%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU677^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:12 AM UTC 2026
% Result : Theorem 69.28s 11.09s
% Output : Refutation 69.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 3473 ( 919 equ; 0 cnn)
% Maximal formula atoms : 195 ( 48 avg)
% Number of connectives : 2228 ( 54 ~; 36 |; 626 &; 688 @)
% ( 6 <=>; 797 =>; 0 <=; 0 <~>)
% Maximal formula depth : 202 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 355 ( 350 usr; 205 con; 0-4 aty)
% ( 10 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 251 ( 156 ^; 69 !; 26 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_243,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_244,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_248,type,
sK4: $i > $o ).
thf(func_def_282,type,
sK38: $i > $i > $o ).
thf(func_def_286,type,
sK42: $i > $i ).
thf(func_def_288,type,
sK44: $i > $i ).
thf(func_def_291,type,
sK47: $i > $o ).
thf(func_def_305,type,
sK61: $i > $o ).
thf(func_def_318,type,
sK74: $i > $i ).
thf(func_def_319,type,
sK75: $i > $i ).
thf(func_def_320,type,
sK76: $i > $i ).
thf(func_def_321,type,
sK77: $i > $i ).
thf(func_def_322,type,
sK78: $i > $i > $i ).
thf(func_def_323,type,
sK79: $i > $i > $i > $i ).
thf(func_def_324,type,
sK80: $i > $i > $i > $i ).
thf(func_def_325,type,
sK81: $i > $i ).
thf(func_def_326,type,
sK82: $i > $i ).
thf(func_def_327,type,
sK83: $i > $i ).
thf(func_def_328,type,
sK84: $i > $i ).
thf(func_def_329,type,
sK85: $i > $i ).
thf(func_def_330,type,
sK86: $i > $i ).
thf(func_def_331,type,
sK87: $i > $i ).
thf(func_def_332,type,
sK88: $i > $i > $i ).
thf(func_def_333,type,
sK89: $i > $i > $i ).
thf(func_def_334,type,
sK90: $i > $i > $i ).
thf(func_def_335,type,
sK91: $i > $i > $i > $i ).
thf(func_def_336,type,
sK92: $i > $i > $i ).
thf(func_def_347,type,
sK103: $i > $i > $i ).
thf(func_def_368,type,
sK124: ( $i > $o ) > $i ).
thf(func_def_369,type,
sK125: $i > $o ).
thf(func_def_370,type,
sK126: $i > $i ).
thf(func_def_379,type,
sK135: $i > ( $i > $o ) > $i ).
thf(func_def_380,type,
sK136: $i > $o ).
thf(func_def_388,type,
sK144: $i > $o ).
thf(func_def_390,type,
sK146: ( $i > $o ) > $i > $i ).
thf(func_def_432,type,
sK188: $i > $o ).
thf(func_def_434,type,
sK190: ( $i > $o ) > $i ).
thf(func_def_435,type,
sK191: ( $i > $o ) > $i ).
thf(func_def_442,type,
sK198: $i > $i > $i ).
thf(func_def_447,type,
sK203: $i > $o ).
thf(func_def_454,type,
sK210: $i > $i > $i ).
thf(func_def_457,type,
sK213: $i > $o ).
thf(func_def_464,type,
sK220: $i > $i > $o ).
thf(func_def_471,type,
sK227: $i > $i ).
thf(func_def_474,type,
sK230: $i > $o ).
thf(func_def_495,type,
sK251: $i > $i > $o ).
thf(func_def_508,type,
sK264: $i > $o ).
thf(func_def_510,type,
sK266: $i > $i > $o ).
thf(func_def_515,type,
sK271: $i > ( $i > $o ) > $i ).
thf(func_def_516,type,
sK272: $i > $o ).
thf(func_def_519,type,
sK275: ( $i > $o ) > $i > $i ).
thf(func_def_520,type,
sK276: ( $i > $o ) > $i > $i ).
thf(func_def_522,type,
sK278: $i > $o ).
thf(func_def_525,type,
sK281: $i > $i > $o ).
thf(func_def_532,type,
sK288: $i > $o ).
thf(func_def_534,type,
sK290: $i > ( $i > $o ) > $i ).
thf(func_def_542,type,
sK298: $i > ( $i > $o ) > $i ).
thf(func_def_543,type,
sK299: $i > $o ).
thf(func_def_557,type,
sK313: $i > $i > $i ).
thf(func_def_570,type,
sK326: $i > $i ).
thf(func_def_574,type,
sK330: $i > $o ).
thf(func_def_575,type,
sK331: $i > $o ).
thf(func_def_576,type,
sK332: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_577,type,
sK333: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_581,type,
sK337: $i > $o ).
thf(func_def_582,type,
sK338: $i > $i ).
thf(func_def_583,type,
sK339: ( $i > $o ) > $i ).
thf(func_def_584,type,
sK340: $i > $i ).
thf(func_def_604,type,
sK360: $i > ( $i > $o ) > $i ).
thf(func_def_605,type,
sK361: $i > ( $i > $o ) > $i ).
thf(func_def_606,type,
sK362: $i > $o ).
thf(func_def_613,type,
sK369: $i > $o ).
thf(func_def_614,type,
sK370: ( $i > $o ) > $i ).
thf(func_def_617,type,
sK373: $i > $o ).
thf(func_def_621,type,
sK377: $i > $i > $i > $i ).
thf(func_def_622,type,
sK378: $i > $i > $i > $i ).
thf(func_def_633,type,
sK389: $i > $i > $i ).
thf(func_def_636,type,
sK392: $i > $i > $i ).
thf(func_def_637,type,
sK393: $i > $i > $i ).
thf(func_def_645,type,
sK401: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_646,type,
sK402: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_647,type,
sK403: $i > $o ).
thf(func_def_648,type,
sK404: $i > $o ).
thf(func_def_649,type,
sK405: $i > $o ).
thf(func_def_651,type,
sK407: $i > ( $i > $o ) > $i ).
thf(func_def_674,type,
sK430: $i > $o ).
thf(func_def_675,type,
sK431: $i > $o ).
thf(func_def_676,type,
sK432: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_677,type,
sK433: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_685,type,
sK441: ( $i > $o ) > $i > $i ).
thf(func_def_687,type,
sK443: $i > $o ).
thf(func_def_707,type,
sK463: $i > $o ).
thf(func_def_709,type,
sK465: ( $i > $o ) > $i > $i ).
thf(func_def_710,type,
sK466: $i > $i > $o ).
thf(func_def_712,type,
sK468: $i > $i ).
thf(func_def_713,type,
sK469: $i > $i ).
thf(func_def_714,type,
sK470: $i > ( $i > $i > $o ) > $i ).
thf(func_def_715,type,
sK471: $i > ( $i > $i > $o ) > $i ).
thf(func_def_716,type,
sK472: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_717,type,
sK473: $i > $o ).
thf(func_def_724,type,
sK480: $i > $o ).
thf(func_def_730,type,
sK486: $i > ( $i > $o ) > $i ).
thf(func_def_731,type,
sK487: $i > $o ).
thf(func_def_735,type,
sK491: $i > $i > $i ).
thf(func_def_742,type,
sK498: $i > $i ).
thf(func_def_744,type,
sK500: $o > $i > $i > $i ).
thf(func_def_749,type,
sK505: $i > $i > $o ).
thf(func_def_753,type,
sK509: ( $i > $o ) > $i > $i > $i ).
thf(func_def_756,type,
sK512: $i > $o ).
thf(func_def_770,type,
sK526: $i > $o ).
thf(func_def_772,type,
sK528: $i > $i > $o ).
thf(func_def_777,type,
sK533: $i > $o ).
thf(func_def_780,type,
sK536: $i > $i ).
thf(func_def_782,type,
sK538: $i > $i > $i ).
thf(func_def_801,type,
ph556:
!>[X0: $tType] : X0 ).
thf(f9451,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9449,f8291]) ).
thf(f8291,plain,
( ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f8287]) ).
thf(f8287,plain,
( ( ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f617,f5039]) ).
thf(f5039,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK243 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK241
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK242 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK241
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK242 ) ) ) ) ) ) )
& ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f4370]) ).
thf(f4370,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK243
@ sK241
@ sK242 )
= $true ),
inference(definition_unfolding,[status(thm)],[f2779,f3354]) ).
thf(f3354,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f3002,f3353,f3007]) ).
thf(f3007,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
thf(f549,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f548]) ).
thf(f548,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f186]) ).
thf(f186,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',breln) ).
thf(f3353,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f3319,f3138]) ).
thf(f3138,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f421]) ).
thf(f421,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f420]) ).
thf(f420,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f156]) ).
thf(f156,axiom,
( singleton
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( ( setadjoin @ X1 @ emptyset )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',singleton) ).
thf(f3319,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
thf(f277,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f276]) ).
thf(f276,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f158]) ).
thf(f158,axiom,
( ex1
= ( ^ [X3: $i,X0: $i > $o] :
( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',ex1) ).
thf(f3002,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f307]) ).
thf(f307,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
& ( breln @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f306]) ).
thf(f306,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
& ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f194]) ).
thf(f194,axiom,
( func
= ( ^ [X3: $i,X4: $i,X12: $i] :
( ( breln @ X3 @ X4 @ X12 )
& ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ex1 @ X4
@ ^ [X2: $i] : ( in @ ( kpair @ X1 @ X2 ) @ X12 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',func) ).
thf(f2779,plain,
( ( func @ sK243 @ sK241 @ sK242 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1225]) ).
thf(f1225,plain,
( ( binintersectI = $true )
& ( ksndpairEq = $true )
& ( emptyinunitempty = $true )
& ( apProp = $true )
& ( powersetI = $true )
& ( powersetsubset = $true )
& ( dpsetconstrER = $true )
& ( binunionRsub = $true )
& ( setadjoinIR = $true )
& ( notsubsetI = $true )
& ( kfstpairEq = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( kpairsurjEq = $true )
& ( notdallE = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( setminusI = $true )
& ( setukpairinjL = $true )
& ( binintersectRsub = $true )
& ( setminusELneg = $true )
& ( nonemptyImpWitness = $true )
& ( foundationAx = $true )
& ( binunionLsub = $true )
& ( setminusILneg = $true )
& ( setbeta = $true )
& ( setukpairIL = $true )
& ( emptyE1 = $true )
& ( setadjoinOr = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( symdiffE = $true )
& ( descrp = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR11 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( powersetAx = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( vacuousDall = $true )
& ( powersetE1 = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dpsetconstrEL1 = $true )
& ( replAx = $true )
& ( upairequniteq = $true )
& ( setminusEL = $true )
& ( emptysetAx = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyset__Cong = $true )
& ( setminusSubset1 = $true )
& ( exuE3e = $true )
& ( setminusSubset2 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectER = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairsurjEq = $true )
& ( setminusERneg = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR12 = $true )
& ( subset2powerset = $true )
& ( binunionE = $true )
& ( setunionE = $true )
& ( singletoninpowunion = $true )
& ( exuI3 = $true )
& ( binintersectSubset1 = $true )
& ( powerset__Cong = $true )
& ( omegaIndAx = $true )
& ( setminusER = $true )
& ( cartprodsndin = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR2 = $true )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( descr__Cong = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( symdiffIneg2 = $true )
& ( singletonprop = $true )
& ( nonemptyI = $true )
& ( infuncsetfunc = $true )
& ( quantDeMorgan4 = $true )
& ( setextsub = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( in__Cong = $true )
& ( setunionE2 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE2 = $true )
& ( symdiffI2 = $true )
& ( binunionIR = $true )
& ( exuI2 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinAx = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( dsetconstrI = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( ex1I = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL2 = $true )
& ( singletoninpowerset = $true )
& ( subsetTrans = $true )
& ( kpairp = $true )
& ( binintersectSubset5 = $true )
& ( app = $true )
& ( emptyInPowerset = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( kfstsingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( setadjoinSub = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( setminusLsub = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( binintersectEL = $true )
& ( cartprodpairmemEL = $true )
& ( prop2setE = $true )
& ( emptysetimpfalse = $true )
& ( symdiffIneg1 = $true )
& ( ap2p = $true )
& ( funcImageSingleton = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( emptyinPowerset = $true )
& ( subsetI1 = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( setextAx = $true )
& ( bs114d = $true )
& ( cartprodsndpairEq = $true )
& ( ex1I2 = $true )
& ( ksndsingleton = $true )
& ( subsetE = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset3 = $true )
& ( setukpairIR = $true )
& ( omegaSAx = $true )
& ( dpsetconstrSub = $true )
& ( upairsubunion = $true )
& ( eqimpsubset1 = $true )
& ( exuEu = $true )
& ( setext = $true )
& ( upairset2IR = $true )
& ( secondinupair = $true )
& ( ( func @ sK243 @ sK241 @ sK242 )
= $true )
& ( ( in @ sK242 @ ( funcSet @ sK243 @ sK241 ) )
!= $true )
& ( upairset2E = $true )
& ( noeltsimpempty = $true )
& ( notinemptyset = $true )
& ( omega0Ax = $true )
& ( setunionsingleton = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrI = $true )
& ( sepSubset = $true )
& ( subsetI2 = $true )
& ( setoftrueEq = $true )
& ( powersetE = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( upairsetE = $true )
& ( cartprodfstpairEq = $true )
& ( binunionIL = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton2 = $true )
& ( cartprodmempair = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem1 = $true )
& ( dpsetconstrERa = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem2 = $true )
& ( notequalI1 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR1 = $true )
& ( upairsetIR = $true )
& ( setminusIRneg = $true )
& ( setukpairinjR = $true )
& ( upairinpowunion = $true )
& ( symdiffI1 = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( kpairiskpair = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK241,sK242,sK243])],[f774,f1224]) ).
thf(f1224,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true ) )
=> ( ( ( func @ sK243 @ sK241 @ sK242 )
= $true )
& ( ( in @ sK242 @ ( funcSet @ sK243 @ sK241 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f774,plain,
( ( binintersectI = $true )
& ( ksndpairEq = $true )
& ( emptyinunitempty = $true )
& ( apProp = $true )
& ( powersetI = $true )
& ( powersetsubset = $true )
& ( dpsetconstrER = $true )
& ( binunionRsub = $true )
& ( setadjoinIR = $true )
& ( notsubsetI = $true )
& ( kfstpairEq = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( kpairsurjEq = $true )
& ( notdallE = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( setminusI = $true )
& ( setukpairinjL = $true )
& ( binintersectRsub = $true )
& ( setminusELneg = $true )
& ( nonemptyImpWitness = $true )
& ( foundationAx = $true )
& ( binunionLsub = $true )
& ( setminusILneg = $true )
& ( setbeta = $true )
& ( setukpairIL = $true )
& ( emptyE1 = $true )
& ( setadjoinOr = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( symdiffE = $true )
& ( descrp = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR11 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( powersetAx = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( vacuousDall = $true )
& ( powersetE1 = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dpsetconstrEL1 = $true )
& ( replAx = $true )
& ( upairequniteq = $true )
& ( setminusEL = $true )
& ( emptysetAx = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyset__Cong = $true )
& ( setminusSubset1 = $true )
& ( exuE3e = $true )
& ( setminusSubset2 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectER = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairsurjEq = $true )
& ( setminusERneg = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR12 = $true )
& ( subset2powerset = $true )
& ( binunionE = $true )
& ( setunionE = $true )
& ( singletoninpowunion = $true )
& ( exuI3 = $true )
& ( binintersectSubset1 = $true )
& ( powerset__Cong = $true )
& ( omegaIndAx = $true )
& ( setminusER = $true )
& ( cartprodsndin = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR2 = $true )
& ( setadjoin__Cong = $true )
& ( exuE2 = $true )
& ( descr__Cong = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( symdiffIneg2 = $true )
& ( singletonprop = $true )
& ( nonemptyI = $true )
& ( infuncsetfunc = $true )
& ( quantDeMorgan4 = $true )
& ( setextsub = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( notequalI2 = $true )
& ( cartprodmempair1 = $true )
& ( in__Cong = $true )
& ( setunionE2 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE2 = $true )
& ( symdiffI2 = $true )
& ( binunionIR = $true )
& ( exuI2 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinAx = $true )
& ( notdexE = $true )
& ( ex1E1 = $true )
& ( dsetconstrI = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( ex1I = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL2 = $true )
& ( singletoninpowerset = $true )
& ( subsetTrans = $true )
& ( kpairp = $true )
& ( binintersectSubset5 = $true )
& ( app = $true )
& ( emptyInPowerset = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( kfstsingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( setadjoinSub = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( setminusLsub = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( binintersectEL = $true )
& ( cartprodpairmemEL = $true )
& ( prop2setE = $true )
& ( emptysetimpfalse = $true )
& ( symdiffIneg1 = $true )
& ( ap2p = $true )
& ( funcImageSingleton = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( emptyinPowerset = $true )
& ( subsetI1 = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( setextAx = $true )
& ( bs114d = $true )
& ( cartprodsndpairEq = $true )
& ( ex1I2 = $true )
& ( ksndsingleton = $true )
& ( subsetE = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset3 = $true )
& ( setukpairIR = $true )
& ( omegaSAx = $true )
& ( dpsetconstrSub = $true )
& ( upairsubunion = $true )
& ( eqimpsubset1 = $true )
& ( exuEu = $true )
& ( setext = $true )
& ( upairset2IR = $true )
& ( secondinupair = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true ) )
& ( upairset2E = $true )
& ( noeltsimpempty = $true )
& ( notinemptyset = $true )
& ( omega0Ax = $true )
& ( setunionsingleton = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrI = $true )
& ( sepSubset = $true )
& ( subsetI2 = $true )
& ( setoftrueEq = $true )
& ( powersetE = $true )
& ( subsetRefl = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( upairsetE = $true )
& ( cartprodfstpairEq = $true )
& ( binunionIL = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton2 = $true )
& ( cartprodmempair = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem1 = $true )
& ( dpsetconstrERa = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem2 = $true )
& ( notequalI1 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR1 = $true )
& ( upairsetIR = $true )
& ( setminusIRneg = $true )
& ( setukpairinjR = $true )
& ( upairinpowunion = $true )
& ( symdiffI1 = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( kpairiskpair = $true ) ),
inference(flattening,[status(thm)],[f773]) ).
thf(f773,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
!= $true ) )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f399]) ).
thf(f399,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
=> ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f398]) ).
thf(f398,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X2 @ X0 @ X1 )
=> ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f203]) ).
thf(f203,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ! [X4: $i,X13: $i,X3: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ( in @ X13 @ ( funcSet @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f202]) ).
thf(f202,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ! [X4: $i,X13: $i,X3: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ( in @ X13 @ ( funcSet @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',funcinfuncset) ).
thf(f617,plain,
! [X2: $o,X1: $o] :
( ( $false
= ( X1
& X2 ) )
| ( $true = X2 ) ),
introduced(definition,[],[logical_and_proxy_axiom]) ).
thf(f9449,plain,
( ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f9447]) ).
thf(f9447,plain,
( ( $true != $true )
| ( ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f8305,f4865]) ).
thf(f4865,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4267]) ).
thf(f4267,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2639,f2742]) ).
thf(f2742,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f1225]) ).
thf(f2639,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1096]) ).
thf(f1096,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( subset @ sK162 @ sK161 )
= $true )
& ( ( in @ sK162 @ ( powerset @ sK161 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161,sK162])],[f1094,f1095]) ).
thf(f1095,plain,
( ? [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
=> ( ( ( subset @ sK162 @ sK161 )
= $true )
& ( ( in @ sK162 @ ( powerset @ sK161 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1094,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1093]) ).
thf(f1093,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f839]) ).
thf(f839,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f559]) ).
thf(f559,plain,
( ( powersetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f558]) ).
thf(f558,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f95]) ).
thf(f95,axiom,
( powersetI1
= ( ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',powersetI1) ).
thf(f8305,plain,
( ( in @ sK242 @ ( powerset @ ( cartprod @ sK243 @ sK241 ) ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f8304,f5039]) ).
thf(f8304,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK243 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ sK241
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK242 ) ) )
& ( in @ Y1
@ ( dsetconstr @ sK241
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ sK242 ) ) ) ) ) ) )
& ( subset @ sK242 @ ( cartprod @ sK243 @ sK241 ) ) )
!= $true )
| ( ( in @ sK242 @ ( powerset @ ( cartprod @ sK243 @ sK241 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f8297]) ).
thf(f8297,plain,
( ( ( in @ sK242 @ ( powerset @ ( cartprod @ sK243 @ sK241 ) ) )
!= $true )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK243 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK241
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK241
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK243 @ sK241 ) ) )
@ sK242 )
!= $true ) ),
inference(superposition,[status(thm)],[f5055,f4863]) ).
thf(f4863,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f4862]) ).
thf(f4862,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4395]) ).
thf(f4395,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true != $true )
| ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2961,f2909]) ).
thf(f2909,plain,
setbeta = $true,
inference(cnf_transformation,[status(thm)],[f1225]) ).
thf(f2961,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( setbeta != $true ) ),
inference(cnf_transformation,[status(thm)],[f1261]) ).
thf(f1261,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( setbeta != $true ) )
& ( ( setbeta = $true )
| ( ( ( in @ sK265 @ sK263 )
= $true )
& ( ( sK264 @ sK265 )
!= ( in @ sK265
@ ( dsetconstr @ sK263
@ ^ [Y0: $i] : ( sK264 @ Y0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK263,sK264,sK265])],[f1259,f1260]) ).
thf(f1260,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( ( X4 @ X5 )
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) )
=> ( ( ( in @ sK265 @ sK263 )
= $true )
& ( ( sK264 @ sK265 )
!= ( in @ sK265
@ ( dsetconstr @ sK263
@ ^ [Y0: $i] : ( sK264 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1259,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( setbeta != $true ) )
& ( ( setbeta = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( ( X4 @ X5 )
!= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1258]) ).
thf(f1258,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( setbeta != $true ) )
& ( ( setbeta = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f699]) ).
thf(f699,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
<=> ( setbeta = $true ) ),
inference(ennf_transformation,[status(thm)],[f295]) ).
thf(f295,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
<=> ( setbeta = $true ) ),
inference(fool_elimination,[status(thm)],[f294]) ).
thf(f294,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
<=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= setbeta ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,axiom,
! [X3: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
<=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) )
= setbeta ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',setbeta) ).
thf(f5055,plain,
( ( in @ sK242
@ ( dsetconstr @ ( powerset @ ( cartprod @ sK243 @ sK241 ) )
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK243 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ sK241
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ sK241
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ sK243 @ sK241 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f4371]) ).
thf(f4371,plain,
( ( in @ sK242
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) )
@ sK243
@ sK241 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f2778,f3355]) ).
thf(f3355,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) )
& ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1
@ Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2986,f3354]) ).
thf(f2986,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
thf(f432,plain,
( funcSet
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y2: $i] : ( func @ Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f431]) ).
thf(f431,plain,
( funcSet
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X0 @ X1 ) )
@ ^ [X2: $i] : ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f195]) ).
thf(f195,axiom,
( funcSet
= ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X3 @ X4 ) )
@ ^ [X13: $i] : ( func @ X3 @ X4 @ X13 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',funcSet) ).
thf(f2778,plain,
( ( in @ sK242 @ ( funcSet @ sK243 @ sK241 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU677^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:30:54 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU677^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Functions - Lambda Abstraction
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : (! A:i.! B:i.! f:i.func A B f -> in f (funcSet A B))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC179g [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.80 v8.2.0, 0.92 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 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
% 0.18/0.45 % Syntax : Number of formulae : 431 ( 201 unt; 229 typ; 201 def)
% 0.18/0.45 % Number of atoms : 1062 ( 294 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 195 ( 5 avg)
% 0.18/0.45 % Number of connectives : 1925 ( 47 ~; 7 |; 36 &;1355 @)
% 0.18/0.45 % ( 14 <=>; 466 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 201 ( 2 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 232 ( 229 usr; 197 con; 0-4 aty)
% 0.18/0.45 % Number of variables : 626 ( 71 ^; 519 !; 36 ?; 626 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=231
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu_type,type,
% 0.18/0.45 exu: ( $i > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu,definition,
% 0.18/0.45 ( exu
% 0.18/0.45 = ( ^ [Xphi: $i > $o] :
% 0.18/0.45 ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx_type,type,
% 0.18/0.45 setextAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx,definition,
% 0.18/0.45 ( setextAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 <=> ( in @ Xx @ B ) )
% 0.18/0.45 => ( A = B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx_type,type,
% 0.18/0.45 emptysetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx,definition,
% 0.18/0.45 ( emptysetAx
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin_type,type,
% 0.18/0.45 setadjoin: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx_type,type,
% 0.18/0.45 setadjoinAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx,definition,
% 0.18/0.45 ( setadjoinAx
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 <=> ( ( Xy = Xx )
% 0.18/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx_type,type,
% 0.18/0.45 powersetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx,definition,
% 0.18/0.45 ( powersetAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.45 <=> ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunion_type,type,
% 0.18/0.45 setunion: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx_type,type,
% 0.18/0.45 setunionAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx,definition,
% 0.18/0.45 ( setunionAx
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.45 <=> ? [B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omega_type,type,
% 0.18/0.45 omega: $i ).
% 0.18/0.45
% 0.18/0.45 thf(omega0Ax_type,type,
% 0.18/0.45 omega0Ax: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omega0Ax,definition,
% 0.18/0.45 ( omega0Ax
% 0.18/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omegaSAx_type,type,
% 0.18/0.45 omegaSAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omegaSAx,definition,
% 0.18/0.45 ( omegaSAx
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ omega )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(omegaIndAx_type,type,
% 0.18/0.45 omegaIndAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(omegaIndAx,definition,
% 0.18/0.45 ( omegaIndAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( ( in @ emptyset @ A )
% 0.18/0.45 & ! [Xx: $i] :
% 0.18/0.45 ( ( ( in @ Xx @ omega )
% 0.18/0.45 & ( in @ Xx @ A ) )
% 0.18/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ omega )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(replAx_type,type,
% 0.18/0.45 replAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(replAx,definition,
% 0.18/0.45 ( replAx
% 0.18/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( exu
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.45 => ? [B: $i] :
% 0.18/0.45 ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 <=> ? [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ A )
% 0.18/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx_type,type,
% 0.18/0.45 foundationAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(foundationAx,definition,
% 0.18/0.45 ( foundationAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.45 => ? [B: $i] :
% 0.18/0.45 ( ( in @ B @ A )
% 0.18/0.45 & ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(wellorderingAx_type,type,
% 0.18/0.45 wellorderingAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(wellorderingAx,definition,
% 0.18/0.45 ( wellorderingAx
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ? [B: $i] :
% 0.18/0.45 ( ! [C: $i] :
% 0.18/0.45 ( ( in @ C @ B )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ A ) ) )
% 0.18/0.45 & ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( ( in @ Xx @ A )
% 0.18/0.45 & ( in @ Xy @ A ) )
% 0.18/0.45 => ( ! [C: $i] :
% 0.18/0.45 ( ( in @ C @ B )
% 0.18/0.45 => ( ( in @ Xx @ C )
% 0.18/0.45 <=> ( in @ Xy @ C ) ) )
% 0.18/0.45 => ( Xx = Xy ) ) )
% 0.18/0.45 & ! [C: $i,D: $i] :
% 0.18/0.45 ( ( ( in @ C @ B )
% 0.18/0.45 & ( in @ D @ B ) )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ D ) )
% 0.18/0.45 | ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ D )
% 0.18/0.45 => ( in @ Xx @ C ) ) ) )
% 0.18/0.45 & ! [C: $i] :
% 0.18/0.45 ( ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ C )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.45 => ? [D: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ D @ B )
% 0.18/0.45 & ( in @ Xx @ C )
% 0.18/0.45 & ~ ? [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ D )
% 0.18/0.45 & ( in @ Xy @ C ) )
% 0.18/0.45 & ! [E: $i] :
% 0.18/0.45 ( ( in @ E @ B )
% 0.18/0.45 => ( ! [Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ E )
% 0.18/0.45 => ( in @ Xy @ D ) )
% 0.18/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(descr_type,type,
% 0.18/0.45 descr: ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(descrp_type,type,
% 0.18/0.45 descrp: $o ).
% 0.18/0.45
% 0.18/0.45 thf(descrp,definition,
% 0.18/0.45 ( descrp
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ( Xphi
% 0.18/0.45 @ ( descr
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstr_type,type,
% 0.18/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI_type,type,
% 0.18/0.45 dsetconstrI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrI,definition,
% 0.18/0.45 ( dsetconstrI
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 => ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL_type,type,
% 0.18/0.45 dsetconstrEL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrEL,definition,
% 0.18/0.45 ( dsetconstrEL
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER_type,type,
% 0.18/0.45 dsetconstrER: $o ).
% 0.18/0.45
% 0.18/0.45 thf(dsetconstrER,definition,
% 0.18/0.45 ( dsetconstrER
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE1_type,type,
% 0.18/0.45 exuE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE1,definition,
% 0.18/0.45 ( exuE1
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set_type,type,
% 0.18/0.45 prop2set: $o > $i ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setE_type,type,
% 0.18/0.45 prop2setE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setE,definition,
% 0.18/0.45 ( prop2setE
% 0.18/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.45 => Xphi ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetE_type,type,
% 0.18/0.45 emptysetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetE,definition,
% 0.18/0.45 ( emptysetE
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetimpfalse_type,type,
% 0.18/0.45 emptysetimpfalse: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetimpfalse,definition,
% 0.18/0.45 ( emptysetimpfalse
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => $false ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notinemptyset_type,type,
% 0.18/0.45 notinemptyset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notinemptyset,definition,
% 0.18/0.45 ( notinemptyset
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3e_type,type,
% 0.18/0.45 exuE3e: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3e,definition,
% 0.18/0.45 ( exuE3e
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setext_type,type,
% 0.18/0.45 setext: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setext,definition,
% 0.18/0.45 ( setext
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ B ) )
% 0.18/0.45 => ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyI_type,type,
% 0.18/0.45 emptyI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyI,definition,
% 0.18/0.45 ( emptyI
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ A )
% 0.18/0.45 => ( A = emptyset ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(noeltsimpempty_type,type,
% 0.18/0.45 noeltsimpempty: $o ).
% 0.18/0.45
% 0.18/0.45 thf(noeltsimpempty,definition,
% 0.18/0.45 ( noeltsimpempty
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ A )
% 0.18/0.45 => ( A = emptyset ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setbeta_type,type,
% 0.18/0.45 setbeta: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setbeta,definition,
% 0.18/0.45 ( setbeta
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( in @ Xx
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty_type,type,
% 0.18/0.45 nonempty: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonempty,definition,
% 0.18/0.45 ( nonempty
% 0.18/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1_type,type,
% 0.18/0.45 nonemptyE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyE1,definition,
% 0.18/0.45 ( nonemptyE1
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI_type,type,
% 0.18/0.45 nonemptyI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI,definition,
% 0.18/0.45 ( nonemptyI
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 => ( nonempty
% 0.18/0.45 @ ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI1_type,type,
% 0.18/0.45 nonemptyI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyI1,definition,
% 0.18/0.45 ( nonemptyI1
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIL_type,type,
% 0.18/0.45 setadjoinIL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIL,definition,
% 0.18/0.45 ( setadjoinIL
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinunitempty_type,type,
% 0.18/0.45 emptyinunitempty: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinunitempty,definition,
% 0.18/0.45 ( emptyinunitempty
% 0.18/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIR_type,type,
% 0.18/0.45 setadjoinIR: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinIR,definition,
% 0.18/0.45 ( setadjoinIR
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ A )
% 0.18/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinE_type,type,
% 0.18/0.45 setadjoinE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinE,definition,
% 0.18/0.45 ( setadjoinE
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 => ! [Xphi: $o] :
% 0.18/0.45 ( ( ( Xy = Xx )
% 0.18/0.45 => Xphi )
% 0.18/0.45 => ( ( ( in @ Xy @ A )
% 0.18/0.45 => Xphi )
% 0.18/0.45 => Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinOr_type,type,
% 0.18/0.45 setadjoinOr: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinOr,definition,
% 0.18/0.45 ( setadjoinOr
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 => ( ( Xy = Xx )
% 0.18/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setoftrueEq_type,type,
% 0.18/0.45 setoftrueEq: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setoftrueEq,definition,
% 0.18/0.45 ( setoftrueEq
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : $true )
% 0.18/0.45 = A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powersetI_type,type,
% 0.18/0.45 powersetI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetI,definition,
% 0.18/0.45 ( powersetI
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) )
% 0.18/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinPowerset_type,type,
% 0.18/0.45 emptyinPowerset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyinPowerset,definition,
% 0.18/0.45 ( emptyinPowerset
% 0.18/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyInPowerset_type,type,
% 0.18/0.45 emptyInPowerset: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyInPowerset,definition,
% 0.18/0.45 ( emptyInPowerset
% 0.18/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powersetE_type,type,
% 0.18/0.45 powersetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetE,definition,
% 0.18/0.45 ( powersetE
% 0.18/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.45 => ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI_type,type,
% 0.18/0.45 setunionI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI,definition,
% 0.18/0.45 ( setunionI
% 0.18/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( ( in @ B @ A )
% 0.18/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunionE_type,type,
% 0.18/0.45 setunionE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionE,definition,
% 0.18/0.45 ( setunionE
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.45 => ! [Xphi: $o] :
% 0.18/0.45 ( ! [B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( ( in @ B @ A )
% 0.18/0.45 => Xphi ) )
% 0.18/0.45 => Xphi ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(subPowSU_type,type,
% 0.18/0.45 subPowSU: $o ).
% 0.18/0.45
% 0.18/0.45 thf(subPowSU,definition,
% 0.18/0.45 ( subPowSU
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE2_type,type,
% 0.18/0.45 exuE2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE2,definition,
% 0.18/0.45 ( exuE2
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyImpWitness_type,type,
% 0.18/0.45 nonemptyImpWitness: $o ).
% 0.18/0.45
% 0.18/0.45 thf(nonemptyImpWitness,definition,
% 0.18/0.45 ( nonemptyImpWitness
% 0.18/0.45 = ( ! [A: $i] :
% 0.18/0.45 ( ( nonempty @ A )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & $true ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(uniqinunit_type,type,
% 0.18/0.45 uniqinunit: $o ).
% 0.18/0.45
% 0.18/0.45 thf(uniqinunit,definition,
% 0.18/0.45 ( uniqinunit
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notinsingleton_type,type,
% 0.18/0.45 notinsingleton: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notinsingleton,definition,
% 0.18/0.45 ( notinsingleton
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx != Xy )
% 0.18/0.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(eqinunit_type,type,
% 0.18/0.45 eqinunit: $o ).
% 0.18/0.45
% 0.18/0.45 thf(eqinunit,definition,
% 0.18/0.45 ( eqinunit
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(singletonsswitch_type,type,
% 0.18/0.45 singletonsswitch: $o ).
