%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU601^1 : 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 : n029.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 09:35:32 AM UTC 2026
% Result : Theorem 6.45s 2.19s
% Output : Refutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 2457 ( 684 equ; 0 cnn)
% Maximal formula atoms : 120 ( 64 avg)
% Number of connectives : 1352 ( 68 ~; 31 |; 374 &; 273 @)
% ( 3 <=>; 603 =>; 0 <=; 0 <~>)
% Maximal formula depth : 127 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 275 ( 272 usr; 124 con; 0-4 aty)
% Number of variables : 103 ( 34 ^; 51 !; 18 ?; 103 :)
% 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_149,type,
sP0: $i > $i > $o ).
thf(func_def_151,type,
sP2: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_152,type,
sP3: $i > ( $i > $i > $o ) > $o ).
thf(func_def_154,type,
sP5: ( $i > $o ) > $o ).
thf(func_def_155,type,
sP6: ( $i > $o ) > $i > $o ).
thf(func_def_157,type,
sP8: $i > ( $i > $o ) > $o ).
thf(func_def_160,type,
sP11: $o > $i > $i > $o ).
thf(func_def_161,type,
sP12: $i > $i > $i > $o ).
thf(func_def_162,type,
sP13: ( $i > $o ) > $o ).
thf(func_def_163,type,
sP14: $i > $i > $o ).
thf(func_def_165,type,
sP16: $i > $i > $i > $o ).
thf(func_def_169,type,
sP20: ( $i > $o ) > $o ).
thf(func_def_171,type,
sP22: $i > $o ).
thf(func_def_172,type,
sP23: $i > $i > $o > $o ).
thf(func_def_173,type,
sP24: ( $i > $o ) > $o ).
thf(func_def_174,type,
sP25: $i > $i > $i > $o ).
thf(func_def_175,type,
sP26: $i > $i > $o ).
thf(func_def_176,type,
sP27: $i > $o ).
thf(func_def_177,type,
sP28: $i > $i > $o ).
thf(func_def_178,type,
sP29: $i > $i > $o ).
thf(func_def_179,type,
sP30: $i > $i > $o ).
thf(func_def_181,type,
sP32: $i > $i > $o > $o ).
thf(func_def_183,type,
sP34: ( $i > $o ) > $o ).
thf(func_def_184,type,
sP35: ( $i > $o ) > $i > $o ).
thf(func_def_186,type,
sP37: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_188,type,
sP39: ( $i > $o ) > $i > $o ).
thf(func_def_190,type,
sP41: $i > ( $i > $o ) > $o ).
thf(func_def_192,type,
sP43: ( $i > $o ) > $i > $o ).
thf(func_def_194,type,
sP45: $i > $i > $o ).
thf(func_def_196,type,
sP47: $i > $o ).
thf(func_def_197,type,
sP48: $i > $o ).
thf(func_def_212,type,
sK63: $i > $i > $i ).
thf(func_def_216,type,
sK67: $i > $i > $o ).
thf(func_def_218,type,
sK69: $i > ( $i > $i > $o ) > $i ).
thf(func_def_219,type,
sK70: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_220,type,
sK71: $i > ( $i > $i > $o ) > $i ).
thf(func_def_221,type,
sK72: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_222,type,
sK73: $i > ( $i > $o ) > $i ).
thf(func_def_223,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_224,type,
sK75: $i > $o ).
thf(func_def_225,type,
sK76: $i > $o ).
thf(func_def_229,type,
sK80: $i > $i ).
thf(func_def_244,type,
sK95: $i > $o ).
thf(func_def_256,type,
sK107: $i > $o ).
thf(func_def_257,type,
sK108: ( $i > $o ) > $i > $i ).
thf(func_def_258,type,
sK109: ( $i > $o ) > $i > $i ).
thf(func_def_261,type,
sK112: $i > $o ).
thf(func_def_265,type,
sK116: $i > $o ).
thf(func_def_269,type,
sK120: $i > $o ).
thf(func_def_272,type,
sK123: $i > $o ).
thf(func_def_279,type,
sK130: $i > $i ).
thf(func_def_287,type,
sK138: $i > $o ).
thf(func_def_288,type,
sK139: ( $i > $o ) > $i > $i ).
thf(func_def_289,type,
sK140: $i > ( $i > $o ) > $i ).
thf(func_def_294,type,
sK145: $i > $i > $i ).
thf(func_def_299,type,
sK150: $i > $o ).
thf(func_def_304,type,
sK155: $i > $i > $i > $o ).
thf(func_def_308,type,
sK159: ( $i > $o ) > $i ).
thf(func_def_309,type,
sK160: $i > ( $i > $o ) > $i ).
thf(func_def_310,type,
sK161: $i > $o ).
thf(func_def_313,type,
sK164: $i > $i > $i ).
thf(func_def_320,type,
sK171: $i > $o ).
thf(func_def_325,type,
sK176: $i > $i ).
thf(func_def_330,type,
sK181: $i > $o ).
thf(func_def_331,type,
sK182: $i > $o ).
thf(func_def_332,type,
sK183: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_333,type,
sK184: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_334,type,
sK185: $i > $o ).
thf(func_def_335,type,
sK186: $i > $o ).
thf(func_def_336,type,
sK187: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_337,type,
sK188: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_342,type,
sK193: $i > ( $i > $o ) > $i ).
thf(func_def_343,type,
sK194: ( $i > $o ) > $i ).
thf(func_def_344,type,
sK195: $i > $o ).
thf(func_def_348,type,
sK199: $i > $i > $i ).
thf(func_def_349,type,
sK200: $i > $i > $i ).
thf(func_def_350,type,
sK201: $i > $i ).
thf(func_def_353,type,
sK204: $i > $i > $o > $i ).
thf(func_def_358,type,
sK209: ( $i > $o ) > $i ).
thf(func_def_359,type,
sK210: $i > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK211: $i > $o ).
thf(func_def_362,type,
sK213: $i > $o ).
thf(func_def_365,type,
sK216: $i > $i ).
thf(func_def_367,type,
sK218: $i > $i > $i ).
thf(func_def_368,type,
sK219: $i > $i > $i ).
thf(func_def_369,type,
sK220: $i > $i > $i > $i ).
thf(func_def_370,type,
sK221: $i > $i > $i ).
thf(func_def_371,type,
sK222: $i > $i > $i ).
thf(func_def_372,type,
sK223: $i > $i > $i ).
thf(func_def_373,type,
sK224: $i > $i > $i ).
thf(func_def_374,type,
sK225: $i > $i > $i ).
thf(func_def_375,type,
sK226: $i > $i ).
thf(func_def_376,type,
sK227: $i > $i ).
thf(func_def_377,type,
sK228: $i > $i ).
thf(func_def_378,type,
sK229: $i > $i ).
thf(func_def_379,type,
sK230: $i > $i > $i ).
thf(func_def_380,type,
sK231: $i > $i > $i ).
thf(func_def_381,type,
sK232: $i > $i > $i ).
thf(func_def_382,type,
sK233: $i > $i > $i > $i ).
thf(func_def_383,type,
sK234: $i > $i > $i > $i ).
thf(func_def_384,type,
sK235: $i > $i ).
thf(func_def_392,type,
sK243: ( $i > $o ) > $i ).
thf(func_def_393,type,
sK244: $i > $o ).
thf(func_def_396,type,
sK247: $i > $i > $i ).
thf(func_def_420,type,
sK271: ( $i > $o ) > $i ).
thf(func_def_421,type,
sK272: ( $i > $o ) > $i ).
thf(func_def_422,type,
sK273: $i > $o ).
thf(func_def_427,type,
sK278: $i > $i > $i ).
thf(func_def_431,type,
sK282: $i > $o ).
thf(func_def_432,type,
sK283: ( $i > $o ) > $i > $i ).
thf(func_def_433,type,
sK284: ( $i > $o ) > $i > $i ).
thf(func_def_438,type,
sK289: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_439,type,
sK290: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_442,type,
sK293: $i > $o ).
thf(func_def_443,type,
sK294: $i > $o ).
thf(func_def_446,type,
sK297: $i > $o ).
thf(func_def_449,type,
sK300: $i > $i > $i ).
thf(func_def_451,type,
sK302: $i > $o ).
thf(func_def_452,type,
sK303: ( $i > $o ) > $i > $i ).
thf(func_def_453,type,
sK304: ( $i > $o ) > $i > $i ).
thf(func_def_454,type,
sK305: $i > $o ).
thf(func_def_456,type,
sK307: $i > ( $i > $o ) > $i ).
thf(func_def_457,type,
sK308: $i > ( $i > $o ) > $i ).
thf(func_def_460,type,
sK311: $i > $o ).
thf(func_def_462,type,
sK313: $i > ( $i > $o ) > $i ).
thf(func_def_463,type,
sK314: ( $i > $o ) > $i > $i ).
thf(func_def_481,type,
sK332: $i > $o ).
thf(func_def_500,type,
sK351: $i > $i > $i ).
thf(func_def_501,type,
sK352: $i > $i > $i ).
thf(func_def_506,type,
sK357: $i > $o ).
thf(func_def_507,type,
sK358: $i > $i ).
thf(func_def_508,type,
sK359: $i > $i ).
thf(func_def_513,type,
ph364:
!>[X0: $tType] : X0 ).
thf(f3610,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3609,f1643]) ).
thf(f1643,plain,
( ( in @ sK251 @ sK252 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( uniqinunit = $true )
& ( subPowSU = $true )
& ( omegaSAx = $true )
& ( upairsetIR = $true )
& ( setadjoinSub = $true )
& ( upairsetE = $true )
& ( exuI2 = $true )
& ( prop2setE = $true )
& ( subsetE2 = $true )
& ( setoftrueEq = $true )
& ( binunionRsub = $true )
& ( binunionIR = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( notinsingleton = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( nonemptyE1 = $true )
& ( emptysetE = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset5 = $true )
& ( omega__Cong = $true )
& ( binintersectSubset1 = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( binintersectSubset2 = $true )
& ( sepInPowerset = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( binintersectRsub = $true )
& ( noeltsimpempty = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( prop2set2propI = $true )
& ( setadjoin__Cong = $true )
& ( omegaIndAx = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrI = $true )
& ( binunionE = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( powersetE = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( quantDeMorgan4 = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset3 = $true )
& ( emptyset__Cong = $true )
& ( dsetconstrER = $true )
& ( ( in @ sK251 @ sK253 )
= $true )
& ( ( in @ sK251 @ sK252 )
!= $true )
& ( $true
!= ( in @ sK251 @ ( setminus @ sK253 @ sK252 ) ) )
& ( powersetAx = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( emptysetsubset = $true )
& ( emptyE1 = $true )
& ( setadjoinSub2 = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( sepSubset = $true )
& ( exuE3u = $true )
& ( inPowerset = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( wellorderingAx = $true )
& ( powersetsubset = $true )
& ( binunionEcases = $true )
& ( exuEu = $true )
& ( setunionI = $true )
& ( powersetI = $true )
& ( binintersectEL = $true )
& ( upairset2IR = $true )
& ( singletonsswitch = $true )
& ( foundationAx = $true )
& ( binintersectI = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan2 = $true )
& ( exuI1 = $true )
& ( replAx = $true )
& ( subsetE = $true )
& ( binunionLsub = $true )
& ( exuE2 = $true )
& ( powersetI1 = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( disjointsetsI1 = $true )
& ( descrp = $true )
& ( exu__Cong = $true )
& ( setbeta = $true )
& ( quantDeMorgan1 = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( powerset__Cong = $true )
& ( notdexE = $true )
& ( subsetRefl = $true )
& ( notequalI1 = $true )
& ( vacuousDall = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetI2 = $true )
& ( setunion__Cong = $true )
& ( setunionAx = $true )
& ( setext = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( notequalI2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK251,sK252,sK253])],[f472,f1004]) ).
thf(f1004,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
=> ( ( ( in @ sK251 @ sK253 )
= $true )
& ( ( in @ sK251 @ sK252 )
!= $true )
& ( $true
!= ( in @ sK251 @ ( setminus @ sK253 @ sK252 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f472,plain,
( ( uniqinunit = $true )
& ( subPowSU = $true )
& ( omegaSAx = $true )
& ( upairsetIR = $true )
& ( setadjoinSub = $true )
& ( upairsetE = $true )
& ( exuI2 = $true )
& ( prop2setE = $true )
& ( subsetE2 = $true )
& ( setoftrueEq = $true )
& ( binunionRsub = $true )
& ( binunionIR = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( notinsingleton = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( nonemptyE1 = $true )
& ( emptysetE = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset5 = $true )
& ( omega__Cong = $true )
& ( binintersectSubset1 = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( binintersectSubset2 = $true )
& ( sepInPowerset = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( binintersectRsub = $true )
& ( noeltsimpempty = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( prop2set2propI = $true )
& ( setadjoin__Cong = $true )
& ( omegaIndAx = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrI = $true )
& ( binunionE = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( powersetE = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( quantDeMorgan4 = $true )
& ( subset2powerset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset3 = $true )
& ( emptyset__Cong = $true )
& ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
& ( powersetAx = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( binintersectSubset4 = $true )
& ( emptysetsubset = $true )
& ( emptyE1 = $true )
& ( setadjoinSub2 = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( sepSubset = $true )
& ( exuE3u = $true )
& ( inPowerset = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( wellorderingAx = $true )
& ( powersetsubset = $true )
& ( binunionEcases = $true )
& ( exuEu = $true )
& ( setunionI = $true )
& ( powersetI = $true )
& ( binintersectEL = $true )
& ( upairset2IR = $true )
& ( singletonsswitch = $true )
& ( foundationAx = $true )
& ( binintersectI = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan2 = $true )
& ( exuI1 = $true )
& ( replAx = $true )
& ( subsetE = $true )
& ( binunionLsub = $true )
& ( exuE2 = $true )
& ( powersetI1 = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( disjointsetsI1 = $true )
& ( descrp = $true )
& ( exu__Cong = $true )
& ( setbeta = $true )
& ( quantDeMorgan1 = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( powerset__Cong = $true )
& ( notdexE = $true )
& ( subsetRefl = $true )
& ( notequalI1 = $true )
& ( vacuousDall = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan3 = $true )
& ( subsetI2 = $true )
& ( setunion__Cong = $true )
& ( setunionAx = $true )
& ( setext = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( notequalI2 = $true ) ),
inference(flattening,[status(thm)],[f471]) ).
thf(f471,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ X2 )
= $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)],[f360]) ).
thf(f360,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f125]) ).
thf(f125,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
=> ( ( $true
!= ( in @ X0 @ X1 ) )
=> ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f124]) ).
thf(f124,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ~ ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setminus @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f121]) ).
thf(f121,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
=> ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',setminusI) ).
thf(f3609,plain,
( ( in @ sK251 @ sK252 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f3604,f1644]) ).
thf(f1644,plain,
( ( in @ sK251 @ sK253 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
thf(f3604,plain,
( ( ( in @ sK251 @ sK253 )
!= $true )
| ( ( in @ sK251 @ sK252 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f3603]) ).
thf(f3603,plain,
( ( $true
!= ( ~ ( in @ sK251 @ sK252 ) ) )
| ( ( in @ sK251 @ sK253 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3602]) ).
thf(f3602,plain,
( ( ( in @ sK251 @ sK253 )
!= $true )
| ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK252 )
@ sK251 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3597]) ).
thf(f3597,plain,
( ( ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK252 )
@ sK251 )
!= $true )
| ( $true != $true )
| ( ( in @ sK251 @ sK253 )
!= $true ) ),
inference(superposition,[status(thm)],[f2352,f2269]) ).
thf(f2269,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( dsetconstr @ X4 @ X3 ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2268]) ).
thf(f2268,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) )
| ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1965]) ).
thf(f1965,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) )
| ( $true != $true )
| ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1337,f1657]) ).
thf(f1657,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f1005]) ).
thf(f1337,plain,
! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) )
| ( dsetconstrI != $true ) ),
inference(cnf_transformation,[status(thm)],[f722]) ).
thf(f722,plain,
( ( ( dsetconstrI = $true )
| ( ( ( in @ sK118
@ ( dsetconstr @ sK117
@ ^ [Y0: $i] : ( sK116 @ Y0 ) ) )
!= $true )
& ( $true
= ( in @ sK118 @ sK117 ) )
& ( $true
= ( sK116 @ sK118 ) ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) ) )
| ( dsetconstrI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117,sK118])],[f720,f721]) ).
thf(f721,plain,
( ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( ( in @ sK118
@ ( dsetconstr @ sK117
@ ^ [Y0: $i] : ( sK116 @ Y0 ) ) )
!= $true )
& ( $true
= ( in @ sK118 @ sK117 ) )
& ( $true
= ( sK116 @ sK118 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f720,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( X3 @ X5 ) ) )
| ( dsetconstrI != $true ) ) ),
inference(rectify,[status(thm)],[f719]) ).
thf(f719,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( $true
= ( in @ X2 @ X1 ) )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( X0 @ X2 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f407]) ).
thf(f407,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f406]) ).
thf(f406,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
| ( ( X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f272]) ).
thf(f272,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i > $o,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( ( X0 @ X2 )
= $true )
=> ( $true
= ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f271]) ).
thf(f271,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( dsetconstrI
= ( ! [X0: $i > $o,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',dsetconstrI) ).
thf(f2352,plain,
( $true
!= ( in @ sK251
@ ( dsetconstr @ sK253
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK252 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2101]) ).
thf(f2101,plain,
( $true
!= ( in @ sK251
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK253
@ sK252 ) ) ),
inference(definition_unfolding,[status(thm)],[f1642,f1365]) ).
thf(f1365,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f237]) ).
thf(f237,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) )
= setminus ),
inference(rectify,[status(thm)],[f120]) ).
thf(f120,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ X3
@ ^ [X1: $i] :
~ ( in @ X1 @ X4 ) ) )
= setminus ),
file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',setminus) ).
thf(f1642,plain,
( $true
!= ( in @ sK251 @ ( setminus @ sK253 @ sK252 ) ) ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU601^1 : 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
% 0.11/0.29 % Computer : n029.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:28:14 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.38 ---- Original DTF file ---
% 0.19/0.38 thf(spec,logic,$$dhol).
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 % File : SEU601^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.38 % Domain : Set Theory
% 0.19/0.38 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.19/0.38 % Version : Especial.
% 0.19/0.38 % English : (! A:i.! B:i.! x:i.in x A -> ~(in x B) -> in x (setminus A B))
% 0.19/0.38
% 0.19/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.38 % Source : [Bro08]
% 0.19/0.38 % Names : ZFC103g [Bro08]
% 0.19/0.38
% 0.19/0.38 % Status : Theorem
% 0.19/0.38 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.19/0.38 % Syntax : Number of formulae : 257 ( 120 unt; 136 typ; 120 def)
% 0.19/0.38 % Number of atoms : 637 ( 175 equ; 0 cnn)
% 0.19/0.38 % Maximal formula atoms : 120 ( 5 avg)
% 0.19/0.38 % Number of connectives : 1005 ( 32 ~; 6 |; 28 &; 643 @)
% 0.19/0.38 % ( 14 <=>; 282 =>; 0 <=; 0 <~>)
% 0.19/0.38 % Maximal formula depth : 126 ( 2 avg)
% 0.19/0.38 % Number of types : 2 ( 0 usr)
% 0.19/0.38 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.19/0.38 % Number of symbols : 139 ( 136 usr; 121 con; 0-2 aty)
% 0.19/0.38 % Number of variables : 349 ( 33 ^; 287 !; 29 ?; 349 :)
% 0.19/0.38 % SPC : TH0_THM_EQU_NAR
% 0.19/0.38
% 0.19/0.38 % Comments : http://mathgate.info/detsetitem.php?id=277
% 0.19/0.38 %------------------------------------------------------------------------------
% 0.19/0.38 thf(in_type,type,
% 0.19/0.38 in: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(exu_type,type,
% 0.19/0.38 exu: ( $i > $o ) > $o ).
