.18/0.38 thf(omega0Ax_type,type,
% 0.18/0.38 omega0Ax: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omega0Ax,definition,
% 0.18/0.38 ( omega0Ax
% 0.18/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omegaSAx_type,type,
% 0.18/0.38 omegaSAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omegaSAx,definition,
% 0.18/0.38 ( omegaSAx
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ omega )
% 0.18/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omegaIndAx_type,type,
% 0.18/0.38 omegaIndAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omegaIndAx,definition,
% 0.18/0.38 ( omegaIndAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( ( in @ emptyset @ A )
% 0.18/0.38 & ! [Xx: $i] :
% 0.18/0.38 ( ( ( in @ Xx @ omega )
% 0.18/0.38 & ( in @ Xx @ A ) )
% 0.18/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ omega )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(replAx_type,type,
% 0.18/0.38 replAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(replAx,definition,
% 0.18/0.38 ( replAx
% 0.18/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( exu
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.38 => ? [B: $i] :
% 0.18/0.38 ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 <=> ? [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(foundationAx_type,type,
% 0.18/0.38 foundationAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(foundationAx,definition,
% 0.18/0.38 ( foundationAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.38 => ? [B: $i] :
% 0.18/0.38 ( ( in @ B @ A )
% 0.18/0.38 & ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(wellorderingAx_type,type,
% 0.18/0.38 wellorderingAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(wellorderingAx,definition,
% 0.18/0.38 ( wellorderingAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ? [B: $i] :
% 0.18/0.38 ( ! [C: $i] :
% 0.18/0.38 ( ( in @ C @ B )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ A ) ) )
% 0.18/0.38 & ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( ( in @ Xx @ A )
% 0.18/0.38 & ( in @ Xy @ A ) )
% 0.18/0.38 => ( ! [C: $i] :
% 0.18/0.38 ( ( in @ C @ B )
% 0.18/0.38 => ( ( in @ Xx @ C )
% 0.18/0.38 <=> ( in @ Xy @ C ) ) )
% 0.18/0.38 => ( Xx = Xy ) ) )
% 0.18/0.38 & ! [C: $i,D: $i] :
% 0.18/0.38 ( ( ( in @ C @ B )
% 0.18/0.38 & ( in @ D @ B ) )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ D ) )
% 0.18/0.38 | ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ D )
% 0.18/0.38 => ( in @ Xx @ C ) ) ) )
% 0.18/0.38 & ! [C: $i] :
% 0.18/0.38 ( ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ A ) )
% 0.18/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.38 => ? [D: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ D @ B )
% 0.18/0.38 & ( in @ Xx @ C )
% 0.18/0.38 & ~ ? [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ D )
% 0.18/0.38 & ( in @ Xy @ C ) )
% 0.18/0.38 & ! [E: $i] :
% 0.18/0.38 ( ( in @ E @ B )
% 0.18/0.38 => ( ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ E )
% 0.18/0.38 => ( in @ Xy @ D ) )
% 0.18/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(descr_type,type,
% 0.18/0.38 descr: ( $i > $o ) > $i ).
% 0.18/0.38
% 0.18/0.38 thf(descrp_type,type,
% 0.18/0.38 descrp: $o ).
% 0.18/0.38
% 0.18/0.38 thf(descrp,definition,
% 0.18/0.38 ( descrp
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ( Xphi
% 0.18/0.38 @ ( descr
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstr_type,type,
% 0.18/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrI_type,type,
% 0.18/0.38 dsetconstrI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrI,definition,
% 0.18/0.38 ( dsetconstrI
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 => ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrEL_type,type,
% 0.18/0.38 dsetconstrEL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrEL,definition,
% 0.18/0.38 ( dsetconstrEL
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrER_type,type,
% 0.18/0.38 dsetconstrER: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrER,definition,
% 0.18/0.38 ( dsetconstrER
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE1_type,type,
% 0.18/0.38 exuE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE1,definition,
% 0.18/0.38 ( exuE1
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 & ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(prop2set_type,type,
% 0.18/0.38 prop2set: $o > $i ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setE_type,type,
% 0.18/0.38 prop2setE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setE,definition,
% 0.18/0.38 ( prop2setE
% 0.18/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.38 => Xphi ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetE_type,type,
% 0.18/0.38 emptysetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetE,definition,
% 0.18/0.38 ( emptysetE
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ emptyset )
% 0.18/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetimpfalse_type,type,
% 0.18/0.38 emptysetimpfalse: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetimpfalse,definition,
% 0.18/0.38 ( emptysetimpfalse
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ emptyset )
% 0.18/0.38 => $false ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notinemptyset_type,type,
% 0.18/0.38 notinemptyset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notinemptyset,definition,
% 0.18/0.38 ( notinemptyset
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3e_type,type,
% 0.18/0.38 exuE3e: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3e,definition,
% 0.18/0.38 ( exuE3e
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setext_type,type,
% 0.18/0.38 setext: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setext,definition,
% 0.18/0.38 ( setext
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) )
% 0.18/0.38 => ( A = B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyI_type,type,
% 0.18/0.38 emptyI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyI,definition,
% 0.18/0.38 ( emptyI
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ A )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(noeltsimpempty_type,type,
% 0.18/0.38 noeltsimpempty: $o ).
% 0.18/0.38
% 0.18/0.38 thf(noeltsimpempty,definition,
% 0.18/0.38 ( noeltsimpempty
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ A )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setbeta_type,type,
% 0.18/0.38 setbeta: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setbeta,definition,
% 0.18/0.38 ( setbeta
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonempty_type,type,
% 0.18/0.38 nonempty: $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonempty,definition,
% 0.18/0.38 ( nonempty
% 0.18/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyE1_type,type,
% 0.18/0.38 nonemptyE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyE1,definition,
% 0.18/0.38 ( nonemptyE1
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( nonempty @ A )
% 0.18/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI_type,type,
% 0.18/0.38 nonemptyI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI,definition,
% 0.18/0.38 ( nonemptyI
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 => ( nonempty
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI1_type,type,
% 0.18/0.38 nonemptyI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI1,definition,
% 0.18/0.38 ( nonemptyI1
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIL_type,type,
% 0.18/0.38 setadjoinIL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIL,definition,
% 0.18/0.38 ( setadjoinIL
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinunitempty_type,type,
% 0.18/0.38 emptyinunitempty: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinunitempty,definition,
% 0.18/0.38 ( emptyinunitempty
% 0.18/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIR_type,type,
% 0.18/0.38 setadjoinIR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIR,definition,
% 0.18/0.38 ( setadjoinIR
% 0.18/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinE_type,type,
% 0.18/0.38 setadjoinE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinE,definition,
% 0.18/0.38 ( setadjoinE
% 0.18/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.38 => ! [Xphi: $o] :
% 0.18/0.38 ( ( ( Xy = Xx )
% 0.18/0.38 => Xphi )
% 0.18/0.38 => ( ( ( in @ Xy @ A )
% 0.18/0.38 => Xphi )
% 0.18/0.38 => Xphi ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinOr_type,type,
% 0.18/0.38 setadjoinOr: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinOr,definition,
% 0.18/0.38 ( setadjoinOr
% 0.18/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.38 => ( ( Xy = Xx )
% 0.18/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setoftrueEq_type,type,
% 0.18/0.38 setoftrueEq: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setoftrueEq,definition,
% 0.18/0.38 ( setoftrueEq
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xx: $i] : $true )
% 0.18/0.38 = A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powersetI_type,type,
% 0.18/0.38 powersetI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetI,definition,
% 0.18/0.38 ( powersetI
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) )
% 0.18/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinPowerset_type,type,
% 0.18/0.38 emptyinPowerset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinPowerset,definition,
% 0.18/0.38 ( emptyinPowerset
% 0.18/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyInPowerset_type,type,
% 0.18/0.38 emptyInPowerset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyInPowerset,definition,
% 0.18/0.38 ( emptyInPowerset
% 0.18/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powersetE_type,type,
% 0.18/0.38 powersetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetE,definition,
% 0.18/0.38 ( powersetE
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.38 => ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setunionI_type,type,
% 0.18/0.38 setunionI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setunionI,definition,
% 0.18/0.38 ( setunionI
% 0.18/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( ( in @ B @ A )
% 0.18/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setunionE_type,type,
% 0.18/0.38 setunionE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setunionE,definition,
% 0.18/0.38 ( setunionE
% 0.18/0.38 = ( ! [A: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.38 => ! [Xphi: $o] :
% 0.18/0.38 ( ! [B: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( ( in @ B @ A )
% 0.18/0.38 => Xphi ) )
% 0.18/0.38 => Xphi ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subPowSU_type,type,
% 0.18/0.38 subPowSU: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subPowSU,definition,
% 0.18/0.38 ( subPowSU
% 0.18/0.38 = ( ! [A: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE2_type,type,
% 0.18/0.38 exuE2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE2,definition,
% 0.18/0.38 ( exuE2
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyImpWitness_type,type,
% 0.18/0.38 nonemptyImpWitness: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyImpWitness,definition,
% 0.18/0.38 ( nonemptyImpWitness
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( nonempty @ A )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & $true ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(uniqinunit_type,type,
% 0.18/0.38 uniqinunit: $o ).
% 0.18/0.38
% 0.18/0.38 thf(uniqinunit,definition,
% 0.18/0.38 ( uniqinunit
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notinsingleton_type,type,
% 0.18/0.38 notinsingleton: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notinsingleton,definition,
% 0.18/0.38 ( notinsingleton
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx != Xy )
% 0.18/0.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(eqinunit_type,type,
% 0.18/0.38 eqinunit: $o ).
% 0.18/0.38
% 0.18/0.38 thf(eqinunit,definition,
% 0.18/0.38 ( eqinunit
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(singletonsswitch_type,type,
% 0.18/0.38 singletonsswitch: $o ).
% 0.18/0.38
% 0.18/0.38 thf(singletonsswitch,definition,
% 0.18/0.38 ( singletonsswitch
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetE_type,type,
% 0.18/0.38 upairsetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetE,definition,
% 0.18/0.38 ( upairsetE
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.38 => ( ( Xz = Xx )
% 0.18/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetIL_type,type,
% 0.18/0.38 upairsetIL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetIL,definition,
% 0.18/0.38 ( upairsetIL
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetIR_type,type,
% 0.18/0.38 upairsetIR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(upairsetIR,definition,
% 0.18/0.38 ( upairsetIR
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyE1_type,type,
% 0.18/0.38 emptyE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyE1,definition,
% 0.18/0.38 ( emptyE1
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ( Xphi @ Xx ) )
% 0.18/0.38 => ( ( ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 = emptyset )
% 0.18/0.38 => $false ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(vacuousDall_type,type,
% 0.18/0.38 vacuousDall: $o ).
% 0.18/0.38
% 0.18/0.38 thf(vacuousDall,definition,
% 0.18/0.38 ( vacuousDall
% 0.18/0.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ emptyset )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan1_type,type,
% 0.18/0.38 quantDeMorgan1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan1,definition,
% 0.18/0.38 ( quantDeMorgan1
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ~ ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan2_type,type,
% 0.18/0.38 quantDeMorgan2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan2,definition,
% 0.18/0.38 ( quantDeMorgan2
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ~ ( Xphi @ Xx ) )
% 0.18/0.38 => ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan3_type,type,
% 0.18/0.38 quantDeMorgan3: $o ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan3,definition,
% 0.18/0.38 ( quantDeMorgan3
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ( Xphi @ Xx ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan4_type,type,
% 0.18/0.38 quantDeMorgan4: $o ).
% 0.18/0.38
% 0.18/0.38 thf(quantDeMorgan4,definition,
% 0.18/0.38 ( quantDeMorgan4
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ~ ( Xphi @ Xx ) )
% 0.18/0.38 => ~ ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setI_type,type,
% 0.18/0.38 prop2setI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setI,definition,
% 0.18/0.38 ( prop2setI
% 0.18/0.38 = ( ! [Xphi: $o] :
% 0.18/0.38 ( Xphi
% 0.18/0.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(set2prop_type,type,
% 0.18/0.38 set2prop: $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(prop2set2propI_type,type,
% 0.18/0.38 prop2set2propI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(prop2set2propI,definition,
% 0.18/0.38 ( prop2set2propI
% 0.18/0.38 = ( ! [Xphi: $o] :
% 0.18/0.38 ( Xphi
% 0.18/0.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notdexE_type,type,
% 0.18/0.38 notdexE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notdexE,definition,
% 0.18/0.38 ( notdexE
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ( Xphi @ Xx ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notdallE_type,type,
% 0.18/0.38 notdallE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notdallE,definition,
% 0.18/0.38 ( notdallE
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( ~ ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuI1_type,type,
% 0.18/0.38 exuI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuI1,definition,
% 0.18/0.38 ( exuI1
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 & ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) )
% 0.18/0.38 => ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuI3_type,type,
% 0.18/0.38 exuI3: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuI3,definition,
% 0.18/0.38 ( exuI3
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.18/0.38 => ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 => ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) )
% 0.18/0.38 => ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuI2_type,type,
% 0.18/0.38 exuI2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuI2,definition,
% 0.18/0.38 ( exuI2
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ? [Xx: $i] :
% 0.18/0.38 ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 <=> ( Xy = Xx ) )
% 0.18/0.38 => ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(inCongP_type,type,
% 0.18/0.38 inCongP: $o ).
% 0.18/0.38
% 0.18/0.38 thf(inCongP,definition,
% 0.18/0.38 ( inCongP
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(in__Cong_type,type,
% 0.18/0.38 in__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(in__Cong,definition,
% 0.18/0.38 ( in__Cong
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3u_type,type,
% 0.18/0.38 exuE3u: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3u,definition,
% 0.18/0.38 ( exuE3u
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 => ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exu__Cong_type,type,
% 0.18/0.38 exu__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exu__Cong,definition,
% 0.18/0.38 ( exu__Cong
% 0.18/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.38 => ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 <=> ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyset__Cong_type,type,
% 0.18/0.38 emptyset__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyset__Cong,definition,
% 0.18/0.38 ( emptyset__Cong
% 0.18/0.38 = ( emptyset = emptyset ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoin__Cong_type,type,
% 0.18/0.38 setadjoin__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoin__Cong,definition,
% 0.18/0.38 ( setadjoin__Cong
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ! [Xz: $i,Xu: $i] :
% 0.18/0.38 ( ( Xz = Xu )
% 0.18/0.38 => ( ( setadjoin @ Xx @ Xz )
% 0.18/0.38 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powerset__Cong_type,type,
% 0.18/0.38 powerset__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powerset__Cong,definition,
% 0.18/0.38 ( powerset__Cong
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ( ( powerset @ A )
% 0.18/0.38 = ( powerset @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setunion__Cong_type,type,
% 0.18/0.38 setunion__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setunion__Cong,definition,
% 0.18/0.38 ( setunion__Cong
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ( ( setunion @ A )
% 0.18/0.38 = ( setunion @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omega__Cong_type,type,
% 0.18/0.38 omega__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omega__Cong,definition,
% 0.18/0.38 ( omega__Cong
% 0.18/0.38 = ( omega = omega ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuEu_type,type,
% 0.18/0.38 exuEu: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuEu,definition,
% 0.18/0.38 ( exuEu
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 => ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(descr__Cong_type,type,
% 0.18/0.38 descr__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(descr__Cong,definition,
% 0.18/0.38 ( descr__Cong
% 0.18/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( Xx = Xy )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.38 => ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.18/0.38 => ( ( descr
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 = ( descr
% 0.18/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstr__Cong_type,type,
% 0.18/0.38 dsetconstr__Cong: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstr__Cong,definition,
% 0.18/0.38 ( dsetconstr__Cong
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ B )
% 0.18/0.38 => ( ( Xx = Xy )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.18/0.38 => ( ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 = ( dsetconstr @ B
% 0.18/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subset_type,type,
% 0.18/0.38 subset: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(disjoint_type,type,
% 0.18/0.38 disjoint: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(setsmeet_type,type,
% 0.18/0.38 setsmeet: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI1_type,type,
% 0.18/0.38 subsetI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI1,definition,
% 0.18/0.38 ( subsetI1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(eqimpsubset2_type,type,
% 0.18/0.38 eqimpsubset2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(eqimpsubset2,definition,
% 0.18/0.38 ( eqimpsubset2
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(eqimpsubset1_type,type,
% 0.18/0.38 eqimpsubset1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(eqimpsubset1,definition,
% 0.18/0.38 ( eqimpsubset1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( A = B )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI2_type,type,
% 0.18/0.38 subsetI2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetI2,definition,
% 0.18/0.38 ( subsetI2
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetsubset_type,type,
% 0.18/0.38 emptysetsubset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetsubset,definition,
% 0.18/0.38 ( emptysetsubset
% 0.18/0.38 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE_type,type,
% 0.18/0.38 subsetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE,definition,
% 0.18/0.38 ( subsetE
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE2_type,type,
% 0.18/0.38 subsetE2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetE2,definition,
% 0.18/0.38 ( subsetE2
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notsubsetI_type,type,
% 0.18/0.38 notsubsetI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notsubsetI,definition,
% 0.18/0.38 ( notsubsetI
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notequalI1_type,type,
% 0.18/0.38 notequalI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notequalI1,definition,
% 0.18/0.38 ( notequalI1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ~ ( subset @ A @ B )
% 0.18/0.38 => ( A != B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notequalI2_type,type,
% 0.18/0.38 notequalI2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notequalI2,definition,
% 0.18/0.38 ( notequalI2
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ( A != B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetRefl_type,type,
% 0.18/0.38 subsetRefl: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetRefl,definition,
% 0.18/0.38 ( subsetRefl
% 0.18/0.38 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetTrans_type,type,
% 0.18/0.38 subsetTrans: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetTrans,definition,
% 0.18/0.38 ( subsetTrans
% 0.18/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( subset @ B @ C )
% 0.18/0.38 => ( subset @ A @ C ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinSub_type,type,
% 0.18/0.38 setadjoinSub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinSub,definition,
% 0.18/0.38 ( setadjoinSub
% 0.18/0.38 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinSub2_type,type,
% 0.18/0.38 setadjoinSub2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinSub2,definition,
% 0.18/0.38 ( setadjoinSub2
% 0.18/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subset2powerset_type,type,
% 0.18/0.38 subset2powerset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subset2powerset,definition,
% 0.18/0.38 ( subset2powerset
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setextsub_type,type,
% 0.18/0.38 setextsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setextsub,definition,
% 0.18/0.38 ( setextsub
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( subset @ B @ A )
% 0.18/0.38 => ( A = B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(subsetemptysetimpeq_type,type,
% 0.18/0.38 subsetemptysetimpeq: $o ).