% 0.18/0.45
% 0.18/0.45 thf(singletonsswitch,definition,
% 0.18/0.45 ( singletonsswitch
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetE_type,type,
% 0.18/0.45 upairsetE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetE,definition,
% 0.18/0.45 ( upairsetE
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.45 => ( ( Xz = Xx )
% 0.18/0.45 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIL_type,type,
% 0.18/0.45 upairsetIL: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIL,definition,
% 0.18/0.45 ( upairsetIL
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIR_type,type,
% 0.18/0.45 upairsetIR: $o ).
% 0.18/0.45
% 0.18/0.45 thf(upairsetIR,definition,
% 0.18/0.45 ( upairsetIR
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyE1_type,type,
% 0.18/0.45 emptyE1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyE1,definition,
% 0.18/0.45 ( emptyE1
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) )
% 0.18/0.45 => ( ( ( dsetconstr @ A
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 = emptyset )
% 0.18/0.45 => $false ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(vacuousDall_type,type,
% 0.18/0.45 vacuousDall: $o ).
% 0.18/0.45
% 0.18/0.45 thf(vacuousDall,definition,
% 0.18/0.45 ( vacuousDall
% 0.18/0.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ emptyset )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan1_type,type,
% 0.18/0.45 quantDeMorgan1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan1,definition,
% 0.18/0.45 ( quantDeMorgan1
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan2_type,type,
% 0.18/0.45 quantDeMorgan2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan2,definition,
% 0.18/0.45 ( quantDeMorgan2
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ~ ( Xphi @ Xx ) )
% 0.18/0.45 => ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan3_type,type,
% 0.18/0.45 quantDeMorgan3: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan3,definition,
% 0.18/0.45 ( quantDeMorgan3
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan4_type,type,
% 0.18/0.45 quantDeMorgan4: $o ).
% 0.18/0.45
% 0.18/0.45 thf(quantDeMorgan4,definition,
% 0.18/0.45 ( quantDeMorgan4
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ~ ( Xphi @ Xx ) )
% 0.18/0.45 => ~ ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setI_type,type,
% 0.18/0.45 prop2setI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2setI,definition,
% 0.18/0.45 ( prop2setI
% 0.18/0.45 = ( ! [Xphi: $o] :
% 0.18/0.45 ( Xphi
% 0.18/0.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(set2prop_type,type,
% 0.18/0.45 set2prop: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set2propI_type,type,
% 0.18/0.45 prop2set2propI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(prop2set2propI,definition,
% 0.18/0.45 ( prop2set2propI
% 0.18/0.45 = ( ! [Xphi: $o] :
% 0.18/0.45 ( Xphi
% 0.18/0.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notdexE_type,type,
% 0.18/0.45 notdexE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notdexE,definition,
% 0.18/0.45 ( notdexE
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ( Xphi @ Xx ) )
% 0.18/0.45 => ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(notdallE_type,type,
% 0.18/0.45 notdallE: $o ).
% 0.18/0.45
% 0.18/0.45 thf(notdallE,definition,
% 0.18/0.45 ( notdallE
% 0.18/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.45 ( ~ ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 => ( Xphi @ Xx ) )
% 0.18/0.45 => ? [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuI1_type,type,
% 0.18/0.45 exuI1: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuI1,definition,
% 0.18/0.45 ( exuI1
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) )
% 0.18/0.45 => ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuI3_type,type,
% 0.18/0.45 exuI3: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuI3,definition,
% 0.18/0.45 ( exuI3
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.18/0.45 => ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 => ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) )
% 0.18/0.45 => ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuI2_type,type,
% 0.18/0.45 exuI2: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuI2,definition,
% 0.18/0.45 ( exuI2
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ? [Xx: $i] :
% 0.18/0.45 ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 <=> ( Xy = Xx ) )
% 0.18/0.45 => ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(inCongP_type,type,
% 0.18/0.45 inCongP: $o ).
% 0.18/0.45
% 0.18/0.45 thf(inCongP,definition,
% 0.18/0.45 ( inCongP
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( ( in @ Xx @ A )
% 0.18/0.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(in__Cong_type,type,
% 0.18/0.45 in__Cong: $o ).
% 0.18/0.45
% 0.18/0.45 thf(in__Cong,definition,
% 0.18/0.45 ( in__Cong
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( ( in @ Xx @ A )
% 0.18/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3u_type,type,
% 0.18/0.45 exuE3u: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exuE3u,definition,
% 0.18/0.45 ( exuE3u
% 0.18/0.45 = ( ! [Xphi: $i > $o] :
% 0.18/0.45 ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 => ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 => ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(exu__Cong_type,type,
% 0.18/0.45 exu__Cong: $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu__Cong,definition,
% 0.18/0.45 ( exu__Cong
% 0.18/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ( ( Xphi @ Xx )
% 0.18/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.45 => ( ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.45 <=> ( exu
% 0.18/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset__Cong_type,type,
% 0.18/0.45 emptyset__Cong: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset__Cong,definition,
% 0.18/0.45 ( emptyset__Cong
% 0.18/0.45 = ( emptyset = emptyset ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin__Cong_type,type,
% 0.18/0.45 setadjoin__Cong: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin__Cong,definition,
% 0.18/0.45 ( setadjoin__Cong
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xx = Xy )
% 0.18/0.45 => ! [Xz: $i,Xu: $i] :
% 0.18/0.45 ( ( Xz = Xu )
% 0.18/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.18/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(powerset__Cong_type,type,
% 0.18/0.46 powerset__Cong: $o ).
% 0.18/0.46
% 0.18/0.46 thf(powerset__Cong,definition,
% 0.18/0.46 ( powerset__Cong
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( A = B )
% 0.18/0.46 => ( ( powerset @ A )
% 0.18/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setunion__Cong_type,type,
% 0.18/0.46 setunion__Cong: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setunion__Cong,definition,
% 0.18/0.46 ( setunion__Cong
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( A = B )
% 0.18/0.46 => ( ( setunion @ A )
% 0.18/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(omega__Cong_type,type,
% 0.18/0.46 omega__Cong: $o ).
% 0.18/0.46
% 0.18/0.46 thf(omega__Cong,definition,
% 0.18/0.46 ( omega__Cong
% 0.18/0.46 = ( omega = omega ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(exuEu_type,type,
% 0.18/0.46 exuEu: $o ).
% 0.18/0.46
% 0.18/0.46 thf(exuEu,definition,
% 0.18/0.46 ( exuEu
% 0.18/0.46 = ( ! [Xphi: $i > $o] :
% 0.18/0.46 ( ( exu
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 => ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( Xphi @ Xx )
% 0.18/0.46 => ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(descr__Cong_type,type,
% 0.18/0.46 descr__Cong: $o ).
% 0.18/0.46
% 0.18/0.46 thf(descr__Cong,definition,
% 0.18/0.46 ( descr__Cong
% 0.18/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( Xx = Xy )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.18/0.46 => ( ( exu
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 => ( ( exu
% 0.18/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.18/0.46 => ( ( descr
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 = ( descr
% 0.18/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstr__Cong_type,type,
% 0.18/0.46 dsetconstr__Cong: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstr__Cong,definition,
% 0.18/0.46 ( dsetconstr__Cong
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( A = B )
% 0.18/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( Xx = Xy )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.18/0.46 => ( ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 = ( dsetconstr @ B
% 0.18/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subset_type,type,
% 0.18/0.46 subset: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(disjoint_type,type,
% 0.18/0.46 disjoint: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(setsmeet_type,type,
% 0.18/0.46 setsmeet: $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetI1_type,type,
% 0.18/0.46 subsetI1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetI1,definition,
% 0.18/0.46 ( subsetI1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ B ) )
% 0.18/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(eqimpsubset2_type,type,
% 0.18/0.46 eqimpsubset2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(eqimpsubset2,definition,
% 0.18/0.46 ( eqimpsubset2
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( A = B )
% 0.18/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(eqimpsubset1_type,type,
% 0.18/0.46 eqimpsubset1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(eqimpsubset1,definition,
% 0.18/0.46 ( eqimpsubset1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( A = B )
% 0.18/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetI2_type,type,
% 0.18/0.46 subsetI2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetI2,definition,
% 0.18/0.46 ( subsetI2
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ B ) )
% 0.18/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(emptysetsubset_type,type,
% 0.18/0.46 emptysetsubset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(emptysetsubset,definition,
% 0.18/0.46 ( emptysetsubset
% 0.18/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE_type,type,
% 0.18/0.46 subsetE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE,definition,
% 0.18/0.46 ( subsetE
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE2_type,type,
% 0.18/0.46 subsetE2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetE2,definition,
% 0.18/0.46 ( subsetE2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(notsubsetI_type,type,
% 0.18/0.46 notsubsetI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(notsubsetI,definition,
% 0.18/0.46 ( notsubsetI
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(notequalI1_type,type,
% 0.18/0.46 notequalI1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(notequalI1,definition,
% 0.18/0.46 ( notequalI1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ~ ( subset @ A @ B )
% 0.18/0.46 => ( A != B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(notequalI2_type,type,
% 0.18/0.46 notequalI2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(notequalI2,definition,
% 0.18/0.46 ( notequalI2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ( A != B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetRefl_type,type,
% 0.18/0.46 subsetRefl: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetRefl,definition,
% 0.18/0.46 ( subsetRefl
% 0.18/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetTrans_type,type,
% 0.18/0.46 subsetTrans: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetTrans,definition,
% 0.18/0.46 ( subsetTrans
% 0.18/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( subset @ B @ C )
% 0.18/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoinSub_type,type,
% 0.18/0.46 setadjoinSub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoinSub,definition,
% 0.18/0.46 ( setadjoinSub
% 0.18/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoinSub2_type,type,
% 0.18/0.46 setadjoinSub2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setadjoinSub2,definition,
% 0.18/0.46 ( setadjoinSub2
% 0.18/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subset2powerset_type,type,
% 0.18/0.46 subset2powerset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subset2powerset,definition,
% 0.18/0.46 ( subset2powerset
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setextsub_type,type,
% 0.18/0.46 setextsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setextsub,definition,
% 0.18/0.46 ( setextsub
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( subset @ B @ A )
% 0.18/0.46 => ( A = B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(subsetemptysetimpeq_type,type,
% 0.18/0.46 subsetemptysetimpeq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(subsetemptysetimpeq,definition,
% 0.18/0.46 ( subsetemptysetimpeq
% 0.18/0.46 = ( ! [A: $i] :
% 0.18/0.46 ( ( subset @ A @ emptyset )
% 0.18/0.46 => ( A = emptyset ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(powersetI1_type,type,
% 0.18/0.46 powersetI1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(powersetI1,definition,
% 0.18/0.46 ( powersetI1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ B @ A )
% 0.18/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(powersetE1_type,type,
% 0.18/0.46 powersetE1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(powersetE1,definition,
% 0.18/0.46 ( powersetE1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(inPowerset_type,type,
% 0.18/0.46 inPowerset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(inPowerset,definition,
% 0.18/0.46 ( inPowerset
% 0.18/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(powersetsubset_type,type,
% 0.18/0.46 powersetsubset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(powersetsubset,definition,
% 0.18/0.46 ( powersetsubset
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(sepInPowerset_type,type,
% 0.18/0.46 sepInPowerset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(sepInPowerset,definition,
% 0.18/0.46 ( sepInPowerset
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( in
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(sepSubset_type,type,
% 0.18/0.46 sepSubset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(sepSubset,definition,
% 0.18/0.46 ( sepSubset
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( subset
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunion_type,type,
% 0.18/0.46 binunion: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(binunionIL_type,type,
% 0.18/0.46 binunionIL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionIL,definition,
% 0.18/0.46 ( binunionIL
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(upairset2IR_type,type,
% 0.18/0.46 upairset2IR: $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairset2IR,definition,
% 0.18/0.46 ( upairset2IR
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunionIR_type,type,
% 0.18/0.46 binunionIR: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionIR,definition,
% 0.18/0.46 ( binunionIR
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ B )
% 0.18/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunionEcases_type,type,
% 0.18/0.46 binunionEcases: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionEcases,definition,
% 0.18/0.46 ( binunionEcases
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.18/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.46 => ( ( ( in @ Xx @ A )
% 0.18/0.46 => Xphi )
% 0.18/0.46 => ( ( ( in @ Xx @ B )
% 0.18/0.46 => Xphi )
% 0.18/0.46 => Xphi ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunionE_type,type,
% 0.18/0.46 binunionE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionE,definition,
% 0.18/0.46 ( binunionE
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.18/0.46 => ( ( in @ Xx @ A )
% 0.18/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunionLsub_type,type,
% 0.18/0.46 binunionLsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionLsub,definition,
% 0.18/0.46 ( binunionLsub
% 0.18/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binunionRsub_type,type,
% 0.18/0.46 binunionRsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binunionRsub,definition,
% 0.18/0.46 ( binunionRsub
% 0.18/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersect_type,type,
% 0.18/0.46 binintersect: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectI_type,type,
% 0.18/0.46 binintersectI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectI,definition,
% 0.18/0.46 ( binintersectI
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ( in @ Xx @ B )
% 0.18/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset5_type,type,
% 0.18/0.46 binintersectSubset5: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset5,definition,
% 0.18/0.46 ( binintersectSubset5
% 0.18/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.46 ( ( subset @ C @ A )
% 0.18/0.46 => ( ( subset @ C @ B )
% 0.18/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectEL_type,type,
% 0.18/0.46 binintersectEL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectEL,definition,
% 0.18/0.46 ( binintersectEL
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectLsub_type,type,
% 0.18/0.46 binintersectLsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectLsub,definition,
% 0.18/0.46 ( binintersectLsub
% 0.18/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset2_type,type,
% 0.18/0.46 binintersectSubset2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset2,definition,
% 0.18/0.46 ( binintersectSubset2
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( binintersect @ A @ B )
% 0.18/0.46 = A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset3_type,type,
% 0.18/0.46 binintersectSubset3: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset3,definition,
% 0.18/0.46 ( binintersectSubset3
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( ( binintersect @ A @ B )
% 0.18/0.46 = B )
% 0.18/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectER_type,type,
% 0.18/0.46 binintersectER: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectER,definition,
% 0.18/0.46 ( binintersectER
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.18/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(disjointsetsI1_type,type,
% 0.18/0.46 disjointsetsI1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(disjointsetsI1,definition,
% 0.18/0.46 ( disjointsetsI1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ~ ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( in @ Xx @ B ) )
% 0.18/0.46 => ( ( binintersect @ A @ B )
% 0.18/0.46 = emptyset ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectRsub_type,type,
% 0.18/0.46 binintersectRsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectRsub,definition,
% 0.18/0.46 ( binintersectRsub
% 0.18/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset4_type,type,
% 0.18/0.46 binintersectSubset4: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset4,definition,
% 0.18/0.46 ( binintersectSubset4
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ B @ A )
% 0.18/0.46 => ( ( binintersect @ A @ B )
% 0.18/0.46 = B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset1_type,type,
% 0.18/0.46 binintersectSubset1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(binintersectSubset1,definition,
% 0.18/0.46 ( binintersectSubset1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( ( binintersect @ A @ B )
% 0.18/0.46 = A )
% 0.18/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(bs114d_type,type,
% 0.18/0.46 bs114d: $o ).
% 0.18/0.46
% 0.18/0.46 thf(bs114d,definition,
% 0.18/0.46 ( bs114d
% 0.18/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.18/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.18/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(regular_type,type,
% 0.18/0.46 regular: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminus_type,type,
% 0.18/0.46 setminus: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(setminusI_type,type,
% 0.18/0.46 setminusI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusI,definition,
% 0.18/0.46 ( setminusI
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusEL_type,type,
% 0.18/0.46 setminusEL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusEL,definition,
% 0.18/0.46 ( setminusEL
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusER_type,type,
% 0.18/0.46 setminusER: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusER,definition,
% 0.18/0.46 ( setminusER
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusSubset2_type,type,
% 0.18/0.46 setminusSubset2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusSubset2,definition,
% 0.18/0.46 ( setminusSubset2
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( subset @ A @ B )
% 0.18/0.46 => ( ( setminus @ A @ B )
% 0.18/0.46 = emptyset ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusERneg_type,type,
% 0.18/0.46 setminusERneg: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusERneg,definition,
% 0.18/0.46 ( setminusERneg
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.46 => ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusELneg_type,type,
% 0.18/0.46 setminusELneg: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusELneg,definition,
% 0.18/0.46 ( setminusELneg
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusILneg_type,type,
% 0.18/0.46 setminusILneg: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusILneg,definition,
% 0.18/0.46 ( setminusILneg
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ~ ( in @ Xx @ A )
% 0.18/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusIRneg_type,type,
% 0.18/0.46 setminusIRneg: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusIRneg,definition,
% 0.18/0.46 ( setminusIRneg
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ B )
% 0.18/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusLsub_type,type,
% 0.18/0.46 setminusLsub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusLsub,definition,
% 0.18/0.46 ( setminusLsub
% 0.18/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setminusSubset1_type,type,
% 0.18/0.46 setminusSubset1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setminusSubset1,definition,
% 0.18/0.46 ( setminusSubset1
% 0.18/0.46 = ( ! [A: $i,B: $i] :
% 0.18/0.46 ( ( ( setminus @ A @ B )
% 0.18/0.46 = emptyset )
% 0.18/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(symdiff_type,type,
% 0.18/0.46 symdiff: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffE_type,type,
% 0.18/0.46 symdiffE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffE,definition,
% 0.18/0.46 ( symdiffE
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.18/0.46 => ! [Xphi: $o] :
% 0.18/0.46 ( ( ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => Xphi ) )
% 0.18/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.18/0.46 => ( ( in @ Xx @ B )
% 0.18/0.46 => Xphi ) )
% 0.18/0.46 => Xphi ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffI1_type,type,
% 0.18/0.46 symdiffI1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffI1,definition,
% 0.18/0.46 ( symdiffI1
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffI2_type,type,
% 0.18/0.46 symdiffI2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffI2,definition,
% 0.18/0.46 ( symdiffI2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ~ ( in @ Xx @ A )
% 0.18/0.46 => ( ( in @ Xx @ B )
% 0.18/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffIneg1_type,type,
% 0.18/0.46 symdiffIneg1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffIneg1,definition,
% 0.18/0.46 ( symdiffIneg1
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ( in @ Xx @ B )
% 0.18/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffIneg2_type,type,
% 0.18/0.46 symdiffIneg2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(symdiffIneg2,definition,
% 0.18/0.46 ( symdiffIneg2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ~ ( in @ Xx @ A )
% 0.18/0.46 => ( ~ ( in @ Xx @ B )
% 0.18/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(iskpair_type,type,
% 0.18/0.46 iskpair: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(secondinupair_type,type,
% 0.18/0.46 secondinupair: $o ).
% 0.18/0.46
% 0.18/0.46 thf(secondinupair,definition,
% 0.18/0.46 ( secondinupair
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairIL_type,type,
% 0.18/0.46 setukpairIL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairIL,definition,
% 0.18/0.46 ( setukpairIL
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairIR_type,type,
% 0.18/0.46 setukpairIR: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairIR,definition,
% 0.18/0.46 ( setukpairIR
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(kpairiskpair_type,type,
% 0.18/0.46 kpairiskpair: $o ).
% 0.18/0.46
% 0.18/0.46 thf(kpairiskpair,definition,
% 0.18/0.46 ( kpairiskpair
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(kpair_type,type,
% 0.18/0.46 kpair: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(kpairp_type,type,
% 0.18/0.46 kpairp: $o ).
% 0.18/0.46
% 0.18/0.46 thf(kpairp,definition,
% 0.18/0.46 ( kpairp
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprod_type,type,
% 0.18/0.46 cartprod: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(singletonsubset_type,type,
% 0.18/0.46 singletonsubset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(singletonsubset,definition,
% 0.18/0.46 ( singletonsubset
% 0.18/0.46 = ( ! [A: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singletoninpowerset_type,type,
% 0.18/0.46 singletoninpowerset: $o ).
% 0.18/0.46
% 0.18/0.46 thf(singletoninpowerset,definition,
% 0.18/0.46 ( singletoninpowerset
% 0.18/0.46 = ( ! [A: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singletoninpowunion_type,type,
% 0.18/0.46 singletoninpowunion: $o ).
% 0.18/0.46
% 0.18/0.46 thf(singletoninpowunion,definition,
% 0.18/0.46 ( singletoninpowunion
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(upairset2E_type,type,
% 0.18/0.46 upairset2E: $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairset2E,definition,
% 0.18/0.46 ( upairset2E
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.18/0.46 => ( ( Xz = Xx )
% 0.18/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(upairsubunion_type,type,
% 0.18/0.46 upairsubunion: $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairsubunion,definition,
% 0.18/0.46 ( upairsubunion
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(upairinpowunion_type,type,
% 0.18/0.46 upairinpowunion: $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairinpowunion,definition,
% 0.18/0.46 ( upairinpowunion
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem1_type,type,
% 0.18/0.46 ubforcartprodlem1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem1,definition,
% 0.18/0.46 ( ubforcartprodlem1
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem2_type,type,
% 0.18/0.46 ubforcartprodlem2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem2,definition,
% 0.18/0.46 ( ubforcartprodlem2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem3_type,type,
% 0.18/0.46 ubforcartprodlem3: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ubforcartprodlem3,definition,
% 0.18/0.46 ( ubforcartprodlem3
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairin_type,type,
% 0.18/0.46 cartprodpairin: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairin,definition,
% 0.18/0.46 ( cartprodpairin
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempair1_type,type,
% 0.18/0.46 cartprodmempair1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempair1,definition,
% 0.18/0.46 ( cartprodmempair1
% 0.18/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ? [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 & ( Xu
% 0.18/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempair_type,type,
% 0.18/0.46 cartprodmempair: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempair,definition,
% 0.18/0.46 ( cartprodmempair
% 0.18/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setunionE2_type,type,
% 0.18/0.46 setunionE2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setunionE2,definition,
% 0.18/0.46 ( setunionE2
% 0.18/0.46 = ( ! [A: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.46 => ? [X: $i] :
% 0.18/0.46 ( ( in @ X @ A )
% 0.18/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton1_type,type,
% 0.18/0.46 setunionsingleton1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton1,definition,
% 0.18/0.46 ( setunionsingleton1
% 0.18/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton2_type,type,
% 0.18/0.46 setunionsingleton2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton2,definition,
% 0.18/0.46 ( setunionsingleton2
% 0.18/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton_type,type,
% 0.18/0.46 setunionsingleton: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setunionsingleton,definition,
% 0.18/0.46 ( setunionsingleton
% 0.18/0.46 = ( ! [Xx: $i] :
% 0.18/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.18/0.46 = Xx ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singleton_type,type,
% 0.18/0.46 singleton: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(singleton,definition,
% 0.18/0.46 ( singleton
% 0.18/0.46 = ( ^ [A: $i] :
% 0.18/0.46 ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( A
% 0.18/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singletonprop_type,type,
% 0.18/0.46 singletonprop: $o ).
% 0.18/0.46
% 0.18/0.46 thf(singletonprop,definition,
% 0.18/0.46 ( singletonprop
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 => ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) )
% 0.18/0.46 => ( ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( Xphi @ Xx ) )
% 0.18/0.46 => ( singleton
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1_type,type,
% 0.18/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1,definition,
% 0.18/0.46 ( ex1
% 0.18/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( singleton
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1E1_type,type,
% 0.18/0.46 ex1E1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1E1,definition,
% 0.18/0.46 ( ex1E1
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( ( ex1 @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 => ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I_type,type,
% 0.18/0.46 ex1I: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I,definition,
% 0.18/0.46 ( ex1I
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 => ( ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xy = Xx ) ) )
% 0.18/0.46 => ( ex1 @ A
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I2_type,type,
% 0.18/0.46 ex1I2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ex1I2,definition,
% 0.18/0.46 ( ex1I2
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 => ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) )
% 0.18/0.46 => ( ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 & ( Xphi @ Xx ) )
% 0.18/0.46 => ( ex1 @ A
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(singletonsuniq_type,type,
% 0.18/0.46 singletonsuniq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(singletonsuniq,definition,
% 0.18/0.46 ( singletonsuniq
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.18/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(atmost1p_type,type,
% 0.18/0.46 atmost1p: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(atleast2p_type,type,
% 0.18/0.46 atleast2p: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(atmost2p_type,type,
% 0.18/0.46 atmost2p: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairsetp_type,type,
% 0.18/0.46 upairsetp: $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL1_type,type,
% 0.18/0.46 setukpairinjL1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL1,definition,
% 0.18/0.46 ( setukpairinjL1
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(kfstsingleton_type,type,
% 0.18/0.46 kfstsingleton: $o ).
% 0.18/0.46
% 0.18/0.46 thf(kfstsingleton,definition,
% 0.18/0.46 ( kfstsingleton
% 0.18/0.46 = ( ! [Xu: $i] :
% 0.18/0.46 ( ( iskpair @ Xu )
% 0.18/0.46 => ( singleton
% 0.18/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.18/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(theprop_type,type,
% 0.18/0.46 theprop: $o ).
% 0.18/0.46
% 0.18/0.46 thf(theprop,definition,
% 0.18/0.46 ( theprop
% 0.18/0.46 = ( ! [X: $i] :
% 0.18/0.46 ( ( singleton @ X )
% 0.18/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(kfst_type,type,
% 0.18/0.46 kfst: $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(kfstpairEq_type,type,
% 0.18/0.46 kfstpairEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(kfstpairEq,definition,
% 0.18/0.46 ( kfstpairEq
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.18/0.46 = Xx ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodfstin_type,type,
% 0.18/0.46 cartprodfstin: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodfstin,definition,
% 0.18/0.46 ( cartprodfstin
% 0.18/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL2_type,type,
% 0.18/0.46 setukpairinjL2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL2,definition,
% 0.18/0.46 ( setukpairinjL2
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL_type,type,
% 0.18/0.46 setukpairinjL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjL,definition,
% 0.18/0.46 ( setukpairinjL
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.18/0.46 = ( kpair @ Xz @ Xu ) )
% 0.18/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR11_type,type,
% 0.18/0.46 setukpairinjR11: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR11,definition,
% 0.18/0.46 ( setukpairinjR11
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( Xx = Xy )
% 0.18/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR12_type,type,
% 0.18/0.46 setukpairinjR12: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR12,definition,
% 0.18/0.46 ( setukpairinjR12
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( Xx = Xy )
% 0.18/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR1_type,type,
% 0.18/0.46 setukpairinjR1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR1,definition,
% 0.18/0.46 ( setukpairinjR1
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.46 => ( ( Xz = Xu )
% 0.18/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(upairequniteq_type,type,
% 0.18/0.46 upairequniteq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(upairequniteq,definition,
% 0.18/0.46 ( upairequniteq
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.18/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR2_type,type,
% 0.18/0.46 setukpairinjR2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR2,definition,
% 0.18/0.46 ( setukpairinjR2
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.18/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.18/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR_type,type,
% 0.18/0.46 setukpairinjR: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setukpairinjR,definition,
% 0.18/0.46 ( setukpairinjR
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.18/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.18/0.46 = ( kpair @ Xz @ Xu ) )
% 0.18/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ksndsingleton_type,type,
% 0.18/0.46 ksndsingleton: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ksndsingleton,definition,
% 0.18/0.46 ( ksndsingleton
% 0.18/0.46 = ( ! [Xu: $i] :
% 0.18/0.46 ( ( iskpair @ Xu )
% 0.18/0.46 => ( singleton
% 0.18/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.18/0.46 @ ^ [Xx: $i] :
% 0.18/0.46 ( Xu
% 0.18/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ksnd_type,type,
% 0.18/0.46 ksnd: $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(ksndpairEq_type,type,
% 0.18/0.46 ksndpairEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ksndpairEq,definition,
% 0.18/0.46 ( ksndpairEq
% 0.18/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.46 = Xy ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(kpairsurjEq_type,type,
% 0.18/0.46 kpairsurjEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(kpairsurjEq,definition,
% 0.18/0.46 ( kpairsurjEq
% 0.18/0.46 = ( ! [Xu: $i] :
% 0.18/0.46 ( ( iskpair @ Xu )
% 0.18/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.18/0.46 = Xu ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodsndin_type,type,
% 0.18/0.46 cartprodsndin: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodsndin,definition,
% 0.18/0.46 ( cartprodsndin
% 0.18/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairmemEL_type,type,
% 0.18/0.46 cartprodpairmemEL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairmemEL,definition,
% 0.18/0.46 ( cartprodpairmemEL
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairmemER_type,type,
% 0.18/0.46 cartprodpairmemER: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairmemER,definition,
% 0.18/0.46 ( cartprodpairmemER
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempaircEq_type,type,
% 0.18/0.46 cartprodmempaircEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodmempaircEq,definition,
% 0.18/0.46 ( cartprodmempaircEq
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( kpair @ Xx @ Xy )
% 0.18/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodfstpairEq_type,type,
% 0.18/0.46 cartprodfstpairEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodfstpairEq,definition,
% 0.18/0.46 ( cartprodfstpairEq
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.18/0.46 = Xx ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodsndpairEq_type,type,
% 0.18/0.46 cartprodsndpairEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodsndpairEq,definition,
% 0.18/0.46 ( cartprodsndpairEq
% 0.18/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.18/0.46 = Xy ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairsurjEq_type,type,
% 0.18/0.46 cartprodpairsurjEq: $o ).
% 0.18/0.46
% 0.18/0.46 thf(cartprodpairsurjEq,definition,
% 0.18/0.46 ( cartprodpairsurjEq
% 0.18/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.18/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.18/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.18/0.46 = Xu ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(breln_type,type,
% 0.18/0.46 breln: $i > $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(breln,definition,
% 0.18/0.46 ( breln
% 0.18/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstr_type,type,
% 0.18/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrI_type,type,
% 0.18/0.46 dpsetconstrI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrI,definition,
% 0.18/0.46 ( dpsetconstrI
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.18/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrSub_type,type,
% 0.18/0.46 dpsetconstrSub: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrSub,definition,
% 0.18/0.46 ( dpsetconstrSub
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.18/0.46 ( subset
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.18/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(setOfPairsIsBReln_type,type,
% 0.18/0.46 setOfPairsIsBReln: $o ).
% 0.18/0.46
% 0.18/0.46 thf(setOfPairsIsBReln,definition,
% 0.18/0.46 ( setOfPairsIsBReln
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.18/0.46 ( breln @ A @ B
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrERa_type,type,
% 0.18/0.46 dpsetconstrERa: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrERa,definition,
% 0.18/0.46 ( dpsetconstrERa
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ B )
% 0.18/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrEL1_type,type,
% 0.18/0.46 dpsetconstrEL1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrEL1,definition,
% 0.18/0.46 ( dpsetconstrEL1
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrEL2_type,type,
% 0.18/0.46 dpsetconstrEL2: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrEL2,definition,
% 0.18/0.46 ( dpsetconstrEL2
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrER_type,type,
% 0.18/0.46 dpsetconstrER: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dpsetconstrER,definition,
% 0.18/0.46 ( dpsetconstrER
% 0.18/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.18/0.46 @ ( dpsetconstr @ A @ B
% 0.18/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.18/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(func_type,type,
% 0.18/0.46 func: $i > $i > $i > $o ).
% 0.18/0.46
% 0.18/0.46 thf(func,definition,
% 0.18/0.46 ( func
% 0.18/0.46 = ( ^ [A: $i,B: $i,R: $i] :
% 0.18/0.46 ( ( breln @ A @ B @ R )
% 0.18/0.46 & ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ex1 @ B
% 0.18/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(funcSet_type,type,
% 0.18/0.46 funcSet: $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(funcSet,definition,
% 0.18/0.46 ( funcSet
% 0.18/0.46 = ( ^ [A: $i,B: $i] :
% 0.18/0.46 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 0.18/0.46 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(funcImageSingleton_type,type,
% 0.18/0.46 funcImageSingleton: $o ).
% 0.18/0.46
% 0.18/0.46 thf(funcImageSingleton,definition,
% 0.18/0.46 ( funcImageSingleton
% 0.18/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( func @ A @ B @ Xf )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( singleton
% 0.18/0.46 @ ( dsetconstr @ B
% 0.18/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(apProp_type,type,
% 0.18/0.46 apProp: $o ).
% 0.18/0.46
% 0.18/0.46 thf(apProp,definition,
% 0.18/0.46 ( apProp
% 0.18/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( func @ A @ B @ Xf )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in
% 0.18/0.46 @ ( setunion
% 0.18/0.46 @ ( dsetconstr @ B
% 0.18/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.18/0.46 @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ap_type,type,
% 0.18/0.46 ap: $i > $i > $i > $i > $i ).
% 0.18/0.46
% 0.18/0.46 thf(ap,definition,
% 0.18/0.46 ( ap
% 0.18/0.46 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 0.18/0.46 ( setunion
% 0.18/0.46 @ ( dsetconstr @ B
% 0.18/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(app_type,type,
% 0.18/0.46 app: $o ).
% 0.18/0.46
% 0.18/0.46 thf(app,definition,
% 0.18/0.46 ( app
% 0.18/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( func @ A @ B @ Xf )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(infuncsetfunc_type,type,
% 0.18/0.46 infuncsetfunc: $o ).
% 0.18/0.46
% 0.18/0.46 thf(infuncsetfunc,definition,
% 0.18/0.46 ( infuncsetfunc
% 0.18/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(ap2p_type,type,
% 0.18/0.46 ap2p: $o ).