% 0.19/0.38
% 0.19/0.38 thf(exu,definition,
% 0.19/0.38 ( exu
% 0.19/0.38 = ( ^ [Xphi: $i > $o] :
% 0.19/0.38 ? [Xx: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 & ! [Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setextAx_type,type,
% 0.19/0.38 setextAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setextAx,definition,
% 0.19/0.38 ( setextAx
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 <=> ( in @ Xx @ B ) )
% 0.19/0.38 => ( A = B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyset_type,type,
% 0.19/0.38 emptyset: $i ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetAx_type,type,
% 0.19/0.38 emptysetAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetAx,definition,
% 0.19/0.38 ( emptysetAx
% 0.19/0.38 = ( ! [Xx: $i] :
% 0.19/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoin_type,type,
% 0.19/0.38 setadjoin: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinAx_type,type,
% 0.19/0.38 setadjoinAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinAx,definition,
% 0.19/0.38 ( setadjoinAx
% 0.19/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.38 <=> ( ( Xy = Xx )
% 0.19/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powerset_type,type,
% 0.19/0.38 powerset: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(powersetAx_type,type,
% 0.19/0.38 powersetAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetAx,definition,
% 0.19/0.38 ( powersetAx
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.38 <=> ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setunion_type,type,
% 0.19/0.38 setunion: $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(setunionAx_type,type,
% 0.19/0.38 setunionAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setunionAx,definition,
% 0.19/0.38 ( setunionAx
% 0.19/0.38 = ( ! [A: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.38 <=> ? [B: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(omega_type,type,
% 0.19/0.38 omega: $i ).
% 0.19/0.38
% 0.19/0.38 thf(omega0Ax_type,type,
% 0.19/0.38 omega0Ax: $o ).
% 0.19/0.38
% 0.19/0.38 thf(omega0Ax,definition,
% 0.19/0.38 ( omega0Ax
% 0.19/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(omegaSAx_type,type,
% 0.19/0.38 omegaSAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(omegaSAx,definition,
% 0.19/0.38 ( omegaSAx
% 0.19/0.38 = ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ omega )
% 0.19/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(omegaIndAx_type,type,
% 0.19/0.38 omegaIndAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(omegaIndAx,definition,
% 0.19/0.38 ( omegaIndAx
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ( ( in @ emptyset @ A )
% 0.19/0.38 & ! [Xx: $i] :
% 0.19/0.38 ( ( ( in @ Xx @ omega )
% 0.19/0.38 & ( in @ Xx @ A ) )
% 0.19/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.19/0.38 => ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ omega )
% 0.19/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(replAx_type,type,
% 0.19/0.38 replAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(replAx,definition,
% 0.19/0.38 ( replAx
% 0.19/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( exu
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.19/0.38 => ? [B: $i] :
% 0.19/0.38 ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 <=> ? [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ A )
% 0.19/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(foundationAx_type,type,
% 0.19/0.38 foundationAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(foundationAx,definition,
% 0.19/0.38 ( foundationAx
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.38 => ? [B: $i] :
% 0.19/0.38 ( ( in @ B @ A )
% 0.19/0.38 & ~ ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(wellorderingAx_type,type,
% 0.19/0.38 wellorderingAx: $o ).
% 0.19/0.38
% 0.19/0.38 thf(wellorderingAx,definition,
% 0.19/0.38 ( wellorderingAx
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ? [B: $i] :
% 0.19/0.38 ( ! [C: $i] :
% 0.19/0.38 ( ( in @ C @ B )
% 0.19/0.38 => ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ C )
% 0.19/0.38 => ( in @ Xx @ A ) ) )
% 0.19/0.38 & ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( ( in @ Xx @ A )
% 0.19/0.38 & ( in @ Xy @ A ) )
% 0.19/0.38 => ( ! [C: $i] :
% 0.19/0.38 ( ( in @ C @ B )
% 0.19/0.38 => ( ( in @ Xx @ C )
% 0.19/0.38 <=> ( in @ Xy @ C ) ) )
% 0.19/0.38 => ( Xx = Xy ) ) )
% 0.19/0.38 & ! [C: $i,D: $i] :
% 0.19/0.38 ( ( ( in @ C @ B )
% 0.19/0.38 & ( in @ D @ B ) )
% 0.19/0.38 => ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ C )
% 0.19/0.38 => ( in @ Xx @ D ) )
% 0.19/0.38 | ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ D )
% 0.19/0.38 => ( in @ Xx @ C ) ) ) )
% 0.19/0.38 & ! [C: $i] :
% 0.19/0.38 ( ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ C )
% 0.19/0.38 => ( in @ Xx @ A ) )
% 0.19/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.19/0.38 => ? [D: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ D @ B )
% 0.19/0.38 & ( in @ Xx @ C )
% 0.19/0.38 & ~ ? [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ D )
% 0.19/0.38 & ( in @ Xy @ C ) )
% 0.19/0.38 & ! [E: $i] :
% 0.19/0.38 ( ( in @ E @ B )
% 0.19/0.38 => ( ! [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ E )
% 0.19/0.38 => ( in @ Xy @ D ) )
% 0.19/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(descr_type,type,
% 0.19/0.38 descr: ( $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(descrp_type,type,
% 0.19/0.38 descrp: $o ).
% 0.19/0.38
% 0.19/0.38 thf(descrp,definition,
% 0.19/0.38 ( descrp
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ( Xphi
% 0.19/0.38 @ ( descr
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstr_type,type,
% 0.19/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrI_type,type,
% 0.19/0.38 dsetconstrI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrI,definition,
% 0.19/0.38 ( dsetconstrI
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ( Xphi @ Xx )
% 0.19/0.38 => ( in @ Xx
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrEL_type,type,
% 0.19/0.38 dsetconstrEL: $o ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrEL,definition,
% 0.19/0.38 ( dsetconstrEL
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrER_type,type,
% 0.19/0.38 dsetconstrER: $o ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstrER,definition,
% 0.19/0.38 ( dsetconstrER
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuE1_type,type,
% 0.19/0.38 exuE1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuE1,definition,
% 0.19/0.38 ( exuE1
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ? [Xx: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 & ! [Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(prop2set_type,type,
% 0.19/0.38 prop2set: $o > $i ).
% 0.19/0.38
% 0.19/0.38 thf(prop2setE_type,type,
% 0.19/0.38 prop2setE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(prop2setE,definition,
% 0.19/0.38 ( prop2setE
% 0.19/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.19/0.38 => Xphi ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetE_type,type,
% 0.19/0.38 emptysetE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetE,definition,
% 0.19/0.38 ( emptysetE
% 0.19/0.38 = ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ emptyset )
% 0.19/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetimpfalse_type,type,
% 0.19/0.38 emptysetimpfalse: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetimpfalse,definition,
% 0.19/0.38 ( emptysetimpfalse
% 0.19/0.38 = ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ emptyset )
% 0.19/0.38 => $false ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notinemptyset_type,type,
% 0.19/0.38 notinemptyset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notinemptyset,definition,
% 0.19/0.38 ( notinemptyset
% 0.19/0.38 = ( ! [Xx: $i] :
% 0.19/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuE3e_type,type,
% 0.19/0.38 exuE3e: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuE3e,definition,
% 0.19/0.38 ( exuE3e
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setext_type,type,
% 0.19/0.38 setext: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setext,definition,
% 0.19/0.38 ( setext
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) )
% 0.19/0.38 => ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ A ) )
% 0.19/0.38 => ( A = B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyI_type,type,
% 0.19/0.38 emptyI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyI,definition,
% 0.19/0.38 ( emptyI
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ~ ( in @ Xx @ A )
% 0.19/0.38 => ( A = emptyset ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(noeltsimpempty_type,type,
% 0.19/0.38 noeltsimpempty: $o ).
% 0.19/0.38
% 0.19/0.38 thf(noeltsimpempty,definition,
% 0.19/0.38 ( noeltsimpempty
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ~ ( in @ Xx @ A )
% 0.19/0.38 => ( A = emptyset ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setbeta_type,type,
% 0.19/0.38 setbeta: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setbeta,definition,
% 0.19/0.38 ( setbeta
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ( in @ Xx
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(nonempty_type,type,
% 0.19/0.38 nonempty: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(nonempty,definition,
% 0.19/0.38 ( nonempty
% 0.19/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyE1_type,type,
% 0.19/0.38 nonemptyE1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyE1,definition,
% 0.19/0.38 ( nonemptyE1
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ( nonempty @ A )
% 0.19/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyI_type,type,
% 0.19/0.38 nonemptyI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyI,definition,
% 0.19/0.38 ( nonemptyI
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ( Xphi @ Xx )
% 0.19/0.38 => ( nonempty
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyI1_type,type,
% 0.19/0.38 nonemptyI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyI1,definition,
% 0.19/0.38 ( nonemptyI1
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinIL_type,type,
% 0.19/0.38 setadjoinIL: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinIL,definition,
% 0.19/0.38 ( setadjoinIL
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyinunitempty_type,type,
% 0.19/0.38 emptyinunitempty: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyinunitempty,definition,
% 0.19/0.38 ( emptyinunitempty
% 0.19/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinIR_type,type,
% 0.19/0.38 setadjoinIR: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinIR,definition,
% 0.19/0.38 ( setadjoinIR
% 0.19/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ A )
% 0.19/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinE_type,type,
% 0.19/0.38 setadjoinE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinE,definition,
% 0.19/0.38 ( setadjoinE
% 0.19/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.38 => ! [Xphi: $o] :
% 0.19/0.38 ( ( ( Xy = Xx )
% 0.19/0.38 => Xphi )
% 0.19/0.38 => ( ( ( in @ Xy @ A )
% 0.19/0.38 => Xphi )
% 0.19/0.38 => Xphi ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinOr_type,type,
% 0.19/0.38 setadjoinOr: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinOr,definition,
% 0.19/0.38 ( setadjoinOr
% 0.19/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.38 => ( ( Xy = Xx )
% 0.19/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setoftrueEq_type,type,
% 0.19/0.38 setoftrueEq: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setoftrueEq,definition,
% 0.19/0.38 ( setoftrueEq
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] : $true )
% 0.19/0.38 = A ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powersetI_type,type,
% 0.19/0.38 powersetI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetI,definition,
% 0.19/0.38 ( powersetI
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ A ) )
% 0.19/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyinPowerset_type,type,
% 0.19/0.38 emptyinPowerset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyinPowerset,definition,
% 0.19/0.38 ( emptyinPowerset
% 0.19/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyInPowerset_type,type,
% 0.19/0.38 emptyInPowerset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyInPowerset,definition,
% 0.19/0.38 ( emptyInPowerset
% 0.19/0.38 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powersetE_type,type,
% 0.19/0.38 powersetE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetE,definition,
% 0.19/0.38 ( powersetE
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.38 => ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setunionI_type,type,
% 0.19/0.38 setunionI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setunionI,definition,
% 0.19/0.38 ( setunionI
% 0.19/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( ( in @ B @ A )
% 0.19/0.38 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setunionE_type,type,
% 0.19/0.38 setunionE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setunionE,definition,
% 0.19/0.38 ( setunionE
% 0.19/0.38 = ( ! [A: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.38 => ! [Xphi: $o] :
% 0.19/0.38 ( ! [B: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( ( in @ B @ A )
% 0.19/0.38 => Xphi ) )
% 0.19/0.38 => Xphi ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subPowSU_type,type,
% 0.19/0.38 subPowSU: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subPowSU,definition,
% 0.19/0.38 ( subPowSU
% 0.19/0.38 = ( ! [A: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuE2_type,type,
% 0.19/0.38 exuE2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuE2,definition,
% 0.19/0.38 ( exuE2
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ? [Xx: $i] :
% 0.19/0.38 ! [Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xy )
% 0.19/0.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyImpWitness_type,type,
% 0.19/0.38 nonemptyImpWitness: $o ).
% 0.19/0.38
% 0.19/0.38 thf(nonemptyImpWitness,definition,
% 0.19/0.38 ( nonemptyImpWitness
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ( nonempty @ A )
% 0.19/0.38 => ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & $true ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(uniqinunit_type,type,
% 0.19/0.38 uniqinunit: $o ).
% 0.19/0.38
% 0.19/0.38 thf(uniqinunit,definition,
% 0.19/0.38 ( uniqinunit
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.38 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notinsingleton_type,type,
% 0.19/0.38 notinsingleton: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notinsingleton,definition,
% 0.19/0.38 ( notinsingleton
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx != Xy )
% 0.19/0.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(eqinunit_type,type,
% 0.19/0.38 eqinunit: $o ).
% 0.19/0.38
% 0.19/0.38 thf(eqinunit,definition,
% 0.19/0.38 ( eqinunit
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(singletonsswitch_type,type,
% 0.19/0.38 singletonsswitch: $o ).
% 0.19/0.38
% 0.19/0.38 thf(singletonsswitch,definition,
% 0.19/0.38 ( singletonsswitch
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetE_type,type,
% 0.19/0.38 upairsetE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetE,definition,
% 0.19/0.38 ( upairsetE
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.38 => ( ( Xz = Xx )
% 0.19/0.38 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetIL_type,type,
% 0.19/0.38 upairsetIL: $o ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetIL,definition,
% 0.19/0.38 ( upairsetIL
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetIR_type,type,
% 0.19/0.38 upairsetIR: $o ).
% 0.19/0.38
% 0.19/0.38 thf(upairsetIR,definition,
% 0.19/0.38 ( upairsetIR
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyE1_type,type,
% 0.19/0.38 emptyE1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyE1,definition,
% 0.19/0.38 ( emptyE1
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ( Xphi @ Xx ) )
% 0.19/0.38 => ( ( ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 = emptyset )
% 0.19/0.38 => $false ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(vacuousDall_type,type,
% 0.19/0.38 vacuousDall: $o ).
% 0.19/0.38
% 0.19/0.38 thf(vacuousDall,definition,
% 0.19/0.38 ( vacuousDall
% 0.19/0.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ emptyset )
% 0.19/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan1_type,type,
% 0.19/0.38 quantDeMorgan1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan1,definition,
% 0.19/0.38 ( quantDeMorgan1
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ~ ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( Xphi @ Xx ) )
% 0.19/0.38 => ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan2_type,type,
% 0.19/0.38 quantDeMorgan2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan2,definition,
% 0.19/0.38 ( quantDeMorgan2
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ~ ( Xphi @ Xx ) )
% 0.19/0.38 => ~ ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan3_type,type,
% 0.19/0.38 quantDeMorgan3: $o ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan3,definition,
% 0.19/0.38 ( quantDeMorgan3
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ~ ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ( Xphi @ Xx ) )
% 0.19/0.38 => ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan4_type,type,
% 0.19/0.38 quantDeMorgan4: $o ).
% 0.19/0.38
% 0.19/0.38 thf(quantDeMorgan4,definition,
% 0.19/0.38 ( quantDeMorgan4
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ~ ( Xphi @ Xx ) )
% 0.19/0.38 => ~ ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(prop2setI_type,type,
% 0.19/0.38 prop2setI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(prop2setI,definition,
% 0.19/0.38 ( prop2setI
% 0.19/0.38 = ( ! [Xphi: $o] :
% 0.19/0.38 ( Xphi
% 0.19/0.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(set2prop_type,type,
% 0.19/0.38 set2prop: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(prop2set2propI_type,type,
% 0.19/0.38 prop2set2propI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(prop2set2propI,definition,
% 0.19/0.38 ( prop2set2propI
% 0.19/0.38 = ( ! [Xphi: $o] :
% 0.19/0.38 ( Xphi
% 0.19/0.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notdexE_type,type,
% 0.19/0.38 notdexE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notdexE,definition,
% 0.19/0.38 ( notdexE
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ~ ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ( Xphi @ Xx ) )
% 0.19/0.38 => ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notdallE_type,type,
% 0.19/0.38 notdallE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notdallE,definition,
% 0.19/0.38 ( notdallE
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( ~ ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( Xphi @ Xx ) )
% 0.19/0.38 => ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuI1_type,type,
% 0.19/0.38 exuI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuI1,definition,
% 0.19/0.38 ( exuI1
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ? [Xx: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 & ! [Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) )
% 0.19/0.38 => ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuI3_type,type,
% 0.19/0.38 exuI3: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuI3,definition,
% 0.19/0.38 ( exuI3
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.19/0.38 => ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 => ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) )
% 0.19/0.38 => ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuI2_type,type,
% 0.19/0.38 exuI2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuI2,definition,
% 0.19/0.38 ( exuI2
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ? [Xx: $i] :
% 0.19/0.38 ! [Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xy )
% 0.19/0.38 <=> ( Xy = Xx ) )
% 0.19/0.38 => ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(inCongP_type,type,
% 0.19/0.38 inCongP: $o ).
% 0.19/0.38
% 0.19/0.38 thf(inCongP,definition,
% 0.19/0.38 ( inCongP
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(in__Cong_type,type,
% 0.19/0.38 in__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(in__Cong,definition,
% 0.19/0.38 ( in__Cong
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ( ( in @ Xx @ A )
% 0.19/0.38 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuE3u_type,type,
% 0.19/0.38 exuE3u: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuE3u,definition,
% 0.19/0.38 ( exuE3u
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 => ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exu__Cong_type,type,
% 0.19/0.38 exu__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exu__Cong,definition,
% 0.19/0.38 ( exu__Cong
% 0.19/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ( ( Xphi @ Xx )
% 0.19/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.38 => ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 <=> ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptyset__Cong_type,type,
% 0.19/0.38 emptyset__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptyset__Cong,definition,
% 0.19/0.38 ( emptyset__Cong
% 0.19/0.38 = ( emptyset = emptyset ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoin__Cong_type,type,
% 0.19/0.38 setadjoin__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoin__Cong,definition,
% 0.19/0.38 ( setadjoin__Cong
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ! [Xz: $i,Xu: $i] :
% 0.19/0.38 ( ( Xz = Xu )
% 0.19/0.38 => ( ( setadjoin @ Xx @ Xz )
% 0.19/0.38 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powerset__Cong_type,type,
% 0.19/0.38 powerset__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powerset__Cong,definition,
% 0.19/0.38 ( powerset__Cong
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ( ( powerset @ A )
% 0.19/0.38 = ( powerset @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setunion__Cong_type,type,
% 0.19/0.38 setunion__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setunion__Cong,definition,
% 0.19/0.38 ( setunion__Cong
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ( ( setunion @ A )
% 0.19/0.38 = ( setunion @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(omega__Cong_type,type,
% 0.19/0.38 omega__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(omega__Cong,definition,
% 0.19/0.38 ( omega__Cong
% 0.19/0.38 = ( omega = omega ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(exuEu_type,type,
% 0.19/0.38 exuEu: $o ).