% 0.18/0.38
% 0.18/0.38 thf(subsetemptysetimpeq,definition,
% 0.18/0.38 ( subsetemptysetimpeq
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( subset @ A @ emptyset )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powersetI1_type,type,
% 0.18/0.38 powersetI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetI1,definition,
% 0.18/0.38 ( powersetI1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ B @ A )
% 0.18/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powersetE1_type,type,
% 0.18/0.38 powersetE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetE1,definition,
% 0.18/0.38 ( powersetE1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(inPowerset_type,type,
% 0.18/0.38 inPowerset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(inPowerset,definition,
% 0.18/0.38 ( inPowerset
% 0.18/0.38 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powersetsubset_type,type,
% 0.18/0.38 powersetsubset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetsubset,definition,
% 0.18/0.38 ( powersetsubset
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sepInPowerset_type,type,
% 0.18/0.38 sepInPowerset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(sepInPowerset,definition,
% 0.18/0.38 ( sepInPowerset
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( in
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 @ ( powerset @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sepSubset_type,type,
% 0.18/0.38 sepSubset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(sepSubset,definition,
% 0.18/0.38 ( sepSubset
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.38 ( subset
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunion_type,type,
% 0.18/0.38 binunion: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIL_type,type,
% 0.18/0.38 binunionIL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIL,definition,
% 0.18/0.38 ( binunionIL
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(upairset2IR_type,type,
% 0.18/0.38 upairset2IR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(upairset2IR,definition,
% 0.18/0.38 ( upairset2IR
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIR_type,type,
% 0.18/0.38 binunionIR: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionIR,definition,
% 0.18/0.38 ( binunionIR
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionEcases_type,type,
% 0.18/0.38 binunionEcases: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionEcases,definition,
% 0.18/0.38 ( binunionEcases
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.18/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.38 => ( ( ( in @ Xx @ A )
% 0.18/0.38 => Xphi )
% 0.18/0.38 => ( ( ( in @ Xx @ B )
% 0.18/0.38 => Xphi )
% 0.18/0.38 => Xphi ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionE_type,type,
% 0.18/0.38 binunionE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionE,definition,
% 0.18/0.38 ( binunionE
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionLsub_type,type,
% 0.18/0.38 binunionLsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionLsub,definition,
% 0.18/0.38 ( binunionLsub
% 0.18/0.38 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binunionRsub_type,type,
% 0.18/0.38 binunionRsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binunionRsub,definition,
% 0.18/0.38 ( binunionRsub
% 0.18/0.38 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersect_type,type,
% 0.18/0.38 binintersect: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectI_type,type,
% 0.18/0.38 binintersectI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectI,definition,
% 0.18/0.38 ( binintersectI
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset5_type,type,
% 0.18/0.38 binintersectSubset5: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset5,definition,
% 0.18/0.38 ( binintersectSubset5
% 0.18/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.38 ( ( subset @ C @ A )
% 0.18/0.38 => ( ( subset @ C @ B )
% 0.18/0.38 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectEL_type,type,
% 0.18/0.38 binintersectEL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectEL,definition,
% 0.18/0.38 ( binintersectEL
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectLsub_type,type,
% 0.18/0.38 binintersectLsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectLsub,definition,
% 0.18/0.38 ( binintersectLsub
% 0.18/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset2_type,type,
% 0.18/0.38 binintersectSubset2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset2,definition,
% 0.18/0.38 ( binintersectSubset2
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( binintersect @ A @ B )
% 0.18/0.38 = A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset3_type,type,
% 0.18/0.38 binintersectSubset3: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset3,definition,
% 0.18/0.38 ( binintersectSubset3
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( ( binintersect @ A @ B )
% 0.18/0.38 = B )
% 0.18/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectER_type,type,
% 0.18/0.38 binintersectER: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectER,definition,
% 0.18/0.38 ( binintersectER
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.38 => ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(disjointsetsI1_type,type,
% 0.18/0.38 disjointsetsI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(disjointsetsI1,definition,
% 0.18/0.38 ( disjointsetsI1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 & ( in @ Xx @ B ) )
% 0.18/0.38 => ( ( binintersect @ A @ B )
% 0.18/0.38 = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectRsub_type,type,
% 0.18/0.38 binintersectRsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectRsub,definition,
% 0.18/0.38 ( binintersectRsub
% 0.18/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset4_type,type,
% 0.18/0.38 binintersectSubset4: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset4,definition,
% 0.18/0.38 ( binintersectSubset4
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ B @ A )
% 0.18/0.38 => ( ( binintersect @ A @ B )
% 0.18/0.38 = B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset1_type,type,
% 0.18/0.38 binintersectSubset1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(binintersectSubset1,definition,
% 0.18/0.38 ( binintersectSubset1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( ( binintersect @ A @ B )
% 0.18/0.38 = A )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(bs114d_type,type,
% 0.18/0.38 bs114d: $o ).
% 0.18/0.38
% 0.18/0.38 thf(bs114d,definition,
% 0.18/0.38 ( bs114d
% 0.18/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.38 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.18/0.38 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(regular_type,type,
% 0.18/0.38 regular: $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminus_type,type,
% 0.18/0.38 setminus: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(setminusI_type,type,
% 0.18/0.38 setminusI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusI,definition,
% 0.18/0.38 ( setminusI
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusEL_type,type,
% 0.18/0.38 setminusEL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusEL,definition,
% 0.18/0.38 ( setminusEL
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusER_type,type,
% 0.18/0.38 setminusER: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusER,definition,
% 0.18/0.38 ( setminusER
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.38 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusSubset2_type,type,
% 0.18/0.38 setminusSubset2: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusSubset2,definition,
% 0.18/0.38 ( setminusSubset2
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( subset @ A @ B )
% 0.18/0.38 => ( ( setminus @ A @ B )
% 0.18/0.38 = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusERneg_type,type,
% 0.18/0.38 setminusERneg: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusERneg,definition,
% 0.18/0.38 ( setminusERneg
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.38 => ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusELneg_type,type,
% 0.18/0.38 setminusELneg: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusELneg,definition,
% 0.18/0.38 ( setminusELneg
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusILneg_type,type,
% 0.18/0.38 setminusILneg: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusILneg,definition,
% 0.18/0.38 ( setminusILneg
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ~ ( in @ Xx @ A )
% 0.18/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusIRneg_type,type,
% 0.18/0.38 setminusIRneg: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusIRneg,definition,
% 0.18/0.38 ( setminusIRneg
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusLsub_type,type,
% 0.18/0.38 setminusLsub: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusLsub,definition,
% 0.18/0.38 ( setminusLsub
% 0.18/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setminusSubset1_type,type,
% 0.18/0.38 setminusSubset1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setminusSubset1,definition,
% 0.18/0.38 ( setminusSubset1
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( ( setminus @ A @ B )
% 0.18/0.38 = emptyset )
% 0.18/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(symdiff_type,type,
% 0.18/0.38 symdiff: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(symdiff,definition,
% 0.18/0.38 ( symdiff
% 0.18/0.38 = ( ^ [A: $i,B: $i] :
% 0.18/0.38 ( dsetconstr @ ( binunion @ A @ B )
% 0.18/0.38 @ ^ [Xx: $i] :
% 0.18/0.38 ( ~ ( in @ Xx @ A )
% 0.18/0.38 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(symdiffE_type,type,
% 0.18/0.38 symdiffE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(symdiffE,definition,
% 0.18/0.38 ( symdiffE
% 0.18/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.18/0.38 => ! [Xphi: $o] :
% 0.18/0.38 ( ( ( in @ Xx @ A )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => Xphi ) )
% 0.18/0.38 => ( ( ~ ( in @ Xx @ A )
% 0.18/0.38 => ( ( in @ Xx @ B )
% 0.18/0.38 => Xphi ) )
% 0.18/0.38 => Xphi ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(symdiffI1,conjecture,
% 0.18/0.38 ( setextAx
% 0.18/0.38 => ( emptysetAx
% 0.18/0.38 => ( setadjoinAx
% 0.18/0.38 => ( powersetAx
% 0.18/0.38 => ( setunionAx
% 0.18/0.38 => ( omega0Ax
% 0.18/0.38 => ( omegaSAx
% 0.18/0.38 => ( omegaIndAx
% 0.18/0.38 => ( replAx
% 0.18/0.38 => ( foundationAx
% 0.18/0.38 => ( wellorderingAx
% 0.18/0.38 => ( descrp
% 0.18/0.38 => ( dsetconstrI
% 0.18/0.38 => ( dsetconstrEL
% 0.18/0.38 => ( dsetconstrER
% 0.18/0.38 => ( exuE1
% 0.18/0.38 => ( prop2setE
% 0.18/0.38 => ( emptysetE
% 0.18/0.38 => ( emptysetimpfalse
% 0.18/0.38 => ( notinemptyset
% 0.18/0.38 => ( exuE3e
% 0.18/0.38 => ( setext
% 0.18/0.38 => ( emptyI
% 0.18/0.38 => ( noeltsimpempty
% 0.18/0.38 => ( setbeta
% 0.18/0.38 => ( nonemptyE1
% 0.18/0.38 => ( nonemptyI
% 0.18/0.38 => ( nonemptyI1
% 0.18/0.38 => ( setadjoinIL
% 0.18/0.38 => ( emptyinunitempty
% 0.18/0.38 => ( setadjoinIR
% 0.18/0.38 => ( setadjoinE
% 0.18/0.38 => ( setadjoinOr
% 0.18/0.38 => ( setoftrueEq
% 0.18/0.38 => ( powersetI
% 0.18/0.38 => ( emptyinPowerset
% 0.18/0.38 => ( emptyInPowerset
% 0.18/0.38 => ( powersetE
% 0.18/0.38 => ( setunionI
% 0.18/0.38 => ( setunionE
% 0.18/0.38 => ( subPowSU
% 0.18/0.38 => ( exuE2
% 0.18/0.38 => ( nonemptyImpWitness
% 0.18/0.38 => ( uniqinunit
% 0.18/0.38 => ( notinsingleton
% 0.18/0.38 => ( eqinunit
% 0.18/0.38 => ( singletonsswitch
% 0.18/0.38 => ( upairsetE
% 0.18/0.38 => ( upairsetIL
% 0.18/0.38 => ( upairsetIR
% 0.18/0.38 => ( emptyE1
% 0.18/0.38 => ( vacuousDall
% 0.18/0.38 => ( quantDeMorgan1
% 0.18/0.38 => ( quantDeMorgan2
% 0.18/0.38 => ( quantDeMorgan3
% 0.18/0.38 => ( quantDeMorgan4
% 0.18/0.38 => ( prop2setI
% 0.18/0.38 => ( prop2set2propI
% 0.18/0.38 => ( notdexE
% 0.18/0.38 => ( notdallE
% 0.18/0.38 => ( exuI1
% 0.18/0.38 => ( exuI3
% 0.18/0.38 => ( exuI2
% 0.18/0.38 => ( inCongP
% 0.18/0.38 => ( in__Cong
% 0.18/0.38 => ( exuE3u
% 0.18/0.38 => ( exu__Cong
% 0.18/0.38 => ( emptyset__Cong
% 0.18/0.38 => ( setadjoin__Cong
% 0.18/0.38 => ( powerset__Cong
% 0.18/0.38 => ( setunion__Cong
% 0.18/0.38 => ( omega__Cong
% 0.18/0.38 => ( exuEu
% 0.18/0.38 => ( descr__Cong
% 0.18/0.38 => ( dsetconstr__Cong
% 0.18/0.38 => ( subsetI1
% 0.18/0.38 => ( eqimpsubset2
% 0.18/0.38 => ( eqimpsubset1
% 0.18/0.38 => ( subsetI2
% 0.18/0.38 => ( emptysetsubset
% 0.18/0.38 => ( subsetE
% 0.18/0.38 => ( subsetE2
% 0.18/0.38 => ( notsubsetI
% 0.18/0.38 => ( notequalI1
% 0.18/0.38 => ( notequalI2
% 0.18/0.38 => ( subsetRefl
% 0.18/0.38 => ( subsetTrans
% 0.18/0.38 => ( setadjoinSub
% 0.18/0.38 => ( setadjoinSub2
% 0.18/0.38 => ( subset2powerset
% 0.18/0.38 => ( setextsub
% 0.18/0.38 => ( subsetemptysetimpeq
% 0.18/0.38 => ( powersetI1
% 0.18/0.38 => ( powersetE1
% 0.18/0.38 => ( inPowerset
% 0.18/0.38 => ( powersetsubset
% 0.18/0.38 => ( sepInPowerset
% 0.18/0.38 => ( sepSubset
% 0.18/0.38 => ( binunionIL
% 0.18/0.38 => ( upairset2IR
% 0.18/0.38 => ( binunionIR
% 0.18/0.38 => ( binunionEcases
% 0.18/0.38 => ( binunionE
% 0.18/0.38 => ( binunionLsub
% 0.18/0.38 => ( binunionRsub
% 0.18/0.38 => ( binintersectI
% 0.18/0.38 => ( binintersectSubset5
% 0.18/0.38 => ( binintersectEL
% 0.18/0.38 => ( binintersectLsub
% 0.18/0.38 => ( binintersectSubset2
% 0.18/0.38 => ( binintersectSubset3
% 0.18/0.38 => ( binintersectER
% 0.18/0.38 => ( disjointsetsI1
% 0.18/0.38 => ( binintersectRsub
% 0.18/0.38 => ( binintersectSubset4
% 0.18/0.38 => ( binintersectSubset1
% 0.18/0.38 => ( bs114d
% 0.18/0.38 => ( setminusI
% 0.18/0.38 => ( setminusEL
% 0.18/0.38 => ( setminusER
% 0.18/0.38 => ( setminusSubset2
% 0.18/0.38 => ( setminusERneg
% 0.18/0.38 => ( setminusELneg
% 0.18/0.38 => ( setminusILneg
% 0.18/0.38 => ( setminusIRneg
% 0.18/0.38 => ( setminusLsub
% 0.18/0.38 => ( setminusSubset1
% 0.18/0.38 => ( symdiffE
% 0.18/0.38 => ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ~ ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 2.23/1.46 ---- Embedded in THF ---
% 2.23/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.23/1.46 %%% Generated on Tue Feb 24 12:28:42 EST 2026
% 2.23/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.23/1.46 %%% Logic specification used:
% 2.23/1.46 %%% thf(spec, logic, $$dhol).
% 2.23/1.46
% 2.23/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2DTF6052.p
% See solution above
% 2.23/1.47 ------------------------
% 2.23/1.49 ---- Cleaned THF ---
% 2.23/1.49 thf(in_type,type,
% 2.23/1.49 in: $i > $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(exu_type,type,
% 2.23/1.49 exu: ( $i > $o ) > $o ).
% 2.23/1.49
% 2.23/1.49 thf(exu,definition,
% 2.23/1.49 ( exu
% 2.23/1.49 = ( ^ [Xphi: $i > $o] :
% 2.23/1.49 ? [Xx: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 & ! [Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setextAx_type,type,
% 2.23/1.49 setextAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setextAx,definition,
% 2.23/1.49 ( setextAx
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 <=> ( in @ Xx @ B ) )
% 2.23/1.49 => ( A = B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyset_type,type,
% 2.23/1.49 emptyset: $i ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetAx_type,type,
% 2.23/1.49 emptysetAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetAx,definition,
% 2.23/1.49 ( emptysetAx
% 2.23/1.49 = ( ! [Xx: $i] :
% 2.23/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoin_type,type,
% 2.23/1.49 setadjoin: $i > $i > $i ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinAx_type,type,
% 2.23/1.49 setadjoinAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinAx,definition,
% 2.23/1.49 ( setadjoinAx
% 2.23/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.23/1.49 <=> ( ( Xy = Xx )
% 2.23/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powerset_type,type,
% 2.23/1.49 powerset: $i > $i ).
% 2.23/1.49
% 2.23/1.49 thf(powersetAx_type,type,
% 2.23/1.49 powersetAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetAx,definition,
% 2.23/1.49 ( powersetAx
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.23/1.49 <=> ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setunion_type,type,
% 2.23/1.49 setunion: $i > $i ).
% 2.23/1.49
% 2.23/1.49 thf(setunionAx_type,type,
% 2.23/1.49 setunionAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setunionAx,definition,
% 2.23/1.49 ( setunionAx
% 2.23/1.49 = ( ! [A: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.23/1.49 <=> ? [B: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 & ( in @ B @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(omega_type,type,
% 2.23/1.49 omega: $i ).
% 2.23/1.49
% 2.23/1.49 thf(omega0Ax_type,type,
% 2.23/1.49 omega0Ax: $o ).