% 0.18/0.46
% 0.18/0.46 thf(ap2p,definition,
% 0.18/0.46 ( ap2p
% 0.18/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(funcinfuncset,conjecture,
% 0.18/0.46 ( setextAx
% 0.18/0.46 => ( emptysetAx
% 0.18/0.46 => ( setadjoinAx
% 0.18/0.46 => ( powersetAx
% 0.18/0.46 => ( setunionAx
% 0.18/0.46 => ( omega0Ax
% 0.18/0.46 => ( omegaSAx
% 0.18/0.46 => ( omegaIndAx
% 0.18/0.46 => ( replAx
% 0.18/0.46 => ( foundationAx
% 0.18/0.46 => ( wellorderingAx
% 0.18/0.46 => ( descrp
% 0.18/0.46 => ( dsetconstrI
% 0.18/0.46 => ( dsetconstrEL
% 0.18/0.46 => ( dsetconstrER
% 0.18/0.46 => ( exuE1
% 0.18/0.46 => ( prop2setE
% 0.18/0.46 => ( emptysetE
% 0.18/0.46 => ( emptysetimpfalse
% 0.18/0.46 => ( notinemptyset
% 0.18/0.46 => ( exuE3e
% 0.18/0.46 => ( setext
% 0.18/0.46 => ( emptyI
% 0.18/0.46 => ( noeltsimpempty
% 0.18/0.46 => ( setbeta
% 0.18/0.46 => ( nonemptyE1
% 0.18/0.46 => ( nonemptyI
% 0.18/0.46 => ( nonemptyI1
% 0.18/0.46 => ( setadjoinIL
% 0.18/0.46 => ( emptyinunitempty
% 0.18/0.46 => ( setadjoinIR
% 0.18/0.46 => ( setadjoinE
% 0.18/0.46 => ( setadjoinOr
% 0.18/0.46 => ( setoftrueEq
% 0.18/0.46 => ( powersetI
% 0.18/0.46 => ( emptyinPowerset
% 0.18/0.46 => ( emptyInPowerset
% 0.18/0.46 => ( powersetE
% 0.18/0.46 => ( setunionI
% 0.18/0.46 => ( setunionE
% 0.18/0.46 => ( subPowSU
% 0.18/0.46 => ( exuE2
% 0.18/0.46 => ( nonemptyImpWitness
% 0.18/0.46 => ( uniqinunit
% 0.18/0.46 => ( notinsingleton
% 0.18/0.46 => ( eqinunit
% 0.18/0.46 => ( singletonsswitch
% 0.18/0.46 => ( upairsetE
% 0.18/0.46 => ( upairsetIL
% 0.18/0.46 => ( upairsetIR
% 0.18/0.46 => ( emptyE1
% 0.18/0.46 => ( vacuousDall
% 0.18/0.46 => ( quantDeMorgan1
% 0.18/0.46 => ( quantDeMorgan2
% 0.18/0.46 => ( quantDeMorgan3
% 0.18/0.46 => ( quantDeMorgan4
% 0.18/0.46 => ( prop2setI
% 0.18/0.46 => ( prop2set2propI
% 0.18/0.46 => ( notdexE
% 0.18/0.46 => ( notdallE
% 0.18/0.46 => ( exuI1
% 0.18/0.46 => ( exuI3
% 0.18/0.46 => ( exuI2
% 0.18/0.46 => ( inCongP
% 0.18/0.46 => ( in__Cong
% 0.18/0.46 => ( exuE3u
% 0.18/0.46 => ( exu__Cong
% 0.18/0.46 => ( emptyset__Cong
% 0.18/0.46 => ( setadjoin__Cong
% 0.18/0.46 => ( powerset__Cong
% 0.18/0.46 => ( setunion__Cong
% 0.18/0.46 => ( omega__Cong
% 0.18/0.46 => ( exuEu
% 0.18/0.46 => ( descr__Cong
% 0.18/0.46 => ( dsetconstr__Cong
% 0.18/0.46 => ( subsetI1
% 0.18/0.46 => ( eqimpsubset2
% 0.18/0.46 => ( eqimpsubset1
% 0.18/0.46 => ( subsetI2
% 0.18/0.46 => ( emptysetsubset
% 0.18/0.46 => ( subsetE
% 0.18/0.46 => ( subsetE2
% 0.18/0.46 => ( notsubsetI
% 0.18/0.46 => ( notequalI1
% 0.18/0.46 => ( notequalI2
% 0.18/0.46 => ( subsetRefl
% 0.18/0.46 => ( subsetTrans
% 0.18/0.46 => ( setadjoinSub
% 0.18/0.46 => ( setadjoinSub2
% 0.18/0.46 => ( subset2powerset
% 0.18/0.46 => ( setextsub
% 0.18/0.46 => ( subsetemptysetimpeq
% 0.18/0.46 => ( powersetI1
% 0.18/0.46 => ( powersetE1
% 0.18/0.46 => ( inPowerset
% 0.18/0.46 => ( powersetsubset
% 0.18/0.46 => ( sepInPowerset
% 0.18/0.46 => ( sepSubset
% 0.18/0.46 => ( binunionIL
% 0.18/0.46 => ( upairset2IR
% 0.18/0.46 => ( binunionIR
% 0.18/0.46 => ( binunionEcases
% 0.18/0.46 => ( binunionE
% 0.18/0.46 => ( binunionLsub
% 0.18/0.46 => ( binunionRsub
% 0.18/0.46 => ( binintersectI
% 0.18/0.46 => ( binintersectSubset5
% 0.18/0.46 => ( binintersectEL
% 0.18/0.46 => ( binintersectLsub
% 0.18/0.46 => ( binintersectSubset2
% 0.18/0.46 => ( binintersectSubset3
% 0.18/0.46 => ( binintersectER
% 0.18/0.46 => ( disjointsetsI1
% 0.18/0.46 => ( binintersectRsub
% 0.18/0.46 => ( binintersectSubset4
% 0.18/0.46 => ( binintersectSubset1
% 0.18/0.46 => ( bs114d
% 0.18/0.46 => ( setminusI
% 0.18/0.46 => ( setminusEL
% 0.18/0.46 => ( setminusER
% 0.18/0.46 => ( setminusSubset2
% 0.18/0.46 => ( setminusERneg
% 0.18/0.46 => ( setminusELneg
% 0.18/0.46 => ( setminusILneg
% 0.18/0.46 => ( setminusIRneg
% 0.18/0.46 => ( setminusLsub
% 0.18/0.46 => ( setminusSubset1
% 0.18/0.46 => ( symdiffE
% 0.18/0.46 => ( symdiffI1
% 0.18/0.46 => ( symdiffI2
% 0.18/0.46 => ( symdiffIneg1
% 0.18/0.46 => ( symdiffIneg2
% 0.18/0.46 => ( secondinupair
% 0.18/0.46 => ( setukpairIL
% 0.18/0.46 => ( setukpairIR
% 0.18/0.46 => ( kpairiskpair
% 0.18/0.46 => ( kpairp
% 0.18/0.46 => ( singletonsubset
% 0.18/0.46 => ( singletoninpowerset
% 0.18/0.46 => ( singletoninpowunion
% 0.18/0.46 => ( upairset2E
% 0.18/0.46 => ( upairsubunion
% 0.18/0.46 => ( upairinpowunion
% 0.18/0.46 => ( ubforcartprodlem1
% 0.18/0.46 => ( ubforcartprodlem2
% 0.18/0.46 => ( ubforcartprodlem3
% 0.18/0.46 => ( cartprodpairin
% 0.18/0.46 => ( cartprodmempair1
% 0.18/0.46 => ( cartprodmempair
% 0.18/0.46 => ( setunionE2
% 0.18/0.46 => ( setunionsingleton1
% 0.18/0.46 => ( setunionsingleton2
% 0.18/0.46 => ( setunionsingleton
% 0.18/0.46 => ( singletonprop
% 0.18/0.46 => ( ex1E1
% 0.18/0.46 => ( ex1I
% 0.18/0.46 => ( ex1I2
% 0.18/0.46 => ( singletonsuniq
% 0.18/0.46 => ( setukpairinjL1
% 0.18/0.46 => ( kfstsingleton
% 0.18/0.46 => ( theprop
% 0.18/0.46 => ( kfstpairEq
% 0.18/0.46 => ( cartprodfstin
% 0.18/0.46 => ( setukpairinjL2
% 0.18/0.46 => ( setukpairinjL
% 0.18/0.46 => ( setukpairinjR11
% 0.18/0.46 => ( setukpairinjR12
% 0.18/0.46 => ( setukpairinjR1
% 0.18/0.46 => ( upairequniteq
% 0.18/0.46 => ( setukpairinjR2
% 0.18/0.46 => ( setukpairinjR
% 0.18/0.46 => ( ksndsingleton
% 0.18/0.46 => ( ksndpairEq
% 0.18/0.46 => ( kpairsurjEq
% 0.18/0.46 => ( cartprodsndin
% 0.18/0.46 => ( cartprodpairmemEL
% 0.18/0.46 => ( cartprodpairmemER
% 0.18/0.46 => ( cartprodmempaircEq
% 0.18/0.46 => ( cartprodfstpairEq
% 0.18/0.46 => ( cartprodsndpairEq
% 0.18/0.46 => ( cartprodpairsurjEq
% 0.18/0.46 => ( dpsetconstrI
% 0.18/0.46 => ( dpsetconstrSub
% 0.18/0.46 => ( setOfPairsIsBReln
% 0.18/0.46 => ( dpsetconstrERa
% 0.18/0.46 => ( dpsetconstrEL1
% 0.18/0.46 => ( dpsetconstrEL2
% 0.18/0.46 => ( dpsetconstrER
% 0.18/0.46 => ( funcImageSingleton
% 0.18/0.46 => ( apProp
% 0.18/0.46 => ( app
% 0.18/0.46 => ( infuncsetfunc
% 0.18/0.46 => ( ap2p
% 0.18/0.46 => ! [A: $i,B: $i,Xf: $i] :
% 0.18/0.46 ( ( func @ A @ B @ Xf )
% 0.18/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 2.36/1.48 ---- Embedded in THF ---
% 2.36/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.36/1.48 %%% Generated on Tue Feb 24 12:30:55 EST 2026
% 2.36/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.36/1.48 %%% Logic specification used:
% 2.36/1.48 %%% thf(spec, logic, $$dhol).
% 2.36/1.48
% 2.36/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2DTF3362.p
% See solution above
% 2.36/1.48 ------------------------
% 2.61/1.50 ---- Cleaned THF ---
% 2.61/1.50 thf(in_type,type,
% 2.61/1.50 in: $i > $i > $o ).
% 2.61/1.50
% 2.61/1.50 thf(exu_type,type,
% 2.61/1.50 exu: ( $i > $o ) > $o ).
% 2.61/1.50
% 2.61/1.50 thf(exu,definition,
% 2.61/1.50 ( exu
% 2.61/1.50 = ( ^ [Xphi: $i > $o] :
% 2.61/1.50 ? [Xx: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 & ! [Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setextAx_type,type,
% 2.61/1.50 setextAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setextAx,definition,
% 2.61/1.50 ( setextAx
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 <=> ( in @ Xx @ B ) )
% 2.61/1.50 => ( A = B ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyset_type,type,
% 2.61/1.50 emptyset: $i ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetAx_type,type,
% 2.61/1.50 emptysetAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetAx,definition,
% 2.61/1.50 ( emptysetAx
% 2.61/1.50 = ( ! [Xx: $i] :
% 2.61/1.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoin_type,type,
% 2.61/1.50 setadjoin: $i > $i > $i ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinAx_type,type,
% 2.61/1.50 setadjoinAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinAx,definition,
% 2.61/1.50 ( setadjoinAx
% 2.61/1.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.61/1.50 <=> ( ( Xy = Xx )
% 2.61/1.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(powerset_type,type,
% 2.61/1.50 powerset: $i > $i ).
% 2.61/1.50
% 2.61/1.50 thf(powersetAx_type,type,
% 2.61/1.50 powersetAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(powersetAx,definition,
% 2.61/1.50 ( powersetAx
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ( in @ B @ ( powerset @ A ) )
% 2.61/1.50 <=> ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setunion_type,type,
% 2.61/1.50 setunion: $i > $i ).
% 2.61/1.50
% 2.61/1.50 thf(setunionAx_type,type,
% 2.61/1.50 setunionAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setunionAx,definition,
% 2.61/1.50 ( setunionAx
% 2.61/1.50 = ( ! [A: $i,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ ( setunion @ A ) )
% 2.61/1.50 <=> ? [B: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 & ( in @ B @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(omega_type,type,
% 2.61/1.50 omega: $i ).
% 2.61/1.50
% 2.61/1.50 thf(omega0Ax_type,type,
% 2.61/1.50 omega0Ax: $o ).
% 2.61/1.50
% 2.61/1.50 thf(omega0Ax,definition,
% 2.61/1.50 ( omega0Ax
% 2.61/1.50 = ( in @ emptyset @ omega ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(omegaSAx_type,type,
% 2.61/1.50 omegaSAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(omegaSAx,definition,
% 2.61/1.50 ( omegaSAx
% 2.61/1.50 = ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ omega )
% 2.61/1.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(omegaIndAx_type,type,
% 2.61/1.50 omegaIndAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(omegaIndAx,definition,
% 2.61/1.50 ( omegaIndAx
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ( ( in @ emptyset @ A )
% 2.61/1.50 & ! [Xx: $i] :
% 2.61/1.50 ( ( ( in @ Xx @ omega )
% 2.61/1.50 & ( in @ Xx @ A ) )
% 2.61/1.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.61/1.50 => ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ omega )
% 2.61/1.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(replAx_type,type,
% 2.61/1.50 replAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(replAx,definition,
% 2.61/1.50 ( replAx
% 2.61/1.50 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( exu
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.61/1.50 => ? [B: $i] :
% 2.61/1.50 ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 <=> ? [Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ A )
% 2.61/1.50 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(foundationAx_type,type,
% 2.61/1.50 foundationAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(foundationAx,definition,
% 2.61/1.50 ( foundationAx
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.61/1.50 => ? [B: $i] :
% 2.61/1.50 ( ( in @ B @ A )
% 2.61/1.50 & ~ ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(wellorderingAx_type,type,
% 2.61/1.50 wellorderingAx: $o ).
% 2.61/1.50
% 2.61/1.50 thf(wellorderingAx,definition,
% 2.61/1.50 ( wellorderingAx
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ? [B: $i] :
% 2.61/1.50 ( ! [C: $i] :
% 2.61/1.50 ( ( in @ C @ B )
% 2.61/1.50 => ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ C )
% 2.61/1.50 => ( in @ Xx @ A ) ) )
% 2.61/1.50 & ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( ( in @ Xx @ A )
% 2.61/1.50 & ( in @ Xy @ A ) )
% 2.61/1.50 => ( ! [C: $i] :
% 2.61/1.50 ( ( in @ C @ B )
% 2.61/1.50 => ( ( in @ Xx @ C )
% 2.61/1.50 <=> ( in @ Xy @ C ) ) )
% 2.61/1.50 => ( Xx = Xy ) ) )
% 2.61/1.50 & ! [C: $i,D: $i] :
% 2.61/1.50 ( ( ( in @ C @ B )
% 2.61/1.50 & ( in @ D @ B ) )
% 2.61/1.50 => ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ C )
% 2.61/1.50 => ( in @ Xx @ D ) )
% 2.61/1.50 | ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ D )
% 2.61/1.50 => ( in @ Xx @ C ) ) ) )
% 2.61/1.50 & ! [C: $i] :
% 2.61/1.50 ( ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ C )
% 2.61/1.50 => ( in @ Xx @ A ) )
% 2.61/1.50 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.61/1.50 => ? [D: $i,Xx: $i] :
% 2.61/1.50 ( ( in @ D @ B )
% 2.61/1.50 & ( in @ Xx @ C )
% 2.61/1.50 & ~ ? [Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ D )
% 2.61/1.50 & ( in @ Xy @ C ) )
% 2.61/1.50 & ! [E: $i] :
% 2.61/1.50 ( ( in @ E @ B )
% 2.61/1.50 => ( ! [Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ E )
% 2.61/1.50 => ( in @ Xy @ D ) )
% 2.61/1.50 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(descr_type,type,
% 2.61/1.50 descr: ( $i > $o ) > $i ).
% 2.61/1.50
% 2.61/1.50 thf(descrp_type,type,
% 2.61/1.50 descrp: $o ).
% 2.61/1.50
% 2.61/1.50 thf(descrp,definition,
% 2.61/1.50 ( descrp
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ( Xphi
% 2.61/1.50 @ ( descr
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstr_type,type,
% 2.61/1.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrI_type,type,
% 2.61/1.50 dsetconstrI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrI,definition,
% 2.61/1.50 ( dsetconstrI
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( ( Xphi @ Xx )
% 2.61/1.50 => ( in @ Xx
% 2.61/1.50 @ ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrEL_type,type,
% 2.61/1.50 dsetconstrEL: $o ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrEL,definition,
% 2.61/1.50 ( dsetconstrEL
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx
% 2.61/1.50 @ ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.61/1.50 => ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrER_type,type,
% 2.61/1.50 dsetconstrER: $o ).
% 2.61/1.50
% 2.61/1.50 thf(dsetconstrER,definition,
% 2.61/1.50 ( dsetconstrER
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx
% 2.61/1.50 @ ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.61/1.50 => ( Xphi @ Xx ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuE1_type,type,
% 2.61/1.50 exuE1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuE1,definition,
% 2.61/1.50 ( exuE1
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ? [Xx: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 & ! [Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(prop2set_type,type,
% 2.61/1.50 prop2set: $o > $i ).
% 2.61/1.50
% 2.61/1.50 thf(prop2setE_type,type,
% 2.61/1.50 prop2setE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(prop2setE,definition,
% 2.61/1.50 ( prop2setE
% 2.61/1.50 = ( ! [Xphi: $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.61/1.50 => Xphi ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetE_type,type,
% 2.61/1.50 emptysetE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetE,definition,
% 2.61/1.50 ( emptysetE
% 2.61/1.50 = ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ emptyset )
% 2.61/1.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetimpfalse_type,type,
% 2.61/1.50 emptysetimpfalse: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptysetimpfalse,definition,
% 2.61/1.50 ( emptysetimpfalse
% 2.61/1.50 = ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ emptyset )
% 2.61/1.50 => $false ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(notinemptyset_type,type,
% 2.61/1.50 notinemptyset: $o ).
% 2.61/1.50
% 2.61/1.50 thf(notinemptyset,definition,
% 2.61/1.50 ( notinemptyset
% 2.61/1.50 = ( ! [Xx: $i] :
% 2.61/1.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuE3e_type,type,
% 2.61/1.50 exuE3e: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuE3e,definition,
% 2.61/1.50 ( exuE3e
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setext_type,type,
% 2.61/1.50 setext: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setext,definition,
% 2.61/1.50 ( setext
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( in @ Xx @ B ) )
% 2.61/1.50 => ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 => ( in @ Xx @ A ) )
% 2.61/1.50 => ( A = B ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyI_type,type,
% 2.61/1.50 emptyI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyI,definition,
% 2.61/1.50 ( emptyI
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ~ ( in @ Xx @ A )
% 2.61/1.50 => ( A = emptyset ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(noeltsimpempty_type,type,
% 2.61/1.50 noeltsimpempty: $o ).
% 2.61/1.50
% 2.61/1.50 thf(noeltsimpempty,definition,
% 2.61/1.50 ( noeltsimpempty
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ~ ( in @ Xx @ A )
% 2.61/1.50 => ( A = emptyset ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setbeta_type,type,
% 2.61/1.50 setbeta: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setbeta,definition,
% 2.61/1.50 ( setbeta
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( ( in @ Xx
% 2.61/1.50 @ ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.61/1.50 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(nonempty_type,type,
% 2.61/1.50 nonempty: $i > $o ).
% 2.61/1.50
% 2.61/1.50 thf(nonempty,definition,
% 2.61/1.50 ( nonempty
% 2.61/1.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyE1_type,type,
% 2.61/1.50 nonemptyE1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyE1,definition,
% 2.61/1.50 ( nonemptyE1
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ( nonempty @ A )
% 2.61/1.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyI_type,type,
% 2.61/1.50 nonemptyI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyI,definition,
% 2.61/1.50 ( nonemptyI
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( ( Xphi @ Xx )
% 2.61/1.50 => ( nonempty
% 2.61/1.50 @ ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyI1_type,type,
% 2.61/1.50 nonemptyI1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyI1,definition,
% 2.61/1.50 ( nonemptyI1
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.61/1.50 => ( nonempty @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinIL_type,type,
% 2.61/1.50 setadjoinIL: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinIL,definition,
% 2.61/1.50 ( setadjoinIL
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyinunitempty_type,type,
% 2.61/1.50 emptyinunitempty: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyinunitempty,definition,
% 2.61/1.50 ( emptyinunitempty
% 2.61/1.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinIR_type,type,
% 2.61/1.50 setadjoinIR: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinIR,definition,
% 2.61/1.50 ( setadjoinIR
% 2.61/1.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ A )
% 2.61/1.50 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinE_type,type,
% 2.61/1.50 setadjoinE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinE,definition,
% 2.61/1.50 ( setadjoinE
% 2.61/1.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.61/1.50 => ! [Xphi: $o] :
% 2.61/1.50 ( ( ( Xy = Xx )
% 2.61/1.50 => Xphi )
% 2.61/1.50 => ( ( ( in @ Xy @ A )
% 2.61/1.50 => Xphi )
% 2.61/1.50 => Xphi ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinOr_type,type,
% 2.61/1.50 setadjoinOr: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoinOr,definition,
% 2.61/1.50 ( setadjoinOr
% 2.61/1.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.61/1.50 => ( ( Xy = Xx )
% 2.61/1.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setoftrueEq_type,type,
% 2.61/1.50 setoftrueEq: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setoftrueEq,definition,
% 2.61/1.50 ( setoftrueEq
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xx: $i] : $true )
% 2.61/1.50 = A ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(powersetI_type,type,
% 2.61/1.50 powersetI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(powersetI,definition,
% 2.61/1.50 ( powersetI
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 => ( in @ Xx @ A ) )
% 2.61/1.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyinPowerset_type,type,
% 2.61/1.50 emptyinPowerset: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyinPowerset,definition,
% 2.61/1.50 ( emptyinPowerset
% 2.61/1.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyInPowerset_type,type,
% 2.61/1.50 emptyInPowerset: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyInPowerset,definition,
% 2.61/1.50 ( emptyInPowerset
% 2.61/1.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(powersetE_type,type,
% 2.61/1.50 powersetE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(powersetE,definition,
% 2.61/1.50 ( powersetE
% 2.61/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.50 ( ( in @ B @ ( powerset @ A ) )
% 2.61/1.50 => ( ( in @ Xx @ B )
% 2.61/1.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setunionI_type,type,
% 2.61/1.50 setunionI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setunionI,definition,
% 2.61/1.50 ( setunionI
% 2.61/1.50 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 => ( ( in @ B @ A )
% 2.61/1.50 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setunionE_type,type,
% 2.61/1.50 setunionE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setunionE,definition,
% 2.61/1.50 ( setunionE
% 2.61/1.50 = ( ! [A: $i,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ ( setunion @ A ) )
% 2.61/1.50 => ! [Xphi: $o] :
% 2.61/1.50 ( ! [B: $i] :
% 2.61/1.50 ( ( in @ Xx @ B )
% 2.61/1.50 => ( ( in @ B @ A )
% 2.61/1.50 => Xphi ) )
% 2.61/1.50 => Xphi ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(subPowSU_type,type,
% 2.61/1.50 subPowSU: $o ).
% 2.61/1.50
% 2.61/1.50 thf(subPowSU,definition,
% 2.61/1.50 ( subPowSU
% 2.61/1.50 = ( ! [A: $i,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuE2_type,type,
% 2.61/1.50 exuE2: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuE2,definition,
% 2.61/1.50 ( exuE2
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ? [Xx: $i] :
% 2.61/1.50 ! [Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xy )
% 2.61/1.50 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyImpWitness_type,type,
% 2.61/1.50 nonemptyImpWitness: $o ).
% 2.61/1.50
% 2.61/1.50 thf(nonemptyImpWitness,definition,
% 2.61/1.50 ( nonemptyImpWitness
% 2.61/1.50 = ( ! [A: $i] :
% 2.61/1.50 ( ( nonempty @ A )
% 2.61/1.50 => ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & $true ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(uniqinunit_type,type,
% 2.61/1.50 uniqinunit: $o ).
% 2.61/1.50
% 2.61/1.50 thf(uniqinunit,definition,
% 2.61/1.50 ( uniqinunit
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.61/1.50 => ( Xx = Xy ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(notinsingleton_type,type,
% 2.61/1.50 notinsingleton: $o ).
% 2.61/1.50
% 2.61/1.50 thf(notinsingleton,definition,
% 2.61/1.50 ( notinsingleton
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx != Xy )
% 2.61/1.50 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(eqinunit_type,type,
% 2.61/1.50 eqinunit: $o ).
% 2.61/1.50
% 2.61/1.50 thf(eqinunit,definition,
% 2.61/1.50 ( eqinunit
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(singletonsswitch_type,type,
% 2.61/1.50 singletonsswitch: $o ).
% 2.61/1.50
% 2.61/1.50 thf(singletonsswitch,definition,
% 2.61/1.50 ( singletonsswitch
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.61/1.50 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetE_type,type,
% 2.61/1.50 upairsetE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetE,definition,
% 2.61/1.50 ( upairsetE
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.61/1.50 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.61/1.50 => ( ( Xz = Xx )
% 2.61/1.50 | ( Xz = Xy ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetIL_type,type,
% 2.61/1.50 upairsetIL: $o ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetIL,definition,
% 2.61/1.50 ( upairsetIL
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetIR_type,type,
% 2.61/1.50 upairsetIR: $o ).
% 2.61/1.50
% 2.61/1.50 thf(upairsetIR,definition,
% 2.61/1.50 ( upairsetIR
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyE1_type,type,
% 2.61/1.50 emptyE1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyE1,definition,
% 2.61/1.50 ( emptyE1
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ( Xphi @ Xx ) )
% 2.61/1.50 => ( ( ( dsetconstr @ A
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 = emptyset )
% 2.61/1.50 => $false ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(vacuousDall_type,type,
% 2.61/1.50 vacuousDall: $o ).
% 2.61/1.50
% 2.61/1.50 thf(vacuousDall,definition,
% 2.61/1.50 ( vacuousDall
% 2.61/1.50 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ emptyset )
% 2.61/1.50 => ( Xphi @ Xx ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan1_type,type,
% 2.61/1.50 quantDeMorgan1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan1,definition,
% 2.61/1.50 ( quantDeMorgan1
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ~ ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( Xphi @ Xx ) )
% 2.61/1.50 => ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan2_type,type,
% 2.61/1.50 quantDeMorgan2: $o ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan2,definition,
% 2.61/1.50 ( quantDeMorgan2
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ~ ( Xphi @ Xx ) )
% 2.61/1.50 => ~ ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan3_type,type,
% 2.61/1.50 quantDeMorgan3: $o ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan3,definition,
% 2.61/1.50 ( quantDeMorgan3
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ~ ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ( Xphi @ Xx ) )
% 2.61/1.50 => ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan4_type,type,
% 2.61/1.50 quantDeMorgan4: $o ).
% 2.61/1.50
% 2.61/1.50 thf(quantDeMorgan4,definition,
% 2.61/1.50 ( quantDeMorgan4
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ~ ( Xphi @ Xx ) )
% 2.61/1.50 => ~ ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(prop2setI_type,type,
% 2.61/1.50 prop2setI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(prop2setI,definition,
% 2.61/1.50 ( prop2setI
% 2.61/1.50 = ( ! [Xphi: $o] :
% 2.61/1.50 ( Xphi
% 2.61/1.50 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(set2prop_type,type,
% 2.61/1.50 set2prop: $i > $o ).
% 2.61/1.50
% 2.61/1.50 thf(prop2set2propI_type,type,
% 2.61/1.50 prop2set2propI: $o ).
% 2.61/1.50
% 2.61/1.50 thf(prop2set2propI,definition,
% 2.61/1.50 ( prop2set2propI
% 2.61/1.50 = ( ! [Xphi: $o] :
% 2.61/1.50 ( Xphi
% 2.61/1.50 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(notdexE_type,type,
% 2.61/1.50 notdexE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(notdexE,definition,
% 2.61/1.50 ( notdexE
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ~ ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ( Xphi @ Xx ) )
% 2.61/1.50 => ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(notdallE_type,type,
% 2.61/1.50 notdallE: $o ).
% 2.61/1.50
% 2.61/1.50 thf(notdallE,definition,
% 2.61/1.50 ( notdallE
% 2.61/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.50 ( ~ ! [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 => ( Xphi @ Xx ) )
% 2.61/1.50 => ? [Xx: $i] :
% 2.61/1.50 ( ( in @ Xx @ A )
% 2.61/1.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuI1_type,type,
% 2.61/1.50 exuI1: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuI1,definition,
% 2.61/1.50 ( exuI1
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ? [Xx: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 & ! [Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) )
% 2.61/1.50 => ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuI3_type,type,
% 2.61/1.50 exuI3: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuI3,definition,
% 2.61/1.50 ( exuI3
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.61/1.50 => ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 => ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) )
% 2.61/1.50 => ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuI2_type,type,
% 2.61/1.50 exuI2: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuI2,definition,
% 2.61/1.50 ( exuI2
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ? [Xx: $i] :
% 2.61/1.50 ! [Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xy )
% 2.61/1.50 <=> ( Xy = Xx ) )
% 2.61/1.50 => ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(inCongP_type,type,
% 2.61/1.50 inCongP: $o ).
% 2.61/1.50
% 2.61/1.50 thf(inCongP,definition,
% 2.61/1.50 ( inCongP
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ( A = B )
% 2.61/1.50 => ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ( ( in @ Xx @ A )
% 2.61/1.50 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(in__Cong_type,type,
% 2.61/1.50 in__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(in__Cong,definition,
% 2.61/1.50 ( in__Cong
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ( A = B )
% 2.61/1.50 => ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ( ( in @ Xx @ A )
% 2.61/1.50 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuE3u_type,type,
% 2.61/1.50 exuE3u: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuE3u,definition,
% 2.61/1.50 ( exuE3u
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 => ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exu__Cong_type,type,
% 2.61/1.50 exu__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exu__Cong,definition,
% 2.61/1.50 ( exu__Cong
% 2.61/1.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.61/1.50 ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ( ( Xphi @ Xx )
% 2.61/1.50 <=> ( Xpsi @ Xy ) ) )
% 2.61/1.50 => ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 <=> ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(emptyset__Cong_type,type,
% 2.61/1.50 emptyset__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(emptyset__Cong,definition,
% 2.61/1.50 ( emptyset__Cong
% 2.61/1.50 = ( emptyset = emptyset ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoin__Cong_type,type,
% 2.61/1.50 setadjoin__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setadjoin__Cong,definition,
% 2.61/1.50 ( setadjoin__Cong
% 2.61/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ! [Xz: $i,Xu: $i] :
% 2.61/1.50 ( ( Xz = Xu )
% 2.61/1.50 => ( ( setadjoin @ Xx @ Xz )
% 2.61/1.50 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(powerset__Cong_type,type,
% 2.61/1.50 powerset__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(powerset__Cong,definition,
% 2.61/1.50 ( powerset__Cong
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ( A = B )
% 2.61/1.50 => ( ( powerset @ A )
% 2.61/1.50 = ( powerset @ B ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(setunion__Cong_type,type,
% 2.61/1.50 setunion__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(setunion__Cong,definition,
% 2.61/1.50 ( setunion__Cong
% 2.61/1.50 = ( ! [A: $i,B: $i] :
% 2.61/1.50 ( ( A = B )
% 2.61/1.50 => ( ( setunion @ A )
% 2.61/1.50 = ( setunion @ B ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(omega__Cong_type,type,
% 2.61/1.50 omega__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(omega__Cong,definition,
% 2.61/1.50 ( omega__Cong
% 2.61/1.50 = ( omega = omega ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(exuEu_type,type,
% 2.61/1.50 exuEu: $o ).
% 2.61/1.50
% 2.61/1.50 thf(exuEu,definition,
% 2.61/1.50 ( exuEu
% 2.61/1.50 = ( ! [Xphi: $i > $o] :
% 2.61/1.50 ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xphi @ Xx )
% 2.61/1.50 => ( ( Xphi @ Xy )
% 2.61/1.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(descr__Cong_type,type,
% 2.61/1.50 descr__Cong: $o ).
% 2.61/1.50
% 2.61/1.50 thf(descr__Cong,definition,
% 2.61/1.50 ( descr__Cong
% 2.61/1.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.61/1.50 ( ! [Xx: $i,Xy: $i] :
% 2.61/1.50 ( ( Xx = Xy )
% 2.61/1.50 => ( ( Xphi @ Xx )
% 2.61/1.50 <=> ( Xpsi @ Xy ) ) )
% 2.61/1.50 => ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 => ( ( exu
% 2.61/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.61/1.50 => ( ( descr
% 2.61/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.50 = ( descr
% 2.61/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dsetconstr__Cong_type,type,
% 2.61/1.51 dsetconstr__Cong: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dsetconstr__Cong,definition,
% 2.61/1.51 ( dsetconstr__Cong
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( A = B )
% 2.61/1.51 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.61/1.51 ( ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( Xx = Xy )
% 2.61/1.51 => ( ( Xphi @ Xx )
% 2.61/1.51 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.61/1.51 => ( ( dsetconstr @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.51 = ( dsetconstr @ B
% 2.61/1.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subset_type,type,
% 2.61/1.51 subset: $i > $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(disjoint_type,type,
% 2.61/1.51 disjoint: $i > $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(setsmeet_type,type,
% 2.61/1.51 setsmeet: $i > $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetI1_type,type,
% 2.61/1.51 subsetI1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetI1,definition,
% 2.61/1.51 ( subsetI1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ Xx @ B ) )
% 2.61/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(eqimpsubset2_type,type,
% 2.61/1.51 eqimpsubset2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(eqimpsubset2,definition,
% 2.61/1.51 ( eqimpsubset2
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( A = B )
% 2.61/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(eqimpsubset1_type,type,
% 2.61/1.51 eqimpsubset1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(eqimpsubset1,definition,
% 2.61/1.51 ( eqimpsubset1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( A = B )
% 2.61/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetI2_type,type,
% 2.61/1.51 subsetI2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetI2,definition,
% 2.61/1.51 ( subsetI2
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ Xx @ B ) )
% 2.61/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(emptysetsubset_type,type,
% 2.61/1.51 emptysetsubset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(emptysetsubset,definition,
% 2.61/1.51 ( emptysetsubset
% 2.61/1.51 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetE_type,type,
% 2.61/1.51 subsetE: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetE,definition,
% 2.61/1.51 ( subsetE
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetE2_type,type,
% 2.61/1.51 subsetE2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetE2,definition,
% 2.61/1.51 ( subsetE2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(notsubsetI_type,type,
% 2.61/1.51 notsubsetI: $o ).