% 0.19/0.38
% 0.19/0.38 thf(exuEu,definition,
% 0.19/0.38 ( exuEu
% 0.19/0.38 = ( ! [Xphi: $i > $o] :
% 0.19/0.38 ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xphi @ Xx )
% 0.19/0.38 => ( ( Xphi @ Xy )
% 0.19/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(descr__Cong_type,type,
% 0.19/0.38 descr__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(descr__Cong,definition,
% 0.19/0.38 ( descr__Cong
% 0.19/0.38 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.38 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.38 ( ( Xx = Xy )
% 0.19/0.38 => ( ( Xphi @ Xx )
% 0.19/0.38 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.38 => ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 => ( ( exu
% 0.19/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.38 => ( ( descr
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 = ( descr
% 0.19/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstr__Cong_type,type,
% 0.19/0.38 dsetconstr__Cong: $o ).
% 0.19/0.38
% 0.19/0.38 thf(dsetconstr__Cong,definition,
% 0.19/0.38 ( dsetconstr__Cong
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ! [Xy: $i] :
% 0.19/0.38 ( ( in @ Xy @ B )
% 0.19/0.38 => ( ( Xx = Xy )
% 0.19/0.38 => ( ( Xphi @ Xx )
% 0.19/0.38 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.19/0.38 => ( ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 = ( dsetconstr @ B
% 0.19/0.38 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subset_type,type,
% 0.19/0.38 subset: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(disjoint_type,type,
% 0.19/0.38 disjoint: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(setsmeet_type,type,
% 0.19/0.38 setsmeet: $i > $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetI1_type,type,
% 0.19/0.38 subsetI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetI1,definition,
% 0.19/0.38 ( subsetI1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) )
% 0.19/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(eqimpsubset2_type,type,
% 0.19/0.38 eqimpsubset2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(eqimpsubset2,definition,
% 0.19/0.38 ( eqimpsubset2
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(eqimpsubset1_type,type,
% 0.19/0.38 eqimpsubset1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(eqimpsubset1,definition,
% 0.19/0.38 ( eqimpsubset1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( A = B )
% 0.19/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetI2_type,type,
% 0.19/0.38 subsetI2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetI2,definition,
% 0.19/0.38 ( subsetI2
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ! [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) )
% 0.19/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetsubset_type,type,
% 0.19/0.38 emptysetsubset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(emptysetsubset,definition,
% 0.19/0.38 ( emptysetsubset
% 0.19/0.38 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetE_type,type,
% 0.19/0.38 subsetE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetE,definition,
% 0.19/0.38 ( subsetE
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetE2_type,type,
% 0.19/0.38 subsetE2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetE2,definition,
% 0.19/0.38 ( subsetE2
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( ~ ( in @ Xx @ B )
% 0.19/0.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notsubsetI_type,type,
% 0.19/0.38 notsubsetI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notsubsetI,definition,
% 0.19/0.38 ( notsubsetI
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ~ ( in @ Xx @ B )
% 0.19/0.38 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notequalI1_type,type,
% 0.19/0.38 notequalI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notequalI1,definition,
% 0.19/0.38 ( notequalI1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ~ ( subset @ A @ B )
% 0.19/0.38 => ( A != B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(notequalI2_type,type,
% 0.19/0.38 notequalI2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(notequalI2,definition,
% 0.19/0.38 ( notequalI2
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ~ ( in @ Xx @ B )
% 0.19/0.38 => ( A != B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetRefl_type,type,
% 0.19/0.38 subsetRefl: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetRefl,definition,
% 0.19/0.38 ( subsetRefl
% 0.19/0.38 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetTrans_type,type,
% 0.19/0.38 subsetTrans: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetTrans,definition,
% 0.19/0.38 ( subsetTrans
% 0.19/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( ( subset @ B @ C )
% 0.19/0.38 => ( subset @ A @ C ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinSub_type,type,
% 0.19/0.38 setadjoinSub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinSub,definition,
% 0.19/0.38 ( setadjoinSub
% 0.19/0.38 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinSub2_type,type,
% 0.19/0.38 setadjoinSub2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setadjoinSub2,definition,
% 0.19/0.38 ( setadjoinSub2
% 0.19/0.38 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subset2powerset_type,type,
% 0.19/0.38 subset2powerset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subset2powerset,definition,
% 0.19/0.38 ( subset2powerset
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setextsub_type,type,
% 0.19/0.38 setextsub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(setextsub,definition,
% 0.19/0.38 ( setextsub
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( ( subset @ B @ A )
% 0.19/0.38 => ( A = B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(subsetemptysetimpeq_type,type,
% 0.19/0.38 subsetemptysetimpeq: $o ).
% 0.19/0.38
% 0.19/0.38 thf(subsetemptysetimpeq,definition,
% 0.19/0.38 ( subsetemptysetimpeq
% 0.19/0.38 = ( ! [A: $i] :
% 0.19/0.38 ( ( subset @ A @ emptyset )
% 0.19/0.38 => ( A = emptyset ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powersetI1_type,type,
% 0.19/0.38 powersetI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetI1,definition,
% 0.19/0.38 ( powersetI1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ B @ A )
% 0.19/0.38 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powersetE1_type,type,
% 0.19/0.38 powersetE1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetE1,definition,
% 0.19/0.38 ( powersetE1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(inPowerset_type,type,
% 0.19/0.38 inPowerset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(inPowerset,definition,
% 0.19/0.38 ( inPowerset
% 0.19/0.38 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(powersetsubset_type,type,
% 0.19/0.38 powersetsubset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(powersetsubset,definition,
% 0.19/0.38 ( powersetsubset
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(sepInPowerset_type,type,
% 0.19/0.38 sepInPowerset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(sepInPowerset,definition,
% 0.19/0.38 ( sepInPowerset
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( in
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 @ ( powerset @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(sepSubset_type,type,
% 0.19/0.38 sepSubset: $o ).
% 0.19/0.38
% 0.19/0.38 thf(sepSubset,definition,
% 0.19/0.38 ( sepSubset
% 0.19/0.38 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.38 ( subset
% 0.19/0.38 @ ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.38 @ A ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunion_type,type,
% 0.19/0.38 binunion: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(binunionIL_type,type,
% 0.19/0.38 binunionIL: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionIL,definition,
% 0.19/0.38 ( binunionIL
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(upairset2IR_type,type,
% 0.19/0.38 upairset2IR: $o ).
% 0.19/0.38
% 0.19/0.38 thf(upairset2IR,definition,
% 0.19/0.38 ( upairset2IR
% 0.19/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunionIR_type,type,
% 0.19/0.38 binunionIR: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionIR,definition,
% 0.19/0.38 ( binunionIR
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunionEcases_type,type,
% 0.19/0.38 binunionEcases: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionEcases,definition,
% 0.19/0.38 ( binunionEcases
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.38 => ( ( ( in @ Xx @ A )
% 0.19/0.38 => Xphi )
% 0.19/0.38 => ( ( ( in @ Xx @ B )
% 0.19/0.38 => Xphi )
% 0.19/0.38 => Xphi ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunionE_type,type,
% 0.19/0.38 binunionE: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionE,definition,
% 0.19/0.38 ( binunionE
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.38 => ( ( in @ Xx @ A )
% 0.19/0.38 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunionLsub_type,type,
% 0.19/0.38 binunionLsub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionLsub,definition,
% 0.19/0.38 ( binunionLsub
% 0.19/0.38 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binunionRsub_type,type,
% 0.19/0.38 binunionRsub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binunionRsub,definition,
% 0.19/0.38 ( binunionRsub
% 0.19/0.38 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersect_type,type,
% 0.19/0.38 binintersect: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectI_type,type,
% 0.19/0.38 binintersectI: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectI,definition,
% 0.19/0.38 ( binintersectI
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 => ( ( in @ Xx @ B )
% 0.19/0.38 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset5_type,type,
% 0.19/0.38 binintersectSubset5: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset5,definition,
% 0.19/0.38 ( binintersectSubset5
% 0.19/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.38 ( ( subset @ C @ A )
% 0.19/0.38 => ( ( subset @ C @ B )
% 0.19/0.38 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectEL_type,type,
% 0.19/0.38 binintersectEL: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectEL,definition,
% 0.19/0.38 ( binintersectEL
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectLsub_type,type,
% 0.19/0.38 binintersectLsub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectLsub,definition,
% 0.19/0.38 ( binintersectLsub
% 0.19/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset2_type,type,
% 0.19/0.38 binintersectSubset2: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset2,definition,
% 0.19/0.38 ( binintersectSubset2
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ A @ B )
% 0.19/0.38 => ( ( binintersect @ A @ B )
% 0.19/0.38 = A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset3_type,type,
% 0.19/0.38 binintersectSubset3: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset3,definition,
% 0.19/0.38 ( binintersectSubset3
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( ( binintersect @ A @ B )
% 0.19/0.38 = B )
% 0.19/0.38 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectER_type,type,
% 0.19/0.38 binintersectER: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectER,definition,
% 0.19/0.38 ( binintersectER
% 0.19/0.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.38 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(disjointsetsI1_type,type,
% 0.19/0.38 disjointsetsI1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(disjointsetsI1,definition,
% 0.19/0.38 ( disjointsetsI1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ~ ? [Xx: $i] :
% 0.19/0.38 ( ( in @ Xx @ A )
% 0.19/0.38 & ( in @ Xx @ B ) )
% 0.19/0.38 => ( ( binintersect @ A @ B )
% 0.19/0.38 = emptyset ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectRsub_type,type,
% 0.19/0.38 binintersectRsub: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectRsub,definition,
% 0.19/0.38 ( binintersectRsub
% 0.19/0.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset4_type,type,
% 0.19/0.38 binintersectSubset4: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset4,definition,
% 0.19/0.38 ( binintersectSubset4
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( subset @ B @ A )
% 0.19/0.38 => ( ( binintersect @ A @ B )
% 0.19/0.38 = B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset1_type,type,
% 0.19/0.38 binintersectSubset1: $o ).
% 0.19/0.38
% 0.19/0.38 thf(binintersectSubset1,definition,
% 0.19/0.38 ( binintersectSubset1
% 0.19/0.38 = ( ! [A: $i,B: $i] :
% 0.19/0.38 ( ( ( binintersect @ A @ B )
% 0.19/0.38 = A )
% 0.19/0.38 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(bs114d_type,type,
% 0.19/0.38 bs114d: $o ).
% 0.19/0.38
% 0.19/0.38 thf(bs114d,definition,
% 0.19/0.38 ( bs114d
% 0.19/0.38 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.38 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.19/0.38 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(regular_type,type,
% 0.19/0.38 regular: $i > $o ).
% 0.19/0.38
% 0.19/0.38 thf(setminus_type,type,
% 0.19/0.38 setminus: $i > $i > $i ).
% 0.19/0.38
% 0.19/0.38 thf(setminus,definition,
% 0.19/0.38 ( setminus
% 0.19/0.38 = ( ^ [A: $i,B: $i] :
% 0.19/0.38 ( dsetconstr @ A
% 0.19/0.38 @ ^ [Xx: $i] :
% 0.19/0.38 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.38
% 0.19/0.38 thf(setminusI,conjecture,
% 0.19/0.38 ( setextAx
% 0.19/0.38 => ( emptysetAx
% 0.19/0.38 => ( setadjoinAx
% 0.19/0.38 => ( powersetAx
% 0.19/0.38 => ( setunionAx
% 0.19/0.38 => ( omega0Ax
% 0.19/0.38 => ( omegaSAx
% 0.19/0.38 => ( omegaIndAx
% 0.19/0.38 => ( replAx
% 0.19/0.38 => ( foundationAx
% 0.19/0.38 => ( wellorderingAx
% 0.19/0.38 => ( descrp
% 0.19/0.38 => ( dsetconstrI
% 0.19/0.38 => ( dsetconstrEL
% 0.19/0.38 => ( dsetconstrER
% 0.19/0.38 => ( exuE1
% 0.19/0.38 => ( prop2setE
% 0.19/0.38 => ( emptysetE
% 0.19/0.38 => ( emptysetimpfalse
% 0.19/0.38 => ( notinemptyset
% 0.19/0.38 => ( exuE3e
% 0.19/0.38 => ( setext
% 0.19/0.38 => ( emptyI
% 0.19/0.38 => ( noeltsimpempty
% 0.19/0.38 => ( setbeta
% 0.19/0.38 => ( nonemptyE1
% 0.19/0.38 => ( nonemptyI
% 0.19/0.39 => ( nonemptyI1
% 0.19/0.39 => ( setadjoinIL
% 0.19/0.39 => ( emptyinunitempty
% 0.19/0.39 => ( setadjoinIR
% 0.19/0.39 => ( setadjoinE
% 0.19/0.39 => ( setadjoinOr
% 0.19/0.39 => ( setoftrueEq
% 0.19/0.39 => ( powersetI
% 0.19/0.39 => ( emptyinPowerset
% 0.19/0.39 => ( emptyInPowerset
% 0.19/0.39 => ( powersetE
% 0.19/0.39 => ( setunionI
% 0.19/0.39 => ( setunionE
% 0.19/0.39 => ( subPowSU
% 0.19/0.39 => ( exuE2
% 0.19/0.39 => ( nonemptyImpWitness
% 0.19/0.39 => ( uniqinunit
% 0.19/0.39 => ( notinsingleton
% 0.19/0.39 => ( eqinunit
% 0.19/0.39 => ( singletonsswitch
% 0.19/0.39 => ( upairsetE
% 0.19/0.39 => ( upairsetIL
% 0.19/0.39 => ( upairsetIR
% 0.19/0.39 => ( emptyE1
% 0.19/0.39 => ( vacuousDall
% 0.19/0.39 => ( quantDeMorgan1
% 0.19/0.39 => ( quantDeMorgan2
% 0.19/0.39 => ( quantDeMorgan3
% 0.19/0.39 => ( quantDeMorgan4
% 0.19/0.39 => ( prop2setI
% 0.19/0.39 => ( prop2set2propI
% 0.19/0.39 => ( notdexE
% 0.19/0.39 => ( notdallE
% 0.19/0.39 => ( exuI1
% 0.19/0.39 => ( exuI3
% 0.19/0.39 => ( exuI2
% 0.19/0.39 => ( inCongP
% 0.19/0.39 => ( in__Cong
% 0.19/0.39 => ( exuE3u
% 0.19/0.39 => ( exu__Cong
% 0.19/0.39 => ( emptyset__Cong
% 0.19/0.39 => ( setadjoin__Cong
% 0.19/0.39 => ( powerset__Cong
% 0.19/0.39 => ( setunion__Cong
% 0.19/0.39 => ( omega__Cong
% 0.19/0.39 => ( exuEu
% 0.19/0.39 => ( descr__Cong
% 0.19/0.39 => ( dsetconstr__Cong
% 0.19/0.39 => ( subsetI1
% 0.19/0.39 => ( eqimpsubset2
% 0.19/0.39 => ( eqimpsubset1
% 0.19/0.39 => ( subsetI2
% 0.19/0.39 => ( emptysetsubset
% 0.19/0.39 => ( subsetE
% 0.19/0.39 => ( subsetE2
% 0.19/0.39 => ( notsubsetI
% 0.19/0.39 => ( notequalI1
% 0.19/0.39 => ( notequalI2
% 0.19/0.39 => ( subsetRefl
% 0.19/0.39 => ( subsetTrans
% 0.19/0.39 => ( setadjoinSub
% 0.19/0.39 => ( setadjoinSub2
% 0.19/0.39 => ( subset2powerset
% 0.19/0.39 => ( setextsub
% 0.19/0.39 => ( subsetemptysetimpeq
% 0.19/0.39 => ( powersetI1
% 0.19/0.39 => ( powersetE1
% 0.19/0.39 => ( inPowerset
% 0.19/0.39 => ( powersetsubset
% 0.19/0.39 => ( sepInPowerset
% 0.19/0.39 => ( sepSubset
% 0.19/0.39 => ( binunionIL
% 0.19/0.39 => ( upairset2IR
% 0.19/0.39 => ( binunionIR
% 0.19/0.39 => ( binunionEcases
% 0.19/0.39 => ( binunionE
% 0.19/0.39 => ( binunionLsub
% 0.19/0.39 => ( binunionRsub
% 0.19/0.39 => ( binintersectI
% 0.19/0.39 => ( binintersectSubset5
% 0.19/0.39 => ( binintersectEL
% 0.19/0.39 => ( binintersectLsub
% 0.19/0.39 => ( binintersectSubset2
% 0.19/0.39 => ( binintersectSubset3
% 0.19/0.39 => ( binintersectER
% 0.19/0.39 => ( disjointsetsI1
% 0.19/0.39 => ( binintersectRsub
% 0.19/0.39 => ( binintersectSubset4
% 0.19/0.39 => ( binintersectSubset1
% 0.19/0.39 => ( bs114d
% 0.19/0.39 => ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ~ ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 2.19/1.49 ---- Embedded in THF ---
% 2.19/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.19/1.49 %%% Generated on Tue Feb 24 12:28:15 EST 2026
% 2.19/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.19/1.49 %%% Logic specification used:
% 2.19/1.49 %%% thf(spec, logic, $$dhol).
% 2.19/1.49
% 2.19/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2DTF7545.p
% See solution above
% 2.19/1.49 ------------------------
% 2.47/1.52 ---- Cleaned THF ---
% 2.47/1.52 thf(in_type,type,
% 2.47/1.52 in: $i > $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(exu_type,type,
% 2.47/1.52 exu: ( $i > $o ) > $o ).
% 2.47/1.52
% 2.47/1.52 thf(exu,definition,
% 2.47/1.52 ( exu
% 2.47/1.52 = ( ^ [Xphi: $i > $o] :
% 2.47/1.52 ? [Xx: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 & ! [Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setextAx_type,type,
% 2.47/1.52 setextAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setextAx,definition,
% 2.47/1.52 ( setextAx
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 <=> ( in @ Xx @ B ) )
% 2.47/1.52 => ( A = B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyset_type,type,
% 2.47/1.52 emptyset: $i ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetAx_type,type,
% 2.47/1.52 emptysetAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetAx,definition,
% 2.47/1.52 ( emptysetAx
% 2.47/1.52 = ( ! [Xx: $i] :
% 2.47/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoin_type,type,
% 2.47/1.52 setadjoin: $i > $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinAx_type,type,
% 2.47/1.52 setadjoinAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinAx,definition,
% 2.47/1.52 ( setadjoinAx
% 2.47/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.47/1.52 <=> ( ( Xy = Xx )
% 2.47/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powerset_type,type,
% 2.47/1.52 powerset: $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(powersetAx_type,type,
% 2.47/1.52 powersetAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetAx,definition,
% 2.47/1.52 ( powersetAx
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.47/1.52 <=> ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setunion_type,type,
% 2.47/1.52 setunion: $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(setunionAx_type,type,
% 2.47/1.52 setunionAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setunionAx,definition,
% 2.47/1.52 ( setunionAx
% 2.47/1.52 = ( ! [A: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.47/1.52 <=> ? [B: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(omega_type,type,
% 2.47/1.52 omega: $i ).
% 2.47/1.52
% 2.47/1.52 thf(omega0Ax_type,type,
% 2.47/1.52 omega0Ax: $o ).