% 2.23/1.49
% 2.23/1.49 thf(omega0Ax,definition,
% 2.23/1.49 ( omega0Ax
% 2.23/1.49 = ( in @ emptyset @ omega ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(omegaSAx_type,type,
% 2.23/1.49 omegaSAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(omegaSAx,definition,
% 2.23/1.49 ( omegaSAx
% 2.23/1.49 = ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ omega )
% 2.23/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(omegaIndAx_type,type,
% 2.23/1.49 omegaIndAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(omegaIndAx,definition,
% 2.23/1.49 ( omegaIndAx
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ( ( in @ emptyset @ A )
% 2.23/1.49 & ! [Xx: $i] :
% 2.23/1.49 ( ( ( in @ Xx @ omega )
% 2.23/1.49 & ( in @ Xx @ A ) )
% 2.23/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.23/1.49 => ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ omega )
% 2.23/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(replAx_type,type,
% 2.23/1.49 replAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(replAx,definition,
% 2.23/1.49 ( replAx
% 2.23/1.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( exu
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.23/1.49 => ? [B: $i] :
% 2.23/1.49 ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 <=> ? [Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ A )
% 2.23/1.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(foundationAx_type,type,
% 2.23/1.49 foundationAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(foundationAx,definition,
% 2.23/1.49 ( foundationAx
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.23/1.49 => ? [B: $i] :
% 2.23/1.49 ( ( in @ B @ A )
% 2.23/1.49 & ~ ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(wellorderingAx_type,type,
% 2.23/1.49 wellorderingAx: $o ).
% 2.23/1.49
% 2.23/1.49 thf(wellorderingAx,definition,
% 2.23/1.49 ( wellorderingAx
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ? [B: $i] :
% 2.23/1.49 ( ! [C: $i] :
% 2.23/1.49 ( ( in @ C @ B )
% 2.23/1.49 => ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ C )
% 2.23/1.49 => ( in @ Xx @ A ) ) )
% 2.23/1.49 & ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( ( in @ Xx @ A )
% 2.23/1.49 & ( in @ Xy @ A ) )
% 2.23/1.49 => ( ! [C: $i] :
% 2.23/1.49 ( ( in @ C @ B )
% 2.23/1.49 => ( ( in @ Xx @ C )
% 2.23/1.49 <=> ( in @ Xy @ C ) ) )
% 2.23/1.49 => ( Xx = Xy ) ) )
% 2.23/1.49 & ! [C: $i,D: $i] :
% 2.23/1.49 ( ( ( in @ C @ B )
% 2.23/1.49 & ( in @ D @ B ) )
% 2.23/1.49 => ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ C )
% 2.23/1.49 => ( in @ Xx @ D ) )
% 2.23/1.49 | ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ D )
% 2.23/1.49 => ( in @ Xx @ C ) ) ) )
% 2.23/1.49 & ! [C: $i] :
% 2.23/1.49 ( ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ C )
% 2.23/1.49 => ( in @ Xx @ A ) )
% 2.23/1.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.23/1.49 => ? [D: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ D @ B )
% 2.23/1.49 & ( in @ Xx @ C )
% 2.23/1.49 & ~ ? [Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ D )
% 2.23/1.49 & ( in @ Xy @ C ) )
% 2.23/1.49 & ! [E: $i] :
% 2.23/1.49 ( ( in @ E @ B )
% 2.23/1.49 => ( ! [Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ E )
% 2.23/1.49 => ( in @ Xy @ D ) )
% 2.23/1.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(descr_type,type,
% 2.23/1.49 descr: ( $i > $o ) > $i ).
% 2.23/1.49
% 2.23/1.49 thf(descrp_type,type,
% 2.23/1.49 descrp: $o ).
% 2.23/1.49
% 2.23/1.49 thf(descrp,definition,
% 2.23/1.49 ( descrp
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ( Xphi
% 2.23/1.49 @ ( descr
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstr_type,type,
% 2.23/1.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrI_type,type,
% 2.23/1.49 dsetconstrI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrI,definition,
% 2.23/1.49 ( dsetconstrI
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( ( Xphi @ Xx )
% 2.23/1.49 => ( in @ Xx
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrEL_type,type,
% 2.23/1.49 dsetconstrEL: $o ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrEL,definition,
% 2.23/1.49 ( dsetconstrEL
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.23/1.49 => ( in @ Xx @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrER_type,type,
% 2.23/1.49 dsetconstrER: $o ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstrER,definition,
% 2.23/1.49 ( dsetconstrER
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.23/1.49 => ( Xphi @ Xx ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuE1_type,type,
% 2.23/1.49 exuE1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuE1,definition,
% 2.23/1.49 ( exuE1
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ? [Xx: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 & ! [Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(prop2set_type,type,
% 2.23/1.49 prop2set: $o > $i ).
% 2.23/1.49
% 2.23/1.49 thf(prop2setE_type,type,
% 2.23/1.49 prop2setE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(prop2setE,definition,
% 2.23/1.49 ( prop2setE
% 2.23/1.49 = ( ! [Xphi: $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.23/1.49 => Xphi ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetE_type,type,
% 2.23/1.49 emptysetE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetE,definition,
% 2.23/1.49 ( emptysetE
% 2.23/1.49 = ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ emptyset )
% 2.23/1.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetimpfalse_type,type,
% 2.23/1.49 emptysetimpfalse: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetimpfalse,definition,
% 2.23/1.49 ( emptysetimpfalse
% 2.23/1.49 = ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ emptyset )
% 2.23/1.49 => $false ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notinemptyset_type,type,
% 2.23/1.49 notinemptyset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notinemptyset,definition,
% 2.23/1.49 ( notinemptyset
% 2.23/1.49 = ( ! [Xx: $i] :
% 2.23/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuE3e_type,type,
% 2.23/1.49 exuE3e: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuE3e,definition,
% 2.23/1.49 ( exuE3e
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setext_type,type,
% 2.23/1.49 setext: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setext,definition,
% 2.23/1.49 ( setext
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ B ) )
% 2.23/1.49 => ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( in @ Xx @ A ) )
% 2.23/1.49 => ( A = B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyI_type,type,
% 2.23/1.49 emptyI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyI,definition,
% 2.23/1.49 ( emptyI
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ~ ( in @ Xx @ A )
% 2.23/1.49 => ( A = emptyset ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(noeltsimpempty_type,type,
% 2.23/1.49 noeltsimpempty: $o ).
% 2.23/1.49
% 2.23/1.49 thf(noeltsimpempty,definition,
% 2.23/1.49 ( noeltsimpempty
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ~ ( in @ Xx @ A )
% 2.23/1.49 => ( A = emptyset ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setbeta_type,type,
% 2.23/1.49 setbeta: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setbeta,definition,
% 2.23/1.49 ( setbeta
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( ( in @ Xx
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.23/1.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(nonempty_type,type,
% 2.23/1.49 nonempty: $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(nonempty,definition,
% 2.23/1.49 ( nonempty
% 2.23/1.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyE1_type,type,
% 2.23/1.49 nonemptyE1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyE1,definition,
% 2.23/1.49 ( nonemptyE1
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ( nonempty @ A )
% 2.23/1.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyI_type,type,
% 2.23/1.49 nonemptyI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyI,definition,
% 2.23/1.49 ( nonemptyI
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( ( Xphi @ Xx )
% 2.23/1.49 => ( nonempty
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyI1_type,type,
% 2.23/1.49 nonemptyI1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyI1,definition,
% 2.23/1.49 ( nonemptyI1
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.23/1.49 => ( nonempty @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinIL_type,type,
% 2.23/1.49 setadjoinIL: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinIL,definition,
% 2.23/1.49 ( setadjoinIL
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyinunitempty_type,type,
% 2.23/1.49 emptyinunitempty: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyinunitempty,definition,
% 2.23/1.49 ( emptyinunitempty
% 2.23/1.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinIR_type,type,
% 2.23/1.49 setadjoinIR: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinIR,definition,
% 2.23/1.49 ( setadjoinIR
% 2.23/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ A )
% 2.23/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinE_type,type,
% 2.23/1.49 setadjoinE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinE,definition,
% 2.23/1.49 ( setadjoinE
% 2.23/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.23/1.49 => ! [Xphi: $o] :
% 2.23/1.49 ( ( ( Xy = Xx )
% 2.23/1.49 => Xphi )
% 2.23/1.49 => ( ( ( in @ Xy @ A )
% 2.23/1.49 => Xphi )
% 2.23/1.49 => Xphi ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinOr_type,type,
% 2.23/1.49 setadjoinOr: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinOr,definition,
% 2.23/1.49 ( setadjoinOr
% 2.23/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.23/1.49 => ( ( Xy = Xx )
% 2.23/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setoftrueEq_type,type,
% 2.23/1.49 setoftrueEq: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setoftrueEq,definition,
% 2.23/1.49 ( setoftrueEq
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xx: $i] : $true )
% 2.23/1.49 = A ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powersetI_type,type,
% 2.23/1.49 powersetI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetI,definition,
% 2.23/1.49 ( powersetI
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( in @ Xx @ A ) )
% 2.23/1.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyinPowerset_type,type,
% 2.23/1.49 emptyinPowerset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyinPowerset,definition,
% 2.23/1.49 ( emptyinPowerset
% 2.23/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyInPowerset_type,type,
% 2.23/1.49 emptyInPowerset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyInPowerset,definition,
% 2.23/1.49 ( emptyInPowerset
% 2.23/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powersetE_type,type,
% 2.23/1.49 powersetE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetE,definition,
% 2.23/1.49 ( powersetE
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.23/1.49 => ( ( in @ Xx @ B )
% 2.23/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setunionI_type,type,
% 2.23/1.49 setunionI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setunionI,definition,
% 2.23/1.49 ( setunionI
% 2.23/1.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( ( in @ B @ A )
% 2.23/1.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setunionE_type,type,
% 2.23/1.49 setunionE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setunionE,definition,
% 2.23/1.49 ( setunionE
% 2.23/1.49 = ( ! [A: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.23/1.49 => ! [Xphi: $o] :
% 2.23/1.49 ( ! [B: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( ( in @ B @ A )
% 2.23/1.49 => Xphi ) )
% 2.23/1.49 => Xphi ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subPowSU_type,type,
% 2.23/1.49 subPowSU: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subPowSU,definition,
% 2.23/1.49 ( subPowSU
% 2.23/1.49 = ( ! [A: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuE2_type,type,
% 2.23/1.49 exuE2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuE2,definition,
% 2.23/1.49 ( exuE2
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ? [Xx: $i] :
% 2.23/1.49 ! [Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xy )
% 2.23/1.49 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyImpWitness_type,type,
% 2.23/1.49 nonemptyImpWitness: $o ).
% 2.23/1.49
% 2.23/1.49 thf(nonemptyImpWitness,definition,
% 2.23/1.49 ( nonemptyImpWitness
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ( nonempty @ A )
% 2.23/1.49 => ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & $true ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(uniqinunit_type,type,
% 2.23/1.49 uniqinunit: $o ).
% 2.23/1.49
% 2.23/1.49 thf(uniqinunit,definition,
% 2.23/1.49 ( uniqinunit
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.23/1.49 => ( Xx = Xy ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notinsingleton_type,type,
% 2.23/1.49 notinsingleton: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notinsingleton,definition,
% 2.23/1.49 ( notinsingleton
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx != Xy )
% 2.23/1.49 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(eqinunit_type,type,
% 2.23/1.49 eqinunit: $o ).
% 2.23/1.49
% 2.23/1.49 thf(eqinunit,definition,
% 2.23/1.49 ( eqinunit
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(singletonsswitch_type,type,
% 2.23/1.49 singletonsswitch: $o ).
% 2.23/1.49
% 2.23/1.49 thf(singletonsswitch,definition,
% 2.23/1.49 ( singletonsswitch
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.23/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetE_type,type,
% 2.23/1.49 upairsetE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetE,definition,
% 2.23/1.49 ( upairsetE
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.23/1.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.23/1.49 => ( ( Xz = Xx )
% 2.23/1.49 | ( Xz = Xy ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetIL_type,type,
% 2.23/1.49 upairsetIL: $o ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetIL,definition,
% 2.23/1.49 ( upairsetIL
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetIR_type,type,
% 2.23/1.49 upairsetIR: $o ).
% 2.23/1.49
% 2.23/1.49 thf(upairsetIR,definition,
% 2.23/1.49 ( upairsetIR
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyE1_type,type,
% 2.23/1.49 emptyE1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyE1,definition,
% 2.23/1.49 ( emptyE1
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ( Xphi @ Xx ) )
% 2.23/1.49 => ( ( ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 = emptyset )
% 2.23/1.49 => $false ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(vacuousDall_type,type,
% 2.23/1.49 vacuousDall: $o ).
% 2.23/1.49
% 2.23/1.49 thf(vacuousDall,definition,
% 2.23/1.49 ( vacuousDall
% 2.23/1.49 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ emptyset )
% 2.23/1.49 => ( Xphi @ Xx ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan1_type,type,
% 2.23/1.49 quantDeMorgan1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan1,definition,
% 2.23/1.49 ( quantDeMorgan1
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ~ ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( Xphi @ Xx ) )
% 2.23/1.49 => ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan2_type,type,
% 2.23/1.49 quantDeMorgan2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan2,definition,
% 2.23/1.49 ( quantDeMorgan2
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ~ ( Xphi @ Xx ) )
% 2.23/1.49 => ~ ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan3_type,type,
% 2.23/1.49 quantDeMorgan3: $o ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan3,definition,
% 2.23/1.49 ( quantDeMorgan3
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ~ ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ( Xphi @ Xx ) )
% 2.23/1.49 => ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan4_type,type,
% 2.23/1.49 quantDeMorgan4: $o ).
% 2.23/1.49
% 2.23/1.49 thf(quantDeMorgan4,definition,
% 2.23/1.49 ( quantDeMorgan4
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ~ ( Xphi @ Xx ) )
% 2.23/1.49 => ~ ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(prop2setI_type,type,
% 2.23/1.49 prop2setI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(prop2setI,definition,
% 2.23/1.49 ( prop2setI
% 2.23/1.49 = ( ! [Xphi: $o] :
% 2.23/1.49 ( Xphi
% 2.23/1.49 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(set2prop_type,type,
% 2.23/1.49 set2prop: $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(prop2set2propI_type,type,
% 2.23/1.49 prop2set2propI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(prop2set2propI,definition,
% 2.23/1.49 ( prop2set2propI
% 2.23/1.49 = ( ! [Xphi: $o] :
% 2.23/1.49 ( Xphi
% 2.23/1.49 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notdexE_type,type,
% 2.23/1.49 notdexE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notdexE,definition,
% 2.23/1.49 ( notdexE
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ~ ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ( Xphi @ Xx ) )
% 2.23/1.49 => ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notdallE_type,type,
% 2.23/1.49 notdallE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notdallE,definition,
% 2.23/1.49 ( notdallE
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( ~ ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( Xphi @ Xx ) )
% 2.23/1.49 => ? [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuI1_type,type,
% 2.23/1.49 exuI1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuI1,definition,
% 2.23/1.49 ( exuI1
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ? [Xx: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 & ! [Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) )
% 2.23/1.49 => ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuI3_type,type,
% 2.23/1.49 exuI3: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuI3,definition,
% 2.23/1.49 ( exuI3
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.23/1.49 => ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 => ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) )
% 2.23/1.49 => ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuI2_type,type,
% 2.23/1.49 exuI2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuI2,definition,
% 2.23/1.49 ( exuI2
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ? [Xx: $i] :
% 2.23/1.49 ! [Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xy )
% 2.23/1.49 <=> ( Xy = Xx ) )
% 2.23/1.49 => ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(inCongP_type,type,
% 2.23/1.49 inCongP: $o ).
% 2.23/1.49
% 2.23/1.49 thf(inCongP,definition,
% 2.23/1.49 ( inCongP
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(in__Cong_type,type,
% 2.23/1.49 in__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(in__Cong,definition,
% 2.23/1.49 ( in__Cong
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ( ( in @ Xx @ A )
% 2.23/1.49 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuE3u_type,type,
% 2.23/1.49 exuE3u: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuE3u,definition,
% 2.23/1.49 ( exuE3u
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 => ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exu__Cong_type,type,
% 2.23/1.49 exu__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exu__Cong,definition,
% 2.23/1.49 ( exu__Cong
% 2.23/1.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.23/1.49 ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ( ( Xphi @ Xx )
% 2.23/1.49 <=> ( Xpsi @ Xy ) ) )
% 2.23/1.49 => ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 <=> ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptyset__Cong_type,type,
% 2.23/1.49 emptyset__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptyset__Cong,definition,
% 2.23/1.49 ( emptyset__Cong
% 2.23/1.49 = ( emptyset = emptyset ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoin__Cong_type,type,
% 2.23/1.49 setadjoin__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoin__Cong,definition,
% 2.23/1.49 ( setadjoin__Cong
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ! [Xz: $i,Xu: $i] :
% 2.23/1.49 ( ( Xz = Xu )
% 2.23/1.49 => ( ( setadjoin @ Xx @ Xz )
% 2.23/1.49 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powerset__Cong_type,type,
% 2.23/1.49 powerset__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powerset__Cong,definition,
% 2.23/1.49 ( powerset__Cong
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ( ( powerset @ A )
% 2.23/1.49 = ( powerset @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setunion__Cong_type,type,
% 2.23/1.49 setunion__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setunion__Cong,definition,
% 2.23/1.49 ( setunion__Cong
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ( ( setunion @ A )
% 2.23/1.49 = ( setunion @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(omega__Cong_type,type,
% 2.23/1.49 omega__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(omega__Cong,definition,
% 2.23/1.49 ( omega__Cong
% 2.23/1.49 = ( omega = omega ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(exuEu_type,type,
% 2.23/1.49 exuEu: $o ).
% 2.23/1.49
% 2.23/1.49 thf(exuEu,definition,
% 2.23/1.49 ( exuEu
% 2.23/1.49 = ( ! [Xphi: $i > $o] :
% 2.23/1.49 ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xphi @ Xx )
% 2.23/1.49 => ( ( Xphi @ Xy )
% 2.23/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(descr__Cong_type,type,
% 2.23/1.49 descr__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(descr__Cong,definition,
% 2.23/1.49 ( descr__Cong
% 2.23/1.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.23/1.49 ( ! [Xx: $i,Xy: $i] :
% 2.23/1.49 ( ( Xx = Xy )
% 2.23/1.49 => ( ( Xphi @ Xx )
% 2.23/1.49 <=> ( Xpsi @ Xy ) ) )
% 2.23/1.49 => ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 => ( ( exu
% 2.23/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.23/1.49 => ( ( descr
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 = ( descr
% 2.23/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstr__Cong_type,type,
% 2.23/1.49 dsetconstr__Cong: $o ).