% 2.61/1.51
% 2.61/1.51 thf(notsubsetI,definition,
% 2.61/1.51 ( notsubsetI
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(notequalI1_type,type,
% 2.61/1.51 notequalI1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(notequalI1,definition,
% 2.61/1.51 ( notequalI1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ~ ( subset @ A @ B )
% 2.61/1.51 => ( A != B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(notequalI2_type,type,
% 2.61/1.51 notequalI2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(notequalI2,definition,
% 2.61/1.51 ( notequalI2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ( A != B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetRefl_type,type,
% 2.61/1.51 subsetRefl: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetRefl,definition,
% 2.61/1.51 ( subsetRefl
% 2.61/1.51 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetTrans_type,type,
% 2.61/1.51 subsetTrans: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetTrans,definition,
% 2.61/1.51 ( subsetTrans
% 2.61/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ( subset @ B @ C )
% 2.61/1.51 => ( subset @ A @ C ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setadjoinSub_type,type,
% 2.61/1.51 setadjoinSub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setadjoinSub,definition,
% 2.61/1.51 ( setadjoinSub
% 2.61/1.51 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setadjoinSub2_type,type,
% 2.61/1.51 setadjoinSub2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setadjoinSub2,definition,
% 2.61/1.51 ( setadjoinSub2
% 2.61/1.51 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subset2powerset_type,type,
% 2.61/1.51 subset2powerset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subset2powerset,definition,
% 2.61/1.51 ( subset2powerset
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setextsub_type,type,
% 2.61/1.51 setextsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setextsub,definition,
% 2.61/1.51 ( setextsub
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ( subset @ B @ A )
% 2.61/1.51 => ( A = B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(subsetemptysetimpeq_type,type,
% 2.61/1.51 subsetemptysetimpeq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(subsetemptysetimpeq,definition,
% 2.61/1.51 ( subsetemptysetimpeq
% 2.61/1.51 = ( ! [A: $i] :
% 2.61/1.51 ( ( subset @ A @ emptyset )
% 2.61/1.51 => ( A = emptyset ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(powersetI1_type,type,
% 2.61/1.51 powersetI1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(powersetI1,definition,
% 2.61/1.51 ( powersetI1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ B @ A )
% 2.61/1.51 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(powersetE1_type,type,
% 2.61/1.51 powersetE1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(powersetE1,definition,
% 2.61/1.51 ( powersetE1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( in @ B @ ( powerset @ A ) )
% 2.61/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(inPowerset_type,type,
% 2.61/1.51 inPowerset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(inPowerset,definition,
% 2.61/1.51 ( inPowerset
% 2.61/1.51 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(powersetsubset_type,type,
% 2.61/1.51 powersetsubset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(powersetsubset,definition,
% 2.61/1.51 ( powersetsubset
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(sepInPowerset_type,type,
% 2.61/1.51 sepInPowerset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(sepInPowerset,definition,
% 2.61/1.51 ( sepInPowerset
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( in
% 2.61/1.51 @ ( dsetconstr @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.51 @ ( powerset @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(sepSubset_type,type,
% 2.61/1.51 sepSubset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(sepSubset,definition,
% 2.61/1.51 ( sepSubset
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( subset
% 2.61/1.51 @ ( dsetconstr @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.51 @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunion_type,type,
% 2.61/1.51 binunion: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(binunionIL_type,type,
% 2.61/1.51 binunionIL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionIL,definition,
% 2.61/1.51 ( binunionIL
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(upairset2IR_type,type,
% 2.61/1.51 upairset2IR: $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairset2IR,definition,
% 2.61/1.51 ( upairset2IR
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunionIR_type,type,
% 2.61/1.51 binunionIR: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionIR,definition,
% 2.61/1.51 ( binunionIR
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ B )
% 2.61/1.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunionEcases_type,type,
% 2.61/1.51 binunionEcases: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionEcases,definition,
% 2.61/1.51 ( binunionEcases
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.61/1.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.61/1.51 => ( ( ( in @ Xx @ A )
% 2.61/1.51 => Xphi )
% 2.61/1.51 => ( ( ( in @ Xx @ B )
% 2.61/1.51 => Xphi )
% 2.61/1.51 => Xphi ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunionE_type,type,
% 2.61/1.51 binunionE: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionE,definition,
% 2.61/1.51 ( binunionE
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.61/1.51 => ( ( in @ Xx @ A )
% 2.61/1.51 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunionLsub_type,type,
% 2.61/1.51 binunionLsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionLsub,definition,
% 2.61/1.51 ( binunionLsub
% 2.61/1.51 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binunionRsub_type,type,
% 2.61/1.51 binunionRsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binunionRsub,definition,
% 2.61/1.51 ( binunionRsub
% 2.61/1.51 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersect_type,type,
% 2.61/1.51 binintersect: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectI_type,type,
% 2.61/1.51 binintersectI: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectI,definition,
% 2.61/1.51 ( binintersectI
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ( in @ Xx @ B )
% 2.61/1.51 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset5_type,type,
% 2.61/1.51 binintersectSubset5: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset5,definition,
% 2.61/1.51 ( binintersectSubset5
% 2.61/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.61/1.51 ( ( subset @ C @ A )
% 2.61/1.51 => ( ( subset @ C @ B )
% 2.61/1.51 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectEL_type,type,
% 2.61/1.51 binintersectEL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectEL,definition,
% 2.61/1.51 ( binintersectEL
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.61/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectLsub_type,type,
% 2.61/1.51 binintersectLsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectLsub,definition,
% 2.61/1.51 ( binintersectLsub
% 2.61/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset2_type,type,
% 2.61/1.51 binintersectSubset2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset2,definition,
% 2.61/1.51 ( binintersectSubset2
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ( binintersect @ A @ B )
% 2.61/1.51 = A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset3_type,type,
% 2.61/1.51 binintersectSubset3: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset3,definition,
% 2.61/1.51 ( binintersectSubset3
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( ( binintersect @ A @ B )
% 2.61/1.51 = B )
% 2.61/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectER_type,type,
% 2.61/1.51 binintersectER: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectER,definition,
% 2.61/1.51 ( binintersectER
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.61/1.51 => ( in @ Xx @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(disjointsetsI1_type,type,
% 2.61/1.51 disjointsetsI1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(disjointsetsI1,definition,
% 2.61/1.51 ( disjointsetsI1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ~ ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ( in @ Xx @ B ) )
% 2.61/1.51 => ( ( binintersect @ A @ B )
% 2.61/1.51 = emptyset ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectRsub_type,type,
% 2.61/1.51 binintersectRsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectRsub,definition,
% 2.61/1.51 ( binintersectRsub
% 2.61/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset4_type,type,
% 2.61/1.51 binintersectSubset4: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset4,definition,
% 2.61/1.51 ( binintersectSubset4
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ B @ A )
% 2.61/1.51 => ( ( binintersect @ A @ B )
% 2.61/1.51 = B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset1_type,type,
% 2.61/1.51 binintersectSubset1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(binintersectSubset1,definition,
% 2.61/1.51 ( binintersectSubset1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( ( binintersect @ A @ B )
% 2.61/1.51 = A )
% 2.61/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(bs114d_type,type,
% 2.61/1.51 bs114d: $o ).
% 2.61/1.51
% 2.61/1.51 thf(bs114d,definition,
% 2.61/1.51 ( bs114d
% 2.61/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.61/1.51 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.61/1.51 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(regular_type,type,
% 2.61/1.51 regular: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminus_type,type,
% 2.61/1.51 setminus: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(setminusI_type,type,
% 2.61/1.51 setminusI: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusI,definition,
% 2.61/1.51 ( setminusI
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusEL_type,type,
% 2.61/1.51 setminusEL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusEL,definition,
% 2.61/1.51 ( setminusEL
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.61/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusER_type,type,
% 2.61/1.51 setminusER: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusER,definition,
% 2.61/1.51 ( setminusER
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.61/1.51 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusSubset2_type,type,
% 2.61/1.51 setminusSubset2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusSubset2,definition,
% 2.61/1.51 ( setminusSubset2
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( subset @ A @ B )
% 2.61/1.51 => ( ( setminus @ A @ B )
% 2.61/1.51 = emptyset ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusERneg_type,type,
% 2.61/1.51 setminusERneg: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusERneg,definition,
% 2.61/1.51 ( setminusERneg
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.61/1.51 => ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusELneg_type,type,
% 2.61/1.51 setminusELneg: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusELneg,definition,
% 2.61/1.51 ( setminusELneg
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusILneg_type,type,
% 2.61/1.51 setminusILneg: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusILneg,definition,
% 2.61/1.51 ( setminusILneg
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ~ ( in @ Xx @ A )
% 2.61/1.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusIRneg_type,type,
% 2.61/1.51 setminusIRneg: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusIRneg,definition,
% 2.61/1.51 ( setminusIRneg
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ B )
% 2.61/1.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusLsub_type,type,
% 2.61/1.51 setminusLsub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusLsub,definition,
% 2.61/1.51 ( setminusLsub
% 2.61/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setminusSubset1_type,type,
% 2.61/1.51 setminusSubset1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setminusSubset1,definition,
% 2.61/1.51 ( setminusSubset1
% 2.61/1.51 = ( ! [A: $i,B: $i] :
% 2.61/1.51 ( ( ( setminus @ A @ B )
% 2.61/1.51 = emptyset )
% 2.61/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(symdiff_type,type,
% 2.61/1.51 symdiff: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffE_type,type,
% 2.61/1.51 symdiffE: $o ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffE,definition,
% 2.61/1.51 ( symdiffE
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.61/1.51 => ! [Xphi: $o] :
% 2.61/1.51 ( ( ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => Xphi ) )
% 2.61/1.51 => ( ( ~ ( in @ Xx @ A )
% 2.61/1.51 => ( ( in @ Xx @ B )
% 2.61/1.51 => Xphi ) )
% 2.61/1.51 => Xphi ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffI1_type,type,
% 2.61/1.51 symdiffI1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffI1,definition,
% 2.61/1.51 ( symdiffI1
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffI2_type,type,
% 2.61/1.51 symdiffI2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffI2,definition,
% 2.61/1.51 ( symdiffI2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ~ ( in @ Xx @ A )
% 2.61/1.51 => ( ( in @ Xx @ B )
% 2.61/1.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffIneg1_type,type,
% 2.61/1.51 symdiffIneg1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffIneg1,definition,
% 2.61/1.51 ( symdiffIneg1
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ( in @ Xx @ B )
% 2.61/1.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffIneg2_type,type,
% 2.61/1.51 symdiffIneg2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(symdiffIneg2,definition,
% 2.61/1.51 ( symdiffIneg2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ~ ( in @ Xx @ A )
% 2.61/1.51 => ( ~ ( in @ Xx @ B )
% 2.61/1.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(iskpair_type,type,
% 2.61/1.51 iskpair: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(secondinupair_type,type,
% 2.61/1.51 secondinupair: $o ).
% 2.61/1.51
% 2.61/1.51 thf(secondinupair,definition,
% 2.61/1.51 ( secondinupair
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairIL_type,type,
% 2.61/1.51 setukpairIL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairIL,definition,
% 2.61/1.51 ( setukpairIL
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairIR_type,type,
% 2.61/1.51 setukpairIR: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairIR,definition,
% 2.61/1.51 ( setukpairIR
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(kpairiskpair_type,type,
% 2.61/1.51 kpairiskpair: $o ).
% 2.61/1.51
% 2.61/1.51 thf(kpairiskpair,definition,
% 2.61/1.51 ( kpairiskpair
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(kpair_type,type,
% 2.61/1.51 kpair: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(kpairp_type,type,
% 2.61/1.51 kpairp: $o ).
% 2.61/1.51
% 2.61/1.51 thf(kpairp,definition,
% 2.61/1.51 ( kpairp
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprod_type,type,
% 2.61/1.51 cartprod: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(singletonsubset_type,type,
% 2.61/1.51 singletonsubset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(singletonsubset,definition,
% 2.61/1.51 ( singletonsubset
% 2.61/1.51 = ( ! [A: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(singletoninpowerset_type,type,
% 2.61/1.51 singletoninpowerset: $o ).
% 2.61/1.51
% 2.61/1.51 thf(singletoninpowerset,definition,
% 2.61/1.51 ( singletoninpowerset
% 2.61/1.51 = ( ! [A: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(singletoninpowunion_type,type,
% 2.61/1.51 singletoninpowunion: $o ).
% 2.61/1.51
% 2.61/1.51 thf(singletoninpowunion,definition,
% 2.61/1.51 ( singletoninpowunion
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(upairset2E_type,type,
% 2.61/1.51 upairset2E: $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairset2E,definition,
% 2.61/1.51 ( upairset2E
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.61/1.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.61/1.51 => ( ( Xz = Xx )
% 2.61/1.51 | ( Xz = Xy ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(upairsubunion_type,type,
% 2.61/1.51 upairsubunion: $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairsubunion,definition,
% 2.61/1.51 ( upairsubunion
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(upairinpowunion_type,type,
% 2.61/1.51 upairinpowunion: $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairinpowunion,definition,
% 2.61/1.51 ( upairinpowunion
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem1_type,type,
% 2.61/1.51 ubforcartprodlem1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem1,definition,
% 2.61/1.51 ( ubforcartprodlem1
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem2_type,type,
% 2.61/1.51 ubforcartprodlem2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem2,definition,
% 2.61/1.51 ( ubforcartprodlem2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem3_type,type,
% 2.61/1.51 ubforcartprodlem3: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ubforcartprodlem3,definition,
% 2.61/1.51 ( ubforcartprodlem3
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairin_type,type,
% 2.61/1.51 cartprodpairin: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairin,definition,
% 2.61/1.51 ( cartprodpairin
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempair1_type,type,
% 2.61/1.51 cartprodmempair1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempair1,definition,
% 2.61/1.51 ( cartprodmempair1
% 2.61/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.61/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ? [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 & ( Xu
% 2.61/1.51 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempair_type,type,
% 2.61/1.51 cartprodmempair: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempair,definition,
% 2.61/1.51 ( cartprodmempair
% 2.61/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.61/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( iskpair @ Xu ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setunionE2_type,type,
% 2.61/1.51 setunionE2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setunionE2,definition,
% 2.61/1.51 ( setunionE2
% 2.61/1.51 = ( ! [A: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ ( setunion @ A ) )
% 2.61/1.51 => ? [X: $i] :
% 2.61/1.51 ( ( in @ X @ A )
% 2.61/1.51 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton1_type,type,
% 2.61/1.51 setunionsingleton1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton1,definition,
% 2.61/1.51 ( setunionsingleton1
% 2.61/1.51 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton2_type,type,
% 2.61/1.51 setunionsingleton2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton2,definition,
% 2.61/1.51 ( setunionsingleton2
% 2.61/1.51 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton_type,type,
% 2.61/1.51 setunionsingleton: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setunionsingleton,definition,
% 2.61/1.51 ( setunionsingleton
% 2.61/1.51 = ( ! [Xx: $i] :
% 2.61/1.51 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.61/1.51 = Xx ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(singleton_type,type,
% 2.61/1.51 singleton: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(singleton,definition,
% 2.61/1.51 ( singleton
% 2.61/1.51 = ( ^ [A: $i] :
% 2.61/1.51 ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ( A
% 2.61/1.51 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(singletonprop_type,type,
% 2.61/1.51 singletonprop: $o ).
% 2.61/1.51
% 2.61/1.51 thf(singletonprop,definition,
% 2.61/1.51 ( singletonprop
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ A )
% 2.61/1.51 => ( ( Xphi @ Xx )
% 2.61/1.51 => ( ( Xphi @ Xy )
% 2.61/1.51 => ( Xx = Xy ) ) ) ) )
% 2.61/1.51 => ( ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ( Xphi @ Xx ) )
% 2.61/1.51 => ( singleton
% 2.61/1.51 @ ( dsetconstr @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ex1_type,type,
% 2.61/1.51 ex1: $i > ( $i > $o ) > $o ).
% 2.61/1.51
% 2.61/1.51 thf(ex1,definition,
% 2.61/1.51 ( ex1
% 2.61/1.51 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( singleton
% 2.61/1.51 @ ( dsetconstr @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ex1E1_type,type,
% 2.61/1.51 ex1E1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ex1E1,definition,
% 2.61/1.51 ( ex1E1
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( ( ex1 @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.61/1.51 => ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ex1I_type,type,
% 2.61/1.51 ex1I: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ex1I,definition,
% 2.61/1.51 ( ex1I
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ( Xphi @ Xx )
% 2.61/1.51 => ( ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ A )
% 2.61/1.51 => ( ( Xphi @ Xy )
% 2.61/1.51 => ( Xy = Xx ) ) )
% 2.61/1.51 => ( ex1 @ A
% 2.61/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ex1I2_type,type,
% 2.61/1.51 ex1I2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ex1I2,definition,
% 2.61/1.51 ( ex1I2
% 2.61/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.61/1.51 ( ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ A )
% 2.61/1.51 => ( ( Xphi @ Xx )
% 2.61/1.51 => ( ( Xphi @ Xy )
% 2.61/1.51 => ( Xx = Xy ) ) ) ) )
% 2.61/1.51 => ( ? [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 & ( Xphi @ Xx ) )
% 2.61/1.51 => ( ex1 @ A
% 2.61/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(singletonsuniq_type,type,
% 2.61/1.51 singletonsuniq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(singletonsuniq,definition,
% 2.61/1.51 ( singletonsuniq
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( ( setadjoin @ Xx @ emptyset )
% 2.61/1.51 = ( setadjoin @ Xy @ emptyset ) )
% 2.61/1.51 => ( Xx = Xy ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(atmost1p_type,type,
% 2.61/1.51 atmost1p: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(atleast2p_type,type,
% 2.61/1.51 atleast2p: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(atmost2p_type,type,
% 2.61/1.51 atmost2p: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairsetp_type,type,
% 2.61/1.51 upairsetp: $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL1_type,type,
% 2.61/1.51 setukpairinjL1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL1,definition,
% 2.61/1.51 ( setukpairinjL1
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.61/1.51 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.61/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(kfstsingleton_type,type,
% 2.61/1.51 kfstsingleton: $o ).
% 2.61/1.51
% 2.61/1.51 thf(kfstsingleton,definition,
% 2.61/1.51 ( kfstsingleton
% 2.61/1.51 = ( ! [Xu: $i] :
% 2.61/1.51 ( ( iskpair @ Xu )
% 2.61/1.51 => ( singleton
% 2.61/1.51 @ ( dsetconstr @ ( setunion @ Xu )
% 2.61/1.51 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(theprop_type,type,
% 2.61/1.51 theprop: $o ).
% 2.61/1.51
% 2.61/1.51 thf(theprop,definition,
% 2.61/1.51 ( theprop
% 2.61/1.51 = ( ! [X: $i] :
% 2.61/1.51 ( ( singleton @ X )
% 2.61/1.51 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(kfst_type,type,
% 2.61/1.51 kfst: $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(kfstpairEq_type,type,
% 2.61/1.51 kfstpairEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(kfstpairEq,definition,
% 2.61/1.51 ( kfstpairEq
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.61/1.51 = Xx ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodfstin_type,type,
% 2.61/1.51 cartprodfstin: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodfstin,definition,
% 2.61/1.51 ( cartprodfstin
% 2.61/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.61/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL2_type,type,
% 2.61/1.51 setukpairinjL2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL2,definition,
% 2.61/1.51 ( setukpairinjL2
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.61/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.61/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL_type,type,
% 2.61/1.51 setukpairinjL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjL,definition,
% 2.61/1.51 ( setukpairinjL
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.61/1.51 ( ( ( kpair @ Xx @ Xy )
% 2.61/1.51 = ( kpair @ Xz @ Xu ) )
% 2.61/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR11_type,type,
% 2.61/1.51 setukpairinjR11: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR11,definition,
% 2.61/1.51 ( setukpairinjR11
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( Xx = Xy )
% 2.61/1.51 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR12_type,type,
% 2.61/1.51 setukpairinjR12: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR12,definition,
% 2.61/1.51 ( setukpairinjR12
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( Xx = Xy )
% 2.61/1.51 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR1_type,type,
% 2.61/1.51 setukpairinjR1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR1,definition,
% 2.61/1.51 ( setukpairinjR1
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.61/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.61/1.51 => ( ( Xz = Xu )
% 2.61/1.51 => ( Xy = Xu ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(upairequniteq_type,type,
% 2.61/1.51 upairequniteq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(upairequniteq,definition,
% 2.61/1.51 ( upairequniteq
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.61/1.51 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ Xz @ emptyset ) )
% 2.61/1.51 => ( Xx = Xy ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR2_type,type,
% 2.61/1.51 setukpairinjR2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR2,definition,
% 2.61/1.51 ( setukpairinjR2
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.61/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.61/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.61/1.51 => ( Xy = Xu ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR_type,type,
% 2.61/1.51 setukpairinjR: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setukpairinjR,definition,
% 2.61/1.51 ( setukpairinjR
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.61/1.51 ( ( ( kpair @ Xx @ Xy )
% 2.61/1.51 = ( kpair @ Xz @ Xu ) )
% 2.61/1.51 => ( Xy = Xu ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ksndsingleton_type,type,
% 2.61/1.51 ksndsingleton: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ksndsingleton,definition,
% 2.61/1.51 ( ksndsingleton
% 2.61/1.51 = ( ! [Xu: $i] :
% 2.61/1.51 ( ( iskpair @ Xu )
% 2.61/1.51 => ( singleton
% 2.61/1.51 @ ( dsetconstr @ ( setunion @ Xu )
% 2.61/1.51 @ ^ [Xx: $i] :
% 2.61/1.51 ( Xu
% 2.61/1.51 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ksnd_type,type,
% 2.61/1.51 ksnd: $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(ksndpairEq_type,type,
% 2.61/1.51 ksndpairEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ksndpairEq,definition,
% 2.61/1.51 ( ksndpairEq
% 2.61/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.61/1.51 = Xy ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(kpairsurjEq_type,type,
% 2.61/1.51 kpairsurjEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(kpairsurjEq,definition,
% 2.61/1.51 ( kpairsurjEq
% 2.61/1.51 = ( ! [Xu: $i] :
% 2.61/1.51 ( ( iskpair @ Xu )
% 2.61/1.51 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.61/1.51 = Xu ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodsndin_type,type,
% 2.61/1.51 cartprodsndin: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodsndin,definition,
% 2.61/1.51 ( cartprodsndin
% 2.61/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.61/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairmemEL_type,type,
% 2.61/1.51 cartprodpairmemEL: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairmemEL,definition,
% 2.61/1.51 ( cartprodpairmemEL
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairmemER_type,type,
% 2.61/1.51 cartprodpairmemER: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairmemER,definition,
% 2.61/1.51 ( cartprodpairmemER
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( in @ Xy @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempaircEq_type,type,
% 2.61/1.51 cartprodmempaircEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodmempaircEq,definition,
% 2.61/1.51 ( cartprodmempaircEq
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( kpair @ Xx @ Xy )
% 2.61/1.51 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodfstpairEq_type,type,
% 2.61/1.51 cartprodfstpairEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodfstpairEq,definition,
% 2.61/1.51 ( cartprodfstpairEq
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.61/1.51 = Xx ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodsndpairEq_type,type,
% 2.61/1.51 cartprodsndpairEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodsndpairEq,definition,
% 2.61/1.51 ( cartprodsndpairEq
% 2.61/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.61/1.51 = Xy ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairsurjEq_type,type,
% 2.61/1.51 cartprodpairsurjEq: $o ).
% 2.61/1.51
% 2.61/1.51 thf(cartprodpairsurjEq,definition,
% 2.61/1.51 ( cartprodpairsurjEq
% 2.61/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.61/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.61/1.51 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.61/1.51 = Xu ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(breln_type,type,
% 2.61/1.51 breln: $i > $i > $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(breln,definition,
% 2.61/1.51 ( breln
% 2.61/1.51 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstr_type,type,
% 2.61/1.51 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrI_type,type,
% 2.61/1.51 dpsetconstrI: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrI,definition,
% 2.61/1.51 ( dpsetconstrI
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( Xphi @ Xx @ Xy )
% 2.61/1.51 => ( in @ ( kpair @ Xx @ Xy )
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrSub_type,type,
% 2.61/1.51 dpsetconstrSub: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrSub,definition,
% 2.61/1.51 ( dpsetconstrSub
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.61/1.51 ( subset
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.61/1.51 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(setOfPairsIsBReln_type,type,
% 2.61/1.51 setOfPairsIsBReln: $o ).
% 2.61/1.51
% 2.61/1.51 thf(setOfPairsIsBReln,definition,
% 2.61/1.51 ( setOfPairsIsBReln
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.61/1.51 ( breln @ A @ B
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrERa_type,type,
% 2.61/1.51 dpsetconstrERa: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrERa,definition,
% 2.61/1.51 ( dpsetconstrERa
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ! [Xy: $i] :
% 2.61/1.51 ( ( in @ Xy @ B )
% 2.61/1.51 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.61/1.51 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrEL1_type,type,
% 2.61/1.51 dpsetconstrEL1: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrEL1,definition,
% 2.61/1.51 ( dpsetconstrEL1
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.61/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrEL2_type,type,
% 2.61/1.51 dpsetconstrEL2: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrEL2,definition,
% 2.61/1.51 ( dpsetconstrEL2
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.61/1.51 => ( in @ Xy @ B ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrER_type,type,
% 2.61/1.51 dpsetconstrER: $o ).
% 2.61/1.51
% 2.61/1.51 thf(dpsetconstrER,definition,
% 2.61/1.51 ( dpsetconstrER
% 2.61/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.61/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.61/1.51 @ ( dpsetconstr @ A @ B
% 2.61/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.61/1.51 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(func_type,type,
% 2.61/1.51 func: $i > $i > $i > $o ).
% 2.61/1.51
% 2.61/1.51 thf(func,definition,
% 2.61/1.51 ( func
% 2.61/1.51 = ( ^ [A: $i,B: $i,R: $i] :
% 2.61/1.51 ( ( breln @ A @ B @ R )
% 2.61/1.51 & ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( ex1 @ B
% 2.61/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(funcSet_type,type,
% 2.61/1.51 funcSet: $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(funcSet,definition,
% 2.61/1.51 ( funcSet
% 2.61/1.51 = ( ^ [A: $i,B: $i] :
% 2.61/1.51 ( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
% 2.61/1.51 @ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(funcImageSingleton_type,type,
% 2.61/1.51 funcImageSingleton: $o ).
% 2.61/1.51
% 2.61/1.51 thf(funcImageSingleton,definition,
% 2.61/1.51 ( funcImageSingleton
% 2.61/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( func @ A @ B @ Xf )
% 2.61/1.51 => ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( singleton
% 2.61/1.51 @ ( dsetconstr @ B
% 2.61/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(apProp_type,type,
% 2.61/1.51 apProp: $o ).
% 2.61/1.51
% 2.61/1.51 thf(apProp,definition,
% 2.61/1.51 ( apProp
% 2.61/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( func @ A @ B @ Xf )
% 2.61/1.51 => ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in
% 2.61/1.51 @ ( setunion
% 2.61/1.51 @ ( dsetconstr @ B
% 2.61/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.61/1.51 @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ap_type,type,
% 2.61/1.51 ap: $i > $i > $i > $i > $i ).
% 2.61/1.51
% 2.61/1.51 thf(ap,definition,
% 2.61/1.51 ( ap
% 2.61/1.51 = ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
% 2.61/1.51 ( setunion
% 2.61/1.51 @ ( dsetconstr @ B
% 2.61/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(app_type,type,
% 2.61/1.51 app: $o ).
% 2.61/1.51
% 2.61/1.51 thf(app,definition,
% 2.61/1.51 ( app
% 2.61/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( func @ A @ B @ Xf )
% 2.61/1.51 => ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(infuncsetfunc_type,type,
% 2.61/1.51 infuncsetfunc: $o ).
% 2.61/1.51
% 2.61/1.51 thf(infuncsetfunc,definition,
% 2.61/1.51 ( infuncsetfunc
% 2.61/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.61/1.51 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(ap2p_type,type,
% 2.61/1.51 ap2p: $o ).
% 2.61/1.51
% 2.61/1.51 thf(ap2p,definition,
% 2.61/1.51 ( ap2p
% 2.61/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.61/1.51 => ! [Xx: $i] :
% 2.61/1.51 ( ( in @ Xx @ A )
% 2.61/1.51 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.61/1.51
% 2.61/1.51 thf(funcinfuncset,conjecture,
% 2.61/1.51 ( setextAx
% 2.61/1.51 => ( emptysetAx
% 2.61/1.51 => ( setadjoinAx
% 2.61/1.51 => ( powersetAx
% 2.61/1.51 => ( setunionAx
% 2.61/1.51 => ( omega0Ax
% 2.61/1.51 => ( omegaSAx
% 2.61/1.51 => ( omegaIndAx
% 2.61/1.51 => ( replAx
% 2.61/1.51 => ( foundationAx
% 2.61/1.51 => ( wellorderingAx
% 2.61/1.51 => ( descrp
% 2.61/1.51 => ( dsetconstrI
% 2.61/1.51 => ( dsetconstrEL
% 2.61/1.51 => ( dsetconstrER
% 2.61/1.51 => ( exuE1
% 2.61/1.51 => ( prop2setE
% 2.61/1.51 => ( emptysetE
% 2.61/1.51 => ( emptysetimpfalse
% 2.61/1.51 => ( notinemptyset
% 2.61/1.51 => ( exuE3e
% 2.61/1.51 => ( setext
% 2.61/1.51 => ( emptyI
% 2.61/1.51 => ( noeltsimpempty
% 2.61/1.51 => ( setbeta
% 2.61/1.51 => ( nonemptyE1
% 2.61/1.51 => ( nonemptyI
% 2.61/1.51 => ( nonemptyI1
% 2.61/1.51 => ( setadjoinIL
% 2.61/1.51 => ( emptyinunitempty
% 2.61/1.51 => ( setadjoinIR
% 2.61/1.51 => ( setadjoinE
% 2.61/1.51 => ( setadjoinOr
% 2.61/1.51 => ( setoftrueEq
% 2.61/1.51 => ( powersetI
% 2.61/1.51 => ( emptyinPowerset
% 2.61/1.51 => ( emptyInPowerset
% 2.61/1.51 => ( powersetE
% 2.61/1.51 => ( setunionI
% 2.61/1.51 => ( setunionE
% 2.61/1.51 => ( subPowSU
% 2.61/1.51 => ( exuE2
% 2.61/1.51 => ( nonemptyImpWitness
% 2.61/1.51 => ( uniqinunit
% 2.61/1.51 => ( notinsingleton
% 2.61/1.51 => ( eqinunit
% 2.61/1.51 => ( singletonsswitch
% 2.61/1.51 => ( upairsetE
% 2.61/1.51 => ( upairsetIL
% 2.61/1.51 => ( upairsetIR
% 2.61/1.51 => ( emptyE1
% 2.61/1.51 => ( vacuousDall
% 2.61/1.51 => ( quantDeMorgan1
% 2.61/1.51 => ( quantDeMorgan2
% 2.61/1.51 => ( quantDeMorgan3
% 2.61/1.51 => ( quantDeMorgan4
% 2.61/1.51 => ( prop2setI
% 2.61/1.51 => ( prop2set2propI
% 2.61/1.51 => ( notdexE
% 2.61/1.51 => ( notdallE
% 2.61/1.51 => ( exuI1
% 2.61/1.51 => ( exuI3
% 2.61/1.51 => ( exuI2
% 2.61/1.51 => ( inCongP
% 2.61/1.51 => ( in__Cong
% 2.61/1.51 => ( exuE3u
% 2.61/1.51 => ( exu__Cong
% 2.61/1.51 => ( emptyset__Cong
% 2.61/1.51 => ( setadjoin__Cong
% 2.61/1.51 => ( powerset__Cong
% 2.61/1.51 => ( setunion__Cong
% 2.61/1.51 => ( omega__Cong
% 2.61/1.51 => ( exuEu
% 2.61/1.51 => ( descr__Cong
% 2.61/1.51 => ( dsetconstr__Cong
% 2.61/1.51 => ( subsetI1
% 2.61/1.51 => ( eqimpsubset2
% 2.61/1.51 => ( eqimpsubset1
% 2.61/1.51 => ( subsetI2
% 2.61/1.51 => ( emptysetsubset
% 2.61/1.51 => ( subsetE
% 2.61/1.51 => ( subsetE2
% 2.61/1.51 => ( notsubsetI
% 2.61/1.51 => ( notequalI1
% 2.61/1.51 => ( notequalI2
% 2.61/1.51 => ( subsetRefl
% 2.61/1.51 => ( subsetTrans
% 2.61/1.51 => ( setadjoinSub
% 2.61/1.51 => ( setadjoinSub2
% 2.61/1.51 => ( subset2powerset
% 2.61/1.51 => ( setextsub
% 2.61/1.51 => ( subsetemptysetimpeq
% 2.61/1.51 => ( powersetI1
% 2.61/1.51 => ( powersetE1
% 2.61/1.51 => ( inPowerset
% 2.61/1.51 => ( powersetsubset
% 2.61/1.51 => ( sepInPowerset
% 2.61/1.51 => ( sepSubset
% 2.61/1.51 => ( binunionIL
% 2.61/1.51 => ( upairset2IR
% 2.61/1.51 => ( binunionIR
% 2.61/1.51 => ( binunionEcases
% 2.61/1.51 => ( binunionE
% 2.61/1.51 => ( binunionLsub
% 2.61/1.51 => ( binunionRsub
% 2.61/1.51 => ( binintersectI
% 2.61/1.51 => ( binintersectSubset5
% 2.61/1.51 => ( binintersectEL
% 2.61/1.51 => ( binintersectLsub
% 2.61/1.51 => ( binintersectSubset2
% 2.61/1.51 => ( binintersectSubset3
% 2.61/1.51 => ( binintersectER
% 2.61/1.51 => ( disjointsetsI1
% 2.61/1.51 => ( binintersectRsub
% 2.61/1.51 => ( binintersectSubset4
% 2.61/1.51 => ( binintersectSubset1
% 2.61/1.51 => ( bs114d
% 2.61/1.51 => ( setminusI
% 2.61/1.51 => ( setminusEL
% 2.61/1.51 => ( setminusER
% 2.61/1.51 => ( setminusSubset2
% 2.61/1.51 => ( setminusERneg
% 2.61/1.51 => ( setminusELneg
% 2.61/1.51 => ( setminusILneg
% 2.61/1.51 => ( setminusIRneg
% 2.61/1.51 => ( setminusLsub
% 2.61/1.51 => ( setminusSubset1
% 2.61/1.51 => ( symdiffE
% 2.61/1.51 => ( symdiffI1
% 2.61/1.51 => ( symdiffI2
% 2.61/1.51 => ( symdiffIneg1
% 2.61/1.51 => ( symdiffIneg2
% 2.61/1.51 => ( secondinupair
% 2.61/1.51 => ( setukpairIL
% 2.61/1.51 => ( setukpairIR
% 2.61/1.51 => ( kpairiskpair
% 2.61/1.51 => ( kpairp
% 2.61/1.51 => ( singletonsubset
% 2.61/1.51 => ( singletoninpowerset
% 2.61/1.51 => ( singletoninpowunion
% 2.61/1.51 => ( upairset2E
% 2.61/1.51 => ( upairsubunion
% 2.61/1.51 => ( upairinpowunion
% 2.61/1.51 => ( ubforcartprodlem1
% 2.61/1.51 => ( ubforcartprodlem2
% 2.61/1.51 => ( ubforcartprodlem3
% 2.61/1.51 => ( cartprodpairin
% 2.61/1.51 => ( cartprodmempair1
% 2.61/1.51 => ( cartprodmempair
% 2.61/1.51 => ( setunionE2
% 2.61/1.51 => ( setunionsingleton1
% 2.61/1.51 => ( setunionsingleton2
% 2.61/1.51 => ( setunionsingleton
% 2.61/1.51 => ( singletonprop
% 2.61/1.51 => ( ex1E1
% 2.61/1.51 => ( ex1I
% 2.61/1.51 => ( ex1I2
% 2.61/1.51 => ( singletonsuniq
% 2.61/1.51 => ( setukpairinjL1
% 2.61/1.51 => ( kfstsingleton
% 2.61/1.51 => ( theprop
% 2.61/1.51 => ( kfstpairEq
% 2.61/1.51 => ( cartprodfstin
% 2.61/1.51 => ( setukpairinjL2
% 2.61/1.51 => ( setukpairinjL
% 2.61/1.51 => ( setukpairinjR11
% 2.61/1.51 => ( setukpairinjR12
% 2.61/1.51 => ( setukpairinjR1
% 2.61/1.51 => ( upairequniteq
% 2.61/1.51 => ( setukpairinjR2
% 2.61/1.51 => ( setukpairinjR
% 2.61/1.51 => ( ksndsingleton
% 2.61/1.51 => ( ksndpairEq
% 2.61/1.51 => ( kpairsurjEq
% 2.61/1.51 => ( cartprodsndin
% 2.61/1.51 => ( cartprodpairmemEL
% 2.61/1.51 => ( cartprodpairmemER
% 2.61/1.51 => ( cartprodmempaircEq
% 2.61/1.51 => ( cartprodfstpairEq
% 2.61/1.51 => ( cartprodsndpairEq
% 2.61/1.51 => ( cartprodpairsurjEq
% 2.61/1.51 => ( dpsetconstrI
% 2.61/1.51 => ( dpsetconstrSub
% 2.61/1.51 => ( setOfPairsIsBReln
% 2.61/1.51 => ( dpsetconstrERa
% 2.61/1.51 => ( dpsetconstrEL1
% 2.61/1.51 => ( dpsetconstrEL2
% 2.61/1.51 => ( dpsetconstrER
% 2.61/1.51 => ( funcImageSingleton
% 2.61/1.51 => ( apProp
% 2.61/1.51 => ( app
% 2.61/1.51 => ( infuncsetfunc
% 2.61/1.51 => ( ap2p
% 2.61/1.51 => ! [A: $i,B: $i,Xf: $i] :
% 2.61/1.51 ( ( func @ A @ B @ Xf )
% 2.61/1.51 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.61/1.51 ------------------------
% 2.61/1.52 % (3598)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_3362 for (2999ds/275Mi)
% 2.61/1.53 % (3599)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/18Mi)
% 2.61/1.53 % (3599)Instruction limit reached!