% 2.47/1.52
% 2.47/1.52 thf(omega0Ax,definition,
% 2.47/1.52 ( omega0Ax
% 2.47/1.52 = ( in @ emptyset @ omega ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(omegaSAx_type,type,
% 2.47/1.52 omegaSAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(omegaSAx,definition,
% 2.47/1.52 ( omegaSAx
% 2.47/1.52 = ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ omega )
% 2.47/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(omegaIndAx_type,type,
% 2.47/1.52 omegaIndAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(omegaIndAx,definition,
% 2.47/1.52 ( omegaIndAx
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ( ( in @ emptyset @ A )
% 2.47/1.52 & ! [Xx: $i] :
% 2.47/1.52 ( ( ( in @ Xx @ omega )
% 2.47/1.52 & ( in @ Xx @ A ) )
% 2.47/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.47/1.52 => ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ omega )
% 2.47/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(replAx_type,type,
% 2.47/1.52 replAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(replAx,definition,
% 2.47/1.52 ( replAx
% 2.47/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( exu
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.47/1.52 => ? [B: $i] :
% 2.47/1.52 ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 <=> ? [Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ A )
% 2.47/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(foundationAx_type,type,
% 2.47/1.52 foundationAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(foundationAx,definition,
% 2.47/1.52 ( foundationAx
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.47/1.52 => ? [B: $i] :
% 2.47/1.52 ( ( in @ B @ A )
% 2.47/1.52 & ~ ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(wellorderingAx_type,type,
% 2.47/1.52 wellorderingAx: $o ).
% 2.47/1.52
% 2.47/1.52 thf(wellorderingAx,definition,
% 2.47/1.52 ( wellorderingAx
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ? [B: $i] :
% 2.47/1.52 ( ! [C: $i] :
% 2.47/1.52 ( ( in @ C @ B )
% 2.47/1.52 => ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ C )
% 2.47/1.52 => ( in @ Xx @ A ) ) )
% 2.47/1.52 & ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( ( in @ Xx @ A )
% 2.47/1.52 & ( in @ Xy @ A ) )
% 2.47/1.52 => ( ! [C: $i] :
% 2.47/1.52 ( ( in @ C @ B )
% 2.47/1.52 => ( ( in @ Xx @ C )
% 2.47/1.52 <=> ( in @ Xy @ C ) ) )
% 2.47/1.52 => ( Xx = Xy ) ) )
% 2.47/1.52 & ! [C: $i,D: $i] :
% 2.47/1.52 ( ( ( in @ C @ B )
% 2.47/1.52 & ( in @ D @ B ) )
% 2.47/1.52 => ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ C )
% 2.47/1.52 => ( in @ Xx @ D ) )
% 2.47/1.52 | ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ D )
% 2.47/1.52 => ( in @ Xx @ C ) ) ) )
% 2.47/1.52 & ! [C: $i] :
% 2.47/1.52 ( ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ C )
% 2.47/1.52 => ( in @ Xx @ A ) )
% 2.47/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.47/1.52 => ? [D: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ D @ B )
% 2.47/1.52 & ( in @ Xx @ C )
% 2.47/1.52 & ~ ? [Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ D )
% 2.47/1.52 & ( in @ Xy @ C ) )
% 2.47/1.52 & ! [E: $i] :
% 2.47/1.52 ( ( in @ E @ B )
% 2.47/1.52 => ( ! [Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ E )
% 2.47/1.52 => ( in @ Xy @ D ) )
% 2.47/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(descr_type,type,
% 2.47/1.52 descr: ( $i > $o ) > $i ).
% 2.47/1.52
% 2.47/1.52 thf(descrp_type,type,
% 2.47/1.52 descrp: $o ).
% 2.47/1.52
% 2.47/1.52 thf(descrp,definition,
% 2.47/1.52 ( descrp
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ( Xphi
% 2.47/1.52 @ ( descr
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstr_type,type,
% 2.47/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrI_type,type,
% 2.47/1.52 dsetconstrI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrI,definition,
% 2.47/1.52 ( dsetconstrI
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ( Xphi @ Xx )
% 2.47/1.52 => ( in @ Xx
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrEL_type,type,
% 2.47/1.52 dsetconstrEL: $o ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrEL,definition,
% 2.47/1.52 ( dsetconstrEL
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.47/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrER_type,type,
% 2.47/1.52 dsetconstrER: $o ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstrER,definition,
% 2.47/1.52 ( dsetconstrER
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.47/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuE1_type,type,
% 2.47/1.52 exuE1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuE1,definition,
% 2.47/1.52 ( exuE1
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ? [Xx: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 & ! [Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(prop2set_type,type,
% 2.47/1.52 prop2set: $o > $i ).
% 2.47/1.52
% 2.47/1.52 thf(prop2setE_type,type,
% 2.47/1.52 prop2setE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(prop2setE,definition,
% 2.47/1.52 ( prop2setE
% 2.47/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.47/1.52 => Xphi ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetE_type,type,
% 2.47/1.52 emptysetE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetE,definition,
% 2.47/1.52 ( emptysetE
% 2.47/1.52 = ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ emptyset )
% 2.47/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetimpfalse_type,type,
% 2.47/1.52 emptysetimpfalse: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetimpfalse,definition,
% 2.47/1.52 ( emptysetimpfalse
% 2.47/1.52 = ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ emptyset )
% 2.47/1.52 => $false ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notinemptyset_type,type,
% 2.47/1.52 notinemptyset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notinemptyset,definition,
% 2.47/1.52 ( notinemptyset
% 2.47/1.52 = ( ! [Xx: $i] :
% 2.47/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuE3e_type,type,
% 2.47/1.52 exuE3e: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuE3e,definition,
% 2.47/1.52 ( exuE3e
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setext_type,type,
% 2.47/1.52 setext: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setext,definition,
% 2.47/1.52 ( setext
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ B ) )
% 2.47/1.52 => ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ A ) )
% 2.47/1.52 => ( A = B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyI_type,type,
% 2.47/1.52 emptyI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyI,definition,
% 2.47/1.52 ( emptyI
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ~ ( in @ Xx @ A )
% 2.47/1.52 => ( A = emptyset ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(noeltsimpempty_type,type,
% 2.47/1.52 noeltsimpempty: $o ).
% 2.47/1.52
% 2.47/1.52 thf(noeltsimpempty,definition,
% 2.47/1.52 ( noeltsimpempty
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ~ ( in @ Xx @ A )
% 2.47/1.52 => ( A = emptyset ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setbeta_type,type,
% 2.47/1.52 setbeta: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setbeta,definition,
% 2.47/1.52 ( setbeta
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ( in @ Xx
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.47/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(nonempty_type,type,
% 2.47/1.52 nonempty: $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(nonempty,definition,
% 2.47/1.52 ( nonempty
% 2.47/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyE1_type,type,
% 2.47/1.52 nonemptyE1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyE1,definition,
% 2.47/1.52 ( nonemptyE1
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ( nonempty @ A )
% 2.47/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyI_type,type,
% 2.47/1.52 nonemptyI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyI,definition,
% 2.47/1.52 ( nonemptyI
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ( Xphi @ Xx )
% 2.47/1.52 => ( nonempty
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyI1_type,type,
% 2.47/1.52 nonemptyI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyI1,definition,
% 2.47/1.52 ( nonemptyI1
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.47/1.52 => ( nonempty @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinIL_type,type,
% 2.47/1.52 setadjoinIL: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinIL,definition,
% 2.47/1.52 ( setadjoinIL
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyinunitempty_type,type,
% 2.47/1.52 emptyinunitempty: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyinunitempty,definition,
% 2.47/1.52 ( emptyinunitempty
% 2.47/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinIR_type,type,
% 2.47/1.52 setadjoinIR: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinIR,definition,
% 2.47/1.52 ( setadjoinIR
% 2.47/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ A )
% 2.47/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinE_type,type,
% 2.47/1.52 setadjoinE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinE,definition,
% 2.47/1.52 ( setadjoinE
% 2.47/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.47/1.52 => ! [Xphi: $o] :
% 2.47/1.52 ( ( ( Xy = Xx )
% 2.47/1.52 => Xphi )
% 2.47/1.52 => ( ( ( in @ Xy @ A )
% 2.47/1.52 => Xphi )
% 2.47/1.52 => Xphi ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinOr_type,type,
% 2.47/1.52 setadjoinOr: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinOr,definition,
% 2.47/1.52 ( setadjoinOr
% 2.47/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.47/1.52 => ( ( Xy = Xx )
% 2.47/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setoftrueEq_type,type,
% 2.47/1.52 setoftrueEq: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setoftrueEq,definition,
% 2.47/1.52 ( setoftrueEq
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] : $true )
% 2.47/1.52 = A ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powersetI_type,type,
% 2.47/1.52 powersetI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetI,definition,
% 2.47/1.52 ( powersetI
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ A ) )
% 2.47/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyinPowerset_type,type,
% 2.47/1.52 emptyinPowerset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyinPowerset,definition,
% 2.47/1.52 ( emptyinPowerset
% 2.47/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyInPowerset_type,type,
% 2.47/1.52 emptyInPowerset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyInPowerset,definition,
% 2.47/1.52 ( emptyInPowerset
% 2.47/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powersetE_type,type,
% 2.47/1.52 powersetE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetE,definition,
% 2.47/1.52 ( powersetE
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.47/1.52 => ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setunionI_type,type,
% 2.47/1.52 setunionI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setunionI,definition,
% 2.47/1.52 ( setunionI
% 2.47/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( ( in @ B @ A )
% 2.47/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setunionE_type,type,
% 2.47/1.52 setunionE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setunionE,definition,
% 2.47/1.52 ( setunionE
% 2.47/1.52 = ( ! [A: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.47/1.52 => ! [Xphi: $o] :
% 2.47/1.52 ( ! [B: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( ( in @ B @ A )
% 2.47/1.52 => Xphi ) )
% 2.47/1.52 => Xphi ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subPowSU_type,type,
% 2.47/1.52 subPowSU: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subPowSU,definition,
% 2.47/1.52 ( subPowSU
% 2.47/1.52 = ( ! [A: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuE2_type,type,
% 2.47/1.52 exuE2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuE2,definition,
% 2.47/1.52 ( exuE2
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ? [Xx: $i] :
% 2.47/1.52 ! [Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xy )
% 2.47/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyImpWitness_type,type,
% 2.47/1.52 nonemptyImpWitness: $o ).
% 2.47/1.52
% 2.47/1.52 thf(nonemptyImpWitness,definition,
% 2.47/1.52 ( nonemptyImpWitness
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ( nonempty @ A )
% 2.47/1.52 => ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & $true ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(uniqinunit_type,type,
% 2.47/1.52 uniqinunit: $o ).
% 2.47/1.52
% 2.47/1.52 thf(uniqinunit,definition,
% 2.47/1.52 ( uniqinunit
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.47/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notinsingleton_type,type,
% 2.47/1.52 notinsingleton: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notinsingleton,definition,
% 2.47/1.52 ( notinsingleton
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx != Xy )
% 2.47/1.52 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(eqinunit_type,type,
% 2.47/1.52 eqinunit: $o ).
% 2.47/1.52
% 2.47/1.52 thf(eqinunit,definition,
% 2.47/1.52 ( eqinunit
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(singletonsswitch_type,type,
% 2.47/1.52 singletonsswitch: $o ).
% 2.47/1.52
% 2.47/1.52 thf(singletonsswitch,definition,
% 2.47/1.52 ( singletonsswitch
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.47/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetE_type,type,
% 2.47/1.52 upairsetE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetE,definition,
% 2.47/1.52 ( upairsetE
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.47/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.47/1.52 => ( ( Xz = Xx )
% 2.47/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetIL_type,type,
% 2.47/1.52 upairsetIL: $o ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetIL,definition,
% 2.47/1.52 ( upairsetIL
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetIR_type,type,
% 2.47/1.52 upairsetIR: $o ).
% 2.47/1.52
% 2.47/1.52 thf(upairsetIR,definition,
% 2.47/1.52 ( upairsetIR
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyE1_type,type,
% 2.47/1.52 emptyE1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyE1,definition,
% 2.47/1.52 ( emptyE1
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ( Xphi @ Xx ) )
% 2.47/1.52 => ( ( ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 = emptyset )
% 2.47/1.52 => $false ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(vacuousDall_type,type,
% 2.47/1.52 vacuousDall: $o ).
% 2.47/1.52
% 2.47/1.52 thf(vacuousDall,definition,
% 2.47/1.52 ( vacuousDall
% 2.47/1.52 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ emptyset )
% 2.47/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan1_type,type,
% 2.47/1.52 quantDeMorgan1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan1,definition,
% 2.47/1.52 ( quantDeMorgan1
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ~ ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( Xphi @ Xx ) )
% 2.47/1.52 => ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan2_type,type,
% 2.47/1.52 quantDeMorgan2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan2,definition,
% 2.47/1.52 ( quantDeMorgan2
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ~ ( Xphi @ Xx ) )
% 2.47/1.52 => ~ ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan3_type,type,
% 2.47/1.52 quantDeMorgan3: $o ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan3,definition,
% 2.47/1.52 ( quantDeMorgan3
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ~ ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ( Xphi @ Xx ) )
% 2.47/1.52 => ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan4_type,type,
% 2.47/1.52 quantDeMorgan4: $o ).
% 2.47/1.52
% 2.47/1.52 thf(quantDeMorgan4,definition,
% 2.47/1.52 ( quantDeMorgan4
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ~ ( Xphi @ Xx ) )
% 2.47/1.52 => ~ ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(prop2setI_type,type,
% 2.47/1.52 prop2setI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(prop2setI,definition,
% 2.47/1.52 ( prop2setI
% 2.47/1.52 = ( ! [Xphi: $o] :
% 2.47/1.52 ( Xphi
% 2.47/1.52 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(set2prop_type,type,
% 2.47/1.52 set2prop: $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(prop2set2propI_type,type,
% 2.47/1.52 prop2set2propI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(prop2set2propI,definition,
% 2.47/1.52 ( prop2set2propI
% 2.47/1.52 = ( ! [Xphi: $o] :
% 2.47/1.52 ( Xphi
% 2.47/1.52 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notdexE_type,type,
% 2.47/1.52 notdexE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notdexE,definition,
% 2.47/1.52 ( notdexE
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ~ ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ( Xphi @ Xx ) )
% 2.47/1.52 => ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notdallE_type,type,
% 2.47/1.52 notdallE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notdallE,definition,
% 2.47/1.52 ( notdallE
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( ~ ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( Xphi @ Xx ) )
% 2.47/1.52 => ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuI1_type,type,
% 2.47/1.52 exuI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuI1,definition,
% 2.47/1.52 ( exuI1
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ? [Xx: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 & ! [Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) )
% 2.47/1.52 => ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuI3_type,type,
% 2.47/1.52 exuI3: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuI3,definition,
% 2.47/1.52 ( exuI3
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.47/1.52 => ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 => ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) )
% 2.47/1.52 => ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuI2_type,type,
% 2.47/1.52 exuI2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuI2,definition,
% 2.47/1.52 ( exuI2
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ? [Xx: $i] :
% 2.47/1.52 ! [Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xy )
% 2.47/1.52 <=> ( Xy = Xx ) )
% 2.47/1.52 => ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(inCongP_type,type,
% 2.47/1.52 inCongP: $o ).
% 2.47/1.52
% 2.47/1.52 thf(inCongP,definition,
% 2.47/1.52 ( inCongP
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(in__Cong_type,type,
% 2.47/1.52 in__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(in__Cong,definition,
% 2.47/1.52 ( in__Cong
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ( ( in @ Xx @ A )
% 2.47/1.52 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuE3u_type,type,
% 2.47/1.52 exuE3u: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuE3u,definition,
% 2.47/1.52 ( exuE3u
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 => ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exu__Cong_type,type,
% 2.47/1.52 exu__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exu__Cong,definition,
% 2.47/1.52 ( exu__Cong
% 2.47/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.47/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ( ( Xphi @ Xx )
% 2.47/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.47/1.52 => ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 <=> ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptyset__Cong_type,type,
% 2.47/1.52 emptyset__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptyset__Cong,definition,
% 2.47/1.52 ( emptyset__Cong
% 2.47/1.52 = ( emptyset = emptyset ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoin__Cong_type,type,
% 2.47/1.52 setadjoin__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoin__Cong,definition,
% 2.47/1.52 ( setadjoin__Cong
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ! [Xz: $i,Xu: $i] :
% 2.47/1.52 ( ( Xz = Xu )
% 2.47/1.52 => ( ( setadjoin @ Xx @ Xz )
% 2.47/1.52 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powerset__Cong_type,type,
% 2.47/1.52 powerset__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powerset__Cong,definition,
% 2.47/1.52 ( powerset__Cong
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ( ( powerset @ A )
% 2.47/1.52 = ( powerset @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setunion__Cong_type,type,
% 2.47/1.52 setunion__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setunion__Cong,definition,
% 2.47/1.52 ( setunion__Cong
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ( ( setunion @ A )
% 2.47/1.52 = ( setunion @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(omega__Cong_type,type,
% 2.47/1.52 omega__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(omega__Cong,definition,
% 2.47/1.52 ( omega__Cong
% 2.47/1.52 = ( omega = omega ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(exuEu_type,type,
% 2.47/1.52 exuEu: $o ).
% 2.47/1.52
% 2.47/1.52 thf(exuEu,definition,
% 2.47/1.52 ( exuEu
% 2.47/1.52 = ( ! [Xphi: $i > $o] :
% 2.47/1.52 ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xphi @ Xx )
% 2.47/1.52 => ( ( Xphi @ Xy )
% 2.47/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(descr__Cong_type,type,
% 2.47/1.52 descr__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(descr__Cong,definition,
% 2.47/1.52 ( descr__Cong
% 2.47/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.47/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.47/1.52 ( ( Xx = Xy )
% 2.47/1.52 => ( ( Xphi @ Xx )
% 2.47/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.47/1.52 => ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 => ( ( exu
% 2.47/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.47/1.52 => ( ( descr
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 = ( descr
% 2.47/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstr__Cong_type,type,
% 2.47/1.52 dsetconstr__Cong: $o ).