% 2.23/1.49
% 2.23/1.49 thf(dsetconstr__Cong,definition,
% 2.23/1.49 ( dsetconstr__Cong
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ! [Xy: $i] :
% 2.23/1.49 ( ( in @ Xy @ B )
% 2.23/1.49 => ( ( Xx = Xy )
% 2.23/1.49 => ( ( Xphi @ Xx )
% 2.23/1.49 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.23/1.49 => ( ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 = ( dsetconstr @ B
% 2.23/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subset_type,type,
% 2.23/1.49 subset: $i > $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(disjoint_type,type,
% 2.23/1.49 disjoint: $i > $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(setsmeet_type,type,
% 2.23/1.49 setsmeet: $i > $i > $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetI1_type,type,
% 2.23/1.49 subsetI1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetI1,definition,
% 2.23/1.49 ( subsetI1
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ B ) )
% 2.23/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(eqimpsubset2_type,type,
% 2.23/1.49 eqimpsubset2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(eqimpsubset2,definition,
% 2.23/1.49 ( eqimpsubset2
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ( subset @ B @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(eqimpsubset1_type,type,
% 2.23/1.49 eqimpsubset1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(eqimpsubset1,definition,
% 2.23/1.49 ( eqimpsubset1
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( A = B )
% 2.23/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetI2_type,type,
% 2.23/1.49 subsetI2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetI2,definition,
% 2.23/1.49 ( subsetI2
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ! [Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ B ) )
% 2.23/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetsubset_type,type,
% 2.23/1.49 emptysetsubset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(emptysetsubset,definition,
% 2.23/1.49 ( emptysetsubset
% 2.23/1.49 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetE_type,type,
% 2.23/1.49 subsetE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetE,definition,
% 2.23/1.49 ( subsetE
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetE2_type,type,
% 2.23/1.49 subsetE2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetE2,definition,
% 2.23/1.49 ( subsetE2
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( ~ ( in @ Xx @ B )
% 2.23/1.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notsubsetI_type,type,
% 2.23/1.49 notsubsetI: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notsubsetI,definition,
% 2.23/1.49 ( notsubsetI
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( ~ ( in @ Xx @ B )
% 2.23/1.49 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notequalI1_type,type,
% 2.23/1.49 notequalI1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notequalI1,definition,
% 2.23/1.49 ( notequalI1
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ~ ( subset @ A @ B )
% 2.23/1.49 => ( A != B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(notequalI2_type,type,
% 2.23/1.49 notequalI2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(notequalI2,definition,
% 2.23/1.49 ( notequalI2
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( ~ ( in @ Xx @ B )
% 2.23/1.49 => ( A != B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetRefl_type,type,
% 2.23/1.49 subsetRefl: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetRefl,definition,
% 2.23/1.49 ( subsetRefl
% 2.23/1.49 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetTrans_type,type,
% 2.23/1.49 subsetTrans: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetTrans,definition,
% 2.23/1.49 ( subsetTrans
% 2.23/1.49 = ( ! [A: $i,B: $i,C: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( ( subset @ B @ C )
% 2.23/1.49 => ( subset @ A @ C ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinSub_type,type,
% 2.23/1.49 setadjoinSub: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinSub,definition,
% 2.23/1.49 ( setadjoinSub
% 2.23/1.49 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinSub2_type,type,
% 2.23/1.49 setadjoinSub2: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setadjoinSub2,definition,
% 2.23/1.49 ( setadjoinSub2
% 2.23/1.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subset2powerset_type,type,
% 2.23/1.49 subset2powerset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subset2powerset,definition,
% 2.23/1.49 ( subset2powerset
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(setextsub_type,type,
% 2.23/1.49 setextsub: $o ).
% 2.23/1.49
% 2.23/1.49 thf(setextsub,definition,
% 2.23/1.49 ( setextsub
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( ( subset @ B @ A )
% 2.23/1.49 => ( A = B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(subsetemptysetimpeq_type,type,
% 2.23/1.49 subsetemptysetimpeq: $o ).
% 2.23/1.49
% 2.23/1.49 thf(subsetemptysetimpeq,definition,
% 2.23/1.49 ( subsetemptysetimpeq
% 2.23/1.49 = ( ! [A: $i] :
% 2.23/1.49 ( ( subset @ A @ emptyset )
% 2.23/1.49 => ( A = emptyset ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powersetI1_type,type,
% 2.23/1.49 powersetI1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetI1,definition,
% 2.23/1.49 ( powersetI1
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( subset @ B @ A )
% 2.23/1.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powersetE1_type,type,
% 2.23/1.49 powersetE1: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetE1,definition,
% 2.23/1.49 ( powersetE1
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.23/1.49 => ( subset @ B @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(inPowerset_type,type,
% 2.23/1.49 inPowerset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(inPowerset,definition,
% 2.23/1.49 ( inPowerset
% 2.23/1.49 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(powersetsubset_type,type,
% 2.23/1.49 powersetsubset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(powersetsubset,definition,
% 2.23/1.49 ( powersetsubset
% 2.23/1.49 = ( ! [A: $i,B: $i] :
% 2.23/1.49 ( ( subset @ A @ B )
% 2.23/1.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(sepInPowerset_type,type,
% 2.23/1.49 sepInPowerset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(sepInPowerset,definition,
% 2.23/1.49 ( sepInPowerset
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( in
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 @ ( powerset @ A ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(sepSubset_type,type,
% 2.23/1.49 sepSubset: $o ).
% 2.23/1.49
% 2.23/1.49 thf(sepSubset,definition,
% 2.23/1.49 ( sepSubset
% 2.23/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.23/1.49 ( subset
% 2.23/1.49 @ ( dsetconstr @ A
% 2.23/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.23/1.49 @ A ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunion_type,type,
% 2.23/1.49 binunion: $i > $i > $i ).
% 2.23/1.49
% 2.23/1.49 thf(binunionIL_type,type,
% 2.23/1.49 binunionIL: $o ).
% 2.23/1.49
% 2.23/1.49 thf(binunionIL,definition,
% 2.23/1.49 ( binunionIL
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ A )
% 2.23/1.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(upairset2IR_type,type,
% 2.23/1.49 upairset2IR: $o ).
% 2.23/1.49
% 2.23/1.49 thf(upairset2IR,definition,
% 2.23/1.49 ( upairset2IR
% 2.23/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunionIR_type,type,
% 2.23/1.49 binunionIR: $o ).
% 2.23/1.49
% 2.23/1.49 thf(binunionIR,definition,
% 2.23/1.49 ( binunionIR
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ B )
% 2.23/1.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunionEcases_type,type,
% 2.23/1.49 binunionEcases: $o ).
% 2.23/1.49
% 2.23/1.49 thf(binunionEcases,definition,
% 2.23/1.49 ( binunionEcases
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.23/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.23/1.49 => ( ( ( in @ Xx @ A )
% 2.23/1.49 => Xphi )
% 2.23/1.49 => ( ( ( in @ Xx @ B )
% 2.23/1.49 => Xphi )
% 2.23/1.49 => Xphi ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunionE_type,type,
% 2.23/1.49 binunionE: $o ).
% 2.23/1.49
% 2.23/1.49 thf(binunionE,definition,
% 2.23/1.49 ( binunionE
% 2.23/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.23/1.49 => ( ( in @ Xx @ A )
% 2.23/1.49 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunionLsub_type,type,
% 2.23/1.49 binunionLsub: $o ).
% 2.23/1.49
% 2.23/1.49 thf(binunionLsub,definition,
% 2.23/1.49 ( binunionLsub
% 2.23/1.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.23/1.49
% 2.23/1.49 thf(binunionRsub_type,type,
% 2.23/1.50 binunionRsub: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binunionRsub,definition,
% 2.23/1.50 ( binunionRsub
% 2.23/1.50 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersect_type,type,
% 2.23/1.50 binintersect: $i > $i > $i ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectI_type,type,
% 2.23/1.50 binintersectI: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectI,definition,
% 2.23/1.50 ( binintersectI
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ A )
% 2.23/1.50 => ( ( in @ Xx @ B )
% 2.23/1.50 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset5_type,type,
% 2.23/1.50 binintersectSubset5: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset5,definition,
% 2.23/1.50 ( binintersectSubset5
% 2.23/1.50 = ( ! [A: $i,B: $i,C: $i] :
% 2.23/1.50 ( ( subset @ C @ A )
% 2.23/1.50 => ( ( subset @ C @ B )
% 2.23/1.50 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectEL_type,type,
% 2.23/1.50 binintersectEL: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectEL,definition,
% 2.23/1.50 ( binintersectEL
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.23/1.50 => ( in @ Xx @ A ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectLsub_type,type,
% 2.23/1.50 binintersectLsub: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectLsub,definition,
% 2.23/1.50 ( binintersectLsub
% 2.23/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset2_type,type,
% 2.23/1.50 binintersectSubset2: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset2,definition,
% 2.23/1.50 ( binintersectSubset2
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( subset @ A @ B )
% 2.23/1.50 => ( ( binintersect @ A @ B )
% 2.23/1.50 = A ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset3_type,type,
% 2.23/1.50 binintersectSubset3: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset3,definition,
% 2.23/1.50 ( binintersectSubset3
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( ( binintersect @ A @ B )
% 2.23/1.50 = B )
% 2.23/1.50 => ( subset @ B @ A ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectER_type,type,
% 2.23/1.50 binintersectER: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectER,definition,
% 2.23/1.50 ( binintersectER
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.23/1.50 => ( in @ Xx @ B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(disjointsetsI1_type,type,
% 2.23/1.50 disjointsetsI1: $o ).
% 2.23/1.50
% 2.23/1.50 thf(disjointsetsI1,definition,
% 2.23/1.50 ( disjointsetsI1
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ~ ? [Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ A )
% 2.23/1.50 & ( in @ Xx @ B ) )
% 2.23/1.50 => ( ( binintersect @ A @ B )
% 2.23/1.50 = emptyset ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectRsub_type,type,
% 2.23/1.50 binintersectRsub: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectRsub,definition,
% 2.23/1.50 ( binintersectRsub
% 2.23/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset4_type,type,
% 2.23/1.50 binintersectSubset4: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset4,definition,
% 2.23/1.50 ( binintersectSubset4
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( subset @ B @ A )
% 2.23/1.50 => ( ( binintersect @ A @ B )
% 2.23/1.50 = B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset1_type,type,
% 2.23/1.50 binintersectSubset1: $o ).
% 2.23/1.50
% 2.23/1.50 thf(binintersectSubset1,definition,
% 2.23/1.50 ( binintersectSubset1
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( ( binintersect @ A @ B )
% 2.23/1.50 = A )
% 2.23/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(bs114d_type,type,
% 2.23/1.50 bs114d: $o ).
% 2.23/1.50
% 2.23/1.50 thf(bs114d,definition,
% 2.23/1.50 ( bs114d
% 2.23/1.50 = ( ! [A: $i,B: $i,C: $i] :
% 2.23/1.50 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.23/1.50 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(regular_type,type,
% 2.23/1.50 regular: $i > $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminus_type,type,
% 2.23/1.50 setminus: $i > $i > $i ).
% 2.23/1.50
% 2.23/1.50 thf(setminusI_type,type,
% 2.23/1.50 setminusI: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusI,definition,
% 2.23/1.50 ( setminusI
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ A )
% 2.23/1.50 => ( ~ ( in @ Xx @ B )
% 2.23/1.50 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusEL_type,type,
% 2.23/1.50 setminusEL: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusEL,definition,
% 2.23/1.50 ( setminusEL
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.23/1.50 => ( in @ Xx @ A ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusER_type,type,
% 2.23/1.50 setminusER: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusER,definition,
% 2.23/1.50 ( setminusER
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.23/1.50 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusSubset2_type,type,
% 2.23/1.50 setminusSubset2: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusSubset2,definition,
% 2.23/1.50 ( setminusSubset2
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( subset @ A @ B )
% 2.23/1.50 => ( ( setminus @ A @ B )
% 2.23/1.50 = emptyset ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusERneg_type,type,
% 2.23/1.50 setminusERneg: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusERneg,definition,
% 2.23/1.50 ( setminusERneg
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.23/1.50 => ( ( in @ Xx @ A )
% 2.23/1.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusELneg_type,type,
% 2.23/1.50 setminusELneg: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusELneg,definition,
% 2.23/1.50 ( setminusELneg
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.23/1.50 => ( ~ ( in @ Xx @ B )
% 2.23/1.50 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusILneg_type,type,
% 2.23/1.50 setminusILneg: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusILneg,definition,
% 2.23/1.50 ( setminusILneg
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ~ ( in @ Xx @ A )
% 2.23/1.50 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusIRneg_type,type,
% 2.23/1.50 setminusIRneg: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusIRneg,definition,
% 2.23/1.50 ( setminusIRneg
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ B )
% 2.23/1.50 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusLsub_type,type,
% 2.23/1.50 setminusLsub: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusLsub,definition,
% 2.23/1.50 ( setminusLsub
% 2.23/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(setminusSubset1_type,type,
% 2.23/1.50 setminusSubset1: $o ).
% 2.23/1.50
% 2.23/1.50 thf(setminusSubset1,definition,
% 2.23/1.50 ( setminusSubset1
% 2.23/1.50 = ( ! [A: $i,B: $i] :
% 2.23/1.50 ( ( ( setminus @ A @ B )
% 2.23/1.50 = emptyset )
% 2.23/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(symdiff_type,type,
% 2.23/1.50 symdiff: $i > $i > $i ).
% 2.23/1.50
% 2.23/1.50 thf(symdiff,definition,
% 2.23/1.50 ( symdiff
% 2.23/1.50 = ( ^ [A: $i,B: $i] :
% 2.23/1.50 ( dsetconstr @ ( binunion @ A @ B )
% 2.23/1.50 @ ^ [Xx: $i] :
% 2.23/1.50 ( ~ ( in @ Xx @ A )
% 2.23/1.50 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(symdiffE_type,type,
% 2.23/1.50 symdiffE: $o ).
% 2.23/1.50
% 2.23/1.50 thf(symdiffE,definition,
% 2.23/1.50 ( symdiffE
% 2.23/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.23/1.50 => ! [Xphi: $o] :
% 2.23/1.50 ( ( ( in @ Xx @ A )
% 2.23/1.50 => ( ~ ( in @ Xx @ B )
% 2.23/1.50 => Xphi ) )
% 2.23/1.50 => ( ( ~ ( in @ Xx @ A )
% 2.23/1.50 => ( ( in @ Xx @ B )
% 2.23/1.50 => Xphi ) )
% 2.23/1.50 => Xphi ) ) ) ) ) ).