% 2.61/1.53 % (3599)------------------------------
% 2.61/1.53 % (3599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (3599)Termination reason: Unknown
% 2.61/1.53 % (3599)Termination phase: Property scanning
% 2.61/1.53
% 2.61/1.53 % (3599)Memory used [KB]: 1791
% 2.61/1.53 % (3599)Time elapsed: 0.008 s
% 2.61/1.53 % (3599)Instructions burned: 20 (million)
% 2.61/1.53 % (3599)------------------------------
% 2.61/1.53 % (3599)------------------------------
% 2.61/1.53 % (3593)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/183Mi)
% 2.61/1.53 % (3596)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/2Mi)
% 2.61/1.53 % (3595)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_3362 for (2999ds/27Mi)
% 2.61/1.53 % (3594)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_3362 for (2999ds/4Mi)
% 2.61/1.53 % (3597)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_3362 for (2999ds/2Mi)
% 2.61/1.53 % (3596)Instruction limit reached!
% 2.61/1.53 % (3596)------------------------------
% 2.61/1.53 % (3596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (3596)Termination reason: Unknown
% 2.61/1.53 % (3596)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (3596)Memory used [KB]: 1407
% 2.61/1.53 % (3596)Time elapsed: 0.004 s
% 2.61/1.53 % (3596)Instructions burned: 3 (million)
% 2.61/1.53 % (3596)------------------------------
% 2.61/1.53 % (3596)------------------------------
% 2.61/1.53 % (3597)Instruction limit reached!
% 2.61/1.53 % (3597)------------------------------
% 2.61/1.53 % (3597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (3597)Termination reason: Unknown
% 2.61/1.53 % (3597)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (3597)Memory used [KB]: 1407
% 2.61/1.53 % (3597)Time elapsed: 0.004 s
% 2.61/1.53 % (3597)Instructions burned: 3 (million)
% 2.61/1.53 % (3597)------------------------------
% 2.61/1.53 % (3597)------------------------------
% 2.61/1.53 % (3594)Instruction limit reached!
% 2.61/1.53 % (3594)------------------------------
% 2.61/1.53 % (3594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (3594)Termination reason: Unknown
% 2.61/1.53 % (3594)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (3594)Memory used [KB]: 1407
% 2.61/1.53 % (3594)Time elapsed: 0.004 s
% 2.61/1.53 % (3594)Instructions burned: 5 (million)
% 2.61/1.53 % (3594)------------------------------
% 2.61/1.53 % (3594)------------------------------
% 2.61/1.54 % (3604)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/3Mi)
% 2.61/1.54 % (3604)Instruction limit reached!
% 2.61/1.54 % (3604)------------------------------
% 2.61/1.54 % (3604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.54 % (3604)Termination reason: Unknown
% 2.61/1.54 % (3604)Termination phase: shuffling
% 2.61/1.54
% 2.61/1.54 % (3604)Memory used [KB]: 1407
% 2.61/1.54 % (3604)Time elapsed: 0.003 s
% 2.61/1.54 % (3604)Instructions burned: 5 (million)
% 2.61/1.54 % (3604)------------------------------
% 2.61/1.54 % (3604)------------------------------
% 2.61/1.55 % (3595)Instruction limit reached!
% 2.61/1.55 % (3595)------------------------------
% 2.61/1.55 % (3595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (3595)Termination reason: Unknown
% 2.61/1.55 % (3595)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (3595)Memory used [KB]: 1918
% 2.61/1.55 % (3595)Time elapsed: 0.017 s
% 2.61/1.55 % (3595)Instructions burned: 28 (million)
% 2.61/1.55 % (3595)------------------------------
% 2.61/1.55 % (3595)------------------------------
% 2.61/1.55 % (3606)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_3362 for (2999ds/37Mi)
% 2.61/1.55 % (3607)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_3362 for (2999ds/15Mi)
% 2.61/1.55 % (3609)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_3362 for (2999ds/3Mi)
% 2.61/1.55 % (3614)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_3362 for (2999ds/1041Mi)
% 2.61/1.55 % (3609)Instruction limit reached!
% 2.61/1.55 % (3609)------------------------------
% 2.61/1.55 % (3609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (3609)Termination reason: Unknown
% 2.61/1.55 % (3609)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (3609)Memory used [KB]: 1407
% 2.61/1.55 % (3609)Time elapsed: 0.004 s
% 2.61/1.55 % (3609)Instructions burned: 4 (million)
% 2.61/1.55 % (3609)------------------------------
% 2.61/1.55 % (3609)------------------------------
% 2.61/1.56 % (3607)Instruction limit reached!
% 2.61/1.56 % (3607)------------------------------
% 2.61/1.56 % (3607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.56 % (3607)Termination reason: Unknown
% 2.61/1.56 % (3607)Termination phase: shuffling
% 2.61/1.56
% 2.61/1.56 % (3607)Memory used [KB]: 1663
% 2.61/1.56 % (3607)Time elapsed: 0.012 s
% 2.61/1.56 % (3607)Instructions burned: 16 (million)
% 2.61/1.56 % (3607)------------------------------
% 2.61/1.56 % (3607)------------------------------
% 2.61/1.56 % (3615)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/7Mi)
% 2.61/1.57 % (3616)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/16Mi)
% 2.61/1.57 % (3615)Instruction limit reached!
% 2.61/1.57 % (3615)------------------------------
% 2.61/1.57 % (3615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.57 % (3615)Termination reason: Unknown
% 2.61/1.57 % (3615)Termination phase: shuffling
% 2.61/1.57
% 2.61/1.57 % (3615)Memory used [KB]: 1535
% 2.61/1.57 % (3615)Time elapsed: 0.006 s
% 2.61/1.57 % (3615)Instructions burned: 7 (million)
% 2.61/1.57 % (3615)------------------------------
% 2.61/1.57 % (3615)------------------------------
% 2.61/1.57 % (3606)Instruction limit reached!
% 2.61/1.57 % (3606)------------------------------
% 2.61/1.57 % (3606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.57 % (3606)Termination reason: Unknown
% 2.61/1.57 % (3606)Termination phase: Property scanning
% 2.61/1.57
% 2.61/1.57 % (3606)Memory used [KB]: 2046
% 2.61/1.57 % (3606)Time elapsed: 0.021 s
% 2.61/1.57 % (3606)Instructions burned: 37 (million)
% 2.61/1.57 % (3606)------------------------------
% 2.61/1.57 % (3606)------------------------------
% 2.61/1.57 % (3616)Instruction limit reached!
% 2.61/1.57 % (3616)------------------------------
% 2.61/1.57 % (3616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.57 % (3616)Termination reason: Unknown
% 2.61/1.57 % (3616)Termination phase: shuffling
% 2.61/1.57
% 2.61/1.57 % (3616)Memory used [KB]: 1663
% 2.61/1.57 % (3616)Time elapsed: 0.007 s
% 2.61/1.57 % (3616)Instructions burned: 17 (million)
% 2.61/1.57 % (3616)------------------------------
% 2.61/1.57 % (3616)------------------------------
% 2.61/1.58 % (3625)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_3362 for (2999ds/3Mi)
% 2.61/1.58 % (3625)Instruction limit reached!
% 2.61/1.58 % (3625)------------------------------
% 2.61/1.58 % (3625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.58 % (3625)Termination reason: Unknown
% 2.61/1.58 % (3625)Termination phase: shuffling
% 2.61/1.58
% 2.61/1.58 % (3625)Memory used [KB]: 1407
% 2.61/1.58 % (3625)Time elapsed: 0.003 s
% 2.61/1.58 % (3625)Instructions burned: 3 (million)
% 2.61/1.58 % (3625)------------------------------
% 2.61/1.58 % (3625)------------------------------
% 2.61/1.58 % (3635)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/3Mi)
% 2.61/1.59 % (3635)Instruction limit reached!
% 2.61/1.59 % (3635)------------------------------
% 2.61/1.59 % (3635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.59 % (3635)Termination reason: Unknown
% 2.61/1.59 % (3635)Termination phase: shuffling
% 2.61/1.59
% 2.61/1.59 % (3635)Memory used [KB]: 1407
% 2.61/1.59 % (3635)Time elapsed: 0.003 s
% 2.61/1.59 % (3635)Instructions burned: 5 (million)
% 2.61/1.59 % (3635)------------------------------
% 2.61/1.59 % (3635)------------------------------
% 2.61/1.59 % (3630)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_3362 for (2999ds/3Mi)
% 2.61/1.59 % (3630)Instruction limit reached!
% 2.61/1.59 % (3630)------------------------------
% 2.61/1.59 % (3630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.59 % (3630)Termination reason: Unknown
% 2.61/1.59 % (3630)Termination phase: shuffling
% 2.61/1.59
% 2.61/1.59 % (3630)Memory used [KB]: 1407
% 2.61/1.59 % (3630)Time elapsed: 0.004 s
% 2.61/1.59 % (3630)Instructions burned: 4 (million)
% 2.61/1.59 % (3630)------------------------------
% 2.61/1.59 % (3630)------------------------------
% 2.61/1.59 % (3631)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/7Mi)
% 2.61/1.59 % (3639)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/4Mi)
% 2.61/1.59 % (3639)Instruction limit reached!
% 2.61/1.59 % (3639)------------------------------
% 2.61/1.59 % (3639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.59 % (3639)Termination reason: Unknown
% 2.61/1.59 % (3639)Termination phase: shuffling
% 2.61/1.59
% 2.61/1.59 % (3639)Memory used [KB]: 1407
% 2.61/1.59 % (3639)Time elapsed: 0.003 s
% 2.61/1.59 % (3639)Instructions burned: 5 (million)
% 2.61/1.59 % (3639)------------------------------
% 2.61/1.59 % (3639)------------------------------
% 2.61/1.59 % (3631)Instruction limit reached!
% 2.61/1.59 % (3631)------------------------------
% 2.61/1.59 % (3631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.59 % (3631)Termination reason: Unknown
% 2.61/1.59 % (3631)Termination phase: shuffling
% 2.61/1.59
% 2.61/1.59 % (3631)Memory used [KB]: 1535
% 2.61/1.59 % (3631)Time elapsed: 0.006 s
% 2.61/1.59 % (3631)Instructions burned: 8 (million)
% 2.61/1.59 % (3631)------------------------------
% 2.61/1.59 % (3631)------------------------------
% 2.61/1.59 % (3642)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/18Mi)
% 2.62/1.60 % (3643)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/710Mi)
% 2.62/1.60 % (3642)Instruction limit reached!
% 2.62/1.60 % (3642)------------------------------
% 2.62/1.60 % (3642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.60 % (3642)Termination reason: Unknown
% 2.62/1.60 % (3642)Termination phase: shuffling
% 2.62/1.60
% 2.62/1.60 % (3642)Memory used [KB]: 1791
% 2.62/1.60 % (3642)Time elapsed: 0.007 s
% 2.62/1.60 % (3642)Instructions burned: 21 (million)
% 2.62/1.60 % (3642)------------------------------
% 2.62/1.60 % (3642)------------------------------
% 2.62/1.60 % (3644)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/6Mi)
% 2.62/1.60 % (3644)Instruction limit reached!
% 2.62/1.60 % (3644)------------------------------
% 2.62/1.60 % (3644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.60 % (3644)Termination reason: Unknown
% 2.62/1.60 % (3644)Termination phase: shuffling
% 2.62/1.60
% 2.62/1.60 % (3644)Memory used [KB]: 1535
% 2.62/1.60 % (3644)Time elapsed: 0.004 s
% 2.62/1.60 % (3644)Instructions burned: 7 (million)
% 2.62/1.60 % (3644)------------------------------
% 2.62/1.60 % (3644)------------------------------
% 2.62/1.61 % (3593)Instruction limit reached!
% 2.62/1.61 % (3593)------------------------------
% 2.62/1.61 % (3593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.61 % (3593)Termination reason: Unknown
% 2.62/1.61 % (3593)Termination phase: Saturation
% 2.62/1.61
% 2.62/1.61 % (3593)Memory used [KB]: 7547
% 2.62/1.61 % (3593)Time elapsed: 0.076 s
% 2.62/1.61 % (3593)Instructions burned: 186 (million)
% 2.62/1.61 % (3593)------------------------------
% 2.62/1.61 % (3593)------------------------------
% 2.62/1.61 % (3598)Instruction limit reached!
% 2.62/1.61 % (3598)------------------------------
% 2.62/1.61 % (3598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.61 % (3598)Termination reason: Unknown
% 2.62/1.61 % (3598)Termination phase: Saturation
% 2.62/1.61
% 2.62/1.61 % (3598)Memory used [KB]: 8443
% 2.62/1.61 % (3598)Time elapsed: 0.085 s
% 2.62/1.61 % (3598)Instructions burned: 276 (million)
% 2.62/1.61 % (3598)------------------------------
% 2.62/1.61 % (3598)------------------------------
% 2.62/1.61 % (3645)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_3362 for (2999ds/902Mi)
% 2.62/1.61 % (3651)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_3362 for (2999ds/21Mi)
% 2.62/1.61 % (3656)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/5Mi)
% 2.62/1.62 % (3651)Instruction limit reached!
% 2.62/1.62 % (3651)------------------------------
% 2.62/1.62 % (3651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.62 % (3651)Termination reason: Unknown
% 2.62/1.62 % (3651)Termination phase: shuffling
% 2.62/1.62
% 2.62/1.62 % (3651)Memory used [KB]: 1791
% 2.62/1.62 % (3651)Time elapsed: 0.007 s
% 2.62/1.62 % (3651)Instructions burned: 22 (million)
% 2.62/1.62 % (3651)------------------------------
% 2.62/1.62 % (3651)------------------------------
% 2.62/1.62 % (3656)Instruction limit reached!
% 2.62/1.62 % (3656)------------------------------
% 2.62/1.62 % (3656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.62 % (3656)Termination reason: Unknown
% 2.62/1.62 % (3656)Termination phase: shuffling
% 2.62/1.62
% 2.62/1.62 % (3656)Memory used [KB]: 1535
% 2.62/1.62 % (3656)Time elapsed: 0.004 s
% 2.62/1.62 % (3656)Instructions burned: 8 (million)
% 2.62/1.62 % (3656)------------------------------
% 2.62/1.62 % (3656)------------------------------
% 2.62/1.62 % (3658)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_3362 for (2999ds/6Mi)
% 2.62/1.62 % (3661)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/377Mi)
% 2.62/1.62 % (3658)Instruction limit reached!
% 2.62/1.62 % (3658)------------------------------
% 2.62/1.62 % (3658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.62 % (3658)Termination reason: Unknown
% 2.62/1.62 % (3658)Termination phase: shuffling
% 2.62/1.62
% 2.62/1.62 % (3658)Memory used [KB]: 1535
% 2.62/1.62 % (3658)Time elapsed: 0.004 s
% 2.62/1.62 % (3658)Instructions burned: 8 (million)
% 2.62/1.62 % (3658)------------------------------
% 2.62/1.62 % (3658)------------------------------
% 2.62/1.63 % (3666)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_3362 for (2999ds/779Mi)
% 2.62/1.63 % (3667)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_3362 for (2999ds/19Mi)
% 2.62/1.63 % (3670)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3362 for (2999ds/879Mi)
% 2.62/1.63 % (3667)Instruction limit reached!
% 2.62/1.63 % (3667)------------------------------
% 2.62/1.63 % (3667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.63 % (3667)Termination reason: Unknown
% 2.62/1.63 % (3667)Termination phase: shuffling
% 2.62/1.63
% 2.62/1.63 % (3667)Memory used [KB]: 1791
% 2.62/1.63 % (3667)Time elapsed: 0.008 s
% 2.62/1.63 % (3667)Instructions burned: 21 (million)
% 2.62/1.63 % (3667)------------------------------
% 2.62/1.63 % (3667)------------------------------
% 2.62/1.64 % (3677)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3362 for (2998ds/17Mi)
% 2.62/1.65 % (3677)Instruction limit reached!
% 2.62/1.65 % (3677)------------------------------
% 2.62/1.65 % (3677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.65 % (3677)Termination reason: Unknown
% 2.62/1.65 % (3677)Termination phase: shuffling
% 2.62/1.65
% 2.62/1.65 % (3677)Memory used [KB]: 1663
% 2.62/1.65 % (3677)Time elapsed: 0.006 s
% 2.62/1.65 % (3677)Instructions burned: 17 (million)
% 2.62/1.65 % (3677)------------------------------
% 2.62/1.65 % (3677)------------------------------
% 2.62/1.66 % (3686)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3362 for (2998ds/3Mi)
% 2.62/1.66 % (3686)Instruction limit reached!
% 2.62/1.66 % (3686)------------------------------
% 2.62/1.66 % (3686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.66 % (3686)Termination reason: Unknown
% 2.62/1.66 % (3686)Termination phase: shuffling
% 2.62/1.66
% 2.62/1.66 % (3686)Memory used [KB]: 1407
% 2.62/1.66 % (3686)Time elapsed: 0.002 s
% 2.62/1.66 % (3686)Instructions burned: 4 (million)
% 2.62/1.66 % (3686)------------------------------
% 2.62/1.66 % (3686)------------------------------
% 2.62/1.67 % (3694)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3362 for (2998ds/30Mi)
% 2.62/1.68 % (3694)Instruction limit reached!
% 2.62/1.68 % (3694)------------------------------
% 2.62/1.68 % (3694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.68 % (3694)Termination reason: Unknown
% 2.62/1.68 % (3694)Termination phase: shuffling
% 2.62/1.68
% 2.62/1.68 % (3694)Memory used [KB]: 1918
% 2.62/1.68 % (3694)Time elapsed: 0.011 s
% 2.62/1.68 % (3694)Instructions burned: 31 (million)
% 2.62/1.68 % (3694)------------------------------
% 2.62/1.68 % (3694)------------------------------
% 2.62/1.69 % (3701)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3362 for (2998ds/127Mi)
% 2.62/1.72 % (3701)Instruction limit reached!
% 2.62/1.72 % (3701)------------------------------
% 2.62/1.72 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.72 % (3701)Termination reason: Unknown
% 2.62/1.72 % (3701)Termination phase: Saturation
% 2.62/1.72
% 2.62/1.72 % (3701)Memory used [KB]: 6908
% 2.62/1.72 % (3701)Time elapsed: 0.036 s
% 2.62/1.72 % (3701)Instructions burned: 127 (million)
% 2.62/1.72 % (3701)------------------------------
% 2.62/1.72 % (3701)------------------------------
% 2.62/1.72 % (3661)Instruction limit reached!
% 2.62/1.72 % (3661)------------------------------
% 2.62/1.72 % (3661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.72 % (3661)Termination reason: Unknown
% 2.62/1.72 % (3661)Termination phase: Saturation
% 2.62/1.72
% 2.62/1.72 % (3661)Memory used [KB]: 8443
% 2.62/1.72 % (3661)Time elapsed: 0.108 s
% 2.62/1.72 % (3661)Instructions burned: 377 (million)
% 2.62/1.72 % (3661)------------------------------
% 2.62/1.72 % (3661)------------------------------
% 2.62/1.73 % (3722)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_3362 for (2997ds/3Mi)
% 2.62/1.73 % (3721)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3362 for (2997ds/100Mi)
% 2.62/1.74 % (3722)Instruction limit reached!
% 2.62/1.74 % (3722)------------------------------
% 2.62/1.74 % (3722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.74 % (3722)Termination reason: Unknown
% 2.62/1.74 % (3722)Termination phase: shuffling
% 2.62/1.74
% 2.62/1.74 % (3722)Memory used [KB]: 1407
% 2.62/1.74 % (3722)Time elapsed: 0.003 s
% 2.62/1.74 % (3722)Instructions burned: 5 (million)
% 2.62/1.74 % (3722)------------------------------
% 2.62/1.74 % (3722)------------------------------
% 2.62/1.75 % (3727)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_3362 for (2997ds/20Mi)
% 2.62/1.75 % (3727)Instruction limit reached!
% 2.62/1.75 % (3727)------------------------------
% 2.62/1.75 % (3727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.75 % (3727)Termination reason: Unknown
% 2.62/1.75 % (3727)Termination phase: Property scanning
% 2.62/1.75
% 2.62/1.75 % (3727)Memory used [KB]: 1791
% 2.62/1.75 % (3727)Time elapsed: 0.008 s
% 2.62/1.75 % (3727)Instructions burned: 22 (million)
% 2.62/1.75 % (3727)------------------------------
% 2.62/1.75 % (3727)------------------------------
% 2.62/1.76 % (3737)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_3362 for (2997ds/86Mi)
% 2.62/1.76 % (3721)Instruction limit reached!
% 2.62/1.76 % (3721)------------------------------
% 2.62/1.76 % (3721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.76 % (3721)Termination reason: Unknown
% 2.62/1.76 % (3721)Termination phase: Saturation
% 2.62/1.76
% 2.62/1.76 % (3721)Memory used [KB]: 6780
% 2.62/1.76 % (3721)Time elapsed: 0.029 s
% 2.62/1.76 % (3721)Instructions burned: 102 (million)
% 2.62/1.76 % (3721)------------------------------
% 2.62/1.76 % (3721)------------------------------
% 2.62/1.78 % (3742)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_3362 for (2997ds/107Mi)
% 2.62/1.78 % (3737)Instruction limit reached!
% 2.62/1.78 % (3737)------------------------------
% 2.62/1.78 % (3737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.78 % (3737)Termination reason: Unknown
% 2.62/1.78 % (3737)Termination phase: Property scanning
% 2.62/1.78
% 2.62/1.78 % (3737)Memory used [KB]: 2174
% 2.62/1.78 % (3737)Time elapsed: 0.023 s
% 2.62/1.78 % (3737)Instructions burned: 87 (million)
% 2.62/1.78 % (3737)------------------------------
% 2.62/1.78 % (3737)------------------------------
% 2.62/1.79 % (3750)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_3362 for (2997ds/39Mi)
% 2.62/1.80 % (3750)Instruction limit reached!
% 2.62/1.80 % (3750)------------------------------
% 2.62/1.80 % (3750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.80 % (3750)Termination reason: Unknown
% 2.62/1.80 % (3750)Termination phase: Property scanning
% 2.62/1.80
% 2.62/1.80 % (3750)Memory used [KB]: 2174
% 2.62/1.80 % (3750)Time elapsed: 0.012 s
% 2.62/1.80 % (3750)Instructions burned: 39 (million)
% 2.62/1.80 % (3750)------------------------------
% 2.62/1.80 % (3750)------------------------------
% 2.62/1.81 % (3614)Instruction limit reached!
% 2.62/1.81 % (3614)------------------------------
% 2.62/1.81 % (3614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.81 % (3614)Termination reason: Unknown
% 2.62/1.81 % (3614)Termination phase: Saturation
% 2.62/1.81
% 2.62/1.81 % (3614)Memory used [KB]: 11513
% 2.62/1.81 % (3614)Time elapsed: 0.261 s
% 2.62/1.81 % (3614)Instructions burned: 1042 (million)
% 2.62/1.81 % (3614)------------------------------
% 2.62/1.81 % (3614)------------------------------
% 2.62/1.81 % (3666)Instruction limit reached!
% 2.62/1.81 % (3666)------------------------------
% 2.62/1.81 % (3666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.81 % (3666)Termination reason: Unknown
% 2.62/1.81 % (3666)Termination phase: Saturation
% 2.62/1.81
% 2.62/1.81 % (3666)Memory used [KB]: 7291
% 2.62/1.81 % (3666)Time elapsed: 0.189 s
% 2.62/1.81 % (3666)Instructions burned: 783 (million)
% 2.62/1.81 % (3666)------------------------------
% 2.62/1.81 % (3666)------------------------------
% 2.62/1.81 % (3759)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_3362 for (2997ds/448Mi)
% 2.62/1.82 % (3765)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_3362 for (2997ds/98Mi)
% 2.62/1.82 % (3764)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_3362 for (2997ds/46Mi)
% 2.62/1.83 % (3742)Instruction limit reached!
% 2.62/1.83 % (3742)------------------------------
% 2.62/1.83 % (3742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.83 % (3742)Termination reason: Unknown
% 2.62/1.83 % (3742)Termination phase: Property scanning
% 2.62/1.83
% 2.62/1.83 % (3742)Memory used [KB]: 2174
% 2.62/1.83 % (3742)Time elapsed: 0.053 s
% 2.62/1.83 % (3742)Instructions burned: 107 (million)
% 2.62/1.83 % (3742)------------------------------
% 2.62/1.83 % (3742)------------------------------
% 2.62/1.83 % (3643)Instruction limit reached!
% 2.62/1.83 % (3643)------------------------------
% 2.62/1.83 % (3643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.83 % (3643)Termination reason: Unknown
% 2.62/1.83 % (3643)Termination phase: Saturation
% 2.62/1.83
% 2.62/1.83 % (3643)Memory used [KB]: 9466
% 2.62/1.83 % (3643)Time elapsed: 0.237 s
% 2.62/1.83 % (3643)Instructions burned: 711 (million)
% 2.62/1.83 % (3643)------------------------------
% 2.62/1.83 % (3643)------------------------------
% 2.62/1.84 % (3764)Instruction limit reached!
% 2.62/1.84 % (3764)------------------------------
% 2.62/1.84 % (3764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.84 % (3764)Termination reason: Unknown
% 2.62/1.84 % (3764)Termination phase: Property scanning
% 2.62/1.84
% 2.62/1.84 % (3764)Memory used [KB]: 1918
% 2.62/1.84 % (3764)Time elapsed: 0.014 s
% 2.62/1.84 % (3764)Instructions burned: 47 (million)
% 2.62/1.84 % (3764)------------------------------
% 2.62/1.84 % (3764)------------------------------
% 2.62/1.84 % (3772)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_3362 for (2996ds/149Mi)
% 2.62/1.85 % (3773)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3362 for (2996ds/39Mi)
% 2.62/1.85 % (3765)Instruction limit reached!
% 2.62/1.85 % (3765)------------------------------
% 2.62/1.85 % (3765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.85 % (3765)Termination reason: Unknown
% 2.62/1.85 % (3765)Termination phase: Property scanning
% 2.62/1.85
% 2.62/1.85 % (3765)Memory used [KB]: 2302
% 2.62/1.85 % (3765)Time elapsed: 0.026 s
% 2.62/1.85 % (3765)Instructions burned: 98 (million)
% 2.62/1.85 % (3765)------------------------------
% 2.62/1.85 % (3765)------------------------------
% 2.62/1.85 % (3771)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_3362 for (2996ds/507Mi)
% 2.62/1.86 % (3773)Instruction limit reached!
% 2.62/1.86 % (3773)------------------------------
% 2.62/1.86 % (3773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.86 % (3773)Termination reason: Unknown
% 2.62/1.86 % (3773)Termination phase: Property scanning
% 2.62/1.86
% 2.62/1.86 % (3773)Memory used [KB]: 2046
% 2.62/1.86 % (3773)Time elapsed: 0.012 s
% 2.62/1.86 % (3773)Instructions burned: 40 (million)
% 2.62/1.86 % (3773)------------------------------
% 2.62/1.86 % (3773)------------------------------
% 2.62/1.86 % (3782)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_3362 for (2996ds/6Mi)
% 2.62/1.86 % (3782)Instruction limit reached!
% 2.62/1.86 % (3782)------------------------------
% 2.62/1.86 % (3782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.86 % (3782)Termination reason: Unknown
% 2.62/1.86 % (3782)Termination phase: shuffling
% 2.62/1.86
% 2.62/1.86 % (3782)Memory used [KB]: 1407
% 2.62/1.86 % (3782)Time elapsed: 0.003 s
% 2.62/1.86 % (3782)Instructions burned: 7 (million)
% 2.62/1.86 % (3782)------------------------------
% 2.62/1.86 % (3782)------------------------------
% 2.62/1.87 % (3789)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_3362 for (2996ds/1087Mi)
% 2.62/1.87 % (3792)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3362 for (2996ds/47Mi)
% 2.62/1.88 % (3792)Instruction limit reached!
% 2.62/1.88 % (3792)------------------------------
% 2.62/1.88 % (3792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.88 % (3792)Termination reason: Unknown
% 2.62/1.88 % (3792)Termination phase: Preprocessing 2
% 2.62/1.88
% 2.62/1.88 % (3792)Memory used [KB]: 2046
% 2.62/1.88 % (3792)Time elapsed: 0.015 s
% 2.62/1.88 % (3792)Instructions burned: 50 (million)
% 2.62/1.88 % (3792)------------------------------
% 2.62/1.88 % (3792)------------------------------
% 2.62/1.89 % (3772)Instruction limit reached!
% 2.62/1.89 % (3772)------------------------------
% 2.62/1.89 % (3772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.89 % (3772)Termination reason: Unknown
% 2.62/1.89 % (3772)Termination phase: Saturation
% 2.62/1.89
% 2.62/1.89 % (3772)Memory used [KB]: 7291
% 2.62/1.89 % (3772)Time elapsed: 0.042 s
% 2.62/1.89 % (3772)Instructions burned: 150 (million)
% 2.62/1.89 % (3772)------------------------------
% 2.62/1.89 % (3772)------------------------------
% 2.62/1.89 % (3810)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_3362 for (2996ds/44Mi)
% 2.62/1.89 % (3811)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_3362 for (2996ds/432Mi)
% 2.62/1.90 % (3810)Instruction limit reached!
% 2.62/1.90 % (3810)------------------------------
% 2.62/1.90 % (3810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.90 % (3810)Termination reason: Unknown
% 2.62/1.90 % (3810)Termination phase: Property scanning
% 2.62/1.90
% 2.62/1.90 % (3810)Memory used [KB]: 2046
% 2.62/1.90 % (3810)Time elapsed: 0.013 s
% 2.62/1.90 % (3810)Instructions burned: 46 (million)
% 2.62/1.90 % (3810)------------------------------
% 2.62/1.90 % (3810)------------------------------
% 2.62/1.91 % (3819)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3362 for (2996ds/62Mi)
% 2.62/1.91 % (3645)Instruction limit reached!
% 2.62/1.91 % (3645)------------------------------
% 2.62/1.91 % (3645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.91 % (3645)Termination reason: Unknown
% 2.62/1.91 % (3645)Termination phase: Saturation
% 2.62/1.91
% 2.62/1.91 % (3645)Memory used [KB]: 10618
% 2.62/1.91 % (3645)Time elapsed: 0.307 s
% 2.62/1.91 % (3645)Instructions burned: 903 (million)
% 2.62/1.91 % (3645)------------------------------
% 2.62/1.91 % (3645)------------------------------
% 2.62/1.92 % (3670)Instruction limit reached!
% 2.62/1.92 % (3670)------------------------------
% 2.62/1.92 % (3670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.92 % (3670)Termination reason: Unknown
% 2.62/1.92 % (3670)Termination phase: Saturation
% 2.62/1.92
% 2.62/1.92 % (3670)Memory used [KB]: 8443
% 2.62/1.92 % (3670)Time elapsed: 0.296 s
% 2.62/1.92 % (3670)Instructions burned: 882 (million)
% 2.62/1.92 % (3670)------------------------------
% 2.62/1.92 % (3670)------------------------------
% 2.62/1.92 % (3759)Instruction limit reached!
% 2.62/1.92 % (3759)------------------------------
% 2.62/1.92 % (3759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.92 % (3759)Termination reason: Unknown
% 2.62/1.92 % (3759)Termination phase: Saturation
% 2.62/1.92
% 2.62/1.92 % (3759)Memory used [KB]: 7036
% 2.62/1.92 % (3759)Time elapsed: 0.111 s
% 2.62/1.92 % (3759)Instructions burned: 449 (million)
% 2.62/1.92 % (3759)------------------------------
% 2.62/1.92 % (3759)------------------------------
% 2.62/1.93 % (3820)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_3362 for (2995ds/31Mi)
% 2.62/1.93 % (3819)Instruction limit reached!
% 2.62/1.93 % (3819)------------------------------
% 2.62/1.93 % (3819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.93 % (3819)Termination reason: Unknown
% 2.62/1.93 % (3819)Termination phase: Property scanning
% 2.62/1.93
% 2.62/1.93 % (3819)Memory used [KB]: 2174
% 2.62/1.93 % (3819)Time elapsed: 0.018 s
% 2.62/1.93 % (3819)Instructions burned: 64 (million)
% 2.62/1.93 % (3819)------------------------------
% 2.62/1.93 % (3819)------------------------------
% 2.62/1.93 % (3821)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/96Mi)
% 2.62/1.93 % (3822)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_3362 for (2995ds/453Mi)
% 2.62/1.93 % (3820)Instruction limit reached!