% 2.47/1.52
% 2.47/1.52 thf(dsetconstr__Cong,definition,
% 2.47/1.52 ( dsetconstr__Cong
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ! [Xy: $i] :
% 2.47/1.52 ( ( in @ Xy @ B )
% 2.47/1.52 => ( ( Xx = Xy )
% 2.47/1.52 => ( ( Xphi @ Xx )
% 2.47/1.52 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.47/1.52 => ( ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 = ( dsetconstr @ B
% 2.47/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subset_type,type,
% 2.47/1.52 subset: $i > $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(disjoint_type,type,
% 2.47/1.52 disjoint: $i > $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(setsmeet_type,type,
% 2.47/1.52 setsmeet: $i > $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetI1_type,type,
% 2.47/1.52 subsetI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetI1,definition,
% 2.47/1.52 ( subsetI1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ B ) )
% 2.47/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(eqimpsubset2_type,type,
% 2.47/1.52 eqimpsubset2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(eqimpsubset2,definition,
% 2.47/1.52 ( eqimpsubset2
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(eqimpsubset1_type,type,
% 2.47/1.52 eqimpsubset1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(eqimpsubset1,definition,
% 2.47/1.52 ( eqimpsubset1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( A = B )
% 2.47/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetI2_type,type,
% 2.47/1.52 subsetI2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetI2,definition,
% 2.47/1.52 ( subsetI2
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ! [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ B ) )
% 2.47/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetsubset_type,type,
% 2.47/1.52 emptysetsubset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(emptysetsubset,definition,
% 2.47/1.52 ( emptysetsubset
% 2.47/1.52 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetE_type,type,
% 2.47/1.52 subsetE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetE,definition,
% 2.47/1.52 ( subsetE
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetE2_type,type,
% 2.47/1.52 subsetE2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetE2,definition,
% 2.47/1.52 ( subsetE2
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( ~ ( in @ Xx @ B )
% 2.47/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notsubsetI_type,type,
% 2.47/1.52 notsubsetI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notsubsetI,definition,
% 2.47/1.52 ( notsubsetI
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ~ ( in @ Xx @ B )
% 2.47/1.52 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notequalI1_type,type,
% 2.47/1.52 notequalI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notequalI1,definition,
% 2.47/1.52 ( notequalI1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ~ ( subset @ A @ B )
% 2.47/1.52 => ( A != B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(notequalI2_type,type,
% 2.47/1.52 notequalI2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(notequalI2,definition,
% 2.47/1.52 ( notequalI2
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ~ ( in @ Xx @ B )
% 2.47/1.52 => ( A != B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetRefl_type,type,
% 2.47/1.52 subsetRefl: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetRefl,definition,
% 2.47/1.52 ( subsetRefl
% 2.47/1.52 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetTrans_type,type,
% 2.47/1.52 subsetTrans: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetTrans,definition,
% 2.47/1.52 ( subsetTrans
% 2.47/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( ( subset @ B @ C )
% 2.47/1.52 => ( subset @ A @ C ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinSub_type,type,
% 2.47/1.52 setadjoinSub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinSub,definition,
% 2.47/1.52 ( setadjoinSub
% 2.47/1.52 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinSub2_type,type,
% 2.47/1.52 setadjoinSub2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setadjoinSub2,definition,
% 2.47/1.52 ( setadjoinSub2
% 2.47/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subset2powerset_type,type,
% 2.47/1.52 subset2powerset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subset2powerset,definition,
% 2.47/1.52 ( subset2powerset
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setextsub_type,type,
% 2.47/1.52 setextsub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(setextsub,definition,
% 2.47/1.52 ( setextsub
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( ( subset @ B @ A )
% 2.47/1.52 => ( A = B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(subsetemptysetimpeq_type,type,
% 2.47/1.52 subsetemptysetimpeq: $o ).
% 2.47/1.52
% 2.47/1.52 thf(subsetemptysetimpeq,definition,
% 2.47/1.52 ( subsetemptysetimpeq
% 2.47/1.52 = ( ! [A: $i] :
% 2.47/1.52 ( ( subset @ A @ emptyset )
% 2.47/1.52 => ( A = emptyset ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powersetI1_type,type,
% 2.47/1.52 powersetI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetI1,definition,
% 2.47/1.52 ( powersetI1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ B @ A )
% 2.47/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powersetE1_type,type,
% 2.47/1.52 powersetE1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetE1,definition,
% 2.47/1.52 ( powersetE1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.47/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(inPowerset_type,type,
% 2.47/1.52 inPowerset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(inPowerset,definition,
% 2.47/1.52 ( inPowerset
% 2.47/1.52 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(powersetsubset_type,type,
% 2.47/1.52 powersetsubset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(powersetsubset,definition,
% 2.47/1.52 ( powersetsubset
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(sepInPowerset_type,type,
% 2.47/1.52 sepInPowerset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(sepInPowerset,definition,
% 2.47/1.52 ( sepInPowerset
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( in
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 @ ( powerset @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(sepSubset_type,type,
% 2.47/1.52 sepSubset: $o ).
% 2.47/1.52
% 2.47/1.52 thf(sepSubset,definition,
% 2.47/1.52 ( sepSubset
% 2.47/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.47/1.52 ( subset
% 2.47/1.52 @ ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.47/1.52 @ A ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunion_type,type,
% 2.47/1.52 binunion: $i > $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(binunionIL_type,type,
% 2.47/1.52 binunionIL: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionIL,definition,
% 2.47/1.52 ( binunionIL
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(upairset2IR_type,type,
% 2.47/1.52 upairset2IR: $o ).
% 2.47/1.52
% 2.47/1.52 thf(upairset2IR,definition,
% 2.47/1.52 ( upairset2IR
% 2.47/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunionIR_type,type,
% 2.47/1.52 binunionIR: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionIR,definition,
% 2.47/1.52 ( binunionIR
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunionEcases_type,type,
% 2.47/1.52 binunionEcases: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionEcases,definition,
% 2.47/1.52 ( binunionEcases
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.47/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.47/1.52 => ( ( ( in @ Xx @ A )
% 2.47/1.52 => Xphi )
% 2.47/1.52 => ( ( ( in @ Xx @ B )
% 2.47/1.52 => Xphi )
% 2.47/1.52 => Xphi ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunionE_type,type,
% 2.47/1.52 binunionE: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionE,definition,
% 2.47/1.52 ( binunionE
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.47/1.52 => ( ( in @ Xx @ A )
% 2.47/1.52 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunionLsub_type,type,
% 2.47/1.52 binunionLsub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionLsub,definition,
% 2.47/1.52 ( binunionLsub
% 2.47/1.52 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binunionRsub_type,type,
% 2.47/1.52 binunionRsub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binunionRsub,definition,
% 2.47/1.52 ( binunionRsub
% 2.47/1.52 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersect_type,type,
% 2.47/1.52 binintersect: $i > $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectI_type,type,
% 2.47/1.52 binintersectI: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectI,definition,
% 2.47/1.52 ( binintersectI
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset5_type,type,
% 2.47/1.52 binintersectSubset5: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset5,definition,
% 2.47/1.52 ( binintersectSubset5
% 2.47/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.47/1.52 ( ( subset @ C @ A )
% 2.47/1.52 => ( ( subset @ C @ B )
% 2.47/1.52 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectEL_type,type,
% 2.47/1.52 binintersectEL: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectEL,definition,
% 2.47/1.52 ( binintersectEL
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.47/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectLsub_type,type,
% 2.47/1.52 binintersectLsub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectLsub,definition,
% 2.47/1.52 ( binintersectLsub
% 2.47/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset2_type,type,
% 2.47/1.52 binintersectSubset2: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset2,definition,
% 2.47/1.52 ( binintersectSubset2
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ A @ B )
% 2.47/1.52 => ( ( binintersect @ A @ B )
% 2.47/1.52 = A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset3_type,type,
% 2.47/1.52 binintersectSubset3: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset3,definition,
% 2.47/1.52 ( binintersectSubset3
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( ( binintersect @ A @ B )
% 2.47/1.52 = B )
% 2.47/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectER_type,type,
% 2.47/1.52 binintersectER: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectER,definition,
% 2.47/1.52 ( binintersectER
% 2.47/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.47/1.52 => ( in @ Xx @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(disjointsetsI1_type,type,
% 2.47/1.52 disjointsetsI1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(disjointsetsI1,definition,
% 2.47/1.52 ( disjointsetsI1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ~ ? [Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 & ( in @ Xx @ B ) )
% 2.47/1.52 => ( ( binintersect @ A @ B )
% 2.47/1.52 = emptyset ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectRsub_type,type,
% 2.47/1.52 binintersectRsub: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectRsub,definition,
% 2.47/1.52 ( binintersectRsub
% 2.47/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset4_type,type,
% 2.47/1.52 binintersectSubset4: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset4,definition,
% 2.47/1.52 ( binintersectSubset4
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( subset @ B @ A )
% 2.47/1.52 => ( ( binintersect @ A @ B )
% 2.47/1.52 = B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset1_type,type,
% 2.47/1.52 binintersectSubset1: $o ).
% 2.47/1.52
% 2.47/1.52 thf(binintersectSubset1,definition,
% 2.47/1.52 ( binintersectSubset1
% 2.47/1.52 = ( ! [A: $i,B: $i] :
% 2.47/1.52 ( ( ( binintersect @ A @ B )
% 2.47/1.52 = A )
% 2.47/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(bs114d_type,type,
% 2.47/1.52 bs114d: $o ).
% 2.47/1.52
% 2.47/1.52 thf(bs114d,definition,
% 2.47/1.52 ( bs114d
% 2.47/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.47/1.52 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.47/1.52 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(regular_type,type,
% 2.47/1.52 regular: $i > $o ).
% 2.47/1.52
% 2.47/1.52 thf(setminus_type,type,
% 2.47/1.52 setminus: $i > $i > $i ).
% 2.47/1.52
% 2.47/1.52 thf(setminus,definition,
% 2.47/1.52 ( setminus
% 2.47/1.52 = ( ^ [A: $i,B: $i] :
% 2.47/1.52 ( dsetconstr @ A
% 2.47/1.52 @ ^ [Xx: $i] :
% 2.47/1.52 ~ ( in @ Xx @ B ) ) ) ) ).
% 2.47/1.52
% 2.47/1.52 thf(setminusI,conjecture,
% 2.47/1.52 ( setextAx
% 2.47/1.52 => ( emptysetAx
% 2.47/1.52 => ( setadjoinAx
% 2.47/1.52 => ( powersetAx
% 2.47/1.52 => ( setunionAx
% 2.47/1.52 => ( omega0Ax
% 2.47/1.52 => ( omegaSAx
% 2.47/1.52 => ( omegaIndAx
% 2.47/1.52 => ( replAx
% 2.47/1.52 => ( foundationAx
% 2.47/1.52 => ( wellorderingAx
% 2.47/1.52 => ( descrp
% 2.47/1.52 => ( dsetconstrI
% 2.47/1.52 => ( dsetconstrEL
% 2.47/1.52 => ( dsetconstrER
% 2.47/1.52 => ( exuE1
% 2.47/1.52 => ( prop2setE
% 2.47/1.52 => ( emptysetE
% 2.47/1.52 => ( emptysetimpfalse
% 2.47/1.52 => ( notinemptyset
% 2.47/1.52 => ( exuE3e
% 2.47/1.52 => ( setext
% 2.47/1.52 => ( emptyI
% 2.47/1.52 => ( noeltsimpempty
% 2.47/1.52 => ( setbeta
% 2.47/1.52 => ( nonemptyE1
% 2.47/1.52 => ( nonemptyI
% 2.47/1.52 => ( nonemptyI1
% 2.47/1.52 => ( setadjoinIL
% 2.47/1.52 => ( emptyinunitempty
% 2.47/1.52 => ( setadjoinIR
% 2.47/1.52 => ( setadjoinE
% 2.47/1.52 => ( setadjoinOr
% 2.47/1.52 => ( setoftrueEq
% 2.47/1.52 => ( powersetI
% 2.47/1.52 => ( emptyinPowerset
% 2.47/1.52 => ( emptyInPowerset
% 2.47/1.52 => ( powersetE
% 2.47/1.52 => ( setunionI
% 2.47/1.52 => ( setunionE
% 2.47/1.52 => ( subPowSU
% 2.47/1.52 => ( exuE2
% 2.47/1.52 => ( nonemptyImpWitness
% 2.47/1.52 => ( uniqinunit
% 2.47/1.52 => ( notinsingleton
% 2.47/1.52 => ( eqinunit
% 2.47/1.52 => ( singletonsswitch
% 2.47/1.52 => ( upairsetE
% 2.47/1.52 => ( upairsetIL
% 2.47/1.52 => ( upairsetIR
% 2.47/1.52 => ( emptyE1
% 2.47/1.52 => ( vacuousDall
% 2.47/1.52 => ( quantDeMorgan1
% 2.47/1.52 => ( quantDeMorgan2
% 2.47/1.52 => ( quantDeMorgan3
% 2.47/1.52 => ( quantDeMorgan4
% 2.47/1.52 => ( prop2setI
% 2.47/1.52 => ( prop2set2propI
% 2.47/1.52 => ( notdexE
% 2.47/1.52 => ( notdallE
% 2.47/1.52 => ( exuI1
% 2.47/1.52 => ( exuI3
% 2.47/1.52 => ( exuI2
% 2.47/1.52 => ( inCongP
% 2.47/1.52 => ( in__Cong
% 2.47/1.52 => ( exuE3u
% 2.47/1.52 => ( exu__Cong
% 2.47/1.52 => ( emptyset__Cong
% 2.47/1.52 => ( setadjoin__Cong
% 2.47/1.52 => ( powerset__Cong
% 2.47/1.52 => ( setunion__Cong
% 2.47/1.52 => ( omega__Cong
% 2.47/1.52 => ( exuEu
% 2.47/1.52 => ( descr__Cong
% 2.47/1.52 => ( dsetconstr__Cong
% 2.47/1.52 => ( subsetI1
% 2.47/1.52 => ( eqimpsubset2
% 2.47/1.52 => ( eqimpsubset1
% 2.47/1.52 => ( subsetI2
% 2.47/1.52 => ( emptysetsubset
% 2.47/1.52 => ( subsetE
% 2.47/1.52 => ( subsetE2
% 2.47/1.52 => ( notsubsetI
% 2.47/1.52 => ( notequalI1
% 2.47/1.52 => ( notequalI2
% 2.47/1.52 => ( subsetRefl
% 2.47/1.52 => ( subsetTrans
% 2.47/1.52 => ( setadjoinSub
% 2.47/1.52 => ( setadjoinSub2
% 2.47/1.52 => ( subset2powerset
% 2.47/1.52 => ( setextsub
% 2.47/1.52 => ( subsetemptysetimpeq
% 2.47/1.52 => ( powersetI1
% 2.47/1.52 => ( powersetE1
% 2.47/1.52 => ( inPowerset
% 2.47/1.52 => ( powersetsubset
% 2.47/1.52 => ( sepInPowerset
% 2.47/1.52 => ( sepSubset
% 2.47/1.52 => ( binunionIL
% 2.47/1.52 => ( upairset2IR
% 2.47/1.52 => ( binunionIR
% 2.47/1.52 => ( binunionEcases
% 2.47/1.52 => ( binunionE
% 2.47/1.52 => ( binunionLsub
% 2.47/1.52 => ( binunionRsub
% 2.47/1.52 => ( binintersectI
% 2.47/1.52 => ( binintersectSubset5
% 2.47/1.52 => ( binintersectEL
% 2.47/1.52 => ( binintersectLsub
% 2.47/1.52 => ( binintersectSubset2
% 2.47/1.52 => ( binintersectSubset3
% 2.47/1.52 => ( binintersectER
% 2.47/1.52 => ( disjointsetsI1
% 2.47/1.52 => ( binintersectRsub
% 2.47/1.52 => ( binintersectSubset4
% 2.47/1.52 => ( binintersectSubset1
% 2.47/1.52 => ( bs114d
% 2.47/1.52 => ! [A: $i,B: $i,Xx: $i] :
% 2.47/1.52 ( ( in @ Xx @ A )
% 2.47/1.52 => ( ~ ( in @ Xx @ B )
% 2.47/1.52 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.47/1.52 ------------------------
% 2.47/1.55 % (7645)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_7545 for (2999ds/4Mi)
% 2.47/1.55 % (7648)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_7545 for (2999ds/2Mi)
% 2.47/1.55 % (7647)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/2Mi)
% 2.47/1.55 % (7650)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/18Mi)
% 2.47/1.55 % (7644)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/183Mi)
% 2.47/1.55 % (7649)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_7545 for (2999ds/275Mi)
% 2.47/1.55 % (7646)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_7545 for (2999ds/27Mi)
% 2.47/1.55 % (7647)Instruction limit reached!
% 2.47/1.55 % (7647)------------------------------
% 2.47/1.55 % (7647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (7647)Termination reason: Unknown
% 2.47/1.55 % (7647)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (7647)Memory used [KB]: 1151
% 2.47/1.55 % (7647)Time elapsed: 0.003 s
% 2.47/1.55 % (7647)Instructions burned: 2 (million)
% 2.47/1.55 % (7647)------------------------------
% 2.47/1.55 % (7647)------------------------------
% 2.47/1.55 % (7648)Instruction limit reached!
% 2.47/1.55 % (7648)------------------------------
% 2.47/1.55 % (7648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (7648)Termination reason: Unknown
% 2.47/1.55 % (7648)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (7648)Memory used [KB]: 1151
% 2.47/1.55 % (7648)Time elapsed: 0.003 s
% 2.47/1.55 % (7648)Instructions burned: 3 (million)
% 2.47/1.55 % (7648)------------------------------
% 2.47/1.55 % (7648)------------------------------
% 2.47/1.55 % (7645)Instruction limit reached!
% 2.47/1.55 % (7645)------------------------------
% 2.47/1.55 % (7645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (7645)Termination reason: Unknown
% 2.47/1.55 % (7645)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (7645)Memory used [KB]: 1279
% 2.47/1.55 % (7645)Time elapsed: 0.004 s
% 2.47/1.55 % (7645)Instructions burned: 4 (million)
% 2.47/1.55 % (7645)------------------------------
% 2.47/1.55 % (7645)------------------------------
% 2.47/1.55 % (7650)Instruction limit reached!
% 2.47/1.55 % (7650)------------------------------
% 2.47/1.55 % (7650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (7650)Termination reason: Unknown
% 2.47/1.55 % (7650)Termination phase: Preprocessing 3
% 2.47/1.55
% 2.47/1.55 % (7650)Memory used [KB]: 1535
% 2.47/1.55 % (7650)Time elapsed: 0.011 s
% 2.47/1.55 % (7650)Instructions burned: 19 (million)
% 2.47/1.55 % (7650)------------------------------
% 2.47/1.55 % (7650)------------------------------
% 2.47/1.56 % (7646)Instruction limit reached!
% 2.47/1.56 % (7646)------------------------------
% 2.47/1.56 % (7646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (7646)Termination reason: Unknown
% 2.47/1.56 % (7646)Termination phase: Property scanning
% 2.47/1.56
% 2.47/1.56 % (7646)Memory used [KB]: 1535
% 2.47/1.56 % (7646)Time elapsed: 0.014 s
% 2.47/1.56 % (7646)Instructions burned: 27 (million)
% 2.47/1.56 % (7646)------------------------------
% 2.47/1.56 % (7646)------------------------------
% 2.47/1.56 % (7651)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/3Mi)
% 2.47/1.56 % (7652)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_7545 for (2999ds/37Mi)
% 2.47/1.56 % (7653)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_7545 for (2999ds/15Mi)
% 2.47/1.56 % (7651)Instruction limit reached!
% 2.47/1.56 % (7651)------------------------------
% 2.47/1.56 % (7651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (7651)Termination reason: Unknown
% 2.47/1.56 % (7651)Termination phase: shuffling
% 2.47/1.56
% 2.47/1.56 % (7651)Memory used [KB]: 1151
% 2.47/1.56 % (7651)Time elapsed: 0.003 s
% 2.47/1.56 % (7651)Instructions burned: 4 (million)
% 2.47/1.56 % (7651)------------------------------
% 2.47/1.56 % (7651)------------------------------
% 2.47/1.57 % (7654)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_7545 for (2999ds/3Mi)
% 2.47/1.57 % (7653)Instruction limit reached!
% 2.47/1.57 % (7653)------------------------------
% 2.47/1.57 % (7653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (7653)Termination reason: Unknown
% 2.47/1.57 % (7653)Termination phase: Preprocessing 2
% 2.47/1.57
% 2.47/1.57 % (7653)Memory used [KB]: 1407
% 2.47/1.57 % (7653)Time elapsed: 0.009 s
% 2.47/1.57 % (7653)Instructions burned: 16 (million)
% 2.47/1.57 % (7653)------------------------------
% 2.47/1.57 % (7653)------------------------------
% 2.47/1.57 % (7654)Instruction limit reached!