% 2.23/1.50
% 2.23/1.50 thf(symdiffI1,conjecture,
% 2.23/1.50 ( setextAx
% 2.23/1.50 => ( emptysetAx
% 2.23/1.50 => ( setadjoinAx
% 2.23/1.50 => ( powersetAx
% 2.23/1.50 => ( setunionAx
% 2.23/1.50 => ( omega0Ax
% 2.23/1.50 => ( omegaSAx
% 2.23/1.50 => ( omegaIndAx
% 2.23/1.50 => ( replAx
% 2.23/1.50 => ( foundationAx
% 2.23/1.50 => ( wellorderingAx
% 2.23/1.50 => ( descrp
% 2.23/1.50 => ( dsetconstrI
% 2.23/1.50 => ( dsetconstrEL
% 2.23/1.50 => ( dsetconstrER
% 2.23/1.50 => ( exuE1
% 2.23/1.50 => ( prop2setE
% 2.23/1.50 => ( emptysetE
% 2.23/1.50 => ( emptysetimpfalse
% 2.23/1.50 => ( notinemptyset
% 2.23/1.50 => ( exuE3e
% 2.23/1.50 => ( setext
% 2.23/1.50 => ( emptyI
% 2.23/1.50 => ( noeltsimpempty
% 2.23/1.50 => ( setbeta
% 2.23/1.50 => ( nonemptyE1
% 2.23/1.50 => ( nonemptyI
% 2.23/1.50 => ( nonemptyI1
% 2.23/1.50 => ( setadjoinIL
% 2.23/1.50 => ( emptyinunitempty
% 2.23/1.50 => ( setadjoinIR
% 2.23/1.50 => ( setadjoinE
% 2.23/1.50 => ( setadjoinOr
% 2.23/1.50 => ( setoftrueEq
% 2.23/1.50 => ( powersetI
% 2.23/1.50 => ( emptyinPowerset
% 2.23/1.50 => ( emptyInPowerset
% 2.23/1.50 => ( powersetE
% 2.23/1.50 => ( setunionI
% 2.23/1.50 => ( setunionE
% 2.23/1.50 => ( subPowSU
% 2.23/1.50 => ( exuE2
% 2.23/1.50 => ( nonemptyImpWitness
% 2.23/1.50 => ( uniqinunit
% 2.23/1.50 => ( notinsingleton
% 2.23/1.50 => ( eqinunit
% 2.23/1.50 => ( singletonsswitch
% 2.23/1.50 => ( upairsetE
% 2.23/1.50 => ( upairsetIL
% 2.23/1.50 => ( upairsetIR
% 2.23/1.50 => ( emptyE1
% 2.23/1.50 => ( vacuousDall
% 2.23/1.50 => ( quantDeMorgan1
% 2.23/1.50 => ( quantDeMorgan2
% 2.23/1.50 => ( quantDeMorgan3
% 2.23/1.50 => ( quantDeMorgan4
% 2.23/1.50 => ( prop2setI
% 2.23/1.50 => ( prop2set2propI
% 2.23/1.50 => ( notdexE
% 2.23/1.50 => ( notdallE
% 2.23/1.50 => ( exuI1
% 2.23/1.50 => ( exuI3
% 2.23/1.50 => ( exuI2
% 2.23/1.50 => ( inCongP
% 2.23/1.50 => ( in__Cong
% 2.23/1.50 => ( exuE3u
% 2.23/1.50 => ( exu__Cong
% 2.23/1.50 => ( emptyset__Cong
% 2.23/1.50 => ( setadjoin__Cong
% 2.23/1.50 => ( powerset__Cong
% 2.23/1.50 => ( setunion__Cong
% 2.23/1.50 => ( omega__Cong
% 2.23/1.50 => ( exuEu
% 2.23/1.50 => ( descr__Cong
% 2.23/1.50 => ( dsetconstr__Cong
% 2.23/1.50 => ( subsetI1
% 2.23/1.50 => ( eqimpsubset2
% 2.23/1.50 => ( eqimpsubset1
% 2.23/1.50 => ( subsetI2
% 2.23/1.50 => ( emptysetsubset
% 2.23/1.50 => ( subsetE
% 2.23/1.50 => ( subsetE2
% 2.23/1.50 => ( notsubsetI
% 2.23/1.50 => ( notequalI1
% 2.23/1.50 => ( notequalI2
% 2.23/1.50 => ( subsetRefl
% 2.23/1.50 => ( subsetTrans
% 2.23/1.50 => ( setadjoinSub
% 2.23/1.50 => ( setadjoinSub2
% 2.23/1.50 => ( subset2powerset
% 2.23/1.50 => ( setextsub
% 2.23/1.50 => ( subsetemptysetimpeq
% 2.23/1.50 => ( powersetI1
% 2.23/1.50 => ( powersetE1
% 2.23/1.50 => ( inPowerset
% 2.23/1.50 => ( powersetsubset
% 2.23/1.50 => ( sepInPowerset
% 2.23/1.50 => ( sepSubset
% 2.23/1.50 => ( binunionIL
% 2.23/1.50 => ( upairset2IR
% 2.23/1.50 => ( binunionIR
% 2.23/1.50 => ( binunionEcases
% 2.23/1.50 => ( binunionE
% 2.23/1.50 => ( binunionLsub
% 2.23/1.50 => ( binunionRsub
% 2.23/1.50 => ( binintersectI
% 2.23/1.50 => ( binintersectSubset5
% 2.23/1.50 => ( binintersectEL
% 2.23/1.50 => ( binintersectLsub
% 2.23/1.50 => ( binintersectSubset2
% 2.23/1.50 => ( binintersectSubset3
% 2.23/1.50 => ( binintersectER
% 2.23/1.50 => ( disjointsetsI1
% 2.23/1.50 => ( binintersectRsub
% 2.23/1.50 => ( binintersectSubset4
% 2.23/1.50 => ( binintersectSubset1
% 2.23/1.50 => ( bs114d
% 2.23/1.50 => ( setminusI
% 2.23/1.50 => ( setminusEL
% 2.23/1.50 => ( setminusER
% 2.23/1.50 => ( setminusSubset2
% 2.23/1.50 => ( setminusERneg
% 2.23/1.50 => ( setminusELneg
% 2.23/1.50 => ( setminusILneg
% 2.23/1.50 => ( setminusIRneg
% 2.23/1.50 => ( setminusLsub
% 2.23/1.50 => ( setminusSubset1
% 2.23/1.50 => ( symdiffE
% 2.23/1.50 => ! [A: $i,B: $i,Xx: $i] :
% 2.23/1.50 ( ( in @ Xx @ A )
% 2.23/1.50 => ( ~ ( in @ Xx @ B )
% 2.23/1.50 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.23/1.50 ------------------------
% 2.43/1.52 % (6156)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_6052 for (2999ds/2Mi)
% 2.43/1.52 % (6154)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_6052 for (2999ds/27Mi)
% 2.43/1.52 % (6155)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/2Mi)
% 2.43/1.52 % (6157)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_6052 for (2999ds/275Mi)
% 2.43/1.52 % (6152)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/183Mi)
% 2.43/1.52 % (6153)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_6052 for (2999ds/4Mi)
% 2.43/1.52 % (6158)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/18Mi)
% 2.43/1.52 % (6155)Instruction limit reached!
% 2.43/1.52 % (6155)------------------------------
% 2.43/1.52 % (6155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (6155)Termination reason: Unknown
% 2.43/1.52 % (6155)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (6155)Memory used [KB]: 1151
% 2.43/1.52 % (6155)Time elapsed: 0.003 s
% 2.43/1.52 % (6155)Instructions burned: 3 (million)
% 2.43/1.52 % (6155)------------------------------
% 2.43/1.52 % (6155)------------------------------
% 2.43/1.52 % (6156)Instruction limit reached!
% 2.43/1.52 % (6156)------------------------------
% 2.43/1.52 % (6156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (6156)Termination reason: Unknown
% 2.43/1.52 % (6156)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (6156)Memory used [KB]: 1151
% 2.43/1.52 % (6156)Time elapsed: 0.003 s
% 2.43/1.52 % (6156)Instructions burned: 3 (million)
% 2.43/1.52 % (6156)------------------------------
% 2.43/1.52 % (6156)------------------------------
% 2.43/1.52 % (6153)Instruction limit reached!
% 2.43/1.52 % (6153)------------------------------
% 2.43/1.52 % (6153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (6153)Termination reason: Unknown
% 2.43/1.52 % (6153)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (6153)Memory used [KB]: 1279
% 2.43/1.52 % (6153)Time elapsed: 0.004 s
% 2.43/1.52 % (6153)Instructions burned: 5 (million)
% 2.43/1.52 % (6153)------------------------------
% 2.43/1.52 % (6153)------------------------------
% 2.43/1.53 % (6158)Instruction limit reached!
% 2.43/1.53 % (6158)------------------------------
% 2.43/1.53 % (6158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (6158)Termination reason: Unknown
% 2.43/1.53 % (6158)Termination phase: Preprocessing 2
% 2.43/1.53
% 2.43/1.53 % (6158)Memory used [KB]: 1535
% 2.43/1.53 % (6158)Time elapsed: 0.010 s
% 2.43/1.53 % (6158)Instructions burned: 18 (million)
% 2.43/1.53 % (6158)------------------------------
% 2.43/1.53 % (6158)------------------------------
% 2.43/1.53 % (6154)Instruction limit reached!
% 2.43/1.53 % (6154)------------------------------
% 2.43/1.53 % (6154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (6154)Termination reason: Unknown
% 2.43/1.53 % (6154)Termination phase: Property scanning
% 2.43/1.53
% 2.43/1.53 % (6154)Memory used [KB]: 1663
% 2.43/1.53 % (6154)Time elapsed: 0.014 s
% 2.43/1.53 % (6154)Instructions burned: 27 (million)
% 2.43/1.53 % (6154)------------------------------
% 2.43/1.53 % (6154)------------------------------
% 2.43/1.54 % (6159)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/3Mi)
% 2.43/1.54 % (6160)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_6052 for (2999ds/37Mi)
% 2.43/1.54 % (6161)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_6052 for (2999ds/15Mi)
% 2.43/1.54 % (6159)Instruction limit reached!
% 2.43/1.54 % (6159)------------------------------
% 2.43/1.54 % (6159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.54 % (6159)Termination reason: Unknown
% 2.43/1.54 % (6159)Termination phase: shuffling
% 2.43/1.54
% 2.43/1.54 % (6159)Memory used [KB]: 1151
% 2.43/1.54 % (6159)Time elapsed: 0.003 s
% 2.43/1.54 % (6159)Instructions burned: 3 (million)
% 2.43/1.54 % (6159)------------------------------
% 2.43/1.54 % (6159)------------------------------
% 2.43/1.54 % (6162)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_6052 for (2999ds/3Mi)
% 2.43/1.55 % (6161)Instruction limit reached!
% 2.43/1.55 % (6161)------------------------------
% 2.43/1.55 % (6161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (6161)Termination reason: Unknown
% 2.43/1.55 % (6161)Termination phase: Preprocessing 1
% 2.43/1.55
% 2.43/1.55 % (6161)Memory used [KB]: 1407
% 2.43/1.55 % (6161)Time elapsed: 0.009 s
% 2.43/1.55 % (6161)Instructions burned: 16 (million)
% 2.43/1.55 % (6161)------------------------------
% 2.43/1.55 % (6161)------------------------------
% 2.43/1.55 % (6162)Instruction limit reached!
% 2.43/1.55 % (6162)------------------------------
% 2.43/1.55 % (6162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (6162)Termination reason: Unknown
% 2.43/1.55 % (6162)Termination phase: shuffling
% 2.43/1.55
% 2.43/1.55 % (6162)Memory used [KB]: 1279
% 2.43/1.55 % (6162)Time elapsed: 0.003 s
% 2.43/1.55 % (6162)Instructions burned: 4 (million)
% 2.43/1.55 % (6162)------------------------------
% 2.43/1.55 % (6162)------------------------------
% 2.43/1.55 % (6163)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_6052 for (2999ds/1041Mi)
% 2.43/1.55 % (6160)Instruction limit reached!
% 2.43/1.55 % (6160)------------------------------
% 2.43/1.55 % (6160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (6160)Termination reason: Unknown
% 2.43/1.55 % (6160)Termination phase: Property scanning
% 2.43/1.55
% 2.43/1.55 % (6160)Memory used [KB]: 1663
% 2.43/1.55 % (6160)Time elapsed: 0.018 s
% 2.43/1.55 % (6160)Instructions burned: 38 (million)
% 2.43/1.55 % (6160)------------------------------
% 2.43/1.55 % (6160)------------------------------
% 2.43/1.55 % (6164)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/7Mi)
% 2.43/1.56 % (6164)Instruction limit reached!
% 2.43/1.56 % (6164)------------------------------
% 2.43/1.56 % (6164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.56 % (6164)Termination reason: Unknown
% 2.43/1.56 % (6164)Termination phase: shuffling
% 2.43/1.56
% 2.43/1.56 % (6164)Memory used [KB]: 1279
% 2.43/1.56 % (6164)Time elapsed: 0.005 s
% 2.43/1.56 % (6164)Instructions burned: 8 (million)
% 2.43/1.56 % (6164)------------------------------
% 2.43/1.56 % (6164)------------------------------
% 2.43/1.56 % (6165)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/16Mi)
% 2.43/1.56 % (6166)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_6052 for (2999ds/3Mi)
% 2.43/1.56 % (6166)Instruction limit reached!
% 2.43/1.56 % (6166)------------------------------
% 2.43/1.56 % (6166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.56 % (6166)Termination reason: Unknown
% 2.43/1.56 % (6166)Termination phase: shuffling
% 2.43/1.56
% 2.43/1.56 % (6166)Memory used [KB]: 1279
% 2.43/1.56 % (6166)Time elapsed: 0.003 s
% 2.43/1.56 % (6166)Instructions burned: 3 (million)
% 2.43/1.56 % (6166)------------------------------
% 2.43/1.56 % (6166)------------------------------
% 2.43/1.57 % (6165)Instruction limit reached!
% 2.43/1.57 % (6165)------------------------------
% 2.43/1.57 % (6165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.57 % (6165)Termination reason: Unknown
% 2.43/1.57 % (6165)Termination phase: shuffling
% 2.43/1.57
% 2.43/1.57 % (6165)Memory used [KB]: 1535
% 2.43/1.57 % (6165)Time elapsed: 0.009 s
% 2.43/1.57 % (6165)Instructions burned: 17 (million)
% 2.43/1.57 % (6165)------------------------------
% 2.43/1.57 % (6165)------------------------------
% 2.43/1.57 % (6167)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_6052 for (2999ds/3Mi)
% 2.43/1.57 % (6167)Instruction limit reached!
% 2.43/1.57 % (6167)------------------------------
% 2.43/1.57 % (6167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.57 % (6167)Termination reason: Unknown
% 2.43/1.57 % (6167)Termination phase: shuffling
% 2.43/1.57
% 2.43/1.57 % (6167)Memory used [KB]: 1279
% 2.43/1.57 % (6167)Time elapsed: 0.003 s
% 2.43/1.57 % (6167)Instructions burned: 4 (million)
% 2.43/1.57 % (6167)------------------------------
% 2.43/1.57 % (6167)------------------------------
% 2.43/1.57 % (6168)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/7Mi)
% 2.43/1.58 % (6168)Instruction limit reached!
% 2.43/1.58 % (6168)------------------------------
% 2.43/1.58 % (6168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.58 % (6168)Termination reason: Unknown
% 2.43/1.58 % (6168)Termination phase: shuffling
% 2.43/1.58
% 2.43/1.58 % (6168)Memory used [KB]: 1279
% 2.43/1.58 % (6168)Time elapsed: 0.005 s
% 2.43/1.58 % (6168)Instructions burned: 8 (million)
% 2.43/1.58 % (6168)------------------------------
% 2.43/1.58 % (6168)------------------------------
% 2.43/1.58 % (6169)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/3Mi)
% 2.43/1.58 % (6169)Instruction limit reached!
% 2.43/1.58 % (6169)------------------------------
% 2.43/1.58 % (6169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.58 % (6169)Termination reason: Unknown
% 2.43/1.58 % (6169)Termination phase: shuffling
% 2.43/1.58
% 2.43/1.58 % (6169)Memory used [KB]: 1279
% 2.43/1.58 % (6169)Time elapsed: 0.003 s
% 2.43/1.58 % (6169)Instructions burned: 4 (million)
% 2.43/1.58 % (6169)------------------------------
% 2.43/1.58 % (6169)------------------------------
% 2.43/1.58 % (6170)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/4Mi)
% 2.43/1.59 % (6170)Instruction limit reached!
% 2.43/1.59 % (6170)------------------------------
% 2.43/1.59 % (6170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.59 % (6170)Termination reason: Unknown
% 2.43/1.59 % (6170)Termination phase: shuffling
% 2.43/1.59
% 2.43/1.59 % (6170)Memory used [KB]: 1279
% 2.43/1.59 % (6170)Time elapsed: 0.003 s
% 2.43/1.59 % (6170)Instructions burned: 4 (million)
% 2.43/1.59 % (6170)------------------------------
% 2.43/1.59 % (6170)------------------------------
% 2.43/1.59 % (6171)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/18Mi)
% 2.43/1.59 % (6172)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/710Mi)
% 2.43/1.60 % (6171)Instruction limit reached!
% 2.43/1.60 % (6171)------------------------------
% 2.43/1.60 % (6171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.60 % (6171)Termination reason: Unknown
% 2.43/1.60 % (6171)Termination phase: shuffling
% 2.43/1.60
% 2.43/1.60 % (6171)Memory used [KB]: 1535
% 2.43/1.60 % (6171)Time elapsed: 0.010 s
% 2.43/1.60 % (6171)Instructions burned: 19 (million)
% 2.43/1.60 % (6171)------------------------------
% 2.43/1.60 % (6171)------------------------------
% 2.43/1.60 % (6173)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/6Mi)
% 2.43/1.60 % (6173)Instruction limit reached!
% 2.43/1.60 % (6173)------------------------------
% 2.43/1.60 % (6173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.60 % (6173)Termination reason: Unknown
% 2.43/1.60 % (6173)Termination phase: shuffling
% 2.43/1.60
% 2.43/1.60 % (6173)Memory used [KB]: 1279
% 2.43/1.60 % (6173)Time elapsed: 0.004 s
% 2.43/1.60 % (6173)Instructions burned: 6 (million)
% 2.43/1.60 % (6173)------------------------------
% 2.43/1.60 % (6173)------------------------------
% 2.43/1.60 % (6174)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_6052 for (2999ds/902Mi)
% 2.43/1.60 % (6152)Instruction limit reached!
% 2.43/1.60 % (6152)------------------------------
% 2.43/1.60 % (6152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.60 % (6152)Termination reason: Unknown
% 2.43/1.60 % (6152)Termination phase: Saturation
% 2.43/1.60
% 2.43/1.60 % (6152)Memory used [KB]: 7036
% 2.43/1.60 % (6152)Time elapsed: 0.087 s
% 2.43/1.60 % (6152)Instructions burned: 183 (million)
% 2.43/1.60 % (6152)------------------------------
% 2.43/1.60 % (6152)------------------------------
% 2.43/1.61 % (6175)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_6052 for (2999ds/21Mi)
% 2.43/1.62 % (6176)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6052 for (2999ds/5Mi)
% 2.43/1.62 % (6176)Instruction limit reached!
% 2.43/1.62 % (6176)------------------------------
% 2.43/1.62 % (6176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.62 % (6176)Termination reason: Unknown
% 2.43/1.62 % (6176)Termination phase: shuffling
% 2.43/1.62
% 2.43/1.62 % (6176)Memory used [KB]: 1279
% 2.43/1.62 % (6176)Time elapsed: 0.004 s
% 2.43/1.62 % (6176)Instructions burned: 6 (million)
% 2.43/1.62 % (6176)------------------------------
% 2.43/1.62 % (6176)------------------------------
% 2.43/1.62 % (6175)Instruction limit reached!
% 2.43/1.62 % (6175)------------------------------
% 2.43/1.62 % (6175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.62 % (6175)Termination reason: Unknown
% 2.43/1.62 % (6177)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_6052 for (2998ds/6Mi)
% 2.43/1.62 % (6175)Termination phase: Property scanning
% 2.43/1.62
% 2.43/1.62 % (6175)Memory used [KB]: 1535
% 2.43/1.62 % (6175)Time elapsed: 0.011 s
% 2.43/1.62 % (6175)Instructions burned: 21 (million)
% 2.43/1.62 % (6175)------------------------------
% 2.43/1.62 % (6175)------------------------------
% 2.43/1.62 % (6177)Instruction limit reached!
% 2.43/1.62 % (6177)------------------------------
% 2.43/1.62 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.62 % (6177)Termination reason: Unknown
% 2.43/1.62 % (6177)Termination phase: shuffling
% 2.43/1.62
% 2.43/1.62 % (6177)Memory used [KB]: 1279
% 2.43/1.62 % (6177)Time elapsed: 0.005 s
% 2.43/1.62 % (6177)Instructions burned: 8 (million)
% 2.43/1.62 % (6177)------------------------------
% 2.43/1.62 % (6177)------------------------------
% 2.43/1.63 % (6178)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6052 for (2998ds/377Mi)
% 2.43/1.64 % (6179)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_6052 for (2998ds/779Mi)
% 2.43/1.64 % (6180)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_6052 for (2998ds/19Mi)
% 2.43/1.65 % (6180)Instruction limit reached!