% 2.62/1.93 % (3820)------------------------------
% 2.62/1.93 % (3820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.93 % (3820)Termination reason: Unknown
% 2.62/1.93 % (3820)Termination phase: shuffling
% 2.62/1.93
% 2.62/1.93 % (3820)Memory used [KB]: 1918
% 2.62/1.93 % (3820)Time elapsed: 0.010 s
% 2.62/1.93 % (3820)Instructions burned: 31 (million)
% 2.62/1.93 % (3820)------------------------------
% 2.62/1.93 % (3820)------------------------------
% 2.62/1.94 % (3823)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_3362 for (2995ds/71Mi)
% 2.62/1.94 % (3824)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/83Mi)
% 2.62/1.96 % (3823)Instruction limit reached!
% 2.62/1.96 % (3823)------------------------------
% 2.62/1.96 % (3823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.96 % (3823)Termination reason: Unknown
% 2.62/1.96 % (3823)Termination phase: Function definition elimination
% 2.62/1.96
% 2.62/1.96 % (3823)Memory used [KB]: 2174
% 2.62/1.96 % (3823)Time elapsed: 0.020 s
% 2.62/1.96 % (3823)Instructions burned: 73 (million)
% 2.62/1.96 % (3823)------------------------------
% 2.62/1.96 % (3823)------------------------------
% 2.62/1.96 % (3821)Instruction limit reached!
% 2.62/1.96 % (3821)------------------------------
% 2.62/1.96 % (3821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.96 % (3821)Termination reason: Unknown
% 2.62/1.96 % (3821)Termination phase: Property scanning
% 2.62/1.96
% 2.62/1.96 % (3821)Memory used [KB]: 2174
% 2.62/1.96 % (3821)Time elapsed: 0.027 s
% 2.62/1.96 % (3821)Instructions burned: 96 (million)
% 2.62/1.96 % (3821)------------------------------
% 2.62/1.96 % (3821)------------------------------
% 2.62/1.97 % (3824)Instruction limit reached!
% 2.62/1.97 % (3824)------------------------------
% 2.62/1.97 % (3824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.97 % (3824)Termination reason: Unknown
% 2.62/1.97 % (3824)Termination phase: Property scanning
% 2.62/1.97
% 2.62/1.97 % (3824)Memory used [KB]: 2174
% 2.62/1.97 % (3824)Time elapsed: 0.025 s
% 2.62/1.97 % (3824)Instructions burned: 85 (million)
% 2.62/1.97 % (3824)------------------------------
% 2.62/1.97 % (3824)------------------------------
% 2.62/1.97 % (3825)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/11Mi)
% 2.62/1.97 % (3826)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/41Mi)
% 2.62/1.97 % (3825)Instruction limit reached!
% 2.62/1.97 % (3825)------------------------------
% 2.62/1.97 % (3825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.97 % (3825)Termination reason: Unknown
% 2.62/1.97 % (3825)Termination phase: shuffling
% 2.62/1.97
% 2.62/1.97 % (3825)Memory used [KB]: 1535
% 2.62/1.97 % (3825)Time elapsed: 0.004 s
% 2.62/1.97 % (3825)Instructions burned: 11 (million)
% 2.62/1.97 % (3825)------------------------------
% 2.62/1.97 % (3825)------------------------------
% 2.62/1.98 % (3827)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/6Mi)
% 2.62/1.98 % (3826)Instruction limit reached!
% 2.62/1.98 % (3826)------------------------------
% 2.62/1.98 % (3826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.98 % (3826)Termination reason: Unknown
% 2.62/1.98 % (3826)Termination phase: Property scanning
% 2.62/1.98
% 2.62/1.98 % (3826)Memory used [KB]: 2174
% 2.62/1.98 % (3826)Time elapsed: 0.012 s
% 2.62/1.98 % (3826)Instructions burned: 42 (million)
% 2.62/1.98 % (3826)------------------------------
% 2.62/1.98 % (3826)------------------------------
% 2.62/1.98 % (3827)Instruction limit reached!
% 2.62/1.98 % (3827)------------------------------
% 2.62/1.98 % (3827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.98 % (3827)Termination reason: Unknown
% 2.62/1.98 % (3827)Termination phase: shuffling
% 2.62/1.98
% 2.62/1.98 % (3827)Memory used [KB]: 1535
% 2.62/1.98 % (3827)Time elapsed: 0.004 s
% 2.62/1.98 % (3827)Instructions burned: 7 (million)
% 2.62/1.98 % (3827)------------------------------
% 2.62/1.98 % (3827)------------------------------
% 2.62/1.98 % (3828)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/150Mi)
% 2.62/1.99 % (3829)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/343Mi)
% 2.62/1.99 % (3830)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/109Mi)
% 2.62/2.00 % (3811)Instruction limit reached!
% 2.62/2.00 % (3811)------------------------------
% 2.62/2.00 % (3811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/2.00 % (3811)Termination reason: Unknown
% 2.62/2.00 % (3811)Termination phase: Saturation
% 2.62/2.00
% 2.62/2.00 % (3811)Memory used [KB]: 3070
% 2.62/2.00 % (3811)Time elapsed: 0.108 s
% 2.62/2.00 % (3811)Instructions burned: 432 (million)
% 2.62/2.00 % (3811)------------------------------
% 2.62/2.00 % (3811)------------------------------
% 6.03/2.01 % (3831)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_3362 for (2995ds/253Mi)
% 6.03/2.01 % (3771)Instruction limit reached!
% 6.03/2.01 % (3771)------------------------------
% 6.03/2.01 % (3771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.01 % (3771)Termination reason: Unknown
% 6.03/2.01 % (3771)Termination phase: Saturation
% 6.03/2.01
% 6.03/2.01 % (3771)Memory used [KB]: 7547
% 6.03/2.01 % (3771)Time elapsed: 0.190 s
% 6.03/2.01 % (3771)Instructions burned: 507 (million)
% 6.03/2.01 % (3771)------------------------------
% 6.03/2.01 % (3771)------------------------------
% 6.03/2.02 % (3830)Instruction limit reached!
% 6.03/2.02 % (3830)------------------------------
% 6.03/2.02 % (3830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.02 % (3830)Termination reason: Unknown
% 6.03/2.02 % (3830)Termination phase: Property scanning
% 6.03/2.02
% 6.03/2.02 % (3830)Memory used [KB]: 2174
% 6.03/2.02 % (3830)Time elapsed: 0.030 s
% 6.03/2.02 % (3830)Instructions burned: 111 (million)
% 6.03/2.02 % (3830)------------------------------
% 6.03/2.02 % (3830)------------------------------
% 6.03/2.02 % (3828)Instruction limit reached!
% 6.03/2.02 % (3828)------------------------------
% 6.03/2.02 % (3828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.02 % (3828)Termination reason: Unknown
% 6.03/2.02 % (3828)Termination phase: Saturation
% 6.03/2.02
% 6.03/2.02 % (3828)Memory used [KB]: 8187
% 6.03/2.02 % (3828)Time elapsed: 0.043 s
% 6.03/2.02 % (3828)Instructions burned: 150 (million)
% 6.03/2.02 % (3828)------------------------------
% 6.03/2.02 % (3828)------------------------------
% 6.03/2.02 % (3832)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/140Mi)
% 6.03/2.03 % (3833)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/614Mi)
% 6.03/2.03 % (3834)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/202Mi)
% 6.03/2.04 % (3822)Instruction limit reached!
% 6.03/2.04 % (3822)------------------------------
% 6.03/2.04 % (3822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.04 % (3822)Termination reason: Unknown
% 6.03/2.04 % (3822)Termination phase: Saturation
% 6.03/2.04
% 6.03/2.04 % (3822)Memory used [KB]: 7036
% 6.03/2.04 % (3822)Time elapsed: 0.111 s
% 6.03/2.04 % (3822)Instructions burned: 454 (million)
% 6.03/2.04 % (3822)------------------------------
% 6.03/2.04 % (3822)------------------------------
% 6.03/2.05 % (3835)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/339Mi)
% 6.03/2.06 % (3832)Instruction limit reached!
% 6.03/2.06 % (3832)------------------------------
% 6.03/2.06 % (3832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.06 % (3832)Termination reason: Unknown
% 6.03/2.06 % (3832)Termination phase: Saturation
% 6.03/2.06
% 6.03/2.06 % (3832)Memory used [KB]: 7036
% 6.03/2.06 % (3832)Time elapsed: 0.040 s
% 6.03/2.06 % (3832)Instructions burned: 140 (million)
% 6.03/2.06 % (3832)------------------------------
% 6.03/2.06 % (3832)------------------------------
% 6.03/2.07 % (3836)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/283Mi)
% 6.03/2.09 % (3831)Instruction limit reached!
% 6.03/2.09 % (3831)------------------------------
% 6.03/2.09 % (3831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.09 % (3831)Termination reason: Unknown
% 6.03/2.09 % (3831)Termination phase: Saturation
% 6.03/2.09
% 6.03/2.09 % (3831)Memory used [KB]: 8443
% 6.03/2.09 % (3831)Time elapsed: 0.075 s
% 6.03/2.09 % (3831)Instructions burned: 253 (million)
% 6.03/2.09 % (3831)------------------------------
% 6.03/2.09 % (3831)------------------------------
% 6.03/2.09 % (3834)Instruction limit reached!
% 6.03/2.09 % (3834)------------------------------
% 6.03/2.09 % (3834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.09 % (3834)Termination reason: Unknown
% 6.03/2.09 % (3834)Termination phase: Saturation
% 6.03/2.09
% 6.03/2.09 % (3834)Memory used [KB]: 4605
% 6.03/2.09 % (3834)Time elapsed: 0.059 s
% 6.03/2.09 % (3834)Instructions burned: 203 (million)
% 6.03/2.09 % (3834)------------------------------
% 6.03/2.09 % (3834)------------------------------
% 6.03/2.10 % (3837)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/134Mi)
% 6.03/2.10 % (3838)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3362 for (2994ds/298Mi)
% 6.52/2.13 % (3829)Instruction limit reached!
% 6.52/2.13 % (3829)------------------------------
% 6.52/2.13 % (3829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.13 % (3829)Termination reason: Unknown
% 6.52/2.13 % (3829)Termination phase: Saturation
% 6.52/2.13
% 6.52/2.13 % (3829)Memory used [KB]: 8059
% 6.52/2.13 % (3829)Time elapsed: 0.138 s
% 6.52/2.13 % (3829)Instructions burned: 344 (million)
% 6.52/2.13 % (3829)------------------------------
% 6.52/2.13 % (3829)------------------------------
% 6.52/2.13 % (3837)Instruction limit reached!
% 6.52/2.13 % (3837)------------------------------
% 6.52/2.13 % (3837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.13 % (3837)Termination reason: Unknown
% 6.52/2.13 % (3837)Termination phase: Saturation
% 6.52/2.13
% 6.52/2.13 % (3837)Memory used [KB]: 7036
% 6.52/2.13 % (3837)Time elapsed: 0.036 s
% 6.52/2.13 % (3837)Instructions burned: 136 (million)
% 6.52/2.13 % (3837)------------------------------
% 6.52/2.13 % (3837)------------------------------
% 6.52/2.14 % (3839)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/192Mi)
% 6.52/2.14 % (3840)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/258Mi)
% 6.52/2.15 % (3835)Instruction limit reached!
% 6.52/2.15 % (3835)------------------------------
% 6.52/2.15 % (3835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.15 % (3835)Termination reason: Unknown
% 6.52/2.15 % (3835)Termination phase: Saturation
% 6.52/2.15
% 6.52/2.15 % (3835)Memory used [KB]: 7675
% 6.52/2.15 % (3835)Time elapsed: 0.095 s
% 6.52/2.15 % (3835)Instructions burned: 340 (million)
% 6.52/2.15 % (3835)------------------------------
% 6.52/2.15 % (3835)------------------------------
% 6.52/2.15 % (3836)Instruction limit reached!
% 6.52/2.15 % (3836)------------------------------
% 6.52/2.15 % (3836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.15 % (3836)Termination reason: Unknown
% 6.52/2.15 % (3836)Termination phase: Saturation
% 6.52/2.15
% 6.52/2.15 % (3836)Memory used [KB]: 6908
% 6.52/2.15 % (3836)Time elapsed: 0.077 s
% 6.52/2.15 % (3836)Instructions burned: 285 (million)
% 6.52/2.15 % (3836)------------------------------
% 6.52/2.15 % (3836)------------------------------
% 6.52/2.16 % (3841)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/90Mi)
% 6.52/2.16 % (3842)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/231Mi)
% 6.52/2.18 % (3838)Instruction limit reached!
% 6.52/2.18 % (3838)------------------------------
% 6.52/2.18 % (3838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.18 % (3838)Termination reason: Unknown
% 6.52/2.18 % (3838)Termination phase: Saturation
% 6.52/2.18
% 6.52/2.18 % (3838)Memory used [KB]: 6908
% 6.52/2.18 % (3838)Time elapsed: 0.077 s
% 6.52/2.18 % (3838)Instructions burned: 300 (million)
% 6.52/2.18 % (3838)------------------------------
% 6.52/2.18 % (3838)------------------------------
% 6.52/2.18 % (3841)Instruction limit reached!
% 6.52/2.18 % (3841)------------------------------
% 6.52/2.18 % (3841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.18 % (3841)Termination reason: Unknown
% 6.52/2.18 % (3841)Termination phase: Twee Goal Transformation
% 6.52/2.18
% 6.52/2.18 % (3841)Memory used [KB]: 2558
% 6.52/2.18 % (3841)Time elapsed: 0.026 s
% 6.52/2.18 % (3841)Instructions burned: 92 (million)
% 6.52/2.18 % (3841)------------------------------
% 6.52/2.18 % (3841)------------------------------
% 6.52/2.19 % (3843)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/458Mi)
% 6.52/2.19 % (3844)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_3362 for (2993ds/31Mi)
% 6.52/2.19 % (3839)Instruction limit reached!
% 6.52/2.19 % (3839)------------------------------
% 6.52/2.19 % (3839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.52/2.19 % (3839)Termination reason: Unknown
% 6.52/2.19 % (3839)Termination phase: Saturation
% 6.52/2.19
% 6.52/2.19 % (3839)Memory used [KB]: 7547
% 6.52/2.19 % (3839)Time elapsed: 0.056 s
% 6.52/2.19 % (3839)Instructions burned: 194 (million)
% 6.52/2.19 % (3839)------------------------------
% 6.52/2.19 % (3839)------------------------------
% 7.06/2.20 % (3844)Instruction limit reached!
% 7.06/2.20 % (3844)------------------------------
% 7.06/2.20 % (3844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.20 % (3844)Termination reason: Unknown
% 7.06/2.20 % (3844)Termination phase: Property scanning
% 7.06/2.20
% 7.06/2.20 % (3844)Memory used [KB]: 1918
% 7.06/2.20 % (3844)Time elapsed: 0.010 s
% 7.06/2.20 % (3844)Instructions burned: 32 (million)
% 7.06/2.20 % (3844)------------------------------
% 7.06/2.20 % (3844)------------------------------
% 7.06/2.20 % (3845)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/297Mi)
% 7.06/2.21 % (3833)Instruction limit reached!
% 7.06/2.21 % (3833)------------------------------
% 7.06/2.21 % (3833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.21 % (3833)Termination reason: Unknown
% 7.06/2.21 % (3833)Termination phase: Saturation
% 7.06/2.21
% 7.06/2.21 % (3833)Memory used [KB]: 8699
% 7.06/2.21 % (3833)Time elapsed: 0.180 s
% 7.06/2.21 % (3833)Instructions burned: 614 (million)
% 7.06/2.21 % (3833)------------------------------
% 7.06/2.21 % (3833)------------------------------
% 7.06/2.21 % (3840)Instruction limit reached!
% 7.06/2.21 % (3840)------------------------------
% 7.06/2.21 % (3840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.21 % (3840)Termination reason: Unknown
% 7.06/2.21 % (3840)Termination phase: Saturation
% 7.06/2.21
% 7.06/2.21 % (3840)Memory used [KB]: 7803
% 7.06/2.21 % (3840)Time elapsed: 0.071 s
% 7.06/2.21 % (3840)Instructions burned: 258 (million)
% 7.06/2.21 % (3840)------------------------------
% 7.06/2.21 % (3840)------------------------------
% 7.06/2.21 % (3846)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/987Mi)
% 7.06/2.21 % (3789)Instruction limit reached!
% 7.06/2.21 % (3789)------------------------------
% 7.06/2.21 % (3789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.21 % (3789)Termination reason: Unknown
% 7.06/2.21 % (3789)Termination phase: Saturation
% 7.06/2.21
% 7.06/2.21 % (3789)Memory used [KB]: 10746
% 7.06/2.21 % (3789)Time elapsed: 0.349 s
% 7.06/2.21 % (3789)Instructions burned: 1087 (million)
% 7.06/2.21 % (3789)------------------------------
% 7.06/2.21 % (3789)------------------------------
% 7.06/2.22 % (3847)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/182Mi)
% 7.06/2.22 % (3848)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/182Mi)
% 7.06/2.22 % (3849)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_3362 for (2993ds/154Mi)
% 7.06/2.23 % (3842)Instruction limit reached!
% 7.06/2.23 % (3842)------------------------------
% 7.06/2.23 % (3842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.23 % (3842)Termination reason: Unknown
% 7.06/2.23 % (3842)Termination phase: Saturation
% 7.06/2.23
% 7.06/2.23 % (3842)Memory used [KB]: 12281
% 7.06/2.23 % (3842)Time elapsed: 0.069 s
% 7.06/2.23 % (3842)Instructions burned: 233 (million)
% 7.06/2.23 % (3842)------------------------------
% 7.06/2.23 % (3842)------------------------------
% 7.06/2.24 % (3850)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/79Mi)
% 7.06/2.26 % (3850)Instruction limit reached!
% 7.06/2.26 % (3850)------------------------------
% 7.06/2.26 % (3850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.26 % (3850)Termination reason: Unknown
% 7.06/2.26 % (3850)Termination phase: Property scanning
% 7.06/2.26
% 7.06/2.26 % (3850)Memory used [KB]: 2174
% 7.06/2.26 % (3850)Time elapsed: 0.022 s
% 7.06/2.26 % (3850)Instructions burned: 80 (million)
% 7.06/2.26 % (3850)------------------------------
% 7.06/2.26 % (3850)------------------------------
% 7.06/2.26 % (3849)Instruction limit reached!
% 7.06/2.26 % (3849)------------------------------
% 7.06/2.26 % (3849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.26 % (3849)Termination reason: Unknown
% 7.06/2.26 % (3849)Termination phase: Saturation
% 7.06/2.26
% 7.06/2.26 % (3849)Memory used [KB]: 6908
% 7.06/2.26 % (3849)Time elapsed: 0.041 s
% 7.06/2.26 % (3849)Instructions burned: 156 (million)
% 7.06/2.26 % (3849)------------------------------
% 7.06/2.26 % (3849)------------------------------
% 7.06/2.27 % (3847)Instruction limit reached!
% 7.06/2.27 % (3847)------------------------------
% 7.06/2.27 % (3847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.27 % (3847)Termination reason: Unknown
% 7.06/2.27 % (3847)Termination phase: Saturation
% 7.06/2.27
% 7.06/2.27 % (3847)Memory used [KB]: 7547
% 7.06/2.27 % (3847)Time elapsed: 0.050 s
% 7.06/2.27 % (3847)Instructions burned: 182 (million)
% 7.06/2.27 % (3847)------------------------------
% 7.06/2.27 % (3847)------------------------------
% 7.06/2.27 % (3851)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/216Mi)
% 7.06/2.27 % (3852)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/114Mi)
% 7.06/2.27 % (3848)Instruction limit reached!
% 7.06/2.27 % (3848)------------------------------
% 7.06/2.27 % (3848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.27 % (3848)Termination reason: Unknown
% 7.06/2.27 % (3848)Termination phase: Saturation
% 7.06/2.27
% 7.06/2.27 % (3848)Memory used [KB]: 10234
% 7.06/2.27 % (3848)Time elapsed: 0.055 s
% 7.06/2.27 % (3848)Instructions burned: 184 (million)
% 7.06/2.27 % (3848)------------------------------
% 7.06/2.27 % (3848)------------------------------
% 7.06/2.28 % (3853)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/922Mi)
% 7.06/2.28 % (3845)Instruction limit reached!
% 7.06/2.28 % (3845)------------------------------
% 7.06/2.28 % (3845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.28 % (3845)Termination reason: Unknown
% 7.06/2.28 % (3845)Termination phase: Saturation
% 7.06/2.28
% 7.06/2.28 % (3845)Memory used [KB]: 7547
% 7.06/2.28 % (3845)Time elapsed: 0.078 s
% 7.06/2.28 % (3845)Instructions burned: 299 (million)
% 7.06/2.28 % (3845)------------------------------
% 7.06/2.28 % (3845)------------------------------
% 7.06/2.28 % (3854)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/182Mi)
% 7.06/2.29 % (3855)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/164Mi)
% 7.73/2.30 % (3852)Instruction limit reached!
% 7.73/2.30 % (3852)------------------------------
% 7.73/2.30 % (3852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.30 % (3852)Termination reason: Unknown
% 7.73/2.30 % (3852)Termination phase: Saturation
% 7.73/2.30
% 7.73/2.30 % (3852)Memory used [KB]: 6908
% 7.73/2.30 % (3852)Time elapsed: 0.030 s
% 7.73/2.30 % (3852)Instructions burned: 115 (million)
% 7.73/2.30 % (3852)------------------------------
% 7.73/2.30 % (3852)------------------------------
% 7.73/2.31 % (3856)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/50Mi)
% 7.73/2.32 % (3843)Instruction limit reached!
% 7.73/2.32 % (3843)------------------------------
% 7.73/2.32 % (3843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.32 % (3843)Termination reason: Unknown
% 7.73/2.32 % (3843)Termination phase: Saturation
% 7.73/2.32
% 7.73/2.32 % (3843)Memory used [KB]: 8443
% 7.73/2.32 % (3843)Time elapsed: 0.134 s
% 7.73/2.32 % (3843)Instructions burned: 460 (million)
% 7.73/2.32 % (3843)------------------------------
% 7.73/2.32 % (3843)------------------------------
% 7.73/2.32 % (3851)Instruction limit reached!
% 7.73/2.32 % (3851)------------------------------
% 7.73/2.32 % (3851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.32 % (3851)Termination reason: Unknown
% 7.73/2.32 % (3851)Termination phase: Saturation
% 7.73/2.32
% 7.73/2.32 % (3851)Memory used [KB]: 6908
% 7.73/2.32 % (3851)Time elapsed: 0.055 s
% 7.73/2.32 % (3851)Instructions burned: 218 (million)
% 7.73/2.32 % (3851)------------------------------
% 7.73/2.32 % (3851)------------------------------
% 7.73/2.33 % (3856)Instruction limit reached!
% 7.73/2.33 % (3856)------------------------------
% 7.73/2.33 % (3856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.33 % (3856)Termination reason: Unknown
% 7.73/2.33 % (3856)Termination phase: Preprocessing 3
% 7.73/2.33
% 7.73/2.33 % (3856)Memory used [KB]: 2174
% 7.73/2.33 % (3856)Time elapsed: 0.015 s
% 7.73/2.33 % (3856)Instructions burned: 52 (million)
% 7.73/2.33 % (3856)------------------------------
% 7.73/2.33 % (3856)------------------------------
% 7.73/2.33 % (3857)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/368Mi)
% 7.73/2.33 % (3854)Instruction limit reached!
% 7.73/2.33 % (3854)------------------------------
% 7.73/2.33 % (3854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.33 % (3854)Termination reason: Unknown
% 7.73/2.33 % (3854)Termination phase: Saturation
% 7.73/2.33
% 7.73/2.33 % (3854)Memory used [KB]: 6908
% 7.73/2.33 % (3854)Time elapsed: 0.047 s
% 7.73/2.33 % (3854)Instructions burned: 184 (million)
% 7.73/2.33 % (3854)------------------------------
% 7.73/2.33 % (3854)------------------------------
% 7.73/2.33 % (3855)Instruction limit reached!
% 7.73/2.33 % (3855)------------------------------
% 7.73/2.33 % (3855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.33 % (3855)Termination reason: Unknown
% 7.73/2.33 % (3855)Termination phase: Saturation
% 7.73/2.33
% 7.73/2.33 % (3855)Memory used [KB]: 2558
% 7.73/2.33 % (3855)Time elapsed: 0.044 s
% 7.73/2.33 % (3855)Instructions burned: 166 (million)
% 7.73/2.33 % (3855)------------------------------
% 7.73/2.33 % (3855)------------------------------
% 7.73/2.33 % (3858)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3362 for (2992ds/1021Mi)
% 7.73/2.33 % (3859)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/267Mi)
% 7.73/2.34 % (3860)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/204Mi)
% 7.73/2.34 % (3861)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/26Mi)
% 7.73/2.35 % (3861)Instruction limit reached!
% 7.73/2.35 % (3861)------------------------------
% 7.73/2.35 % (3861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.35 % (3861)Termination reason: Unknown
% 7.73/2.35 % (3861)Termination phase: shuffling
% 7.73/2.35
% 7.73/2.35 % (3861)Memory used [KB]: 1918
% 7.73/2.35 % (3861)Time elapsed: 0.009 s
% 7.73/2.35 % (3861)Instructions burned: 29 (million)
% 7.73/2.35 % (3861)------------------------------
% 7.73/2.35 % (3861)------------------------------
% 7.73/2.36 % (3862)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/53Mi)
% 7.73/2.37 % (3862)Instruction limit reached!
% 7.73/2.37 % (3862)------------------------------
% 7.73/2.37 % (3862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.37 % (3862)Termination reason: Unknown
% 7.73/2.37 % (3862)Termination phase: Property scanning
% 7.73/2.37
% 7.73/2.37 % (3862)Memory used [KB]: 2174
% 7.73/2.37 % (3862)Time elapsed: 0.015 s
% 7.73/2.37 % (3862)Instructions burned: 55 (million)
% 7.73/2.37 % (3862)------------------------------
% 7.73/2.37 % (3862)------------------------------
% 7.73/2.38 % (3863)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/4436Mi)
% 7.73/2.39 % (3860)Instruction limit reached!
% 7.73/2.39 % (3860)------------------------------
% 7.73/2.39 % (3860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.39 % (3860)Termination reason: Unknown
% 7.73/2.39 % (3860)Termination phase: Saturation
% 7.73/2.39
% 7.73/2.39 % (3860)Memory used [KB]: 7419
% 7.73/2.39 % (3860)Time elapsed: 0.054 s
% 7.73/2.39 % (3860)Instructions burned: 205 (million)
% 7.73/2.39 % (3860)------------------------------
% 7.73/2.39 % (3860)------------------------------
% 8.22/2.40 % (3864)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/1539Mi)
% 8.22/2.40 % (3859)Instruction limit reached!
% 8.22/2.40 % (3859)------------------------------
% 8.22/2.40 % (3859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.40 % (3859)Termination reason: Unknown
% 8.22/2.40 % (3859)Termination phase: Saturation
% 8.22/2.40
% 8.22/2.40 % (3859)Memory used [KB]: 6908
% 8.22/2.40 % (3859)Time elapsed: 0.068 s
% 8.22/2.40 % (3859)Instructions burned: 270 (million)
% 8.22/2.40 % (3859)------------------------------
% 8.22/2.40 % (3859)------------------------------
% 8.22/2.41 % (3865)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3362 for (2991ds/408Mi)
% 8.22/2.43 % (3857)Instruction limit reached!
% 8.22/2.43 % (3857)------------------------------
% 8.22/2.43 % (3857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.43 % (3857)Termination reason: Unknown
% 8.22/2.43 % (3857)Termination phase: Saturation
% 8.22/2.43
% 8.22/2.43 % (3857)Memory used [KB]: 8059
% 8.22/2.43 % (3857)Time elapsed: 0.121 s
% 8.22/2.43 % (3857)Instructions burned: 370 (million)
% 8.22/2.43 % (3857)------------------------------
% 8.22/2.43 % (3857)------------------------------
% 8.22/2.44 % (3866)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3362 for (2990ds/5205Mi)
% 8.22/2.45 % (3846)Instruction limit reached!
% 8.22/2.45 % (3846)------------------------------
% 8.22/2.45 % (3846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.45 % (3846)Termination reason: Unknown
% 8.22/2.45 % (3846)Termination phase: Saturation
% 8.22/2.45
% 8.22/2.45 % (3846)Memory used [KB]: 11513
% 8.22/2.45 % (3846)Time elapsed: 0.245 s
% 8.22/2.45 % (3846)Instructions burned: 988 (million)
% 8.22/2.45 % (3846)------------------------------
% 8.22/2.45 % (3846)------------------------------
% 8.22/2.46 % (3867)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3362 for (2990ds/1913Mi)
% 8.66/2.54 % (3865)Instruction limit reached!
% 8.66/2.54 % (3865)------------------------------
% 8.66/2.54 % (3865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.54 % (3865)Termination reason: Unknown
% 8.66/2.54 % (3865)Termination phase: Saturation
% 8.66/2.54
% 8.66/2.54 % (3865)Memory used [KB]: 9722
% 8.66/2.54 % (3865)Time elapsed: 0.129 s
% 8.66/2.54 % (3865)Instructions burned: 409 (million)
% 8.66/2.54 % (3865)------------------------------
% 8.66/2.54 % (3865)------------------------------
% 8.66/2.55 % (3868)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3362 for (2989ds/4350Mi)
% 8.66/2.56 % (3853)Instruction limit reached!
% 8.66/2.56 % (3853)------------------------------
% 8.66/2.56 % (3853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.56 % (3853)Termination reason: Unknown
% 8.66/2.56 % (3853)Termination phase: Saturation
% 8.66/2.56
% 8.66/2.56 % (3853)Memory used [KB]: 10234
% 8.66/2.56 % (3853)Time elapsed: 0.310 s
% 8.66/2.56 % (3853)Instructions burned: 922 (million)
% 8.66/2.56 % (3853)------------------------------
% 8.66/2.56 % (3853)------------------------------
% 8.66/2.57 % (3869)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3362 for (2989ds/68Mi)
% 8.66/2.59 % (3869)Instruction limit reached!
% 8.66/2.59 % (3869)------------------------------
% 8.66/2.59 % (3869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.59 % (3869)Termination reason: Unknown
% 8.66/2.59 % (3869)Termination phase: Property scanning
% 8.66/2.59
% 8.66/2.59 % (3869)Memory used [KB]: 2046
% 8.66/2.59 % (3869)Time elapsed: 0.019 s
% 8.66/2.59 % (3869)Instructions burned: 71 (million)
% 8.66/2.59 % (3869)------------------------------
% 8.66/2.59 % (3869)------------------------------
% 9.12/2.60 % (3870)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3362 for (2989ds/358Mi)
% 9.12/2.65 % (3858)Instruction limit reached!
% 9.12/2.65 % (3858)------------------------------
% 9.12/2.65 % (3858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.65 % (3858)Termination reason: Unknown
% 9.12/2.65 % (3858)Termination phase: Saturation
% 9.12/2.65
% 9.12/2.65 % (3858)Memory used [KB]: 10746
% 9.12/2.65 % (3858)Time elapsed: 0.344 s
% 9.12/2.65 % (3858)Instructions burned: 1023 (million)
% 9.12/2.65 % (3858)------------------------------
% 9.12/2.65 % (3858)------------------------------
% 9.12/2.66 % (3871)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_3362 for (2988ds/31Mi)
% 9.12/2.67 % (3871)Instruction limit reached!
% 9.12/2.67 % (3871)------------------------------
% 9.12/2.67 % (3871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.67 % (3871)Termination reason: Unknown
% 9.12/2.67 % (3871)Termination phase: shuffling
% 9.12/2.67
% 9.12/2.67 % (3871)Memory used [KB]: 1918
% 9.12/2.67 % (3871)Time elapsed: 0.010 s
% 9.12/2.67 % (3871)Instructions burned: 31 (million)
% 9.12/2.67 % (3871)------------------------------
% 9.12/2.67 % (3871)------------------------------
% 9.12/2.68 % (3872)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3362 for (2988ds/279Mi)
% 9.47/2.70 % (3870)Instruction limit reached!
% 9.47/2.70 % (3870)------------------------------
% 9.47/2.70 % (3870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.70 % (3870)Termination reason: Unknown
% 9.47/2.70 % (3870)Termination phase: Saturation
% 9.47/2.70
% 9.47/2.70 % (3870)Memory used [KB]: 8187
% 9.47/2.70 % (3870)Time elapsed: 0.103 s
% 9.47/2.70 % (3870)Instructions burned: 359 (million)
% 9.47/2.70 % (3870)------------------------------
% 9.47/2.70 % (3870)------------------------------
% 9.47/2.71 % (3873)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3362 for (2988ds/258Mi)
% 9.47/2.75 % (3872)Instruction limit reached!
% 9.47/2.75 % (3872)------------------------------
% 9.47/2.75 % (3872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.75 % (3872)Termination reason: Unknown
% 9.47/2.75 % (3872)Termination phase: Saturation
% 9.47/2.75
% 9.47/2.75 % (3872)Memory used [KB]: 7036
% 9.47/2.75 % (3872)Time elapsed: 0.069 s
% 9.47/2.75 % (3872)Instructions burned: 280 (million)
% 9.47/2.75 % (3872)------------------------------
% 9.47/2.75 % (3872)------------------------------
% 9.47/2.76 % (3874)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3362 for (2987ds/26Mi)
% 9.47/2.77 % (3874)Instruction limit reached!
% 9.47/2.77 % (3874)------------------------------
% 9.47/2.77 % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.77 % (3874)Termination reason: Unknown
% 9.47/2.77 % (3874)Termination phase: shuffling
% 9.47/2.77
% 9.47/2.77 % (3874)Memory used [KB]: 1918
% 9.47/2.77 % (3874)Time elapsed: 0.009 s
% 9.47/2.77 % (3874)Instructions burned: 29 (million)
% 9.47/2.77 % (3874)------------------------------
% 9.47/2.77 % (3874)------------------------------
% 9.47/2.77 % (3875)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3362 for (2987ds/995Mi)
% 9.47/2.78 % (3873)Instruction limit reached!
% 9.47/2.78 % (3873)------------------------------
% 9.47/2.78 % (3873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.78 % (3873)Termination reason: Unknown
% 9.47/2.78 % (3873)Termination phase: Saturation
% 9.47/2.78
% 9.47/2.78 % (3873)Memory used [KB]: 8187
% 9.47/2.78 % (3873)Time elapsed: 0.070 s
% 9.47/2.78 % (3873)Instructions burned: 260 (million)
% 9.47/2.78 % (3873)------------------------------
% 9.47/2.78 % (3873)------------------------------
% 9.47/2.79 % (3876)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3362 for (2987ds/373Mi)
% 9.76/2.88 % (3864)Instruction limit reached!