% 2.47/1.57 % (7654)------------------------------
% 2.47/1.57 % (7654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (7654)Termination reason: Unknown
% 2.47/1.57 % (7654)Termination phase: shuffling
% 2.47/1.57
% 2.47/1.57 % (7654)Memory used [KB]: 1151
% 2.47/1.57 % (7654)Time elapsed: 0.003 s
% 2.47/1.57 % (7654)Instructions burned: 4 (million)
% 2.47/1.57 % (7654)------------------------------
% 2.47/1.57 % (7654)------------------------------
% 2.47/1.57 % (7655)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_7545 for (2999ds/1041Mi)
% 2.47/1.58 % (7652)Instruction limit reached!
% 2.47/1.58 % (7652)------------------------------
% 2.47/1.58 % (7652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (7652)Termination reason: Unknown
% 2.47/1.58 % (7652)Termination phase: Property scanning
% 2.47/1.58
% 2.47/1.58 % (7652)Memory used [KB]: 1663
% 2.47/1.58 % (7652)Time elapsed: 0.018 s
% 2.47/1.58 % (7652)Instructions burned: 38 (million)
% 2.47/1.58 % (7652)------------------------------
% 2.47/1.58 % (7652)------------------------------
% 2.47/1.58 % (7656)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/7Mi)
% 2.47/1.58 % (7656)Instruction limit reached!
% 2.47/1.58 % (7656)------------------------------
% 2.47/1.58 % (7656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (7656)Termination reason: Unknown
% 2.47/1.58 % (7656)Termination phase: shuffling
% 2.47/1.58
% 2.47/1.58 % (7656)Memory used [KB]: 1279
% 2.47/1.58 % (7656)Time elapsed: 0.005 s
% 2.47/1.58 % (7656)Instructions burned: 8 (million)
% 2.47/1.58 % (7656)------------------------------
% 2.47/1.58 % (7656)------------------------------
% 2.47/1.59 % (7657)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/16Mi)
% 2.47/1.59 % (7658)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_7545 for (2999ds/3Mi)
% 2.47/1.59 % (7658)Instruction limit reached!
% 2.47/1.59 % (7658)------------------------------
% 2.47/1.59 % (7658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (7658)Termination reason: Unknown
% 2.47/1.59 % (7658)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (7658)Memory used [KB]: 1279
% 2.47/1.59 % (7658)Time elapsed: 0.003 s
% 2.47/1.59 % (7658)Instructions burned: 4 (million)
% 2.47/1.59 % (7658)------------------------------
% 2.47/1.59 % (7658)------------------------------
% 2.47/1.59 % (7657)Instruction limit reached!
% 2.47/1.59 % (7657)------------------------------
% 2.47/1.59 % (7657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.59 % (7657)Termination reason: Unknown
% 2.47/1.59 % (7657)Termination phase: shuffling
% 2.47/1.59
% 2.47/1.59 % (7657)Memory used [KB]: 1535
% 2.47/1.59 % (7657)Time elapsed: 0.009 s
% 2.47/1.59 % (7657)Instructions burned: 17 (million)
% 2.47/1.59 % (7657)------------------------------
% 2.47/1.59 % (7657)------------------------------
% 2.47/1.60 % (7659)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_7545 for (2999ds/3Mi)
% 2.49/1.60 % (7659)Instruction limit reached!
% 2.49/1.60 % (7659)------------------------------
% 2.49/1.60 % (7659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.60 % (7659)Termination reason: Unknown
% 2.49/1.60 % (7659)Termination phase: shuffling
% 2.49/1.60
% 2.49/1.60 % (7659)Memory used [KB]: 1151
% 2.49/1.60 % (7659)Time elapsed: 0.003 s
% 2.49/1.60 % (7659)Instructions burned: 4 (million)
% 2.49/1.60 % (7659)------------------------------
% 2.49/1.60 % (7659)------------------------------
% 2.49/1.60 % (7660)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/7Mi)
% 2.49/1.60 % (7660)Instruction limit reached!
% 2.49/1.60 % (7660)------------------------------
% 2.49/1.60 % (7660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.60 % (7660)Termination reason: Unknown
% 2.49/1.60 % (7660)Termination phase: shuffling
% 2.49/1.60
% 2.49/1.60 % (7660)Memory used [KB]: 1279
% 2.49/1.60 % (7660)Time elapsed: 0.005 s
% 2.49/1.60 % (7660)Instructions burned: 8 (million)
% 2.49/1.60 % (7660)------------------------------
% 2.49/1.60 % (7660)------------------------------
% 2.49/1.61 % (7661)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/3Mi)
% 2.49/1.61 % (7661)Instruction limit reached!
% 2.49/1.61 % (7661)------------------------------
% 2.49/1.61 % (7661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.61 % (7661)Termination reason: Unknown
% 2.49/1.61 % (7661)Termination phase: shuffling
% 2.49/1.61
% 2.49/1.61 % (7661)Memory used [KB]: 1151
% 2.49/1.61 % (7661)Time elapsed: 0.003 s
% 2.49/1.61 % (7661)Instructions burned: 3 (million)
% 2.49/1.61 % (7661)------------------------------
% 2.49/1.61 % (7661)------------------------------
% 2.49/1.61 % (7662)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/4Mi)
% 2.49/1.61 % (7662)Instruction limit reached!
% 2.49/1.61 % (7662)------------------------------
% 2.49/1.61 % (7662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.61 % (7662)Termination reason: Unknown
% 2.49/1.61 % (7662)Termination phase: shuffling
% 2.49/1.61
% 2.49/1.61 % (7662)Memory used [KB]: 1151
% 2.49/1.61 % (7662)Time elapsed: 0.003 s
% 2.49/1.61 % (7662)Instructions burned: 4 (million)
% 2.49/1.61 % (7662)------------------------------
% 2.49/1.61 % (7662)------------------------------
% 2.49/1.61 % (7663)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/18Mi)
% 2.49/1.62 % (7664)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/710Mi)
% 2.49/1.62 % (7663)Instruction limit reached!
% 2.49/1.62 % (7663)------------------------------
% 2.49/1.62 % (7663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.62 % (7663)Termination reason: Unknown
% 2.49/1.62 % (7663)Termination phase: Property scanning
% 2.49/1.62
% 2.49/1.62 % (7663)Memory used [KB]: 1535
% 2.49/1.62 % (7663)Time elapsed: 0.010 s
% 2.49/1.62 % (7663)Instructions burned: 19 (million)
% 2.49/1.62 % (7663)------------------------------
% 2.49/1.62 % (7663)------------------------------
% 2.49/1.62 % (7665)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/6Mi)
% 2.49/1.63 % (7665)Instruction limit reached!
% 2.49/1.63 % (7665)------------------------------
% 2.49/1.63 % (7665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.63 % (7665)Termination reason: Unknown
% 2.49/1.63 % (7665)Termination phase: shuffling
% 2.49/1.63
% 2.49/1.63 % (7665)Memory used [KB]: 1279
% 2.49/1.63 % (7665)Time elapsed: 0.004 s
% 2.49/1.63 % (7665)Instructions burned: 6 (million)
% 2.49/1.63 % (7665)------------------------------
% 2.49/1.63 % (7665)------------------------------
% 2.49/1.63 % (7666)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_7545 for (2999ds/902Mi)
% 2.49/1.63 % (7644)Instruction limit reached!
% 2.49/1.63 % (7644)------------------------------
% 2.49/1.63 % (7644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.63 % (7644)Termination reason: Unknown
% 2.49/1.63 % (7644)Termination phase: Saturation
% 2.49/1.63
% 2.49/1.63 % (7644)Memory used [KB]: 7036
% 2.49/1.63 % (7644)Time elapsed: 0.087 s
% 2.49/1.63 % (7644)Instructions burned: 183 (million)
% 2.49/1.63 % (7644)------------------------------
% 2.49/1.63 % (7644)------------------------------
% 2.49/1.64 % (7667)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_7545 for (2999ds/21Mi)
% 2.49/1.64 % (7668)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7545 for (2999ds/5Mi)
% 2.49/1.64 % (7668)Instruction limit reached!
% 2.49/1.64 % (7668)------------------------------
% 2.49/1.64 % (7668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.64 % (7668)Termination reason: Unknown
% 2.49/1.64 % (7668)Termination phase: shuffling
% 2.49/1.64
% 2.49/1.64 % (7668)Memory used [KB]: 1279
% 2.49/1.64 % (7668)Time elapsed: 0.004 s
% 2.49/1.64 % (7668)Instructions burned: 6 (million)
% 2.49/1.64 % (7668)------------------------------
% 2.49/1.64 % (7668)------------------------------
% 2.49/1.65 % (7667)Instruction limit reached!
% 2.49/1.65 % (7667)------------------------------
% 2.49/1.65 % (7667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.65 % (7667)Termination reason: Unknown
% 2.49/1.65 % (7667)Termination phase: Property scanning
% 2.49/1.65
% 2.49/1.65 % (7667)Memory used [KB]: 1535
% 2.49/1.65 % (7667)Time elapsed: 0.011 s
% 2.49/1.65 % (7667)Instructions burned: 21 (million)
% 2.49/1.65 % (7667)------------------------------
% 2.49/1.65 % (7667)------------------------------
% 2.49/1.65 % (7669)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_7545 for (2999ds/6Mi)
% 2.49/1.65 % (7669)Instruction limit reached!
% 2.49/1.65 % (7669)------------------------------
% 2.49/1.65 % (7669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.65 % (7669)Termination reason: Unknown
% 2.49/1.65 % (7669)Termination phase: shuffling
% 2.49/1.65
% 2.49/1.65 % (7669)Memory used [KB]: 1279
% 2.49/1.65 % (7669)Time elapsed: 0.004 s
% 2.49/1.65 % (7669)Instructions burned: 6 (million)
% 2.49/1.65 % (7669)------------------------------
% 2.49/1.65 % (7669)------------------------------
% 2.49/1.66 % (7670)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7545 for (2998ds/377Mi)
% 2.49/1.66 % (7671)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_7545 for (2998ds/779Mi)
% 2.49/1.66 % (7672)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_7545 for (2998ds/19Mi)
% 2.49/1.67 % (7672)Instruction limit reached!
% 2.49/1.67 % (7672)------------------------------
% 2.49/1.67 % (7672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.67 % (7672)Termination reason: Unknown
% 2.49/1.67 % (7672)Termination phase: Property scanning
% 2.49/1.67
% 2.49/1.67 % (7672)Memory used [KB]: 1535
% 2.49/1.67 % (7672)Time elapsed: 0.010 s
% 2.49/1.67 % (7672)Instructions burned: 19 (million)
% 2.49/1.67 % (7672)------------------------------
% 2.49/1.67 % (7672)------------------------------
% 2.49/1.68 % (7649)Instruction limit reached!
% 2.49/1.68 % (7649)------------------------------
% 2.49/1.68 % (7649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.68 % (7649)Termination reason: Unknown
% 2.49/1.68 % (7649)Termination phase: Saturation
% 2.49/1.68
% 2.49/1.68 % (7649)Memory used [KB]: 7675
% 2.49/1.68 % (7649)Time elapsed: 0.138 s
% 2.49/1.68 % (7649)Instructions burned: 275 (million)
% 2.49/1.68 % (7649)------------------------------
% 2.49/1.68 % (7649)------------------------------
% 2.49/1.69 % (7673)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7545 for (2998ds/879Mi)
% 2.49/1.70 % (7674)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7545 for (2998ds/17Mi)
% 2.49/1.71 % (7674)Instruction limit reached!
% 2.49/1.71 % (7674)------------------------------
% 2.49/1.71 % (7674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.71 % (7674)Termination reason: Unknown
% 2.49/1.71 % (7674)Termination phase: Property scanning
% 2.49/1.71
% 2.49/1.71 % (7674)Memory used [KB]: 1535
% 2.49/1.71 % (7674)Time elapsed: 0.010 s
% 2.49/1.71 % (7674)Instructions burned: 18 (million)
% 2.49/1.71 % (7674)------------------------------
% 2.49/1.71 % (7674)------------------------------
% 2.49/1.72 % (7675)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7545 for (2998ds/3Mi)
% 2.49/1.72 % (7675)Instruction limit reached!
% 2.49/1.72 % (7675)------------------------------
% 2.49/1.72 % (7675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.72 % (7675)Termination reason: Unknown
% 2.49/1.72 % (7675)Termination phase: shuffling
% 2.49/1.72
% 2.49/1.72 % (7675)Memory used [KB]: 1151
% 2.49/1.72 % (7675)Time elapsed: 0.003 s
% 2.49/1.72 % (7675)Instructions burned: 4 (million)
% 2.49/1.72 % (7675)------------------------------
% 2.49/1.72 % (7675)------------------------------
% 2.49/1.74 % (7676)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7545 for (2998ds/30Mi)
% 2.49/1.75 % (7676)Instruction limit reached!
% 2.49/1.75 % (7676)------------------------------
% 2.49/1.75 % (7676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.75 % (7676)Termination reason: Unknown
% 2.49/1.75 % (7676)Termination phase: Property scanning
% 2.49/1.75
% 2.49/1.75 % (7676)Memory used [KB]: 1535
% 2.49/1.75 % (7676)Time elapsed: 0.015 s
% 2.49/1.75 % (7676)Instructions burned: 30 (million)
% 2.49/1.75 % (7676)------------------------------
% 2.49/1.75 % (7676)------------------------------
% 2.49/1.77 % (7677)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7545 for (2997ds/127Mi)
% 2.49/1.83 % (7677)Instruction limit reached!
% 2.49/1.83 % (7677)------------------------------
% 2.49/1.83 % (7677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.83 % (7677)Termination reason: Unknown
% 2.49/1.83 % (7677)Termination phase: Saturation
% 2.49/1.83
% 2.49/1.83 % (7677)Memory used [KB]: 6780
% 2.49/1.83 % (7677)Time elapsed: 0.059 s
% 2.49/1.83 % (7677)Instructions burned: 128 (million)
% 2.49/1.83 % (7677)------------------------------
% 2.49/1.83 % (7677)------------------------------
% 2.49/1.84 % (7670)Instruction limit reached!
% 2.49/1.84 % (7670)------------------------------
% 2.49/1.84 % (7670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.84 % (7678)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7545 for (2997ds/100Mi)
% 2.49/1.84 % (7670)Termination reason: Unknown
% 2.49/1.84 % (7670)Termination phase: Saturation
% 2.49/1.84
% 2.49/1.84 % (7670)Memory used [KB]: 7291
% 2.49/1.84 % (7670)Time elapsed: 0.186 s
% 2.49/1.84 % (7670)Instructions burned: 377 (million)
% 2.49/1.84 % (7670)------------------------------
% 2.49/1.84 % (7670)------------------------------
% 2.49/1.86 % (7679)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_7545 for (2996ds/3Mi)
% 2.49/1.86 % (7679)Instruction limit reached!
% 2.49/1.86 % (7679)------------------------------
% 2.49/1.86 % (7679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.86 % (7679)Termination reason: Unknown
% 2.49/1.86 % (7679)Termination phase: shuffling
% 2.49/1.86
% 2.49/1.86 % (7679)Memory used [KB]: 1151
% 2.49/1.86 % (7679)Time elapsed: 0.003 s
% 2.49/1.86 % (7679)Instructions burned: 3 (million)
% 2.49/1.86 % (7679)------------------------------
% 2.49/1.86 % (7679)------------------------------
% 2.49/1.88 % (7680)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_7545 for (2996ds/20Mi)
% 2.49/1.89 % (7680)Instruction limit reached!
% 2.49/1.89 % (7680)------------------------------
% 2.49/1.89 % (7680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.89 % (7680)Termination reason: Unknown
% 2.49/1.89 % (7680)Termination phase: SInE selection
% 2.49/1.89
% 2.49/1.89 % (7680)Memory used [KB]: 1407
% 2.49/1.89 % (7680)Time elapsed: 0.011 s
% 2.49/1.89 % (7680)Instructions burned: 21 (million)
% 2.49/1.89 % (7680)------------------------------
% 2.49/1.89 % (7680)------------------------------
% 2.49/1.89 % (7678)Instruction limit reached!
% 2.49/1.89 % (7678)------------------------------
% 2.49/1.89 % (7678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.89 % (7678)Termination reason: Unknown
% 2.49/1.89 % (7678)Termination phase: Saturation
% 2.49/1.89
% 2.49/1.89 % (7678)Memory used [KB]: 6268
% 2.49/1.89 % (7678)Time elapsed: 0.048 s
% 2.49/1.89 % (7678)Instructions burned: 101 (million)
% 2.49/1.89 % (7678)------------------------------
% 2.49/1.89 % (7678)------------------------------
% 2.49/1.90 % (7681)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_7545 for (2996ds/86Mi)
% 2.49/1.91 % (7682)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_7545 for (2996ds/107Mi)
% 2.49/1.94 % (7681)Instruction limit reached!
% 2.49/1.94 % (7681)------------------------------
% 2.49/1.94 % (7681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.94 % (7681)Termination reason: Unknown
% 2.49/1.94 % (7681)Termination phase: Saturation
% 2.49/1.94
% 2.49/1.94 % (7681)Memory used [KB]: 6396
% 2.49/1.94 % (7681)Time elapsed: 0.040 s
% 2.49/1.94 % (7681)Instructions burned: 86 (million)
% 2.49/1.94 % (7681)------------------------------
% 2.49/1.94 % (7681)------------------------------
% 2.49/1.94 % (7671)Instruction limit reached!
% 2.49/1.94 % (7671)------------------------------
% 2.49/1.94 % (7671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.94 % (7671)Termination reason: Unknown
% 2.49/1.94 % (7671)Termination phase: Saturation
% 2.49/1.94
% 2.49/1.94 % (7671)Memory used [KB]: 6524
% 2.49/1.94 % (7671)Time elapsed: 0.283 s
% 2.49/1.94 % (7671)Instructions burned: 779 (million)
% 2.49/1.94 % (7671)------------------------------
% 2.49/1.94 % (7671)------------------------------
% 2.49/1.95 % (7682)Instruction limit reached!
% 2.49/1.95 % (7682)------------------------------
% 2.49/1.95 % (7682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.95 % (7682)Termination reason: Unknown
% 2.49/1.95 % (7682)Termination phase: Saturation
% 2.49/1.95
% 2.49/1.95 % (7682)Memory used [KB]: 6652
% 2.49/1.95 % (7682)Time elapsed: 0.050 s
% 2.49/1.95 % (7682)Instructions burned: 109 (million)
% 2.49/1.95 % (7682)------------------------------
% 2.49/1.95 % (7682)------------------------------
% 2.49/1.96 % (7655)Instruction limit reached!
% 2.49/1.96 % (7655)------------------------------
% 2.49/1.96 % (7655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.96 % (7655)Termination reason: Unknown
% 2.49/1.96 % (7655)Termination phase: Saturation
% 2.49/1.96
% 2.49/1.96 % (7655)Memory used [KB]: 8187
% 2.49/1.96 % (7655)Time elapsed: 0.385 s
% 2.49/1.96 % (7655)Instructions burned: 1042 (million)
% 2.49/1.96 % (7655)------------------------------
% 2.49/1.96 % (7655)------------------------------
% 2.49/1.96 % (7683)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_7545 for (2995ds/39Mi)
% 2.49/1.96 % (7684)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_7545 for (2995ds/448Mi)
% 2.49/1.97 % (7685)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_7545 for (2995ds/46Mi)
% 2.49/1.97 % (7686)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_7545 for (2995ds/98Mi)
% 2.49/1.97 % (7664)Instruction limit reached!