% 2.43/1.65 % (6180)------------------------------
% 2.43/1.65 % (6180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.65 % (6180)Termination reason: Unknown
% 2.43/1.65 % (6180)Termination phase: shuffling
% 2.43/1.65
% 2.43/1.65 % (6180)Memory used [KB]: 1535
% 2.43/1.65 % (6180)Time elapsed: 0.010 s
% 2.43/1.65 % (6180)Instructions burned: 19 (million)
% 2.43/1.65 % (6180)------------------------------
% 2.43/1.65 % (6180)------------------------------
% 2.43/1.66 % (6157)Instruction limit reached!
% 2.43/1.66 % (6157)------------------------------
% 2.43/1.66 % (6157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.66 % (6157)Termination reason: Unknown
% 2.43/1.66 % (6157)Termination phase: Saturation
% 2.43/1.66
% 2.43/1.66 % (6157)Memory used [KB]: 7803
% 2.43/1.66 % (6157)Time elapsed: 0.140 s
% 2.43/1.66 % (6157)Instructions burned: 275 (million)
% 2.43/1.66 % (6157)------------------------------
% 2.43/1.66 % (6157)------------------------------
% 2.43/1.67 % (6181)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6052 for (2998ds/879Mi)
% 2.43/1.67 % (6182)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6052 for (2998ds/17Mi)
% 2.43/1.68 % (6182)Instruction limit reached!
% 2.43/1.68 % (6182)------------------------------
% 2.43/1.68 % (6182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.68 % (6182)Termination reason: Unknown
% 2.43/1.68 % (6182)Termination phase: shuffling
% 2.43/1.68
% 2.43/1.68 % (6182)Memory used [KB]: 1535
% 2.43/1.68 % (6182)Time elapsed: 0.010 s
% 2.43/1.68 % (6182)Instructions burned: 18 (million)
% 2.43/1.68 % (6182)------------------------------
% 2.43/1.68 % (6182)------------------------------
% 2.43/1.70 % (6183)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6052 for (2998ds/3Mi)
% 2.43/1.70 % (6183)Instruction limit reached!
% 2.43/1.70 % (6183)------------------------------
% 2.43/1.70 % (6183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.70 % (6183)Termination reason: Unknown
% 2.43/1.70 % (6183)Termination phase: shuffling
% 2.43/1.70
% 2.43/1.70 % (6183)Memory used [KB]: 1151
% 2.43/1.70 % (6183)Time elapsed: 0.003 s
% 2.43/1.70 % (6183)Instructions burned: 3 (million)
% 2.43/1.70 % (6183)------------------------------
% 2.43/1.70 % (6183)------------------------------
% 2.43/1.72 % (6184)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6052 for (2998ds/30Mi)
% 2.43/1.73 % (6184)Instruction limit reached!
% 2.43/1.73 % (6184)------------------------------
% 2.43/1.73 % (6184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.73 % (6184)Termination reason: Unknown
% 2.43/1.73 % (6184)Termination phase: Property scanning
% 2.43/1.73
% 2.43/1.73 % (6184)Memory used [KB]: 1535
% 2.43/1.73 % (6184)Time elapsed: 0.015 s
% 2.43/1.73 % (6184)Instructions burned: 30 (million)
% 2.43/1.73 % (6184)------------------------------
% 2.43/1.73 % (6184)------------------------------
% 2.43/1.75 % (6185)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6052 for (2997ds/127Mi)
% 2.43/1.80 % (6185)Instruction limit reached!
% 2.43/1.80 % (6185)------------------------------
% 2.43/1.80 % (6185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.80 % (6185)Termination reason: Unknown
% 2.43/1.80 % (6185)Termination phase: Saturation
% 2.43/1.80
% 2.43/1.80 % (6185)Memory used [KB]: 6780
% 2.43/1.80 % (6185)Time elapsed: 0.058 s
% 2.43/1.80 % (6185)Instructions burned: 127 (million)
% 2.43/1.80 % (6185)------------------------------
% 2.43/1.80 % (6185)------------------------------
% 2.43/1.82 % (6178)Instruction limit reached!
% 2.43/1.82 % (6178)------------------------------
% 2.43/1.82 % (6178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.82 % (6178)Termination reason: Unknown
% 2.43/1.82 % (6178)Termination phase: Saturation
% 2.43/1.82
% 2.43/1.82 % (6178)Memory used [KB]: 7419
% 2.43/1.82 % (6178)Time elapsed: 0.186 s
% 2.43/1.82 % (6178)Instructions burned: 377 (million)
% 2.43/1.82 % (6178)------------------------------
% 2.43/1.82 % (6178)------------------------------
% 2.43/1.82 % (6186)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6052 for (2997ds/100Mi)
% 2.43/1.83 % (6187)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_6052 for (2996ds/3Mi)
% 2.43/1.84 % (6187)Instruction limit reached!
% 2.43/1.84 % (6187)------------------------------
% 2.43/1.84 % (6187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.84 % (6187)Termination reason: Unknown
% 2.43/1.84 % (6187)Termination phase: shuffling
% 2.43/1.84
% 2.43/1.84 % (6187)Memory used [KB]: 1151
% 2.43/1.84 % (6187)Time elapsed: 0.003 s
% 2.43/1.84 % (6187)Instructions burned: 3 (million)
% 2.43/1.84 % (6187)------------------------------
% 2.43/1.84 % (6187)------------------------------
% 2.43/1.85 % (6188)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_6052 for (2996ds/20Mi)
% 2.43/1.86 % (6188)Instruction limit reached!
% 2.43/1.86 % (6188)------------------------------
% 2.43/1.86 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.86 % (6188)Termination reason: Unknown
% 2.43/1.86 % (6188)Termination phase: SInE selection
% 2.43/1.86
% 2.43/1.86 % (6188)Memory used [KB]: 1407
% 2.43/1.86 % (6188)Time elapsed: 0.011 s
% 2.43/1.86 % (6188)Instructions burned: 21 (million)
% 2.43/1.86 % (6188)------------------------------
% 2.43/1.86 % (6188)------------------------------
% 2.43/1.86 % (6186)Instruction limit reached!
% 2.43/1.86 % (6186)------------------------------
% 2.43/1.86 % (6186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.86 % (6186)Termination reason: Unknown
% 2.43/1.86 % (6186)Termination phase: Saturation
% 2.43/1.86
% 2.43/1.86 % (6186)Memory used [KB]: 6396
% 2.43/1.86 % (6186)Time elapsed: 0.047 s
% 2.43/1.86 % (6186)Instructions burned: 100 (million)
% 2.43/1.86 % (6186)------------------------------
% 2.43/1.86 % (6186)------------------------------
% 2.43/1.88 % (6189)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_6052 for (2996ds/86Mi)
% 2.43/1.88 % (6190)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_6052 for (2996ds/107Mi)
% 2.43/1.92 % (6189)Instruction limit reached!
% 2.43/1.92 % (6189)------------------------------
% 2.43/1.92 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.92 % (6189)Termination reason: Unknown
% 2.43/1.92 % (6189)Termination phase: Saturation
% 2.43/1.92
% 2.43/1.92 % (6189)Memory used [KB]: 6396
% 2.43/1.92 % (6189)Time elapsed: 0.040 s
% 2.43/1.92 % (6189)Instructions burned: 86 (million)
% 2.43/1.92 % (6189)------------------------------
% 2.43/1.92 % (6189)------------------------------
% 2.43/1.92 % (6179)Instruction limit reached!
% 2.43/1.92 % (6179)------------------------------
% 2.43/1.92 % (6179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.92 % (6179)Termination reason: Unknown
% 2.43/1.92 % (6179)Termination phase: Saturation
% 2.43/1.92
% 2.43/1.92 % (6179)Memory used [KB]: 6524
% 2.43/1.92 % (6179)Time elapsed: 0.283 s
% 2.43/1.92 % (6179)Instructions burned: 781 (million)
% 2.43/1.92 % (6179)------------------------------
% 2.43/1.92 % (6179)------------------------------
% 2.43/1.93 % (6190)Instruction limit reached!
% 2.43/1.93 % (6190)------------------------------
% 2.43/1.93 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.93 % (6190)Termination reason: Unknown
% 2.43/1.93 % (6190)Termination phase: Saturation
% 2.43/1.93
% 2.43/1.93 % (6190)Memory used [KB]: 6652
% 2.43/1.93 % (6190)Time elapsed: 0.050 s
% 2.43/1.93 % (6190)Instructions burned: 108 (million)
% 2.43/1.93 % (6190)------------------------------
% 2.43/1.93 % (6190)------------------------------
% 2.43/1.93 % (6163)Instruction limit reached!
% 2.43/1.93 % (6163)------------------------------
% 2.43/1.93 % (6163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.93 % (6163)Termination reason: Unknown
% 2.43/1.93 % (6163)Termination phase: Saturation
% 2.43/1.93
% 2.43/1.93 % (6163)Memory used [KB]: 8699
% 2.43/1.93 % (6163)Time elapsed: 0.384 s
% 2.43/1.93 % (6163)Instructions burned: 1043 (million)
% 2.43/1.93 % (6163)------------------------------
% 2.43/1.93 % (6163)------------------------------
% 2.43/1.93 % (6191)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_6052 for (2995ds/39Mi)
% 2.43/1.93 % (6192)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_6052 for (2995ds/448Mi)
% 2.43/1.94 % (6193)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_6052 for (2995ds/46Mi)
% 2.43/1.95 % (6194)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_6052 for (2995ds/98Mi)
% 2.43/1.95 % (6191)Instruction limit reached!
% 2.43/1.95 % (6191)------------------------------
% 2.43/1.95 % (6191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.95 % (6191)Termination reason: Unknown
% 2.43/1.95 % (6191)Termination phase: Property scanning
% 2.43/1.95
% 2.43/1.95 % (6191)Memory used [KB]: 1663
% 2.43/1.95 % (6191)Time elapsed: 0.019 s
% 2.43/1.95 % (6191)Instructions burned: 39 (million)
% 2.43/1.95 % (6191)------------------------------
% 2.43/1.95 % (6191)------------------------------
% 2.43/1.96 % (6172)Instruction limit reached!
% 2.43/1.96 % (6172)------------------------------
% 2.43/1.96 % (6172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.96 % (6172)Termination reason: Unknown
% 2.43/1.96 % (6172)Termination phase: Saturation
% 2.43/1.96
% 2.43/1.96 % (6172)Memory used [KB]: 9210
% 2.43/1.96 % (6172)Time elapsed: 0.365 s
% 2.43/1.96 % (6172)Instructions burned: 710 (million)
% 2.43/1.96 % (6172)------------------------------
% 2.43/1.96 % (6172)------------------------------
% 2.43/1.97 % (6195)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_6052 for (2995ds/507Mi)
% 2.43/1.97 % (6193)Instruction limit reached!
% 2.43/1.97 % (6193)------------------------------
% 2.43/1.97 % (6193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.97 % (6193)Termination reason: Unknown
% 2.43/1.97 % (6193)Termination phase: Property scanning
% 2.43/1.97
% 2.43/1.97 % (6193)Memory used [KB]: 1663
% 2.43/1.97 % (6193)Time elapsed: 0.022 s
% 2.43/1.97 % (6193)Instructions burned: 47 (million)
% 2.43/1.97 % (6193)------------------------------
% 2.43/1.97 % (6193)------------------------------
% 2.43/1.97 % (6196)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_6052 for (2995ds/149Mi)
% 2.43/1.98 % (6197)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_6052 for (2995ds/39Mi)
% 2.43/1.99 % (6194)Instruction limit reached!
% 2.43/1.99 % (6194)------------------------------
% 2.43/1.99 % (6194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.99 % (6194)Termination reason: Unknown
% 2.43/1.99 % (6194)Termination phase: Saturation
% 2.43/1.99
% 2.43/1.99 % (6194)Memory used [KB]: 1791
% 2.43/1.99 % (6194)Time elapsed: 0.043 s
% 2.43/1.99 % (6194)Instructions burned: 99 (million)
% 2.43/1.99 % (6194)------------------------------
% 2.43/1.99 % (6194)------------------------------
% 2.43/2.00 % (6197)Instruction limit reached!
% 2.43/2.00 % (6197)------------------------------
% 2.43/2.00 % (6197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/2.00 % (6197)Termination reason: Unknown
% 2.43/2.00 % (6197)Termination phase: Property scanning
% 2.43/2.00
% 2.43/2.00 % (6197)Memory used [KB]: 1663
% 2.43/2.00 % (6197)Time elapsed: 0.020 s
% 2.43/2.00 % (6197)Instructions burned: 39 (million)
% 2.43/2.00 % (6197)------------------------------
% 2.43/2.00 % (6197)------------------------------
% 2.43/2.00 % (6198)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_6052 for (2995ds/6Mi)
% 2.43/2.01 % (6198)Instruction limit reached!
% 2.43/2.01 % (6198)------------------------------
% 2.43/2.01 % (6198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/2.01 % (6198)Termination reason: Unknown
% 2.43/2.01 % (6198)Termination phase: shuffling
% 2.43/2.01
% 2.43/2.01 % (6198)Memory used [KB]: 1279
% 2.43/2.01 % (6198)Time elapsed: 0.004 s
% 2.43/2.01 % (6198)Instructions burned: 6 (million)
% 2.43/2.01 % (6198)------------------------------
% 2.43/2.01 % (6198)------------------------------
% 2.43/2.02 % (6199)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_6052 for (2994ds/1087Mi)
% 2.43/2.02 % (6200)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_6052 for (2994ds/47Mi)
% 5.95/2.04 % (6174)Instruction limit reached!
% 5.95/2.04 % (6174)------------------------------
% 5.95/2.04 % (6174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.04 % (6174)Termination reason: Unknown
% 5.95/2.04 % (6174)Termination phase: Saturation
% 5.95/2.04
% 5.95/2.04 % (6174)Memory used [KB]: 10746
% 5.95/2.04 % (6174)Time elapsed: 0.443 s
% 5.95/2.04 % (6174)Instructions burned: 902 (million)
% 5.95/2.04 % (6174)------------------------------
% 5.95/2.04 % (6174)------------------------------
% 5.95/2.04 % (6200)Instruction limit reached!
% 5.95/2.04 % (6200)------------------------------
% 5.95/2.04 % (6200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.04 % (6200)Termination reason: Unknown
% 5.95/2.04 % (6200)Termination phase: Property scanning
% 5.95/2.04
% 5.95/2.04 % (6200)Memory used [KB]: 1791
% 5.95/2.04 % (6200)Time elapsed: 0.023 s
% 5.95/2.04 % (6200)Instructions burned: 47 (million)
% 5.95/2.04 % (6200)------------------------------
% 5.95/2.04 % (6200)------------------------------
% 5.95/2.05 % (6196)Instruction limit reached!
% 5.95/2.05 % (6196)------------------------------
% 5.95/2.05 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.05 % (6196)Termination reason: Unknown
% 5.95/2.05 % (6196)Termination phase: Saturation
% 5.95/2.05
% 5.95/2.05 % (6196)Memory used [KB]: 6908
% 5.95/2.05 % (6196)Time elapsed: 0.075 s
% 5.95/2.05 % (6196)Instructions burned: 150 (million)
% 5.95/2.05 % (6196)------------------------------
% 5.95/2.05 % (6196)------------------------------
% 5.95/2.06 % (6201)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_6052 for (2994ds/44Mi)
% 5.95/2.06 % (6202)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_6052 for (2994ds/432Mi)
% 5.95/2.06 % (6203)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_6052 for (2994ds/62Mi)
% 5.95/2.08 % (6201)Instruction limit reached!
% 5.95/2.08 % (6201)------------------------------
% 5.95/2.08 % (6201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.08 % (6201)Termination reason: Unknown
% 5.95/2.08 % (6201)Termination phase: Property scanning
% 5.95/2.08
% 5.95/2.08 % (6201)Memory used [KB]: 1663
% 5.95/2.08 % (6201)Time elapsed: 0.021 s
% 5.95/2.08 % (6201)Instructions burned: 45 (million)
% 5.95/2.08 % (6201)------------------------------
% 5.95/2.08 % (6201)------------------------------
% 5.95/2.09 % (6203)Instruction limit reached!
% 5.95/2.09 % (6203)------------------------------
% 5.95/2.09 % (6203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.09 % (6203)Termination reason: Unknown
% 5.95/2.09 % (6203)Termination phase: Saturation
% 5.95/2.09
% 5.95/2.09 % (6203)Memory used [KB]: 6268
% 5.95/2.09 % (6203)Time elapsed: 0.029 s
% 5.95/2.09 % (6203)Instructions burned: 63 (million)
% 5.95/2.09 % (6203)------------------------------
% 5.95/2.09 % (6203)------------------------------
% 5.95/2.10 % (6204)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_6052 for (2994ds/31Mi)
% 5.95/2.10 % (6192)Instruction limit reached!
% 5.95/2.10 % (6192)------------------------------
% 5.95/2.10 % (6192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.10 % (6192)Termination reason: Unknown
% 5.95/2.10 % (6192)Termination phase: Saturation
% 5.95/2.10
% 5.95/2.10 % (6192)Memory used [KB]: 6524
% 5.95/2.10 % (6192)Time elapsed: 0.167 s
% 5.95/2.10 % (6192)Instructions burned: 450 (million)
% 5.95/2.10 % (6192)------------------------------
% 5.95/2.10 % (6192)------------------------------
% 5.95/2.10 % (6181)Instruction limit reached!