% 9.76/2.88 % (3864)------------------------------
% 9.76/2.88 % (3864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.88 % (3864)Termination reason: Unknown
% 9.76/2.88 % (3864)Termination phase: Saturation
% 9.76/2.88
% 9.76/2.88 % (3864)Memory used [KB]: 9338
% 9.76/2.88 % (3864)Time elapsed: 0.482 s
% 9.76/2.88 % (3864)Instructions burned: 1540 (million)
% 9.76/2.88 % (3864)------------------------------
% 9.76/2.88 % (3864)------------------------------
% 9.76/2.89 % (3877)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3362 for (2986ds/253Mi)
% 9.76/2.89 % (3876)Instruction limit reached!
% 9.76/2.89 % (3876)------------------------------
% 9.76/2.89 % (3876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.89 % (3876)Termination reason: Unknown
% 9.76/2.89 % (3876)Termination phase: Saturation
% 9.76/2.89
% 9.76/2.89 % (3876)Memory used [KB]: 8059
% 9.76/2.89 % (3876)Time elapsed: 0.104 s
% 9.76/2.89 % (3876)Instructions burned: 373 (million)
% 9.76/2.89 % (3876)------------------------------
% 9.76/2.89 % (3876)------------------------------
% 10.37/2.90 % (3878)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3362 for (2986ds/832Mi)
% 10.37/2.96 % (3877)Instruction limit reached!
% 10.37/2.96 % (3877)------------------------------
% 10.37/2.96 % (3877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.37/2.96 % (3877)Termination reason: Unknown
% 10.37/2.96 % (3877)Termination phase: Saturation
% 10.37/2.96
% 10.37/2.96 % (3877)Memory used [KB]: 7164
% 10.37/2.96 % (3877)Time elapsed: 0.065 s
% 10.37/2.96 % (3877)Instructions burned: 255 (million)
% 10.37/2.96 % (3877)------------------------------
% 10.37/2.96 % (3877)------------------------------
% 10.37/2.97 % (3879)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3362 for (2985ds/668Mi)
% 10.37/3.02 % (3875)Instruction limit reached!
% 10.37/3.02 % (3875)------------------------------
% 10.37/3.02 % (3875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.37/3.02 % (3875)Termination reason: Unknown
% 10.37/3.02 % (3875)Termination phase: Saturation
% 10.37/3.02
% 10.37/3.02 % (3875)Memory used [KB]: 11129
% 10.37/3.02 % (3875)Time elapsed: 0.245 s
% 10.37/3.02 % (3875)Instructions burned: 996 (million)
% 10.37/3.02 % (3875)------------------------------
% 10.37/3.02 % (3875)------------------------------
% 13.12/3.03 % (3880)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3362 for (2985ds/40Mi)
% 13.12/3.04 % (3880)Instruction limit reached!
% 13.12/3.04 % (3880)------------------------------
% 13.12/3.04 % (3880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.12/3.04 % (3880)Termination reason: Unknown
% 13.12/3.04 % (3880)Termination phase: Property scanning
% 13.12/3.04
% 13.12/3.04 % (3880)Memory used [KB]: 2046
% 13.12/3.04 % (3880)Time elapsed: 0.012 s
% 13.12/3.04 % (3880)Instructions burned: 41 (million)
% 13.12/3.04 % (3880)------------------------------
% 13.12/3.04 % (3880)------------------------------
% 13.12/3.05 % (3881)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3362 for (2984ds/294Mi)
% 13.12/3.05 % (3867)Instruction limit reached!
% 13.12/3.05 % (3867)------------------------------
% 13.12/3.05 % (3867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.12/3.05 % (3867)Termination reason: Unknown
% 13.12/3.05 % (3867)Termination phase: Saturation
% 13.12/3.05
% 13.12/3.05 % (3867)Memory used [KB]: 4733
% 13.12/3.05 % (3867)Time elapsed: 0.589 s
% 13.12/3.05 % (3867)Instructions burned: 1914 (million)
% 13.12/3.05 % (3867)------------------------------
% 13.12/3.05 % (3867)------------------------------
% 13.12/3.06 % (3882)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3362 for (2984ds/187Mi)
% 13.12/3.11 % (3882)Instruction limit reached!
% 13.12/3.11 % (3882)------------------------------
% 13.12/3.11 % (3882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.12/3.11 % (3882)Termination reason: Unknown
% 13.12/3.11 % (3882)Termination phase: Saturation
% 13.12/3.11
% 13.12/3.11 % (3882)Memory used [KB]: 7547
% 13.12/3.11 % (3882)Time elapsed: 0.050 s
% 13.12/3.11 % (3882)Instructions burned: 187 (million)
% 13.12/3.11 % (3882)------------------------------
% 13.12/3.11 % (3882)------------------------------
% 13.12/3.12 % (3883)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3362 for (2984ds/371Mi)
% 13.12/3.12 % (3881)Instruction limit reached!
% 13.12/3.12 % (3881)------------------------------
% 13.12/3.12 % (3881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.12/3.12 % (3881)Termination reason: Unknown
% 13.12/3.12 % (3881)Termination phase: Saturation
% 13.12/3.12
% 13.12/3.12 % (3881)Memory used [KB]: 6908
% 13.12/3.12 % (3881)Time elapsed: 0.074 s
% 13.12/3.12 % (3881)Instructions burned: 295 (million)
% 13.12/3.12 % (3881)------------------------------
% 13.12/3.12 % (3881)------------------------------
% 13.84/3.13 % (3879)Instruction limit reached!
% 13.84/3.13 % (3879)------------------------------
% 13.84/3.13 % (3879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.13 % (3879)Termination reason: Unknown
% 13.84/3.13 % (3879)Termination phase: Saturation
% 13.84/3.13
% 13.84/3.13 % (3879)Memory used [KB]: 15351
% 13.84/3.13 % (3879)Time elapsed: 0.166 s
% 13.84/3.13 % (3879)Instructions burned: 668 (million)
% 13.84/3.13 % (3879)------------------------------
% 13.84/3.13 % (3879)------------------------------
% 13.84/3.13 % (3884)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3362 for (2984ds/1827Mi)
% 13.84/3.14 % (3885)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3362 for (2983ds/70Mi)
% 13.84/3.15 % (3878)Instruction limit reached!
% 13.84/3.15 % (3878)------------------------------
% 13.84/3.15 % (3878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.15 % (3878)Termination reason: Unknown
% 13.84/3.15 % (3878)Termination phase: Saturation
% 13.84/3.15
% 13.84/3.15 % (3878)Memory used [KB]: 9722
% 13.84/3.15 % (3878)Time elapsed: 0.252 s
% 13.84/3.15 % (3878)Instructions burned: 832 (million)
% 13.84/3.15 % (3878)------------------------------
% 13.84/3.15 % (3878)------------------------------
% 13.84/3.16 % (3885)Instruction limit reached!
% 13.84/3.16 % (3885)------------------------------
% 13.84/3.16 % (3885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.16 % (3885)Termination reason: Unknown
% 13.84/3.16 % (3885)Termination phase: Function definition elimination
% 13.84/3.16
% 13.84/3.16 % (3885)Memory used [KB]: 2174
% 13.84/3.16 % (3885)Time elapsed: 0.019 s
% 13.84/3.16 % (3885)Instructions burned: 71 (million)
% 13.84/3.16 % (3885)------------------------------
% 13.84/3.16 % (3885)------------------------------
% 13.84/3.16 % (3886)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3362 for (2983ds/316Mi)
% 13.84/3.17 % (3887)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3362 for (2983ds/932Mi)
% 14.14/3.23 % (3883)Instruction limit reached!
% 14.14/3.23 % (3883)------------------------------
% 14.14/3.23 % (3883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.23 % (3883)Termination reason: Unknown
% 14.14/3.23 % (3883)Termination phase: Saturation
% 14.14/3.23
% 14.14/3.23 % (3883)Memory used [KB]: 8443
% 14.14/3.23 % (3883)Time elapsed: 0.108 s
% 14.14/3.23 % (3883)Instructions burned: 371 (million)
% 14.14/3.23 % (3883)------------------------------
% 14.14/3.23 % (3883)------------------------------
% 14.14/3.24 % (3888)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3362 for (2982ds/4714Mi)
% 14.14/3.25 % (3886)Instruction limit reached!
% 14.14/3.25 % (3886)------------------------------
% 14.14/3.25 % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.25 % (3886)Termination reason: Unknown
% 14.14/3.25 % (3886)Termination phase: Saturation
% 14.14/3.25
% 14.14/3.25 % (3886)Memory used [KB]: 7036
% 14.14/3.25 % (3886)Time elapsed: 0.082 s
% 14.14/3.25 % (3886)Instructions burned: 318 (million)
% 14.14/3.25 % (3886)------------------------------
% 14.14/3.25 % (3886)------------------------------
% 14.14/3.26 % (3889)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3362 for (2982ds/8250Mi)
% 14.96/3.41 % (3887)Instruction limit reached!
% 14.96/3.41 % (3887)------------------------------
% 14.96/3.41 % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.96/3.41 % (3887)Termination reason: Unknown
% 14.96/3.41 % (3887)Termination phase: Saturation
% 14.96/3.41
% 14.96/3.41 % (3887)Memory used [KB]: 12281
% 14.96/3.41 % (3887)Time elapsed: 0.241 s
% 14.96/3.41 % (3887)Instructions burned: 933 (million)
% 14.96/3.41 % (3887)------------------------------
% 14.96/3.41 % (3887)------------------------------
% 14.96/3.42 % (3890)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3362 for (2981ds/770Mi)
% 15.80/3.63 % (3890)Instruction limit reached!
% 15.80/3.63 % (3890)------------------------------
% 15.80/3.63 % (3890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.80/3.63 % (3890)Termination reason: Unknown
% 15.80/3.63 % (3890)Termination phase: Saturation
% 15.80/3.63
% 15.80/3.63 % (3890)Memory used [KB]: 7164
% 15.80/3.63 % (3890)Time elapsed: 0.213 s
% 15.80/3.63 % (3890)Instructions burned: 773 (million)
% 15.80/3.63 % (3890)------------------------------
% 15.80/3.63 % (3890)------------------------------
% 15.80/3.64 % (3891)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3362 for (2978ds/794Mi)
% 15.80/3.67 % (3884)Instruction limit reached!
% 15.80/3.67 % (3884)------------------------------
% 15.80/3.67 % (3884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.80/3.67 % (3884)Termination reason: Unknown
% 15.80/3.67 % (3884)Termination phase: Saturation
% 15.80/3.67
% 15.80/3.67 % (3884)Memory used [KB]: 16758
% 15.80/3.67 % (3884)Time elapsed: 0.566 s
% 15.80/3.67 % (3884)Instructions burned: 1829 (million)
% 15.80/3.67 % (3884)------------------------------
% 15.80/3.67 % (3884)------------------------------
% 15.80/3.68 % (3892)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3362 for (2978ds/464Mi)
% 16.88/3.71 % (3866)Instruction limit reached!
% 16.88/3.71 % (3866)------------------------------
% 16.88/3.71 % (3866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.88/3.71 % (3866)Termination reason: Unknown
% 16.88/3.71 % (3866)Termination phase: Saturation
% 16.88/3.71
% 16.88/3.71 % (3866)Memory used [KB]: 11769
% 16.88/3.71 % (3866)Time elapsed: 1.271 s
% 16.88/3.71 % (3866)Instructions burned: 5207 (million)
% 16.88/3.71 % (3866)------------------------------
% 16.88/3.71 % (3866)------------------------------
% 16.88/3.72 % (3893)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3362 for (2978ds/1376Mi)
% 17.11/3.80 % (3863)Instruction limit reached!
% 17.11/3.80 % (3863)------------------------------
% 17.11/3.80 % (3863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.80 % (3863)Termination reason: Unknown
% 17.11/3.80 % (3863)Termination phase: Saturation
% 17.11/3.80
% 17.11/3.80 % (3863)Memory used [KB]: 15095
% 17.11/3.80 % (3863)Time elapsed: 1.418 s
% 17.11/3.80 % (3863)Instructions burned: 4438 (million)
% 17.11/3.80 % (3863)------------------------------
% 17.11/3.80 % (3863)------------------------------
% 17.11/3.81 % (3894)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3362 for (2977ds/906Mi)
% 17.11/3.82 % (3892)Instruction limit reached!
% 17.11/3.82 % (3892)------------------------------
% 17.11/3.82 % (3892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.82 % (3892)Termination reason: Unknown
% 17.11/3.82 % (3892)Termination phase: Saturation
% 17.11/3.82
% 17.11/3.82 % (3892)Memory used [KB]: 8315
% 17.11/3.82 % (3892)Time elapsed: 0.138 s
% 17.11/3.82 % (3892)Instructions burned: 464 (million)
% 17.11/3.82 % (3892)------------------------------
% 17.11/3.82 % (3892)------------------------------
% 17.11/3.83 % (3895)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3362 for (2976ds/434Mi)
% 17.11/3.88 % (3868)Instruction limit reached!
% 17.11/3.88 % (3868)------------------------------
% 17.11/3.88 % (3868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.88 % (3868)Termination reason: Unknown
% 17.11/3.88 % (3868)Termination phase: Saturation
% 17.11/3.88
% 17.11/3.88 % (3868)Memory used [KB]: 12792
% 17.11/3.88 % (3868)Time elapsed: 1.331 s
% 17.11/3.88 % (3868)Instructions burned: 4351 (million)
% 17.11/3.88 % (3868)------------------------------
% 17.11/3.88 % (3868)------------------------------
% 17.11/3.88 % (3891)Instruction limit reached!
% 17.11/3.88 % (3891)------------------------------
% 17.11/3.88 % (3891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.11/3.88 % (3891)Termination reason: Unknown
% 17.11/3.88 % (3891)Termination phase: Saturation
% 17.11/3.88
% 17.11/3.88 % (3891)Memory used [KB]: 5117
% 17.11/3.88 % (3891)Time elapsed: 0.245 s
% 17.11/3.88 % (3891)Instructions burned: 795 (million)
% 17.11/3.88 % (3891)------------------------------
% 17.11/3.88 % (3891)------------------------------
% 17.11/3.89 % (3896)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3362 for (2976ds/865Mi)
% 17.62/3.90 % (3897)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3362 for (2976ds/593Mi)
% 17.62/3.95 % (3895)Refutation not found, non-redundant clauses discarded% (3895)------------------------------
% 17.62/3.95 % (3895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.62/3.95 % (3895)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.62/3.95
% 17.62/3.95 % (3895)Memory used [KB]: 9338
% 17.62/3.95 % (3895)Time elapsed: 0.123 s
% 17.62/3.95 % (3895)Instructions burned: 415 (million)
% 17.62/3.95 % (3895)------------------------------
% 17.62/3.95 % (3895)------------------------------
% 17.62/3.96 % (3898)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3362 for (2975ds/443Mi)
% 20.07/4.06 % (3893)Instruction limit reached!
% 20.07/4.06 % (3893)------------------------------
% 20.07/4.06 % (3893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.06 % (3893)Termination reason: Unknown
% 20.07/4.06 % (3893)Termination phase: Saturation
% 20.07/4.06
% 20.07/4.06 % (3893)Memory used [KB]: 8571
% 20.07/4.06 % (3893)Time elapsed: 0.347 s
% 20.07/4.06 % (3893)Instructions burned: 1380 (million)
% 20.07/4.06 % (3893)------------------------------
% 20.07/4.06 % (3893)------------------------------
% 20.07/4.07 % (3899)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3362 for (2974ds/594Mi)
% 20.07/4.09 % (3894)Instruction limit reached!
% 20.07/4.09 % (3894)------------------------------
% 20.07/4.09 % (3894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.09 % (3894)Termination reason: Unknown
% 20.07/4.09 % (3894)Termination phase: Saturation
% 20.07/4.09
% 20.07/4.09 % (3894)Memory used [KB]: 9850
% 20.07/4.09 % (3894)Time elapsed: 0.279 s
% 20.07/4.09 % (3894)Instructions burned: 907 (million)
% 20.07/4.09 % (3894)------------------------------
% 20.07/4.09 % (3894)------------------------------
% 20.07/4.09 % (3897)Instruction limit reached!
% 20.07/4.09 % (3897)------------------------------
% 20.07/4.09 % (3897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.09 % (3897)Termination reason: Unknown
% 20.07/4.09 % (3897)Termination phase: Saturation
% 20.07/4.09
% 20.07/4.09 % (3897)Memory used [KB]: 7036
% 20.07/4.09 % (3897)Time elapsed: 0.187 s
% 20.07/4.09 % (3897)Instructions burned: 593 (million)
% 20.07/4.09 % (3897)------------------------------
% 20.07/4.09 % (3897)------------------------------
% 20.07/4.09 % (3898)Instruction limit reached!
% 20.07/4.09 % (3898)------------------------------
% 20.07/4.09 % (3898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.09 % (3898)Termination reason: Unknown
% 20.07/4.09 % (3898)Termination phase: Saturation
% 20.07/4.09
% 20.07/4.09 % (3898)Memory used [KB]: 8315
% 20.07/4.09 % (3898)Time elapsed: 0.128 s
% 20.07/4.09 % (3898)Instructions burned: 443 (million)
% 20.07/4.09 % (3898)------------------------------
% 20.07/4.09 % (3898)------------------------------
% 20.07/4.10 % (3900)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3362 for (2974ds/327Mi)
% 20.07/4.10 % (3901)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3362 for (2974ds/5411Mi)
% 20.07/4.10 % (3902)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3362 for (2974ds/1762Mi)
% 20.70/4.14 % (3896)Instruction limit reached!
% 20.70/4.14 % (3896)------------------------------
% 20.70/4.14 % (3896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.70/4.14 % (3896)Termination reason: Unknown
% 20.70/4.14 % (3896)Termination phase: Saturation
% 20.70/4.14
% 20.70/4.14 % (3896)Memory used [KB]: 8699
% 20.70/4.14 % (3896)Time elapsed: 0.247 s
% 20.70/4.14 % (3896)Instructions burned: 867 (million)
% 20.70/4.14 % (3896)------------------------------
% 20.70/4.14 % (3896)------------------------------
% 20.70/4.15 % (3903)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3362 for (2973ds/96Mi)
% 20.70/4.17 % (3903)Instruction limit reached!
% 20.70/4.17 % (3903)------------------------------
% 20.70/4.17 % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.70/4.17 % (3903)Termination reason: Unknown
% 20.70/4.17 % (3903)Termination phase: Property scanning
% 20.70/4.17
% 20.70/4.17 % (3903)Memory used [KB]: 2174
% 20.70/4.17 % (3903)Time elapsed: 0.025 s
% 20.70/4.17 % (3903)Instructions burned: 98 (million)
% 20.70/4.17 % (3903)------------------------------
% 20.70/4.17 % (3903)------------------------------
% 20.70/4.18 % (3904)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3362 for (2973ds/503Mi)
% 20.92/4.20 % (3900)Instruction limit reached!
% 20.92/4.20 % (3900)------------------------------
% 20.92/4.20 % (3900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.20 % (3900)Termination reason: Unknown
% 20.92/4.20 % (3900)Termination phase: Saturation
% 20.92/4.20
% 20.92/4.20 % (3900)Memory used [KB]: 9978
% 20.92/4.20 % (3900)Time elapsed: 0.102 s
% 20.92/4.20 % (3900)Instructions burned: 328 (million)
% 20.92/4.20 % (3900)------------------------------
% 20.92/4.20 % (3900)------------------------------
% 20.92/4.21 % (3905)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3362 for (2973ds/90Mi)
% 20.92/4.23 % (3905)Instruction limit reached!
% 20.92/4.23 % (3905)------------------------------
% 20.92/4.23 % (3905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.23 % (3905)Termination reason: Unknown
% 20.92/4.23 % (3905)Termination phase: Twee Goal Transformation
% 20.92/4.23
% 20.92/4.23 % (3905)Memory used [KB]: 2558
% 20.92/4.23 % (3905)Time elapsed: 0.025 s
% 20.92/4.23 % (3905)Instructions burned: 92 (million)
% 20.92/4.23 % (3905)------------------------------
% 20.92/4.23 % (3905)------------------------------
% 20.92/4.24 % (3906)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3362 for (2972ds/593Mi)
% 20.92/4.25 % (3899)Instruction limit reached!
% 20.92/4.25 % (3899)------------------------------
% 20.92/4.25 % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.25 % (3899)Termination reason: Unknown
% 20.92/4.25 % (3899)Termination phase: Saturation
% 20.92/4.25
% 20.92/4.25 % (3899)Memory used [KB]: 8443
% 20.92/4.25 % (3899)Time elapsed: 0.178 s
% 20.92/4.25 % (3899)Instructions burned: 596 (million)
% 20.92/4.25 % (3899)------------------------------
% 20.92/4.25 % (3899)------------------------------
% 20.92/4.26 % (3907)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3362 for (2972ds/1512Mi)
% 21.46/4.32 % (3904)Instruction limit reached!
% 21.46/4.32 % (3904)------------------------------
% 21.46/4.32 % (3904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.32 % (3904)Termination reason: Unknown
% 21.46/4.32 % (3904)Termination phase: Saturation
% 21.46/4.32
% 21.46/4.32 % (3904)Memory used [KB]: 8443
% 21.46/4.32 % (3904)Time elapsed: 0.147 s
% 21.46/4.32 % (3904)Instructions burned: 504 (million)
% 21.46/4.32 % (3904)------------------------------
% 21.46/4.32 % (3904)------------------------------
% 21.46/4.33 % (3908)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3362 for (2971ds/569Mi)
% 21.46/4.36 % (3888)Refutation not found, non-redundant clauses discarded% (3888)------------------------------
% 21.46/4.36 % (3888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.46/4.36 % (3888)Termination reason: Refutation not found, non-redundant clauses discarded
% 21.46/4.36
% 21.46/4.36 % (3888)Memory used [KB]: 7547
% 21.46/4.36 % (3888)Time elapsed: 1.127 s
% 21.46/4.36 % (3888)Instructions burned: 4671 (million)
% 21.46/4.36 % (3888)------------------------------
% 21.46/4.36 % (3888)------------------------------
% 21.46/4.37 % (3909)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3362 for (2971ds/501Mi)
% 21.80/4.42 % (3906)Instruction limit reached!
% 21.80/4.42 % (3906)------------------------------
% 21.80/4.42 % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.42 % (3906)Termination reason: Unknown
% 21.80/4.42 % (3906)Termination phase: Saturation
% 21.80/4.42
% 21.80/4.42 % (3906)Memory used [KB]: 8699
% 21.80/4.42 % (3906)Time elapsed: 0.177 s
% 21.80/4.42 % (3906)Instructions burned: 596 (million)
% 21.80/4.42 % (3906)------------------------------
% 21.80/4.42 % (3906)------------------------------
% 21.80/4.43 % (3910)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3362 for (2970ds/562Mi)
% 21.80/4.48 % (3908)Instruction limit reached!
% 21.80/4.48 % (3908)------------------------------
% 21.80/4.48 % (3908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.48 % (3908)Termination reason: Unknown
% 21.80/4.48 % (3908)Termination phase: Saturation
% 21.80/4.48
% 21.80/4.48 % (3908)Memory used [KB]: 10618
% 21.80/4.48 % (3908)Time elapsed: 0.144 s
% 21.80/4.48 % (3908)Instructions burned: 570 (million)
% 21.80/4.48 % (3908)------------------------------
% 21.80/4.48 % (3908)------------------------------
% 21.80/4.49 % (3911)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3362 for (2970ds/406Mi)
% 22.24/4.53 % (3909)Instruction limit reached!
% 22.24/4.53 % (3909)------------------------------
% 22.24/4.53 % (3909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.24/4.53 % (3909)Termination reason: Unknown
% 22.24/4.53 % (3909)Termination phase: Saturation
% 22.24/4.53
% 22.24/4.53 % (3909)Memory used [KB]: 9210
% 22.24/4.53 % (3909)Time elapsed: 0.154 s
% 22.24/4.53 % (3909)Instructions burned: 502 (million)
% 22.24/4.53 % (3909)------------------------------
% 22.24/4.53 % (3909)------------------------------
% 22.24/4.53 % (3902)Instruction limit reached!
% 22.24/4.53 % (3902)------------------------------
% 22.24/4.53 % (3902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.24/4.53 % (3902)Termination reason: Unknown
% 22.24/4.53 % (3902)Termination phase: Saturation
% 22.24/4.53
% 22.24/4.53 % (3902)Memory used [KB]: 15223
% 22.24/4.53 % (3902)Time elapsed: 0.434 s
% 22.24/4.53 % (3902)Instructions burned: 1764 (million)
% 22.24/4.53 % (3902)------------------------------
% 22.24/4.53 % (3902)------------------------------
% 22.24/4.54 % (3912)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3362 for (2969ds/582Mi)
% 22.24/4.54 % (3913)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3362 for (2969ds/456Mi)
% 22.24/4.59 % (3910)Instruction limit reached!
% 22.24/4.59 % (3910)------------------------------
% 22.24/4.59 % (3910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.24/4.59 % (3910)Termination reason: Unknown
% 22.24/4.59 % (3910)Termination phase: Saturation
% 22.24/4.59
% 22.24/4.59 % (3910)Memory used [KB]: 8443
% 22.24/4.59 % (3910)Time elapsed: 0.167 s
% 22.24/4.59 % (3910)Instructions burned: 563 (million)
% 22.24/4.59 % (3910)------------------------------
% 22.24/4.59 % (3910)------------------------------
% 23.12/4.60 % (3911)Instruction limit reached!
% 23.12/4.60 % (3911)------------------------------
% 23.12/4.60 % (3911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.12/4.60 % (3911)Termination reason: Unknown
% 23.12/4.60 % (3911)Termination phase: Saturation
% 23.12/4.60
% 23.12/4.60 % (3911)Memory used [KB]: 7291
% 23.12/4.60 % (3911)Time elapsed: 0.111 s
% 23.12/4.60 % (3911)Instructions burned: 408 (million)
% 23.12/4.60 % (3911)------------------------------
% 23.12/4.60 % (3911)------------------------------
% 23.12/4.60 % (3914)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3362 for (2969ds/393Mi)
% 23.12/4.61 % (3915)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3362 for (2969ds/1335Mi)
% 23.12/4.68 % (3913)Instruction limit reached!
% 23.12/4.68 % (3913)------------------------------
% 23.12/4.68 % (3913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.12/4.68 % (3913)Termination reason: Unknown
% 23.12/4.68 % (3913)Termination phase: Saturation
% 23.12/4.68
% 23.12/4.68 % (3913)Memory used [KB]: 8443
% 23.12/4.68 % (3913)Time elapsed: 0.135 s
% 23.12/4.68 % (3913)Instructions burned: 459 (million)
% 23.12/4.68 % (3913)------------------------------
% 23.12/4.68 % (3913)------------------------------
% 23.12/4.69 % (3916)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3362 for (2968ds/3373Mi)
% 23.48/4.71 % (3914)Instruction limit reached!
% 23.48/4.71 % (3914)------------------------------
% 23.48/4.71 % (3914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.71 % (3914)Termination reason: Unknown
% 23.48/4.71 % (3914)Termination phase: Saturation
% 23.48/4.71
% 23.48/4.71 % (3914)Memory used [KB]: 8827
% 23.48/4.71 % (3914)Time elapsed: 0.104 s
% 23.48/4.71 % (3914)Instructions burned: 394 (million)
% 23.48/4.71 % (3914)------------------------------
% 23.48/4.71 % (3914)------------------------------
% 23.48/4.72 % (3917)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3362 for (2968ds/474Mi)
% 23.48/4.72 % (3912)Instruction limit reached!
% 23.48/4.72 % (3912)------------------------------
% 23.48/4.72 % (3912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.72 % (3912)Termination reason: Unknown
% 23.48/4.72 % (3912)Termination phase: Saturation
% 23.48/4.72
% 23.48/4.72 % (3912)Memory used [KB]: 9466
% 23.48/4.72 % (3912)Time elapsed: 0.183 s
% 23.48/4.72 % (3912)Instructions burned: 585 (million)
% 23.48/4.72 % (3912)------------------------------
% 23.48/4.72 % (3912)------------------------------
% 23.48/4.73 % (3918)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3362 for (2968ds/157Mi)
% 23.48/4.73 % (3907)Instruction limit reached!
% 23.48/4.73 % (3907)------------------------------
% 23.48/4.73 % (3907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.73 % (3907)Termination reason: Unknown
% 23.48/4.73 % (3907)Termination phase: Saturation
% 23.48/4.73
% 23.48/4.73 % (3907)Memory used [KB]: 11513
% 23.48/4.73 % (3907)Time elapsed: 0.476 s
% 23.48/4.73 % (3907)Instructions burned: 1513 (million)
% 23.48/4.73 % (3907)------------------------------
% 23.48/4.73 % (3907)------------------------------
% 23.48/4.74 % (3919)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3362 for (2967ds/590Mi)
% 23.48/4.77 % (3918)Instruction limit reached!
% 23.48/4.77 % (3918)------------------------------
% 23.48/4.77 % (3918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.77 % (3918)Termination reason: Unknown
% 23.48/4.77 % (3918)Termination phase: Saturation
% 23.48/4.77
% 23.48/4.77 % (3918)Memory used [KB]: 6908
% 23.48/4.77 % (3918)Time elapsed: 0.040 s
% 23.48/4.77 % (3918)Instructions burned: 158 (million)
% 23.48/4.77 % (3918)------------------------------
% 23.48/4.77 % (3918)------------------------------
% 23.48/4.78 % (3920)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3362 for (2967ds/104Mi)
% 24.43/4.80 % (3920)Instruction limit reached!
% 24.43/4.80 % (3920)------------------------------
% 24.43/4.80 % (3920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.43/4.80 % (3920)Termination reason: Unknown
% 24.43/4.80 % (3920)Termination phase: Saturation
% 24.43/4.80
% 24.43/4.80 % (3920)Memory used [KB]: 6908
% 24.43/4.80 % (3920)Time elapsed: 0.029 s
% 24.43/4.80 % (3920)Instructions burned: 106 (million)
% 24.43/4.80 % (3920)------------------------------
% 24.43/4.80 % (3920)------------------------------
% 24.43/4.81 % (3921)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3362 for (2967ds/414Mi)
% 24.43/4.83 % (3917)Instruction limit reached!
% 24.43/4.83 % (3917)------------------------------
% 24.43/4.83 % (3917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.43/4.83 % (3917)Termination reason: Unknown
% 24.43/4.83 % (3917)Termination phase: Saturation
% 24.43/4.83
% 24.43/4.83 % (3917)Memory used [KB]: 10618
% 24.43/4.83 % (3917)Time elapsed: 0.118 s
% 24.43/4.83 % (3917)Instructions burned: 475 (million)
% 24.43/4.83 % (3917)------------------------------
% 24.43/4.83 % (3917)------------------------------
% 24.43/4.84 % (3922)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3362 for (2966ds/715Mi)
% 24.69/4.91 % (3921)Instruction limit reached!
% 24.69/4.91 % (3921)------------------------------
% 24.69/4.91 % (3921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/4.91 % (3921)Termination reason: Unknown
% 24.69/4.91 % (3921)Termination phase: Saturation
% 24.69/4.91
% 24.69/4.91 % (3921)Memory used [KB]: 6908
% 24.69/4.91 % (3921)Time elapsed: 0.102 s
% 24.69/4.91 % (3921)Instructions burned: 417 (million)
% 24.69/4.91 % (3921)------------------------------
% 24.69/4.91 % (3921)------------------------------
% 24.69/4.92 % (3919)Instruction limit reached!
% 24.69/4.92 % (3919)------------------------------
% 24.69/4.92 % (3919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/4.92 % (3919)Termination reason: Unknown
% 24.69/4.92 % (3919)Termination phase: Saturation
% 24.69/4.92
% 24.69/4.92 % (3919)Memory used [KB]: 9083
% 24.69/4.92 % (3919)Time elapsed: 0.175 s
% 24.69/4.92 % (3919)Instructions burned: 592 (million)
% 24.69/4.92 % (3919)------------------------------
% 24.69/4.92 % (3919)------------------------------
% 24.69/4.92 % (3923)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3362 for (2965ds/961Mi)
% 24.69/4.93 % (3924)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_3362 for (2965ds/1213Mi)
% 24.69/4.97 % (3915)Instruction limit reached!
% 24.69/4.97 % (3915)------------------------------
% 24.69/4.97 % (3915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/4.97 % (3915)Termination reason: Unknown
% 24.69/4.97 % (3915)Termination phase: Saturation
% 24.69/4.97
% 24.69/4.97 % (3915)Memory used [KB]: 8187
% 24.69/4.97 % (3915)Time elapsed: 0.361 s
% 24.69/4.97 % (3915)Instructions burned: 1337 (million)
% 24.69/4.97 % (3915)------------------------------
% 24.69/4.97 % (3915)------------------------------
% 24.69/4.98 % (3925)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3362 for (2965ds/1979Mi)
% 27.13/5.06 % (3922)Instruction limit reached!
% 27.13/5.06 % (3922)------------------------------
% 27.13/5.06 % (3922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.13/5.06 % (3922)Termination reason: Unknown
% 27.13/5.06 % (3922)Termination phase: Saturation
% 27.13/5.06
% 27.13/5.06 % (3922)Memory used [KB]: 4093
% 27.13/5.06 % (3922)Time elapsed: 0.235 s
% 27.13/5.06 % (3922)Instructions burned: 715 (million)
% 27.13/5.06 % (3922)------------------------------
% 27.13/5.06 % (3922)------------------------------
% 27.13/5.07 % (3926)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_3362 for (2964ds/481Mi)
% 27.83/5.19 % (3926)Instruction limit reached!
% 27.83/5.19 % (3926)------------------------------
% 27.83/5.19 % (3926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.83/5.19 % (3926)Termination reason: Unknown
% 27.83/5.19 % (3926)Termination phase: Saturation
% 27.83/5.19
% 27.83/5.19 % (3926)Memory used [KB]: 10746
% 27.83/5.19 % (3926)Time elapsed: 0.124 s
% 27.83/5.19 % (3926)Instructions burned: 482 (million)
% 27.83/5.19 % (3926)------------------------------
% 27.83/5.19 % (3926)------------------------------
% 28.40/5.20 % (3927)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_3362 for (2963ds/783Mi)
% 28.40/5.22 % (3923)Instruction limit reached!