% 2.49/1.97 % (7664)------------------------------
% 2.49/1.97 % (7664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.97 % (7664)Termination reason: Unknown
% 2.49/1.97 % (7664)Termination phase: Saturation
% 2.49/1.97
% 2.49/1.97 % (7664)Memory used [KB]: 8699
% 2.49/1.97 % (7664)Time elapsed: 0.357 s
% 2.49/1.97 % (7664)Instructions burned: 711 (million)
% 2.49/1.97 % (7664)------------------------------
% 2.49/1.97 % (7664)------------------------------
% 2.49/1.98 % (7683)Instruction limit reached!
% 2.49/1.98 % (7683)------------------------------
% 2.49/1.98 % (7683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.98 % (7683)Termination reason: Unknown
% 2.49/1.98 % (7683)Termination phase: Property scanning
% 2.49/1.98
% 2.49/1.98 % (7683)Memory used [KB]: 1535
% 2.49/1.98 % (7683)Time elapsed: 0.019 s
% 2.49/1.98 % (7683)Instructions burned: 40 (million)
% 2.49/1.98 % (7683)------------------------------
% 2.49/1.98 % (7683)------------------------------
% 2.49/1.99 % (7687)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_7545 for (2995ds/507Mi)
% 2.49/1.99 % (7685)Instruction limit reached!
% 2.49/1.99 % (7685)------------------------------
% 2.49/1.99 % (7685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.99 % (7685)Termination reason: Unknown
% 2.49/1.99 % (7685)Termination phase: Twee Goal Transformation
% 2.49/1.99
% 2.49/1.99 % (7685)Memory used [KB]: 1663
% 2.49/1.99 % (7685)Time elapsed: 0.022 s
% 2.49/1.99 % (7685)Instructions burned: 47 (million)
% 2.49/1.99 % (7685)------------------------------
% 2.49/1.99 % (7685)------------------------------
% 2.49/1.99 % (7688)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_7545 for (2995ds/149Mi)
% 2.49/2.01 % (7689)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7545 for (2995ds/39Mi)
% 2.49/2.01 % (7686)Instruction limit reached!
% 2.49/2.01 % (7686)------------------------------
% 2.49/2.01 % (7686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/2.01 % (7686)Termination reason: Unknown
% 2.49/2.01 % (7686)Termination phase: Saturation
% 2.49/2.01
% 2.49/2.01 % (7686)Memory used [KB]: 1791
% 2.49/2.01 % (7686)Time elapsed: 0.043 s
% 2.49/2.01 % (7686)Instructions burned: 99 (million)
% 2.49/2.01 % (7686)------------------------------
% 2.49/2.01 % (7686)------------------------------
% 2.49/2.03 % (7689)Instruction limit reached!
% 2.49/2.03 % (7689)------------------------------
% 2.49/2.03 % (7689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/2.03 % (7689)Termination reason: Unknown
% 2.49/2.03 % (7689)Termination phase: Function definition elimination
% 2.49/2.03
% 2.49/2.03 % (7689)Memory used [KB]: 1663
% 2.49/2.03 % (7689)Time elapsed: 0.020 s
% 2.49/2.03 % (7689)Instructions burned: 41 (million)
% 2.49/2.03 % (7689)------------------------------
% 2.49/2.03 % (7689)------------------------------
% 5.85/2.03 % (7690)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_7545 for (2995ds/6Mi)
% 5.85/2.03 % (7690)Instruction limit reached!
% 5.85/2.03 % (7690)------------------------------
% 5.85/2.03 % (7690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.03 % (7690)Termination reason: Unknown
% 5.85/2.03 % (7690)Termination phase: shuffling
% 5.85/2.03
% 5.85/2.03 % (7690)Memory used [KB]: 1279
% 5.85/2.03 % (7690)Time elapsed: 0.005 s
% 5.85/2.03 % (7690)Instructions burned: 8 (million)
% 5.85/2.03 % (7690)------------------------------
% 5.85/2.03 % (7690)------------------------------
% 5.85/2.04 % (7691)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_7545 for (2995ds/1087Mi)
% 5.85/2.05 % (7692)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7545 for (2994ds/47Mi)
% 5.85/2.06 % (7688)Instruction limit reached!
% 5.85/2.06 % (7688)------------------------------
% 5.85/2.06 % (7688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.06 % (7688)Termination reason: Unknown
% 5.85/2.06 % (7688)Termination phase: Saturation
% 5.85/2.06
% 5.85/2.06 % (7688)Memory used [KB]: 6780
% 5.85/2.06 % (7688)Time elapsed: 0.074 s
% 5.85/2.06 % (7688)Instructions burned: 150 (million)
% 5.85/2.06 % (7688)------------------------------
% 5.85/2.06 % (7688)------------------------------
% 5.85/2.07 % (7692)Instruction limit reached!
% 5.85/2.07 % (7692)------------------------------
% 5.85/2.07 % (7692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.07 % (7692)Termination reason: Unknown
% 5.85/2.07 % (7692)Termination phase: Property scanning
% 5.85/2.07
% 5.85/2.07 % (7692)Memory used [KB]: 1663
% 5.85/2.07 % (7692)Time elapsed: 0.022 s
% 5.85/2.07 % (7692)Instructions burned: 47 (million)
% 5.85/2.07 % (7692)------------------------------
% 5.85/2.07 % (7692)------------------------------
% 5.85/2.08 % (7693)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_7545 for (2994ds/44Mi)
% 5.85/2.08 % (7666)Instruction limit reached!
% 5.85/2.08 % (7666)------------------------------
% 5.85/2.08 % (7666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.08 % (7666)Termination reason: Unknown
% 5.85/2.08 % (7666)Termination phase: Saturation
% 5.85/2.08
% 5.85/2.08 % (7666)Memory used [KB]: 9978
% 5.85/2.08 % (7666)Time elapsed: 0.465 s
% 5.85/2.08 % (7666)Instructions burned: 902 (million)
% 5.85/2.08 % (7666)------------------------------
% 5.85/2.08 % (7666)------------------------------
% 5.85/2.09 % (7694)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_7545 for (2994ds/432Mi)
% 5.85/2.10 % (7695)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7545 for (2994ds/62Mi)
% 5.85/2.10 % (7693)Instruction limit reached!
% 5.85/2.10 % (7693)------------------------------
% 5.85/2.10 % (7693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.10 % (7693)Termination reason: Unknown
% 5.85/2.10 % (7693)Termination phase: Property scanning
% 5.85/2.10
% 5.85/2.10 % (7693)Memory used [KB]: 1663
% 5.85/2.10 % (7693)Time elapsed: 0.021 s
% 5.85/2.10 % (7693)Instructions burned: 45 (million)
% 5.85/2.10 % (7693)------------------------------
% 5.85/2.10 % (7693)------------------------------
% 5.85/2.12 % (7696)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_7545 for (2994ds/31Mi)
% 5.85/2.12 % (7673)Instruction limit reached!
% 5.85/2.12 % (7673)------------------------------
% 5.85/2.12 % (7673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.12 % (7673)Termination reason: Unknown
% 5.85/2.12 % (7673)Termination phase: Saturation
% 5.85/2.12
% 5.85/2.12 % (7673)Memory used [KB]: 7931
% 5.85/2.12 % (7673)Time elapsed: 0.434 s
% 5.85/2.12 % (7673)Instructions burned: 880 (million)
% 5.85/2.12 % (7673)------------------------------
% 5.85/2.12 % (7673)------------------------------
% 5.85/2.12 % (7684)Instruction limit reached!
% 5.85/2.12 % (7684)------------------------------
% 5.85/2.12 % (7684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.12 % (7684)Termination reason: Unknown
% 5.85/2.12 % (7684)Termination phase: Saturation
% 5.85/2.12
% 5.85/2.12 % (7684)Memory used [KB]: 6396
% 5.85/2.12 % (7684)Time elapsed: 0.164 s
% 5.85/2.12 % (7684)Instructions burned: 448 (million)
% 5.85/2.12 % (7684)------------------------------
% 5.85/2.12 % (7684)------------------------------
% 5.85/2.12 % (7695)Instruction limit reached!
% 5.85/2.12 % (7695)------------------------------
% 5.85/2.12 % (7695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.12 % (7695)Termination reason: Unknown
% 5.85/2.12 % (7695)Termination phase: Saturation
% 5.85/2.12
% 5.85/2.12 % (7695)Memory used [KB]: 6140
% 5.85/2.12 % (7695)Time elapsed: 0.028 s
% 5.85/2.12 % (7695)Instructions burned: 62 (million)
% 5.85/2.12 % (7695)------------------------------
% 5.85/2.12 % (7695)------------------------------
% 6.45/2.13 % (7696)Instruction limit reached!
% 6.45/2.13 % (7696)------------------------------
% 6.45/2.13 % (7696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.13 % (7696)Termination reason: Unknown
% 6.45/2.13 % (7696)Termination phase: Property scanning
% 6.45/2.13
% 6.45/2.13 % (7696)Memory used [KB]: 1535
% 6.45/2.13 % (7696)Time elapsed: 0.016 s
% 6.45/2.13 % (7696)Instructions burned: 31 (million)
% 6.45/2.13 % (7696)------------------------------
% 6.45/2.13 % (7696)------------------------------
% 6.45/2.14 % (7697)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7545 for (2994ds/96Mi)
% 6.45/2.14 % (7698)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_7545 for (2994ds/453Mi)
% 6.45/2.14 % (7699)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_7545 for (2994ds/71Mi)
% 6.45/2.15 % (7700)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7545 for (2994ds/83Mi)
% 6.45/2.17 % (7699)Instruction limit reached!
% 6.45/2.17 % (7699)------------------------------
% 6.45/2.17 % (7699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.17 % (7699)Termination reason: Unknown
% 6.45/2.17 % (7699)Termination phase: Saturation
% 6.45/2.17
% 6.45/2.17 % (7699)Memory used [KB]: 6268
% 6.45/2.17 % (7699)Time elapsed: 0.033 s
% 6.45/2.17 % (7699)Instructions burned: 71 (million)
% 6.45/2.17 % (7699)------------------------------
% 6.45/2.17 % (7699)------------------------------
% 6.45/2.18 % (7697)Instruction limit reached!
% 6.45/2.18 % (7697)------------------------------
% 6.45/2.18 % (7697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.18 % (7697)Termination reason: Unknown
% 6.45/2.18 % (7697)Termination phase: Saturation
% 6.45/2.18
% 6.45/2.18 % (7697)Memory used [KB]: 6524
% 6.45/2.18 % (7697)Time elapsed: 0.045 s
% 6.45/2.18 % (7697)Instructions burned: 97 (million)
% 6.45/2.18 % (7697)------------------------------
% 6.45/2.18 % (7697)------------------------------
% 6.45/2.18 % (7700)Instruction limit reached!
% 6.45/2.18 % (7700)------------------------------
% 6.45/2.18 % (7700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.18 % (7700)Termination reason: Unknown
% 6.45/2.18 % (7700)Termination phase: Saturation
% 6.45/2.18
% 6.45/2.18 % (7700)Memory used [KB]: 6268
% 6.45/2.18 % (7700)Time elapsed: 0.038 s
% 6.45/2.18 % (7700)Instructions burned: 84 (million)
% 6.45/2.18 % (7700)------------------------------
% 6.45/2.18 % (7700)------------------------------
% 6.45/2.19 % (7691)First to succeed.
% 6.45/2.19 % (7701)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7545 for (2993ds/11Mi)
% 6.45/2.19 % (7691)Refutation found. Thanks to Tanya!
% 6.45/2.19 % SZS status Theorem for DTF2THF_7545
% 6.45/2.19 % SZS output start Proof for DTF2THF_7545
% 6.45/2.19 thf(func_def_0, type, in: $i > $i > $o).
% 6.45/2.19 thf(func_def_1, type, exu: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 6.45/2.19 thf(func_def_8, type, powerset: $i > $i).
% 6.45/2.19 thf(func_def_10, type, setunion: $i > $i).
% 6.45/2.19 thf(func_def_19, type, descr: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_26, type, prop2set: $o > $i).
% 6.45/2.19 thf(func_def_36, type, nonempty: $i > $o).
% 6.45/2.19 thf(func_def_69, type, set2prop: $i > $o).
% 6.45/2.19 thf(func_def_88, type, subset: $i > $i > $o).
% 6.45/2.19 thf(func_def_89, type, disjoint: $i > $i > $o).
% 6.45/2.19 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 6.45/2.19 thf(func_def_114, type, binunion: $i > $i > $i).
% 6.45/2.19 thf(func_def_122, type, binintersect: $i > $i > $i).
% 6.45/2.19 thf(func_def_135, type, regular: $i > $o).
% 6.45/2.19 thf(func_def_136, type, setminus: $i > $i > $i).
% 6.45/2.19 thf(func_def_149, type, sP0: $i > $i > $o).
% 6.45/2.19 thf(func_def_151, type, sP2: $i > ($i > $i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_152, type, sP3: $i > ($i > $i > $o) > $o).
% 6.45/2.19 thf(func_def_154, type, sP5: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_155, type, sP6: ($i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_157, type, sP8: $i > ($i > $o) > $o).
% 6.45/2.19 thf(func_def_160, type, sP11: $o > $i > $i > $o).
% 6.45/2.19 thf(func_def_161, type, sP12: $i > $i > $i > $o).
% 6.45/2.19 thf(func_def_162, type, sP13: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_163, type, sP14: $i > $i > $o).
% 6.45/2.19 thf(func_def_165, type, sP16: $i > $i > $i > $o).
% 6.45/2.19 thf(func_def_169, type, sP20: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_171, type, sP22: $i > $o).
% 6.45/2.19 thf(func_def_172, type, sP23: $i > $i > $o > $o).
% 6.45/2.19 thf(func_def_173, type, sP24: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_174, type, sP25: $i > $i > $i > $o).
% 6.45/2.19 thf(func_def_175, type, sP26: $i > $i > $o).
% 6.45/2.19 thf(func_def_176, type, sP27: $i > $o).
% 6.45/2.19 thf(func_def_177, type, sP28: $i > $i > $o).
% 6.45/2.19 thf(func_def_178, type, sP29: $i > $i > $o).
% 6.45/2.19 thf(func_def_179, type, sP30: $i > $i > $o).
% 6.45/2.19 thf(func_def_181, type, sP32: $i > $i > $o > $o).
% 6.45/2.19 thf(func_def_183, type, sP34: ($i > $o) > $o).
% 6.45/2.19 thf(func_def_184, type, sP35: ($i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_186, type, sP37: $i > ($i > $o) > ($i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_188, type, sP39: ($i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_190, type, sP41: $i > ($i > $o) > $o).
% 6.45/2.19 thf(func_def_192, type, sP43: ($i > $o) > $i > $o).
% 6.45/2.19 thf(func_def_194, type, sP45: $i > $i > $o).
% 6.45/2.19 thf(func_def_196, type, sP47: $i > $o).
% 6.45/2.19 thf(func_def_197, type, sP48: $i > $o).
% 6.45/2.19 thf(func_def_212, type, sK63: $i > $i > $i).
% 6.45/2.19 thf(func_def_216, type, sK67: $i > $i > $o).
% 6.45/2.19 thf(func_def_218, type, sK69: $i > ($i > $i > $o) > $i).
% 6.45/2.19 thf(func_def_219, type, sK70: $i > $i > ($i > $i > $o) > $i).
% 6.45/2.19 thf(func_def_220, type, sK71: $i > ($i > $i > $o) > $i).
% 6.45/2.19 thf(func_def_221, type, sK72: $i > ($i > $i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_222, type, sK73: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_223, type, sK74: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_224, type, sK75: $i > $o).
% 6.45/2.19 thf(func_def_225, type, sK76: $i > $o).
% 6.45/2.19 thf(func_def_229, type, sK80: $i > $i).
% 6.45/2.19 thf(func_def_244, type, sK95: $i > $o).
% 6.45/2.19 thf(func_def_256, type, sK107: $i > $o).
% 6.45/2.19 thf(func_def_257, type, sK108: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_258, type, sK109: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_261, type, sK112: $i > $o).
% 6.45/2.19 thf(func_def_265, type, sK116: $i > $o).
% 6.45/2.19 thf(func_def_269, type, sK120: $i > $o).
% 6.45/2.19 thf(func_def_272, type, sK123: $i > $o).
% 6.45/2.19 thf(func_def_279, type, sK130: $i > $i).
% 6.45/2.19 thf(func_def_287, type, sK138: $i > $o).
% 6.45/2.19 thf(func_def_288, type, sK139: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_289, type, sK140: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_294, type, sK145: $i > $i > $i).
% 6.45/2.19 thf(func_def_299, type, sK150: $i > $o).
% 6.45/2.19 thf(func_def_304, type, sK155: $i > $i > $i > $o).
% 6.45/2.19 thf(func_def_308, type, sK159: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_309, type, sK160: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_310, type, sK161: $i > $o).
% 6.45/2.19 thf(func_def_313, type, sK164: $i > $i > $i).
% 6.45/2.19 thf(func_def_320, type, sK171: $i > $o).
% 6.45/2.19 thf(func_def_325, type, sK176: $i > $i).
% 6.45/2.19 thf(func_def_330, type, sK181: $i > $o).
% 6.45/2.19 thf(func_def_331, type, sK182: $i > $o).
% 6.45/2.19 thf(func_def_332, type, sK183: ($i > $o) > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_333, type, sK184: ($i > $o) > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_334, type, sK185: $i > $o).
% 6.45/2.19 thf(func_def_335, type, sK186: $i > $o).
% 6.45/2.19 thf(func_def_336, type, sK187: ($i > $o) > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_337, type, sK188: ($i > $o) > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_342, type, sK193: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_343, type, sK194: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_344, type, sK195: $i > $o).
% 6.45/2.19 thf(func_def_348, type, sK199: $i > $i > $i).
% 6.45/2.19 thf(func_def_349, type, sK200: $i > $i > $i).
% 6.45/2.19 thf(func_def_350, type, sK201: $i > $i).
% 6.45/2.19 thf(func_def_353, type, sK204: $i > $i > $o > $i).
% 6.45/2.19 thf(func_def_358, type, sK209: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_359, type, sK210: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_360, type, sK211: $i > $o).
% 6.45/2.19 thf(func_def_362, type, sK213: $i > $o).
% 6.45/2.19 thf(func_def_365, type, sK216: $i > $i).
% 6.45/2.19 thf(func_def_367, type, sK218: $i > $i > $i).
% 6.45/2.19 thf(func_def_368, type, sK219: $i > $i > $i).
% 6.45/2.19 thf(func_def_369, type, sK220: $i > $i > $i > $i).
% 6.45/2.19 thf(func_def_370, type, sK221: $i > $i > $i).
% 6.45/2.19 thf(func_def_371, type, sK222: $i > $i > $i).
% 6.45/2.19 thf(func_def_372, type, sK223: $i > $i > $i).
% 6.45/2.19 thf(func_def_373, type, sK224: $i > $i > $i).