% 5.95/2.10 % (6181)------------------------------
% 5.95/2.10 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.10 % (6181)Termination reason: Unknown
% 5.95/2.10 % (6181)Termination phase: Saturation
% 5.95/2.10
% 5.95/2.10 % (6181)Memory used [KB]: 8059
% 5.95/2.10 % (6181)Time elapsed: 0.438 s
% 5.95/2.10 % (6181)Instructions burned: 880 (million)
% 5.95/2.10 % (6181)------------------------------
% 5.95/2.10 % (6181)------------------------------
% 5.95/2.11 % (6205)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_6052 for (2994ds/96Mi)
% 5.95/2.11 % (6204)Instruction limit reached!
% 5.95/2.11 % (6204)------------------------------
% 5.95/2.11 % (6204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.11 % (6204)Termination reason: Unknown
% 5.95/2.11 % (6204)Termination phase: Preprocessing 3
% 5.95/2.11
% 5.95/2.11 % (6204)Memory used [KB]: 1663
% 5.95/2.11 % (6204)Time elapsed: 0.016 s
% 5.95/2.11 % (6204)Instructions burned: 31 (million)
% 5.95/2.11 % (6204)------------------------------
% 5.95/2.11 % (6204)------------------------------
% 5.95/2.12 % (6206)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_6052 for (2993ds/453Mi)
% 5.95/2.12 % (6207)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_6052 for (2993ds/71Mi)
% 6.46/2.13 % (6208)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_6052 for (2993ds/83Mi)
% 6.46/2.15 % (6207)Instruction limit reached!
% 6.46/2.15 % (6207)------------------------------
% 6.46/2.15 % (6207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.15 % (6207)Termination reason: Unknown
% 6.46/2.15 % (6207)Termination phase: Saturation
% 6.46/2.15
% 6.46/2.15 % (6207)Memory used [KB]: 6268
% 6.46/2.15 % (6207)Time elapsed: 0.033 s
% 6.46/2.15 % (6207)Instructions burned: 71 (million)
% 6.46/2.15 % (6207)------------------------------
% 6.46/2.15 % (6207)------------------------------
% 6.46/2.15 % (6205)Instruction limit reached!
% 6.46/2.15 % (6205)------------------------------
% 6.46/2.15 % (6205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.15 % (6205)Termination reason: Unknown
% 6.46/2.15 % (6205)Termination phase: Saturation
% 6.46/2.15
% 6.46/2.15 % (6205)Memory used [KB]: 6652
% 6.46/2.15 % (6205)Time elapsed: 0.045 s
% 6.46/2.15 % (6205)Instructions burned: 98 (million)
% 6.46/2.15 % (6205)------------------------------
% 6.46/2.15 % (6205)------------------------------
% 6.46/2.16 % (6208)Instruction limit reached!
% 6.46/2.16 % (6208)------------------------------
% 6.46/2.16 % (6208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.16 % (6208)Termination reason: Unknown
% 6.46/2.16 % (6208)Termination phase: Saturation
% 6.46/2.16
% 6.46/2.16 % (6208)Memory used [KB]: 6396
% 6.46/2.16 % (6208)Time elapsed: 0.038 s
% 6.46/2.16 % (6208)Instructions burned: 83 (million)
% 6.46/2.16 % (6208)------------------------------
% 6.46/2.16 % (6208)------------------------------
% 6.46/2.17 % (6209)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_6052 for (2993ds/11Mi)
% 6.46/2.17 % (6210)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_6052 for (2993ds/41Mi)
% 6.46/2.17 % (6209)Instruction limit reached!
% 6.46/2.17 % (6209)------------------------------
% 6.46/2.17 % (6209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.17 % (6209)Termination reason: Unknown
% 6.46/2.17 % (6209)Termination phase: shuffling
% 6.46/2.17
% 6.46/2.17 % (6209)Memory used [KB]: 1407
% 6.46/2.17 % (6209)Time elapsed: 0.007 s
% 6.46/2.17 % (6209)Instructions burned: 12 (million)
% 6.46/2.17 % (6209)------------------------------
% 6.46/2.17 % (6209)------------------------------
% 6.46/2.18 % (6211)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6052 for (2993ds/6Mi)
% 6.46/2.18 % (6211)Instruction limit reached!
% 6.46/2.18 % (6211)------------------------------
% 6.46/2.18 % (6211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.18 % (6211)Termination reason: Unknown
% 6.46/2.18 % (6211)Termination phase: shuffling
% 6.46/2.18
% 6.46/2.18 % (6211)Memory used [KB]: 1279
% 6.46/2.18 % (6211)Time elapsed: 0.004 s
% 6.46/2.18 % (6211)Instructions burned: 6 (million)
% 6.46/2.18 % (6211)------------------------------
% 6.46/2.18 % (6211)------------------------------
% 6.46/2.18 % (6210)Instruction limit reached!
% 6.46/2.18 % (6210)------------------------------
% 6.46/2.18 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.18 % (6210)Termination reason: Unknown
% 6.46/2.18 % (6210)Termination phase: Property scanning
% 6.46/2.18
% 6.46/2.18 % (6210)Memory used [KB]: 1663
% 6.46/2.18 % (6210)Time elapsed: 0.020 s
% 6.46/2.18 % (6210)Instructions burned: 43 (million)
% 6.46/2.18 % (6210)------------------------------
% 6.46/2.18 % (6210)------------------------------
% 6.46/2.19 % (6212)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_6052 for (2993ds/150Mi)
% 6.46/2.19 % (6199)First to succeed.
% 6.46/2.19 % (6199)Refutation found. Thanks to Tanya!
% 6.46/2.19 % SZS status Theorem for DTF2THF_6052
% 6.46/2.19 % SZS output start Proof for DTF2THF_6052
% 6.46/2.19 thf(func_def_0, type, in: $i > $i > $o).
% 6.46/2.19 thf(func_def_1, type, exu: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 6.46/2.19 thf(func_def_8, type, powerset: $i > $i).
% 6.46/2.19 thf(func_def_10, type, setunion: $i > $i).
% 6.46/2.19 thf(func_def_19, type, descr: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_26, type, prop2set: $o > $i).
% 6.46/2.19 thf(func_def_36, type, nonempty: $i > $o).
% 6.46/2.19 thf(func_def_69, type, set2prop: $i > $o).
% 6.46/2.19 thf(func_def_88, type, subset: $i > $i > $o).
% 6.46/2.19 thf(func_def_89, type, disjoint: $i > $i > $o).
% 6.46/2.19 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 6.46/2.19 thf(func_def_114, type, binunion: $i > $i > $i).
% 6.46/2.19 thf(func_def_122, type, binintersect: $i > $i > $i).
% 6.46/2.19 thf(func_def_135, type, regular: $i > $o).
% 6.46/2.19 thf(func_def_136, type, setminus: $i > $i > $i).
% 6.46/2.19 thf(func_def_147, type, symdiff: $i > $i > $i).
% 6.46/2.19 thf(func_def_162, type, sP0: $i > $i > $o > $o).
% 6.46/2.19 thf(func_def_164, type, sP2: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_165, type, sP3: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_167, type, sP5: $i > $i > $o).
% 6.46/2.19 thf(func_def_170, type, sP8: ($i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_172, type, sP10: $i > $i > $i > $o).
% 6.46/2.19 thf(func_def_173, type, sP11: $i > $i > $o).
% 6.46/2.19 thf(func_def_174, type, sP12: $i > $i > $o).
% 6.46/2.19 thf(func_def_175, type, sP13: $i > $i > $o).
% 6.46/2.19 thf(func_def_176, type, sP14: $i > $o).
% 6.46/2.19 thf(func_def_177, type, sP15: $i > $i > $o).
% 6.46/2.19 thf(func_def_178, type, sP16: $o > $i > $i > $o).
% 6.46/2.19 thf(func_def_180, type, sP18: $i > $o).
% 6.46/2.19 thf(func_def_181, type, sP19: $i > $o).
% 6.46/2.19 thf(func_def_182, type, sP20: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_183, type, sP21: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_184, type, sP22: $i > $i > $o).
% 6.46/2.19 thf(func_def_187, type, sP25: $o > $i > $i > $i > $o).
% 6.46/2.19 thf(func_def_188, type, sP26: $i > $o > $i > $i > $o).
% 6.46/2.19 thf(func_def_189, type, sP27: $i > ($i > $o) > $o).
% 6.46/2.19 thf(func_def_191, type, sP29: ($i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_193, type, sP31: $i > ($i > $i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_194, type, sP32: $i > ($i > $i > $o) > $o).
% 6.46/2.19 thf(func_def_197, type, sP35: $i > ($i > $o) > ($i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_198, type, sP36: ($i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_200, type, sP38: $i > $o).
% 6.46/2.19 thf(func_def_201, type, sP39: ($i > $o) > $o).
% 6.46/2.19 thf(func_def_202, type, sP40: ($i > $o) > $i > $o).
% 6.46/2.19 thf(func_def_204, type, sP42: $i > $i > $o > $o).
% 6.46/2.19 thf(func_def_205, type, sP43: $i > $i > $i > $o).
% 6.46/2.19 thf(func_def_206, type, sP44: $i > $i > $i > $o).
% 6.46/2.19 thf(func_def_209, type, sP47: $i > $i > $o).
% 6.46/2.19 thf(func_def_211, type, sP49: $i > ($i > $o) > $o).
% 6.46/2.19 thf(func_def_233, type, sK71: $i > $i).
% 6.46/2.19 thf(func_def_242, type, sK80: $i > $i > $i).
% 6.46/2.19 thf(func_def_247, type, sK85: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_248, type, sK86: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_249, type, sK87: $i > $o).
% 6.46/2.19 thf(func_def_250, type, sK88: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_251, type, sK89: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_252, type, sK90: $i > $o).
% 6.46/2.19 thf(func_def_257, type, sK95: $i > $o).
% 6.46/2.19 thf(func_def_264, type, sK102: $i > $o).
% 6.46/2.19 thf(func_def_265, type, sK103: $i > $o).
% 6.46/2.19 thf(func_def_266, type, sK104: ($i > $o) > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_267, type, sK105: ($i > $o) > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_272, type, sK110: $i > $o).
% 6.46/2.19 thf(func_def_275, type, sK113: $i > $i > $i).
% 6.46/2.19 thf(func_def_279, type, sK117: $i > $i > $i).
% 6.46/2.19 thf(func_def_292, type, sK130: $i > $o).
% 6.46/2.19 thf(func_def_293, type, sK131: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_294, type, sK132: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_306, type, sK144: $i > $o).
% 6.46/2.19 thf(func_def_309, type, sK147: $i > $i > $i).
% 6.46/2.19 thf(func_def_310, type, sK148: $i > $i > $i).
% 6.46/2.19 thf(func_def_311, type, sK149: $i > $i > $i > $i).
% 6.46/2.19 thf(func_def_312, type, sK150: $i > $i).
% 6.46/2.19 thf(func_def_313, type, sK151: $i > $i).
% 6.46/2.19 thf(func_def_314, type, sK152: $i > $i).
% 6.46/2.19 thf(func_def_315, type, sK153: $i > $i).
% 6.46/2.19 thf(func_def_316, type, sK154: $i > $i > $i).
% 6.46/2.19 thf(func_def_317, type, sK155: $i > $i > $i).
% 6.46/2.19 thf(func_def_318, type, sK156: $i > $i > $i).
% 6.46/2.19 thf(func_def_319, type, sK157: $i > $i > $i).
% 6.46/2.19 thf(func_def_320, type, sK158: $i > $i > $i).
% 6.46/2.19 thf(func_def_321, type, sK159: $i > $i > $i).
% 6.46/2.19 thf(func_def_322, type, sK160: $i > $i > $i).
% 6.46/2.19 thf(func_def_323, type, sK161: $i > $i > $i).
% 6.46/2.19 thf(func_def_324, type, sK162: $i > $i > $i > $i).
% 6.46/2.19 thf(func_def_325, type, sK163: $i > $i > $i > $i).
% 6.46/2.19 thf(func_def_327, type, sK165: $i > $i).
% 6.46/2.19 thf(func_def_328, type, sK166: $o > $i > $i > $i).
% 6.46/2.19 thf(func_def_332, type, sK170: $i > $o).
% 6.46/2.19 thf(func_def_334, type, sK172: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_335, type, sK173: $i > $o).
% 6.46/2.19 thf(func_def_344, type, sK182: $i > $o).
% 6.46/2.19 thf(func_def_350, type, sK188: $i > $i > $i).
% 6.46/2.19 thf(func_def_353, type, sK191: $i > $o).
% 6.46/2.19 thf(func_def_363, type, sK201: $i > $o).
% 6.46/2.19 thf(func_def_368, type, sK206: $i > $i).
% 6.46/2.19 thf(func_def_369, type, sK207: $i > $i).
% 6.46/2.19 thf(func_def_380, type, sK218: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_381, type, sK219: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_382, type, sK220: $i > $o).
% 6.46/2.19 thf(func_def_383, type, sK221: $i > $o).
% 6.46/2.19 thf(func_def_393, type, sK231: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_394, type, sK232: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_395, type, sK233: $i > $o).
% 6.46/2.19 thf(func_def_404, type, sK242: $i > $i).
% 6.46/2.19 thf(func_def_408, type, sK246: $i > $i > $i).
% 6.46/2.19 thf(func_def_416, type, sK254: $i > $i > $i).
% 6.46/2.19 thf(func_def_436, type, sK274: $i > $o).
% 6.46/2.19 thf(func_def_438, type, sK276: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_439, type, sK277: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_444, type, sK282: $i > $o).
% 6.46/2.19 thf(func_def_445, type, sK283: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_446, type, sK284: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_450, type, sK288: $i > $o).
% 6.46/2.19 thf(func_def_458, type, sK296: $i > $i > $o).
% 6.46/2.19 thf(func_def_459, type, sK297: ($i > $i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_460, type, sK298: $i > $i > ($i > $i > $o) > $i).
% 6.46/2.19 thf(func_def_461, type, sK299: $i > ($i > $i > $o) > $i).
% 6.46/2.19 thf(func_def_462, type, sK300: $i > ($i > $i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_465, type, sK303: $i > $i > $i).
% 6.46/2.19 thf(func_def_476, type, sK314: $i > ($i > $o) > ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_477, type, sK315: $i > ($i > $o) > ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_480, type, sK318: $i > $o).
% 6.46/2.19 thf(func_def_481, type, sK319: $i > $o).
% 6.46/2.19 thf(func_def_483, type, sK321: $i > $o).
% 6.46/2.19 thf(func_def_484, type, sK322: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_485, type, sK323: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_486, type, sK324: $i > $o).
% 6.46/2.19 thf(func_def_490, type, sK328: $i > $i > $i).
% 6.46/2.19 thf(func_def_491, type, sK329: $i > $i).
% 6.46/2.19 thf(func_def_497, type, sK335: $i > $o).
% 6.46/2.19 thf(func_def_499, type, sK337: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_500, type, sK338: ($i > $o) > $i).
% 6.46/2.19 thf(func_def_501, type, sK339: $i > $o).
% 6.46/2.19 thf(func_def_504, type, sK342: $i > $o).
% 6.46/2.19 thf(func_def_505, type, sK343: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_506, type, sK344: ($i > $o) > $i > $i).
% 6.46/2.19 thf(func_def_514, type, sK352: $i > $o).
% 6.46/2.19 thf(func_def_517, type, sK355: $i > $i > $i > $o).
% 6.46/2.19 thf(func_def_524, type, sK362: $i > $i).
% 6.46/2.19 thf(func_def_529, type, sK367: $i > $o).
% 6.46/2.19 thf(func_def_530, type, sK368: $i > $o).
% 6.46/2.19 thf(func_def_531, type, sK369: ($i > $o) > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_532, type, sK370: ($i > $o) > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_535, type, sK373: $i > $i > $i).
% 6.46/2.19 thf(func_def_536, type, sK374: $i > $i > $i).
% 6.46/2.19 thf(func_def_547, type, sK385: $i > $o).
% 6.46/2.19 thf(func_def_549, type, sK387: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_550, type, sK388: $i > ($i > $o) > $i).
% 6.46/2.19 thf(func_def_554, type, sK392: $i > $i).
% 6.46/2.19 thf(func_def_559, type, ph397: !>[X0: $tType]:(X0)).
% 6.46/2.19 thf(f3961,plain,(
% 6.46/2.19 $false),
% 6.46/2.19 inference(subsumption_resolution,[status(thm)],[f3959,f1465])).
% 6.46/2.19 thf(f1465,plain,(
% 6.46/2.19 ((in @ sK75 @ sK76) = $true)),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f682])).
% 6.46/2.19 thf(f682,plain,(
% 6.46/2.19 (eqimpsubset1 = $true) & (setminusSubset2 = $true) & (replAx = $true) & (notdexE = $true) & (subsetI2 = $true) & (subsetTrans = $true) & (setextAx = $true) & (binunionLsub = $true) & (descr__Cong = $true) & (exuI3 = $true) & (quantDeMorgan4 = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (binunionIL = $true) & (binintersectER = $true) & (quantDeMorgan2 = $true) & (setminusER = $true) & (binunionE = $true) & (notdallE = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (emptysetimpfalse = $true) & (emptyInPowerset = $true) & (setminusEL = $true) & (exuE2 = $true) & (setext = $true) & (powersetI1 = $true) & (nonemptyE1 = $true) & (emptyE1 = $true) & (setunionE = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (quantDeMorgan1 = $true) & (nonemptyImpWitness = $true) & (((in @ sK75 @ sK77) != $true) & ((in @ sK75 @ sK76) = $true) & ($true != (in @ sK75 @ (symdiff @ sK76 @ sK77)))) & (binintersectSubset1 = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (powerset__Cong = $true) & (setminusI = $true) & (setminusILneg = $true) & (upairset2IR = $true) & (eqinunit = $true) & (exuI2 = $true) & (exuI1 = $true) & (binunionIR = $true) & (emptyinPowerset = $true) & (omega0Ax = $true) & (eqimpsubset2 = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (powersetI = $true) & (dsetconstrER = $true) & (emptyinunitempty = $true) & (setminusLsub = $true) & (noeltsimpempty = $true) & (powersetE1 = $true) & (setoftrueEq = $true) & (exuEu = $true) & (symdiffE = $true) & (upairsetE = $true) & (upairsetIR = $true) & (binintersectI = $true) & (subsetE = $true) & (subsetRefl = $true) & (nonemptyI1 = $true) & (exuE3u = $true) & (exuE3e = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (binintersectSubset2 = $true) & (emptyset__Cong = $true) & (inPowerset = $true) & (uniqinunit = $true) & (sepInPowerset = $true) & (binintersectSubset4 = $true) & (nonemptyI = $true) & (powersetAx = $true) & (inCongP = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (quantDeMorgan3 = $true) & (binintersectEL = $true) & (dsetconstrEL = $true) & (upairsetIL = $true) & (subset2powerset = $true) & (powersetE = $true) & (binunionEcases = $true) & (emptysetE = $true) & (exuE1 = $true) & (setadjoinIR = $true) & (subsetE2 = $true) & (setminusSubset1 = $true) & (subPowSU = $true) & (bs114d = $true) & (setminusELneg = $true) & (dsetconstrI = $true) & (binintersectRsub = $true) & (binunionRsub = $true) & (setunionAx = $true) & (omegaSAx = $true) & (notequalI2 = $true) & (prop2setE = $true) & (notinemptyset = $true) & (setadjoinSub = $true) & (exu__Cong = $true) & (setadjoinIL = $true) & (emptysetAx = $true) & (vacuousDall = $true) & (dsetconstr__Cong = $true) & (emptyI = $true) & (subsetemptysetimpeq = $true) & (setminusIRneg = $true) & (binintersectSubset5 = $true) & (disjointsetsI1 = $true) & (wellorderingAx = $true) & (setminusERneg = $true) & (setunion__Cong = $true) & (singletonsswitch = $true) & (subsetI1 = $true) & (powersetsubset = $true) & (setadjoinSub2 = $true) & (setbeta = $true) & (binintersectLsub = $true) & (sepSubset = $true) & (descrp = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (setextsub = $true)),
% 6.46/2.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76,sK77])],[f464,f681])).
% 6.46/2.19 thf(f681,plain,(
% 6.46/2.19 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) => (((in @ sK75 @ sK77) != $true) & ((in @ sK75 @ sK76) = $true) & ($true != (in @ sK75 @ (symdiff @ sK76 @ sK77))))),
% 6.46/2.19 introduced(definition,[],[choice_axiom])).
% 6.46/2.19 thf(f464,plain,(
% 6.46/2.19 (eqimpsubset1 = $true) & (setminusSubset2 = $true) & (replAx = $true) & (notdexE = $true) & (subsetI2 = $true) & (subsetTrans = $true) & (setextAx = $true) & (binunionLsub = $true) & (descr__Cong = $true) & (exuI3 = $true) & (quantDeMorgan4 = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (binunionIL = $true) & (binintersectER = $true) & (quantDeMorgan2 = $true) & (setminusER = $true) & (binunionE = $true) & (notdallE = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (emptysetimpfalse = $true) & (emptyInPowerset = $true) & (setminusEL = $true) & (exuE2 = $true) & (setext = $true) & (powersetI1 = $true) & (nonemptyE1 = $true) & (emptyE1 = $true) & (setunionE = $true) & (omega__Cong = $true) & (emptysetsubset = $true) & (quantDeMorgan1 = $true) & (nonemptyImpWitness = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) & (binintersectSubset1 = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (powerset__Cong = $true) & (setminusI = $true) & (setminusILneg = $true) & (upairset2IR = $true) & (eqinunit = $true) & (exuI2 = $true) & (exuI1 = $true) & (binunionIR = $true) & (emptyinPowerset = $true) & (omega0Ax = $true) & (eqimpsubset2 = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (powersetI = $true) & (dsetconstrER = $true) & (emptyinunitempty = $true) & (setminusLsub = $true) & (noeltsimpempty = $true) & (powersetE1 = $true) & (setoftrueEq = $true) & (exuEu = $true) & (symdiffE = $true) & (upairsetE = $true) & (upairsetIR = $true) & (binintersectI = $true) & (subsetE = $true) & (subsetRefl = $true) & (nonemptyI1 = $true) & (exuE3u = $true) & (exuE3e = $true) & (notsubsetI = $true) & (notequalI1 = $true) & (binintersectSubset2 = $true) & (emptyset__Cong = $true) & (inPowerset = $true) & (uniqinunit = $true) & (sepInPowerset = $true) & (binintersectSubset4 = $true) & (nonemptyI = $true) & (powersetAx = $true) & (inCongP = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (quantDeMorgan3 = $true) & (binintersectEL = $true) & (dsetconstrEL = $true) & (upairsetIL = $true) & (subset2powerset = $true) & (powersetE = $true) & (binunionEcases = $true) & (emptysetE = $true) & (exuE1 = $true) & (setadjoinIR = $true) & (subsetE2 = $true) & (setminusSubset1 = $true) & (subPowSU = $true) & (bs114d = $true) & (setminusELneg = $true) & (dsetconstrI = $true) & (binintersectRsub = $true) & (binunionRsub = $true) & (setunionAx = $true) & (omegaSAx = $true) & (notequalI2 = $true) & (prop2setE = $true) & (notinemptyset = $true) & (setadjoinSub = $true) & (exu__Cong = $true) & (setadjoinIL = $true) & (emptysetAx = $true) & (vacuousDall = $true) & (dsetconstr__Cong = $true) & (emptyI = $true) & (subsetemptysetimpeq = $true) & (setminusIRneg = $true) & (binintersectSubset5 = $true) & (disjointsetsI1 = $true) & (wellorderingAx = $true) & (setminusERneg = $true) & (setunion__Cong = $true) & (singletonsswitch = $true) & (subsetI1 = $true) & (powersetsubset = $true) & (setadjoinSub2 = $true) & (setbeta = $true) & (binintersectLsub = $true) & (sepSubset = $true) & (descrp = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (setextsub = $true)),
% 6.46/2.19 inference(flattening,[status(thm)],[f463])).
% 6.46/2.19 thf(f463,plain,(
% 6.46/2.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (symdiff @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true)) & ((in @ X0 @ X1) = $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)),
% 6.46/2.19 inference(ennf_transformation,[status(thm)],[f393])).
% 6.46/2.19 thf(f393,plain,(
% 6.46/2.19 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ((in @ X0 @ (symdiff @ X1 @ X2)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.46/2.19 inference(flattening,[status(thm)],[f185])).
% 6.46/2.19 thf(f185,plain,(
% 6.46/2.19 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ((in @ X0 @ (symdiff @ X1 @ X2)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.46/2.19 inference(fool_elimination,[status(thm)],[f184])).
% 6.46/2.19 thf(f184,plain,(
% 6.46/2.19 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.46/2.19 inference(rectify,[status(thm)],[f133])).
% 6.46/2.19 thf(f133,negated_conjecture,(
% 6.46/2.19 ~(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 => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.46/2.19 inference(negated_conjecture,[status(cth)],[f132])).
% 6.46/2.19 thf(f132,conjecture,(
% 6.46/2.19 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 => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.46/2.19 file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',symdiffI1)).
% 6.46/2.19 thf(f3959,plain,(
% 6.46/2.19 ((in @ sK75 @ sK76) != $true)),
% 6.46/2.19 inference(trivial_inequality_removal,[status(thm)],[f3955])).
% 6.46/2.19 thf(f3955,plain,(
% 6.46/2.19 ((in @ sK75 @ sK76) != $true) | ($true != $true)),
% 6.46/2.19 inference(superposition,[status(thm)],[f3954,f2612])).
% 6.46/2.19 thf(f2612,plain,(
% 6.46/2.19 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true)) )),
% 6.46/2.19 inference(trivial_inequality_removal,[status(thm)],[f2329])).
% 6.46/2.19 thf(f2329,plain,(
% 6.46/2.19 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true)) )),
% 6.46/2.19 inference(definition_unfolding,[status(thm)],[f1892,f1487])).
% 6.46/2.19 thf(f1487,plain,(
% 6.46/2.19 (binunionIL = $true)),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f682])).
% 6.46/2.19 thf(f1892,plain,(
% 6.46/2.19 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true) | (binunionIL != $true)) )),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f1154])).
% 6.46/2.19 thf(f1154,plain,(
% 6.46/2.19 ((binunionIL = $true) | (((in @ sK310 @ (binunion @ sK311 @ sK309)) != $true) & ($true = (in @ sK310 @ sK311)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true)) | (binunionIL != $true))),
% 6.46/2.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK309,sK310,sK311])],[f1152,f1153])).
% 6.46/2.19 thf(f1153,plain,(
% 6.46/2.19 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) != $true) & ($true = (in @ X1 @ X2))) => (((in @ sK310 @ (binunion @ sK311 @ sK309)) != $true) & ($true = (in @ sK310 @ sK311)))),
% 6.46/2.19 introduced(definition,[],[choice_axiom])).
% 6.46/2.19 thf(f1152,plain,(
% 6.46/2.19 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) != $true) & ($true = (in @ X1 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (binunion @ X5 @ X3)) = $true) | ((in @ X4 @ X5) != $true)) | (binunionIL != $true))),
% 6.46/2.19 inference(rectify,[status(thm)],[f1151])).
% 6.46/2.19 thf(f1151,plain,(
% 6.46/2.19 ((binunionIL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) != $true) & ($true = (in @ X1 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) = $true) | ($true != (in @ X1 @ X2))) | (binunionIL != $true))),
% 6.46/2.19 inference(nnf_transformation,[status(thm)],[f533])).
% 6.46/2.19 thf(f533,plain,(
% 6.46/2.19 (binunionIL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (binunion @ X2 @ X0)) = $true) | ($true != (in @ X1 @ X2)))),
% 6.46/2.19 inference(ennf_transformation,[status(thm)],[f310])).
% 6.46/2.19 thf(f310,plain,(
% 6.46/2.19 (binunionIL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X2)) => ((in @ X1 @ (binunion @ X2 @ X0)) = $true))),
% 6.46/2.19 inference(fool_elimination,[status(thm)],[f309])).
% 6.46/2.19 thf(f309,plain,(
% 6.46/2.19 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (in @ X1 @ (binunion @ X2 @ X0))))),
% 6.46/2.19 inference(rectify,[status(thm)],[f101])).
% 6.46/2.19 thf(f101,axiom,(
% 6.46/2.19 (binunionIL = ! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))))),
% 6.46/2.19 file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',binunionIL)).
% 6.46/2.19 thf(f3954,plain,(
% 6.46/2.19 ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true)),
% 6.46/2.19 inference(subsumption_resolution,[status(thm)],[f3952,f1466])).
% 6.46/2.19 thf(f1466,plain,(
% 6.46/2.19 ((in @ sK75 @ sK77) != $true)),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f682])).
% 6.46/2.19 thf(f3952,plain,(
% 6.46/2.19 ((in @ sK75 @ sK77) = $true) | ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true)),
% 6.46/2.19 inference(not_proxy_clausification,[status(thm)],[f3949])).
% 6.46/2.19 thf(f3949,plain,(
% 6.46/2.19 ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true) | ((~ (in @ sK75 @ sK77)) = $false)),
% 6.46/2.19 inference(binary_proxy_clausification,[status(thm)],[f3948])).
% 6.46/2.19 thf(f3948,plain,(
% 6.46/2.19 ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true) | ($true != ((~ (in @ sK75 @ sK76)) | (~ (in @ sK75 @ sK77))))),
% 6.46/2.19 inference(beta_eta_normalization,[status(thm)],[f3947])).
% 6.46/2.19 thf(f3947,plain,(
% 6.46/2.19 ($true != ((^[Y0 : $i]: ((~ (in @ Y0 @ sK76)) | (~ (in @ Y0 @ sK77)))) @ sK75)) | ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true)),
% 6.46/2.19 inference(trivial_inequality_removal,[status(thm)],[f3945])).
% 6.46/2.19 thf(f3945,plain,(
% 6.46/2.19 ((in @ sK75 @ (binunion @ sK76 @ sK77)) != $true) | ($true != ((^[Y0 : $i]: ((~ (in @ Y0 @ sK76)) | (~ (in @ Y0 @ sK77)))) @ sK75)) | ($true != $true)),
% 6.46/2.19 inference(superposition,[status(thm)],[f2592,f2553])).
% 6.46/2.19 thf(f2553,plain,(
% 6.46/2.19 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ X2)) = $true) | ((X2 @ X1) != $true) | ((in @ X1 @ X0) != $true)) )),
% 6.46/2.19 inference(beta_eta_normalization,[status(thm)],[f2552])).
% 6.46/2.19 thf(f2552,plain,(
% 6.46/2.19 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X1) != $true) | ((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)) )),
% 6.46/2.19 inference(trivial_inequality_removal,[status(thm)],[f2200])).
% 6.46/2.19 thf(f2200,plain,(
% 6.46/2.19 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) )),
% 6.46/2.19 inference(definition_unfolding,[status(thm)],[f1704,f1402])).
% 6.46/2.19 thf(f1402,plain,(
% 6.46/2.19 (dsetconstrI = $true)),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f682])).
% 6.46/2.19 thf(f1704,plain,(
% 6.46/2.19 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true) | (dsetconstrI != $true)) )),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f930])).
% 6.46/2.19 thf(f930,plain,(
% 6.46/2.19 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | (((in @ sK200 @ sK199) = $true) & ((in @ sK200 @ (dsetconstr @ sK199 @ (^[Y0 : $i]: (sK201 @ Y0)))) != $true) & ((sK201 @ sK200) = $true)))),
% 6.46/2.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK199,sK200,sK201])],[f928,f929])).
% 6.46/2.19 thf(f929,plain,(
% 6.46/2.19 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ X3) = $true) & ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true = (X5 @ X4))) => (((in @ sK200 @ sK199) = $true) & ((in @ sK200 @ (dsetconstr @ sK199 @ (^[Y0 : $i]: (sK201 @ Y0)))) != $true) & ((sK201 @ sK200) = $true))),
% 6.46/2.19 introduced(definition,[],[choice_axiom])).
% 6.46/2.19 thf(f928,plain,(
% 6.46/2.19 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X4 @ X3) = $true) & ($true != (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true = (X5 @ X4))))),
% 6.46/2.19 inference(rectify,[status(thm)],[f927])).
% 6.46/2.19 thf(f927,plain,(
% 6.46/2.19 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) = $true) & ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) & ((X2 @ X1) = $true)))),
% 6.46/2.19 inference(nnf_transformation,[status(thm)],[f556])).
% 6.46/2.19 thf(f556,plain,(
% 6.46/2.19 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) <=> (dsetconstrI = $true)),
% 6.46/2.19 inference(flattening,[status(thm)],[f555])).
% 6.46/2.19 thf(f555,plain,(
% 6.46/2.19 ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X1) != $true)) | ((in @ X1 @ X0) != $true)) <=> (dsetconstrI = $true)),
% 6.46/2.19 inference(ennf_transformation,[status(thm)],[f277])).
% 6.46/2.19 thf(f277,plain,(
% 6.46/2.19 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X1 @ X0) = $true) => (((X2 @ X1) = $true) => ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true))) <=> (dsetconstrI = $true)),
% 6.46/2.19 inference(fool_elimination,[status(thm)],[f276])).
% 6.46/2.19 thf(f276,plain,(
% 6.46/2.19 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 6.46/2.19 inference(rectify,[status(thm)],[f14])).
% 6.46/2.19 thf(f14,axiom,(
% 6.46/2.19 (! [X3 : $i,X1 : $i,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = dsetconstrI)),
% 6.46/2.19 file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',dsetconstrI)).
% 6.46/2.19 thf(f2592,plain,(
% 6.46/2.19 ((in @ sK75 @ (dsetconstr @ (binunion @ sK76 @ sK77) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK76)) | (~ (in @ Y0 @ sK77)))))) != $true)),
% 6.46/2.19 inference(beta_eta_normalization,[status(thm)],[f2072])).
% 6.46/2.19 thf(f2072,plain,(
% 6.46/2.19 ((in @ sK75 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))) @ sK76 @ sK77)) != $true)),
% 6.46/2.19 inference(definition_unfolding,[status(thm)],[f1464,f1794])).
% 6.46/2.19 thf(f1794,plain,(
% 6.46/2.19 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f306])).
% 6.46/2.19 thf(f306,plain,(
% 6.46/2.19 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) | (~ (in @ Y2 @ Y1)))))))))),
% 6.46/2.19 inference(fool_elimination,[status(thm)],[f305])).
% 6.46/2.19 thf(f305,plain,(
% 6.46/2.19 (symdiff = (^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X1) | ~(in @ X2 @ X0))))))),
% 6.46/2.19 inference(rectify,[status(thm)],[f130])).
% 6.46/2.19 thf(f130,axiom,(
% 6.46/2.19 (symdiff = (^[X3 : $i, X4 : $i] : (dsetconstr @ (binunion @ X3 @ X4) @ (^[X1 : $i] : (~(in @ X1 @ X4) | ~(in @ X1 @ X3))))))),
% 6.46/2.19 file('/export/starexec/sandbox/tmp/tmp.jeWnLKwpeY/DTF2THF_6052.p',symdiff)).
% 6.46/2.19 thf(f1464,plain,(
% 6.46/2.19 ($true != (in @ sK75 @ (symdiff @ sK76 @ sK77)))),
% 6.46/2.19 inference(cnf_transformation,[status(thm)],[f682])).
% 6.46/2.19 % SZS output end Proof for DTF2THF_6052
% 6.46/2.19 % (6199)------------------------------
% 6.46/2.19 % (6199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.19 % (6199)Termination reason: Refutation
% 6.46/2.19
% 6.46/2.19 % (6199)Memory used [KB]: 8443
% 6.46/2.19 % (6199)Time elapsed: 0.177 s
% 6.46/2.19 % (6199)Instructions burned: 336 (million)
% 6.46/2.19 % (6199)------------------------------
% 6.46/2.19 % (6199)------------------------------
% 6.46/2.19 % (6151)Success in time 0.69 s
%------------------------------------------------------------------------------