% 6.45/2.19 thf(func_def_374, type, sK225: $i > $i > $i).
% 6.45/2.19 thf(func_def_375, type, sK226: $i > $i).
% 6.45/2.19 thf(func_def_376, type, sK227: $i > $i).
% 6.45/2.19 thf(func_def_377, type, sK228: $i > $i).
% 6.45/2.19 thf(func_def_378, type, sK229: $i > $i).
% 6.45/2.19 thf(func_def_379, type, sK230: $i > $i > $i).
% 6.45/2.19 thf(func_def_380, type, sK231: $i > $i > $i).
% 6.45/2.19 thf(func_def_381, type, sK232: $i > $i > $i).
% 6.45/2.19 thf(func_def_382, type, sK233: $i > $i > $i > $i).
% 6.45/2.19 thf(func_def_383, type, sK234: $i > $i > $i > $i).
% 6.45/2.19 thf(func_def_384, type, sK235: $i > $i).
% 6.45/2.19 thf(func_def_392, type, sK243: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_393, type, sK244: $i > $o).
% 6.45/2.19 thf(func_def_396, type, sK247: $i > $i > $i).
% 6.45/2.19 thf(func_def_420, type, sK271: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_421, type, sK272: ($i > $o) > $i).
% 6.45/2.19 thf(func_def_422, type, sK273: $i > $o).
% 6.45/2.19 thf(func_def_427, type, sK278: $i > $i > $i).
% 6.45/2.19 thf(func_def_431, type, sK282: $i > $o).
% 6.45/2.19 thf(func_def_432, type, sK283: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_433, type, sK284: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_438, type, sK289: $i > ($i > $o) > ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_439, type, sK290: $i > ($i > $o) > ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_442, type, sK293: $i > $o).
% 6.45/2.19 thf(func_def_443, type, sK294: $i > $o).
% 6.45/2.19 thf(func_def_446, type, sK297: $i > $o).
% 6.45/2.19 thf(func_def_449, type, sK300: $i > $i > $i).
% 6.45/2.19 thf(func_def_451, type, sK302: $i > $o).
% 6.45/2.19 thf(func_def_452, type, sK303: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_453, type, sK304: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_454, type, sK305: $i > $o).
% 6.45/2.19 thf(func_def_456, type, sK307: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_457, type, sK308: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_460, type, sK311: $i > $o).
% 6.45/2.19 thf(func_def_462, type, sK313: $i > ($i > $o) > $i).
% 6.45/2.19 thf(func_def_463, type, sK314: ($i > $o) > $i > $i).
% 6.45/2.19 thf(func_def_481, type, sK332: $i > $o).
% 6.45/2.19 thf(func_def_500, type, sK351: $i > $i > $i).
% 6.45/2.19 thf(func_def_501, type, sK352: $i > $i > $i).
% 6.45/2.19 thf(func_def_506, type, sK357: $i > $o).
% 6.45/2.19 thf(func_def_507, type, sK358: $i > $i).
% 6.45/2.19 thf(func_def_508, type, sK359: $i > $i).
% 6.45/2.19 thf(func_def_513, type, ph364: !>[X0: $tType]:(X0)).
% 6.45/2.19 thf(f3610,plain,(
% 6.45/2.19 $false),
% 6.45/2.19 inference(subsumption_resolution,[status(thm)],[f3609,f1643])).
% 6.45/2.19 thf(f1643,plain,(
% 6.45/2.19 ((in @ sK251 @ sK252) != $true)),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f1005])).
% 6.45/2.19 thf(f1005,plain,(
% 6.45/2.19 (uniqinunit = $true) & (subPowSU = $true) & (omegaSAx = $true) & (upairsetIR = $true) & (setadjoinSub = $true) & (upairsetE = $true) & (exuI2 = $true) & (prop2setE = $true) & (subsetE2 = $true) & (setoftrueEq = $true) & (binunionRsub = $true) & (binunionIR = $true) & (eqimpsubset2 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (nonemptyImpWitness = $true) & (notinsingleton = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (nonemptyE1 = $true) & (emptysetE = $true) & (emptyInPowerset = $true) & (bs114d = $true) & (setadjoinIL = $true) & (binintersectSubset5 = $true) & (omega__Cong = $true) & (binintersectSubset1 = $true) & (setextAx = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (binintersectSubset2 = $true) & (sepInPowerset = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (binintersectRsub = $true) & (noeltsimpempty = $true) & (subsetI1 = $true) & (in__Cong = $true) & (prop2set2propI = $true) & (setadjoin__Cong = $true) & (omegaIndAx = $true) & (nonemptyI1 = $true) & (dsetconstrI = $true) & (binunionE = $true) & (subsetemptysetimpeq = $true) & (upairsetIL = $true) & (powersetE = $true) & (inCongP = $true) & (powersetE1 = $true) & (quantDeMorgan4 = $true) & (subset2powerset = $true) & (notsubsetI = $true) & (binintersectSubset3 = $true) & (emptyset__Cong = $true) & (dsetconstrER = $true) & (((in @ sK251 @ sK253) = $true) & ((in @ sK251 @ sK252) != $true) & ($true != (in @ sK251 @ (setminus @ sK253 @ sK252)))) & (powersetAx = $true) & (exuE3e = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (emptysetsubset = $true) & (emptyE1 = $true) & (setadjoinSub2 = $true) & (exuE1 = $true) & (setunionE = $true) & (exuI3 = $true) & (dsetconstrEL = $true) & (notdallE = $true) & (sepSubset = $true) & (exuE3u = $true) & (inPowerset = $true) & (eqinunit = $true) & (setadjoinOr = $true) & (wellorderingAx = $true) & (powersetsubset = $true) & (binunionEcases = $true) & (exuEu = $true) & (setunionI = $true) & (powersetI = $true) & (binintersectEL = $true) & (upairset2IR = $true) & (singletonsswitch = $true) & (foundationAx = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (quantDeMorgan2 = $true) & (exuI1 = $true) & (replAx = $true) & (subsetE = $true) & (binunionLsub = $true) & (exuE2 = $true) & (powersetI1 = $true) & (binunionIL = $true) & (setextsub = $true) & (disjointsetsI1 = $true) & (descrp = $true) & (exu__Cong = $true) & (setbeta = $true) & (quantDeMorgan1 = $true) & (omega0Ax = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (powerset__Cong = $true) & (notdexE = $true) & (subsetRefl = $true) & (notequalI1 = $true) & (vacuousDall = $true) & (setadjoinAx = $true) & (quantDeMorgan3 = $true) & (subsetI2 = $true) & (setunion__Cong = $true) & (setunionAx = $true) & (setext = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (notequalI2 = $true)),
% 6.45/2.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK251,sK252,sK253])],[f472,f1004])).
% 6.45/2.19 thf(f1004,plain,(
% 6.45/2.19 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ($true != (in @ X0 @ X1)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) => (((in @ sK251 @ sK253) = $true) & ((in @ sK251 @ sK252) != $true) & ($true != (in @ sK251 @ (setminus @ sK253 @ sK252))))),
% 6.45/2.19 introduced(definition,[],[choice_axiom])).
% 6.45/2.19 thf(f472,plain,(
% 6.45/2.19 (uniqinunit = $true) & (subPowSU = $true) & (omegaSAx = $true) & (upairsetIR = $true) & (setadjoinSub = $true) & (upairsetE = $true) & (exuI2 = $true) & (prop2setE = $true) & (subsetE2 = $true) & (setoftrueEq = $true) & (binunionRsub = $true) & (binunionIR = $true) & (eqimpsubset2 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (nonemptyImpWitness = $true) & (notinsingleton = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (nonemptyE1 = $true) & (emptysetE = $true) & (emptyInPowerset = $true) & (bs114d = $true) & (setadjoinIL = $true) & (binintersectSubset5 = $true) & (omega__Cong = $true) & (binintersectSubset1 = $true) & (setextAx = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (binintersectSubset2 = $true) & (sepInPowerset = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (binintersectRsub = $true) & (noeltsimpempty = $true) & (subsetI1 = $true) & (in__Cong = $true) & (prop2set2propI = $true) & (setadjoin__Cong = $true) & (omegaIndAx = $true) & (nonemptyI1 = $true) & (dsetconstrI = $true) & (binunionE = $true) & (subsetemptysetimpeq = $true) & (upairsetIL = $true) & (powersetE = $true) & (inCongP = $true) & (powersetE1 = $true) & (quantDeMorgan4 = $true) & (subset2powerset = $true) & (notsubsetI = $true) & (binintersectSubset3 = $true) & (emptyset__Cong = $true) & (dsetconstrER = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) & ($true != (in @ X0 @ X1)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) & (powersetAx = $true) & (exuE3e = $true) & (setadjoinIR = $true) & (binintersectSubset4 = $true) & (emptysetsubset = $true) & (emptyE1 = $true) & (setadjoinSub2 = $true) & (exuE1 = $true) & (setunionE = $true) & (exuI3 = $true) & (dsetconstrEL = $true) & (notdallE = $true) & (sepSubset = $true) & (exuE3u = $true) & (inPowerset = $true) & (eqinunit = $true) & (setadjoinOr = $true) & (wellorderingAx = $true) & (powersetsubset = $true) & (binunionEcases = $true) & (exuEu = $true) & (setunionI = $true) & (powersetI = $true) & (binintersectEL = $true) & (upairset2IR = $true) & (singletonsswitch = $true) & (foundationAx = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (quantDeMorgan2 = $true) & (exuI1 = $true) & (replAx = $true) & (subsetE = $true) & (binunionLsub = $true) & (exuE2 = $true) & (powersetI1 = $true) & (binunionIL = $true) & (setextsub = $true) & (disjointsetsI1 = $true) & (descrp = $true) & (exu__Cong = $true) & (setbeta = $true) & (quantDeMorgan1 = $true) & (omega0Ax = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (powerset__Cong = $true) & (notdexE = $true) & (subsetRefl = $true) & (notequalI1 = $true) & (vacuousDall = $true) & (setadjoinAx = $true) & (quantDeMorgan3 = $true) & (subsetI2 = $true) & (setunion__Cong = $true) & (setunionAx = $true) & (setext = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (notequalI2 = $true)),
% 6.45/2.19 inference(flattening,[status(thm)],[f471])).
% 6.45/2.19 thf(f471,plain,(
% 6.45/2.19 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1)) != $true) & ($true != (in @ X0 @ X1))) & ((in @ X0 @ X2) = $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)),
% 6.45/2.19 inference(ennf_transformation,[status(thm)],[f360])).
% 6.45/2.19 thf(f360,plain,(
% 6.45/2.19 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (($true != (in @ X0 @ X1)) => ((in @ X0 @ (setminus @ X2 @ X1)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.45/2.19 inference(flattening,[status(thm)],[f125])).
% 6.45/2.19 thf(f125,plain,(
% 6.45/2.19 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) = $true) => (~($true = (in @ X0 @ X1)) => ((in @ X0 @ (setminus @ X2 @ X1)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.45/2.19 inference(fool_elimination,[status(thm)],[f124])).
% 6.45/2.19 thf(f124,plain,(
% 6.45/2.19 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.45/2.19 inference(rectify,[status(thm)],[f122])).
% 6.45/2.19 thf(f122,negated_conjecture,(
% 6.45/2.19 ~(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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.45/2.19 inference(negated_conjecture,[status(cth)],[f121])).
% 6.45/2.19 thf(f121,conjecture,(
% 6.45/2.19 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 => ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.45/2.19 file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',setminusI)).
% 6.45/2.19 thf(f3609,plain,(
% 6.45/2.19 ((in @ sK251 @ sK252) = $true)),
% 6.45/2.19 inference(subsumption_resolution,[status(thm)],[f3604,f1644])).
% 6.45/2.19 thf(f1644,plain,(
% 6.45/2.19 ((in @ sK251 @ sK253) = $true)),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f1005])).
% 6.45/2.19 thf(f3604,plain,(
% 6.45/2.19 ((in @ sK251 @ sK253) != $true) | ((in @ sK251 @ sK252) = $true)),
% 6.45/2.19 inference(not_proxy_clausification,[status(thm)],[f3603])).
% 6.45/2.19 thf(f3603,plain,(
% 6.45/2.19 ($true != (~ (in @ sK251 @ sK252))) | ((in @ sK251 @ sK253) != $true)),
% 6.45/2.19 inference(beta_eta_normalization,[status(thm)],[f3602])).
% 6.45/2.19 thf(f3602,plain,(
% 6.45/2.19 ((in @ sK251 @ sK253) != $true) | (((^[Y0 : $i]: (~ (in @ Y0 @ sK252))) @ sK251) != $true)),
% 6.45/2.19 inference(trivial_inequality_removal,[status(thm)],[f3597])).
% 6.45/2.19 thf(f3597,plain,(
% 6.45/2.19 (((^[Y0 : $i]: (~ (in @ Y0 @ sK252))) @ sK251) != $true) | ($true != $true) | ((in @ sK251 @ sK253) != $true)),
% 6.45/2.19 inference(superposition,[status(thm)],[f2352,f2269])).
% 6.45/2.19 thf(f2269,plain,(
% 6.45/2.19 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (dsetconstr @ X4 @ X3))) | ((in @ X5 @ X4) != $true) | ($true != (X3 @ X5))) )),
% 6.45/2.19 inference(beta_eta_normalization,[status(thm)],[f2268])).
% 6.45/2.19 thf(f2268,plain,(
% 6.45/2.19 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ($true != (X3 @ X5)) | ($true = (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) )),
% 6.45/2.19 inference(trivial_inequality_removal,[status(thm)],[f1965])).
% 6.45/2.19 thf(f1965,plain,(
% 6.45/2.19 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ X4) != $true) | ($true != (X3 @ X5)) | ($true != $true) | ($true = (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))))) )),
% 6.45/2.19 inference(definition_unfolding,[status(thm)],[f1337,f1657])).
% 6.45/2.19 thf(f1657,plain,(
% 6.45/2.19 (dsetconstrI = $true)),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f1005])).
% 6.45/2.19 thf(f1337,plain,(
% 6.45/2.19 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ((in @ X5 @ X4) != $true) | ($true != (X3 @ X5)) | (dsetconstrI != $true)) )),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f722])).
% 6.45/2.19 thf(f722,plain,(
% 6.45/2.19 ((dsetconstrI = $true) | (((in @ sK118 @ (dsetconstr @ sK117 @ (^[Y0 : $i]: (sK116 @ Y0)))) != $true) & ($true = (in @ sK118 @ sK117)) & ($true = (sK116 @ sK118)))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ((in @ X5 @ X4) != $true) | ($true != (X3 @ X5))) | (dsetconstrI != $true))),
% 6.45/2.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117,sK118])],[f720,f721])).
% 6.45/2.19 thf(f721,plain,(
% 6.45/2.19 ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) & ($true = (in @ X2 @ X1)) & ((X0 @ X2) = $true)) => (((in @ sK118 @ (dsetconstr @ sK117 @ (^[Y0 : $i]: (sK116 @ Y0)))) != $true) & ($true = (in @ sK118 @ sK117)) & ($true = (sK116 @ sK118)))),
% 6.45/2.19 introduced(definition,[],[choice_axiom])).
% 6.45/2.19 thf(f720,plain,(
% 6.45/2.19 ((dsetconstrI = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) & ($true = (in @ X2 @ X1)) & ((X0 @ X2) = $true))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0))))) | ((in @ X5 @ X4) != $true) | ($true != (X3 @ X5))) | (dsetconstrI != $true))),
% 6.45/2.19 inference(rectify,[status(thm)],[f719])).
% 6.45/2.19 thf(f719,plain,(
% 6.45/2.19 ((dsetconstrI = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) & ($true = (in @ X2 @ X1)) & ((X0 @ X2) = $true))) & (! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | ($true != (in @ X2 @ X1)) | ((X0 @ X2) != $true)) | (dsetconstrI != $true))),
% 6.45/2.19 inference(nnf_transformation,[status(thm)],[f407])).
% 6.45/2.19 thf(f407,plain,(
% 6.45/2.19 (dsetconstrI = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | ($true != (in @ X2 @ X1)) | ((X0 @ X2) != $true))),
% 6.45/2.19 inference(flattening,[status(thm)],[f406])).
% 6.45/2.19 thf(f406,plain,(
% 6.45/2.19 (dsetconstrI = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) | ((X0 @ X2) != $true)) | ($true != (in @ X2 @ X1)))),
% 6.45/2.19 inference(ennf_transformation,[status(thm)],[f272])).
% 6.45/2.19 thf(f272,plain,(
% 6.45/2.19 (dsetconstrI = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => (((X0 @ X2) = $true) => ($true = (in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))))),
% 6.45/2.19 inference(fool_elimination,[status(thm)],[f271])).
% 6.45/2.19 thf(f271,plain,(
% 6.45/2.19 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 6.45/2.19 inference(rectify,[status(thm)],[f14])).
% 6.45/2.19 thf(f14,axiom,(
% 6.45/2.19 (dsetconstrI = ! [X0 : $i > $o,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 6.45/2.19 file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',dsetconstrI)).
% 6.45/2.19 thf(f2352,plain,(
% 6.45/2.19 ($true != (in @ sK251 @ (dsetconstr @ sK253 @ (^[Y0 : $i]: (~ (in @ Y0 @ sK252))))))),
% 6.45/2.19 inference(beta_eta_normalization,[status(thm)],[f2101])).
% 6.45/2.19 thf(f2101,plain,(
% 6.45/2.19 ($true != (in @ sK251 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))) @ sK253 @ sK252)))),
% 6.45/2.19 inference(definition_unfolding,[status(thm)],[f1642,f1365])).
% 6.45/2.19 thf(f1365,plain,(
% 6.45/2.19 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f237])).
% 6.45/2.19 thf(f237,plain,(
% 6.45/2.19 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 6.45/2.19 inference(fool_elimination,[status(thm)],[f236])).
% 6.45/2.19 thf(f236,plain,(
% 6.45/2.19 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X1))))) = setminus)),
% 6.45/2.19 inference(rectify,[status(thm)],[f120])).
% 6.45/2.19 thf(f120,axiom,(
% 6.45/2.19 ((^[X3 : $i, X4 : $i] : (dsetconstr @ X3 @ (^[X1 : $i] : (~(in @ X1 @ X4))))) = setminus)),
% 6.45/2.19 file('/export/starexec/sandbox/tmp/tmp.sy2j5HuxXp/DTF2THF_7545.p',setminus)).
% 6.45/2.19 thf(f1642,plain,(
% 6.45/2.19 ($true != (in @ sK251 @ (setminus @ sK253 @ sK252)))),
% 6.45/2.19 inference(cnf_transformation,[status(thm)],[f1005])).
% 6.45/2.19 % SZS output end Proof for DTF2THF_7545
% 6.45/2.19 % (7691)------------------------------
% 6.45/2.19 % (7691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.19 % (7691)Termination reason: Refutation
% 6.45/2.19
% 6.45/2.19 % (7691)Memory used [KB]: 8187
% 6.45/2.19 % (7691)Time elapsed: 0.147 s
% 6.45/2.19 % (7691)Instructions burned: 280 (million)
% 6.45/2.19 % (7691)------------------------------
% 6.45/2.19 % (7691)------------------------------
% 6.45/2.19 % (7643)Success in time 0.654 s
%------------------------------------------------------------------------------