% 28.40/5.22 % (3923)------------------------------
% 28.40/5.22 % (3923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.40/5.22 % (3923)Termination reason: Unknown
% 28.40/5.22 % (3923)Termination phase: Saturation
% 28.40/5.22
% 28.40/5.22 % (3923)Memory used [KB]: 8699
% 28.40/5.22 % (3923)Time elapsed: 0.299 s
% 28.40/5.22 % (3923)Instructions burned: 962 (million)
% 28.40/5.22 % (3923)------------------------------
% 28.40/5.22 % (3923)------------------------------
% 28.40/5.23 % (3928)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_3362 for (2962ds/432Mi)
% 28.93/5.30 % (3924)Instruction limit reached!
% 28.93/5.30 % (3924)------------------------------
% 28.93/5.30 % (3924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.93/5.30 % (3924)Termination reason: Unknown
% 28.93/5.30 % (3924)Termination phase: Saturation
% 28.93/5.30
% 28.93/5.30 % (3924)Memory used [KB]: 12537
% 28.93/5.30 % (3924)Time elapsed: 0.377 s
% 28.93/5.30 % (3924)Instructions burned: 1215 (million)
% 28.93/5.30 % (3924)------------------------------
% 28.93/5.30 % (3924)------------------------------
% 28.93/5.31 % (3929)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_3362 for (2962ds/1670Mi)
% 28.93/5.36 % (3928)Instruction limit reached!
% 28.93/5.36 % (3928)------------------------------
% 28.93/5.36 % (3928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.93/5.36 % (3928)Termination reason: Unknown
% 28.93/5.36 % (3928)Termination phase: Saturation
% 28.93/5.36
% 28.93/5.36 % (3928)Memory used [KB]: 8315
% 28.93/5.36 % (3928)Time elapsed: 0.127 s
% 28.93/5.36 % (3928)Instructions burned: 433 (million)
% 28.93/5.36 % (3928)------------------------------
% 28.93/5.36 % (3928)------------------------------
% 28.93/5.37 % (3930)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_3362 for (2961ds/90Mi)
% 28.93/5.39 % (3930)Instruction limit reached!
% 28.93/5.39 % (3930)------------------------------
% 28.93/5.39 % (3930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.93/5.39 % (3930)Termination reason: Unknown
% 28.93/5.39 % (3930)Termination phase: Property scanning
% 28.93/5.39
% 28.93/5.39 % (3930)Memory used [KB]: 2174
% 28.93/5.39 % (3930)Time elapsed: 0.024 s
% 28.93/5.39 % (3930)Instructions burned: 91 (million)
% 28.93/5.39 % (3930)------------------------------
% 28.93/5.39 % (3930)------------------------------
% 29.51/5.40 % (3931)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3362 for (2961ds/346Mi)
% 29.51/5.44 % (3927)Instruction limit reached!
% 29.51/5.44 % (3927)------------------------------
% 29.51/5.44 % (3927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.51/5.44 % (3927)Termination reason: Unknown
% 29.51/5.44 % (3927)Termination phase: Saturation
% 29.51/5.44
% 29.51/5.44 % (3927)Memory used [KB]: 10490
% 29.51/5.44 % (3927)Time elapsed: 0.245 s
% 29.51/5.44 % (3927)Instructions burned: 785 (million)
% 29.51/5.44 % (3927)------------------------------
% 29.51/5.44 % (3927)------------------------------
% 29.51/5.45 % (3932)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_3362 for (2960ds/401Mi)
% 29.51/5.48 % (3931)Instruction limit reached!
% 29.51/5.48 % (3931)------------------------------
% 29.51/5.48 % (3931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.51/5.48 % (3931)Termination reason: Unknown
% 29.51/5.48 % (3931)Termination phase: Saturation
% 29.51/5.48
% 29.51/5.48 % (3931)Memory used [KB]: 8443
% 29.51/5.48 % (3931)Time elapsed: 0.086 s
% 29.51/5.48 % (3931)Instructions burned: 346 (million)
% 29.51/5.48 % (3931)------------------------------
% 29.51/5.48 % (3931)------------------------------
% 29.51/5.49 % (3933)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_3362 for (2960ds/6454Mi)
% 30.26/5.55 % (3932)Instruction limit reached!
% 30.26/5.55 % (3932)------------------------------
% 30.26/5.55 % (3932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.55 % (3932)Termination reason: Unknown
% 30.26/5.55 % (3932)Termination phase: Saturation
% 30.26/5.55
% 30.26/5.55 % (3932)Memory used [KB]: 7036
% 30.26/5.55 % (3932)Time elapsed: 0.099 s
% 30.26/5.55 % (3932)Instructions burned: 404 (million)
% 30.26/5.55 % (3932)------------------------------
% 30.26/5.55 % (3932)------------------------------
% 30.26/5.56 % (3934)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_3362 for (2959ds/283Mi)
% 30.26/5.58 % (3925)Instruction limit reached!
% 30.26/5.58 % (3925)------------------------------
% 30.26/5.58 % (3925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.58 % (3925)Termination reason: Unknown
% 30.26/5.58 % (3925)Termination phase: Saturation
% 30.26/5.58
% 30.26/5.58 % (3925)Memory used [KB]: 9338
% 30.26/5.58 % (3925)Time elapsed: 0.603 s
% 30.26/5.58 % (3925)Instructions burned: 1979 (million)
% 30.26/5.58 % (3925)------------------------------
% 30.26/5.58 % (3925)------------------------------
% 30.26/5.59 % (3935)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_3362 for (2959ds/865Mi)
% 30.78/5.64 % (3934)Instruction limit reached!
% 30.78/5.64 % (3934)------------------------------
% 30.78/5.64 % (3934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.78/5.64 % (3934)Termination reason: Unknown
% 30.78/5.64 % (3934)Termination phase: Saturation
% 30.78/5.64
% 30.78/5.64 % (3934)Memory used [KB]: 7931
% 30.78/5.64 % (3934)Time elapsed: 0.078 s
% 30.78/5.64 % (3934)Instructions burned: 284 (million)
% 30.78/5.64 % (3934)------------------------------
% 30.78/5.64 % (3934)------------------------------
% 30.78/5.65 % (3936)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_3362 for (2958ds/4528Mi)
% 31.16/5.70 % (3916)Instruction limit reached!
% 31.16/5.70 % (3916)------------------------------
% 31.16/5.70 % (3916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.16/5.70 % (3916)Termination reason: Unknown
% 31.16/5.70 % (3916)Termination phase: Saturation
% 31.16/5.70
% 31.16/5.70 % (3916)Memory used [KB]: 11897
% 31.16/5.70 % (3916)Time elapsed: 1.019 s
% 31.16/5.70 % (3916)Instructions burned: 3375 (million)
% 31.16/5.70 % (3916)------------------------------
% 31.16/5.70 % (3916)------------------------------
% 31.16/5.71 % (3937)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_3362 for (2958ds/1001Mi)
% 31.16/5.73 % (3929)Instruction limit reached!
% 31.16/5.73 % (3929)------------------------------
% 31.16/5.73 % (3929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.16/5.73 % (3929)Termination reason: Unknown
% 31.16/5.73 % (3929)Termination phase: Saturation
% 31.16/5.73
% 31.16/5.73 % (3929)Memory used [KB]: 12153
% 31.16/5.73 % (3929)Time elapsed: 0.415 s
% 31.16/5.73 % (3929)Instructions burned: 1671 (million)
% 31.16/5.73 % (3929)------------------------------
% 31.16/5.73 % (3929)------------------------------
% 31.16/5.74 % (3938)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_3362 for (2957ds/102Mi)
% 31.16/5.74 % (3936)Refutation not found, incomplete strategy
% 31.16/5.74 % (3936)------------------------------
% 31.16/5.74 % (3936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.16/5.74 % (3936)Termination reason: Refutation not found, incomplete strategy
% 31.16/5.74
% 31.16/5.74
% 31.16/5.74 % (3936)Memory used [KB]: 2430
% 31.16/5.74 % (3936)Time elapsed: 0.093 s
% 31.16/5.74 % (3936)Instructions burned: 347 (million)
% 31.16/5.74 % (3936)------------------------------
% 31.16/5.74 % (3936)------------------------------
% 31.16/5.75 % (3939)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_3362 for (2957ds/952Mi)
% 31.16/5.76 % (3938)Instruction limit reached!
% 31.16/5.76 % (3938)------------------------------
% 31.16/5.76 % (3938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.16/5.76 % (3938)Termination reason: Unknown
% 31.16/5.76 % (3938)Termination phase: Saturation
% 31.16/5.76
% 31.16/5.76 % (3938)Memory used [KB]: 6780
% 31.16/5.76 % (3938)Time elapsed: 0.027 s
% 31.16/5.76 % (3938)Instructions burned: 102 (million)
% 31.16/5.76 % (3938)------------------------------
% 31.16/5.76 % (3938)------------------------------
% 31.16/5.77 % (3940)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_3362 for (2957ds/578Mi)
% 31.16/5.78 % (3901)Instruction limit reached!
% 31.16/5.78 % (3901)------------------------------
% 31.16/5.78 % (3901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.16/5.78 % (3901)Termination reason: Unknown
% 31.16/5.78 % (3901)Termination phase: Saturation
% 31.16/5.78
% 31.16/5.78 % (3901)Memory used [KB]: 15991
% 31.16/5.78 % (3901)Time elapsed: 1.684 s
% 31.16/5.78 % (3901)Instructions burned: 5413 (million)
% 31.16/5.78 % (3901)------------------------------
% 31.16/5.78 % (3901)------------------------------
% 31.16/5.79 % (3941)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3362 for (2957ds/643Mi)
% 31.93/5.83 % (3935)Instruction limit reached!
% 31.93/5.83 % (3935)------------------------------
% 31.93/5.83 % (3935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/5.83 % (3935)Termination reason: Unknown
% 31.93/5.83 % (3935)Termination phase: Saturation
% 31.93/5.83
% 31.93/5.83 % (3935)Memory used [KB]: 8315
% 31.93/5.83 % (3935)Time elapsed: 0.240 s
% 31.93/5.83 % (3935)Instructions burned: 865 (million)
% 31.93/5.83 % (3935)------------------------------
% 31.93/5.83 % (3935)------------------------------
% 31.93/5.84 % (3942)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_3362 for (2956ds/865Mi)
% 31.93/5.89 % (3889)Instruction limit reached!
% 31.93/5.89 % (3889)------------------------------
% 31.93/5.89 % (3889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/5.89 % (3889)Termination reason: Unknown
% 31.93/5.89 % (3889)Termination phase: Saturation
% 31.93/5.89
% 31.93/5.89 % (3889)Memory used [KB]: 24178
% 31.93/5.89 % (3889)Time elapsed: 2.637 s
% 31.93/5.89 % (3889)Instructions burned: 8253 (million)
% 31.93/5.89 % (3889)------------------------------
% 31.93/5.89 % (3889)------------------------------
% 32.29/5.90 % (3943)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_3362 for (2956ds/1174Mi)
% 32.29/5.91 % (3940)Instruction limit reached!
% 32.29/5.91 % (3940)------------------------------
% 32.29/5.91 % (3940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.29/5.91 % (3940)Termination reason: Unknown
% 32.29/5.91 % (3940)Termination phase: Saturation
% 32.29/5.91
% 32.29/5.91 % (3940)Memory used [KB]: 8443
% 32.29/5.91 % (3940)Time elapsed: 0.134 s
% 32.29/5.91 % (3940)Instructions burned: 582 (million)
% 32.29/5.91 % (3940)------------------------------
% 32.29/5.91 % (3940)------------------------------
% 32.29/5.92 % (3944)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_3362 for (2956ds/644Mi)
% 32.29/5.94 % (3937)Instruction limit reached!
% 32.29/5.94 % (3937)------------------------------
% 32.29/5.94 % (3937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.29/5.94 % (3937)Termination reason: Unknown
% 32.29/5.94 % (3937)Termination phase: Saturation
% 32.29/5.94
% 32.29/5.94 % (3937)Memory used [KB]: 8059
% 32.29/5.94 % (3937)Time elapsed: 0.230 s
% 32.29/5.94 % (3937)Instructions burned: 1006 (million)
% 32.29/5.94 % (3937)------------------------------
% 32.29/5.94 % (3937)------------------------------
% 32.29/5.95 % (3941)Instruction limit reached!
% 32.29/5.95 % (3941)------------------------------
% 32.29/5.95 % (3941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.29/5.95 % (3941)Termination reason: Unknown
% 32.29/5.95 % (3941)Termination phase: Saturation
% 32.29/5.95
% 32.29/5.95 % (3941)Memory used [KB]: 10874
% 32.29/5.95 % (3941)Time elapsed: 0.161 s
% 32.29/5.95 % (3941)Instructions burned: 645 (million)
% 32.29/5.95 % (3941)------------------------------
% 32.29/5.95 % (3941)------------------------------
% 32.29/5.95 % (3945)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_3362 for (2955ds/1201Mi)
% 32.29/5.96 % (3946)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_3362 for (2955ds/1046Mi)
% 34.17/6.04 % (3939)Instruction limit reached!
% 34.17/6.04 % (3939)------------------------------
% 34.17/6.04 % (3939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.04 % (3939)Termination reason: Unknown
% 34.17/6.04 % (3939)Termination phase: Saturation
% 34.17/6.04
% 34.17/6.04 % (3939)Memory used [KB]: 9850
% 34.17/6.04 % (3939)Time elapsed: 0.292 s
% 34.17/6.04 % (3939)Instructions burned: 953 (million)
% 34.17/6.04 % (3939)------------------------------
% 34.17/6.04 % (3939)------------------------------
% 34.17/6.05 % (3947)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_3362 for (2954ds/222Mi)
% 34.17/6.08 % (3942)Instruction limit reached!
% 34.17/6.08 % (3942)------------------------------
% 34.17/6.08 % (3942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.08 % (3942)Termination reason: Unknown
% 34.17/6.08 % (3942)Termination phase: Saturation
% 34.17/6.08
% 34.17/6.08 % (3942)Memory used [KB]: 7291
% 34.17/6.08 % (3942)Time elapsed: 0.240 s
% 34.17/6.08 % (3942)Instructions burned: 866 (million)
% 34.17/6.08 % (3942)------------------------------
% 34.17/6.08 % (3942)------------------------------
% 34.17/6.09 % (3948)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3362 for (2954ds/68Mi)
% 34.17/6.10 % (3948)Instruction limit reached!
% 34.17/6.10 % (3948)------------------------------
% 34.17/6.10 % (3948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.10 % (3948)Termination reason: Unknown
% 34.17/6.10 % (3948)Termination phase: Property scanning
% 34.17/6.10
% 34.17/6.10 % (3948)Memory used [KB]: 2046
% 34.17/6.10 % (3948)Time elapsed: 0.019 s
% 34.17/6.10 % (3948)Instructions burned: 72 (million)
% 34.17/6.10 % (3948)------------------------------
% 34.17/6.10 % (3948)------------------------------
% 34.17/6.11 % (3947)Instruction limit reached!
% 34.17/6.11 % (3947)------------------------------
% 34.17/6.11 % (3947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.11 % (3947)Termination reason: Unknown
% 34.17/6.11 % (3947)Termination phase: Saturation
% 34.17/6.11
% 34.17/6.11 % (3947)Memory used [KB]: 6908
% 34.17/6.11 % (3947)Time elapsed: 0.057 s
% 34.17/6.11 % (3947)Instructions burned: 225 (million)
% 34.17/6.11 % (3947)------------------------------
% 34.17/6.11 % (3947)------------------------------
% 34.17/6.11 % (3944)Instruction limit reached!
% 34.17/6.11 % (3944)------------------------------
% 34.17/6.11 % (3944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.17/6.11 % (3944)Termination reason: Unknown
% 34.17/6.11 % (3944)Termination phase: Saturation
% 34.17/6.11
% 34.17/6.11 % (3944)Memory used [KB]: 7675
% 34.17/6.11 % (3944)Time elapsed: 0.192 s
% 34.17/6.11 % (3944)Instructions burned: 645 (million)
% 34.17/6.11 % (3944)------------------------------
% 34.17/6.11 % (3944)------------------------------
% 34.17/6.11 % (3949)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_3362 for (2954ds/454Mi)
% 34.17/6.12 % (3950)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3362 for (2954ds/360Mi)
% 34.17/6.12 % (3951)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3362 for (2954ds/157Mi)
% 34.88/6.16 % (3951)Instruction limit reached!
% 34.88/6.16 % (3951)------------------------------
% 34.88/6.16 % (3951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.88/6.16 % (3951)Termination reason: Unknown
% 34.88/6.16 % (3951)Termination phase: Saturation
% 34.88/6.16
% 34.88/6.16 % (3951)Memory used [KB]: 6908
% 34.88/6.16 % (3951)Time elapsed: 0.042 s
% 34.88/6.16 % (3951)Instructions burned: 160 (million)
% 34.88/6.16 % (3951)------------------------------
% 34.88/6.16 % (3951)------------------------------
% 34.88/6.17 % (3952)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_3362 for (2953ds/5061Mi)
% 35.22/6.21 % (3950)Instruction limit reached!
% 35.22/6.21 % (3950)------------------------------
% 35.22/6.21 % (3950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.21 % (3950)Termination reason: Unknown
% 35.22/6.21 % (3950)Termination phase: Saturation
% 35.22/6.21
% 35.22/6.21 % (3950)Memory used [KB]: 7036
% 35.22/6.21 % (3950)Time elapsed: 0.091 s
% 35.22/6.21 % (3950)Instructions burned: 363 (million)
% 35.22/6.21 % (3950)------------------------------
% 35.22/6.21 % (3950)------------------------------
% 35.22/6.21 % (3946)Instruction limit reached!
% 35.22/6.21 % (3946)------------------------------
% 35.22/6.21 % (3946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.21 % (3946)Termination reason: Unknown
% 35.22/6.21 % (3946)Termination phase: Saturation
% 35.22/6.21
% 35.22/6.21 % (3946)Memory used [KB]: 7291
% 35.22/6.21 % (3946)Time elapsed: 0.251 s
% 35.22/6.21 % (3946)Instructions burned: 1046 (million)
% 35.22/6.21 % (3946)------------------------------
% 35.22/6.21 % (3946)------------------------------
% 35.22/6.21 % (3953)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_3362 for (2953ds/2401Mi)
% 35.22/6.22 % (3954)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_3362 for (2953ds/5798Mi)
% 35.22/6.23 % (3949)Instruction limit reached!
% 35.22/6.23 % (3949)------------------------------
% 35.22/6.23 % (3949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.23 % (3949)Termination reason: Unknown
% 35.22/6.23 % (3949)Termination phase: Saturation
% 35.22/6.23
% 35.22/6.23 % (3949)Memory used [KB]: 15223
% 35.22/6.23 % (3949)Time elapsed: 0.116 s
% 35.22/6.23 % (3949)Instructions burned: 457 (million)
% 35.22/6.23 % (3949)------------------------------
% 35.22/6.23 % (3949)------------------------------
% 35.22/6.24 % (3955)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3362 for (2952ds/346Mi)
% 35.22/6.26 % (3943)Instruction limit reached!
% 35.22/6.26 % (3943)------------------------------
% 35.22/6.26 % (3943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.26 % (3943)Termination reason: Unknown
% 35.22/6.26 % (3943)Termination phase: Saturation
% 35.22/6.26
% 35.22/6.26 % (3943)Memory used [KB]: 8827
% 35.22/6.26 % (3943)Time elapsed: 0.357 s
% 35.22/6.26 % (3943)Instructions burned: 1176 (million)
% 35.22/6.26 % (3943)------------------------------
% 35.22/6.26 % (3943)------------------------------
% 35.22/6.27 % (3956)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_3362 for (2952ds/1321Mi)
% 35.22/6.27 % (3945)Refutation not found, non-redundant clauses discarded% (3945)------------------------------
% 35.22/6.27 % (3945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.27 % (3945)Termination reason: Refutation not found, non-redundant clauses discarded
% 35.22/6.27
% 35.22/6.27 % (3945)Memory used [KB]: 9722
% 35.22/6.27 % (3945)Time elapsed: 0.322 s
% 35.22/6.27 % (3945)Instructions burned: 1166 (million)
% 35.22/6.27 % (3945)------------------------------
% 35.22/6.27 % (3945)------------------------------
% 35.22/6.28 % (3957)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_3362 for (2952ds/1312Mi)
% 35.72/6.32 % (3955)Instruction limit reached!
% 35.72/6.32 % (3955)------------------------------
% 35.72/6.32 % (3955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.72/6.32 % (3955)Termination reason: Unknown
% 35.72/6.32 % (3955)Termination phase: Saturation
% 35.72/6.32
% 35.72/6.32 % (3955)Memory used [KB]: 8443
% 35.72/6.32 % (3955)Time elapsed: 0.087 s
% 35.72/6.32 % (3955)Instructions burned: 348 (million)
% 35.72/6.32 % (3955)------------------------------
% 35.72/6.32 % (3955)------------------------------
% 35.72/6.33 % (3958)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_3362 for (2951ds/672Mi)
% 36.03/6.53 % (3958)Instruction limit reached!
% 36.03/6.53 % (3958)------------------------------
% 36.03/6.53 % (3958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.03/6.53 % (3958)Termination reason: Unknown
% 36.03/6.53 % (3958)Termination phase: Saturation
% 36.03/6.53
% 36.03/6.53 % (3958)Memory used [KB]: 9594
% 36.03/6.53 % (3958)Time elapsed: 0.202 s
% 36.03/6.53 % (3958)Instructions burned: 673 (million)
% 36.03/6.53 % (3958)------------------------------
% 36.03/6.53 % (3958)------------------------------
% 36.03/6.54 % (3959)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_3362 for (2949ds/1897Mi)
% 36.34/6.61 % (3957)Instruction limit reached!
% 36.34/6.61 % (3957)------------------------------
% 36.34/6.61 % (3957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.34/6.61 % (3957)Termination reason: Unknown
% 36.34/6.62 % (3957)Termination phase: Saturation
% 36.34/6.62
% 36.34/6.62 % (3957)Memory used [KB]: 11385
% 36.34/6.62 % (3957)Time elapsed: 0.332 s
% 36.34/6.62 % (3957)Instructions burned: 1315 (million)
% 36.34/6.62 % (3957)------------------------------
% 36.34/6.62 % (3957)------------------------------
% 36.34/6.63 % (3960)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_3362 for (2949ds/1202Mi)
% 36.34/6.66 % (3956)Instruction limit reached!
% 36.34/6.66 % (3956)------------------------------
% 36.34/6.66 % (3956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.34/6.66 % (3956)Termination reason: Unknown
% 36.34/6.66 % (3956)Termination phase: Saturation
% 36.34/6.66
% 36.34/6.66 % (3956)Memory used [KB]: 6524
% 36.34/6.66 % (3956)Time elapsed: 0.397 s
% 36.34/6.66 % (3956)Instructions burned: 1323 (million)
% 36.34/6.66 % (3956)------------------------------
% 36.34/6.66 % (3956)------------------------------
% 36.34/6.67 % (3961)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_3362 for (2948ds/1493Mi)
% 37.39/6.94 % (3953)Instruction limit reached!
% 37.39/6.94 % (3953)------------------------------
% 37.39/6.94 % (3953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.94 % (3953)Termination reason: Unknown
% 37.39/6.94 % (3953)Termination phase: Saturation
% 37.39/6.94
% 37.39/6.94 % (3953)Memory used [KB]: 8827
% 37.39/6.94 % (3953)Time elapsed: 0.727 s
% 37.39/6.94 % (3953)Instructions burned: 2401 (million)
% 37.39/6.94 % (3953)------------------------------
% 37.39/6.94 % (3953)------------------------------
% 37.39/6.95 % (3962)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_3362 for (2945ds/7679Mi)
% 37.39/6.98 % (3960)Instruction limit reached!
% 37.39/6.98 % (3960)------------------------------
% 37.39/6.98 % (3960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.98 % (3960)Termination reason: Unknown
% 37.39/6.98 % (3960)Termination phase: Saturation
% 37.39/6.98
% 37.39/6.98 % (3960)Memory used [KB]: 6652
% 37.39/6.98 % (3960)Time elapsed: 0.356 s
% 37.39/6.98 % (3960)Instructions burned: 1202 (million)
% 37.39/6.98 % (3960)------------------------------
% 37.39/6.98 % (3960)------------------------------
% 37.39/6.99 % (3963)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_3362 for (2945ds/340Mi)
% 41.18/7.03 % (3961)Instruction limit reached!
% 41.18/7.03 % (3961)------------------------------
% 41.18/7.03 % (3961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.18/7.03 % (3961)Termination reason: Unknown
% 41.18/7.03 % (3961)Termination phase: Saturation
% 41.18/7.03
% 41.18/7.03 % (3961)Memory used [KB]: 7164
% 41.18/7.03 % (3961)Time elapsed: 0.356 s
% 41.18/7.03 % (3961)Instructions burned: 1497 (million)
% 41.18/7.03 % (3961)------------------------------
% 41.18/7.03 % (3961)------------------------------
% 41.18/7.04 % (3964)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_3362 for (2944ds/3672Mi)
% 41.18/7.09 % (3963)Instruction limit reached!
% 41.18/7.09 % (3963)------------------------------
% 41.18/7.09 % (3963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.18/7.09 % (3963)Termination reason: Unknown
% 41.18/7.09 % (3963)Termination phase: Saturation
% 41.18/7.09
% 41.18/7.09 % (3963)Memory used [KB]: 9466
% 41.18/7.09 % (3963)Time elapsed: 0.101 s
% 41.18/7.09 % (3963)Instructions burned: 342 (million)
% 41.18/7.09 % (3963)------------------------------
% 41.18/7.09 % (3963)------------------------------
% 41.18/7.10 % (3965)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_3362 for (2944ds/1535Mi)
% 41.83/7.15 % (3959)Instruction limit reached!
% 41.83/7.15 % (3959)------------------------------
% 41.83/7.15 % (3959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.83/7.15 % (3959)Termination reason: Unknown
% 41.83/7.15 % (3959)Termination phase: Saturation
% 41.83/7.15
% 41.83/7.15 % (3959)Memory used [KB]: 12409
% 41.83/7.15 % (3959)Time elapsed: 0.603 s
% 41.83/7.15 % (3959)Instructions burned: 1899 (million)
% 41.83/7.15 % (3959)------------------------------
% 41.83/7.15 % (3959)------------------------------
% 41.83/7.16 % (3966)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_3362 for (2943ds/4637Mi)
% 42.95/7.41 % (3952)Instruction limit reached!
% 42.95/7.41 % (3952)------------------------------
% 42.95/7.41 % (3952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.95/7.41 % (3952)Termination reason: Unknown
% 42.95/7.41 % (3952)Termination phase: Saturation
% 42.95/7.41
% 42.95/7.41 % (3952)Memory used [KB]: 9338
% 42.95/7.41 % (3952)Time elapsed: 1.244 s
% 42.95/7.41 % (3952)Instructions burned: 5061 (million)
% 42.95/7.41 % (3952)------------------------------
% 42.95/7.41 % (3952)------------------------------
% 42.95/7.42 % (3967)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_3362 for (2941ds/3174Mi)
% 42.95/7.47 % (3965)Instruction limit reached!
% 42.95/7.47 % (3965)------------------------------
% 42.95/7.47 % (3965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.95/7.47 % (3965)Termination reason: Unknown
% 42.95/7.47 % (3965)Termination phase: Saturation
% 42.95/7.47
% 42.95/7.47 % (3965)Memory used [KB]: 11769
% 42.95/7.47 % (3965)Time elapsed: 0.374 s
% 42.95/7.47 % (3965)Instructions burned: 1536 (million)
% 42.95/7.47 % (3965)------------------------------
% 42.95/7.47 % (3965)------------------------------
% 42.95/7.48 % (3968)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3362 for (2940ds/307Mi)
% 43.65/7.51 % (3933)Instruction limit reached!
% 43.65/7.51 % (3933)------------------------------
% 43.65/7.51 % (3933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.65/7.51 % (3933)Termination reason: Unknown
% 43.65/7.51 % (3933)Termination phase: Saturation
% 43.65/7.51
% 43.65/7.51 % (3933)Memory used [KB]: 12025
% 43.65/7.51 % (3933)Time elapsed: 2.013 s
% 43.65/7.51 % (3933)Instructions burned: 6457 (million)
% 43.65/7.51 % (3933)------------------------------
% 43.65/7.51 % (3933)------------------------------
% 43.65/7.52 % (3969)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_3362 for (2940ds/3619Mi)
% 43.65/7.56 % (3968)Instruction limit reached!
% 43.65/7.56 % (3968)------------------------------
% 43.65/7.56 % (3968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.65/7.56 % (3968)Termination reason: Unknown
% 43.65/7.56 % (3968)Termination phase: Saturation
% 43.65/7.56
% 43.65/7.56 % (3968)Memory used [KB]: 7036
% 43.65/7.56 % (3968)Time elapsed: 0.077 s
% 43.65/7.56 % (3968)Instructions burned: 308 (million)
% 43.65/7.56 % (3968)------------------------------
% 43.65/7.56 % (3968)------------------------------
% 43.65/7.57 % (3970)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_3362 for (2939ds/2325Mi)
% 44.57/8.01 % (3954)Instruction limit reached!
% 44.57/8.01 % (3954)------------------------------
% 44.57/8.01 % (3954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.57/8.01 % (3954)Termination reason: Unknown
% 44.57/8.01 % (3954)Termination phase: Saturation
% 44.57/8.01
% 44.57/8.01 % (3954)Memory used [KB]: 12792
% 44.57/8.01 % (3954)Time elapsed: 1.794 s
% 44.57/8.01 % (3954)Instructions burned: 5798 (million)
% 44.57/8.01 % (3954)------------------------------
% 44.57/8.01 % (3954)------------------------------
% 48.21/8.02 % (3971)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_3362 for (2934ds/2341Mi)
% 48.85/8.17 % (3964)Instruction limit reached!
% 48.85/8.17 % (3964)------------------------------
% 48.85/8.17 % (3964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.85/8.17 % (3964)Termination reason: Unknown
% 48.85/8.17 % (3964)Termination phase: Saturation
% 48.85/8.17
% 48.85/8.17 % (3964)Memory used [KB]: 11641
% 48.85/8.17 % (3964)Time elapsed: 1.136 s
% 48.85/8.17 % (3964)Instructions burned: 3672 (million)
% 48.85/8.17 % (3964)------------------------------
% 48.85/8.17 % (3964)------------------------------
% 48.85/8.18 % (3972)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_3362 for (2933ds/7257Mi)
% 49.27/8.26 % (3970)Instruction limit reached!
% 49.27/8.26 % (3970)------------------------------
% 49.27/8.26 % (3970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.27/8.26 % (3970)Termination reason: Unknown
% 49.27/8.26 % (3970)Termination phase: Saturation
% 49.27/8.26
% 49.27/8.26 % (3970)Memory used [KB]: 14839
% 49.27/8.26 % (3970)Time elapsed: 0.694 s
% 49.27/8.26 % (3970)Instructions burned: 2326 (million)
% 49.27/8.26 % (3970)------------------------------
% 49.27/8.26 % (3970)------------------------------
% 49.27/8.27 % (3973)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_3362 for (2932ds/3710Mi)
% 49.74/8.38 % (3967)Instruction limit reached!
% 49.74/8.38 % (3967)------------------------------
% 49.74/8.38 % (3967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.74/8.38 % (3967)Termination reason: Unknown
% 49.74/8.38 % (3967)Termination phase: Saturation
% 49.74/8.38
% 49.74/8.38 % (3967)Memory used [KB]: 19189
% 49.74/8.38 % (3967)Time elapsed: 0.957 s
% 49.74/8.38 % (3967)Instructions burned: 3177 (million)
% 49.74/8.38 % (3967)------------------------------
% 49.74/8.38 % (3967)------------------------------
% 49.74/8.39 % (3974)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_3362 for (2931ds/326Mi)
% 50.13/8.48 % (3974)Instruction limit reached!
% 50.13/8.48 % (3974)------------------------------
% 50.13/8.48 % (3974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.13/8.48 % (3974)Termination reason: Unknown
% 50.13/8.48 % (3974)Termination phase: Saturation
% 50.13/8.48
% 50.13/8.48 % (3974)Memory used [KB]: 8059
% 50.13/8.48 % (3974)Time elapsed: 0.099 s
% 50.13/8.48 % (3974)Instructions burned: 327 (million)
% 50.13/8.48 % (3974)------------------------------
% 50.13/8.48 % (3974)------------------------------
% 50.13/8.49 % (3975)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_3362 for (2930ds/1100Mi)
% 50.55/8.58 % (3966)Instruction limit reached!
% 50.55/8.58 % (3966)------------------------------
% 50.55/8.58 % (3966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.55/8.58 % (3966)Termination reason: Unknown
% 50.55/8.58 % (3966)Termination phase: Saturation
% 50.55/8.58
% 50.55/8.58 % (3966)Memory used [KB]: 10362
% 50.55/8.58 % (3966)Time elapsed: 1.422 s
% 50.55/8.58 % (3966)Instructions burned: 4638 (million)
% 50.55/8.58 % (3966)------------------------------
% 50.55/8.58 % (3966)------------------------------
% 50.55/8.58 % (3969)Instruction limit reached!
% 50.55/8.58 % (3969)------------------------------
% 50.55/8.58 % (3969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.55/8.58 % (3969)Termination reason: Unknown
% 50.55/8.58 % (3969)Termination phase: Saturation
% 50.55/8.58
% 50.55/8.58 % (3969)Memory used [KB]: 16375
% 50.55/8.58 % (3969)Time elapsed: 1.070 s
% 50.55/8.58 % (3969)Instructions burned: 3620 (million)
% 50.55/8.58 % (3969)------------------------------
% 50.55/8.58 % (3969)------------------------------
% 50.55/8.59 % (3976)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3362 for (2929ds/406Mi)
% 50.55/8.60 % (3977)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_3362 for (2929ds/1871Mi)
% 50.94/8.70 % (3976)Instruction limit reached!
% 50.94/8.70 % (3976)------------------------------
% 50.94/8.70 % (3976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.94/8.70 % (3976)Termination reason: Unknown
% 50.94/8.70 % (3976)Termination phase: Saturation
% 50.94/8.70
% 50.94/8.70 % (3976)Memory used [KB]: 7291
% 50.94/8.70 % (3976)Time elapsed: 0.111 s
% 50.94/8.70 % (3976)Instructions burned: 407 (million)
% 50.94/8.70 % (3976)------------------------------
% 50.94/8.70 % (3976)------------------------------
% 50.94/8.71 % (3978)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_3362 for (2928ds/1194Mi)
% 50.94/8.74 % (3971)Instruction limit reached!
% 50.94/8.74 % (3971)------------------------------
% 50.94/8.74 % (3971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.94/8.74 % (3971)Termination reason: Unknown
% 50.94/8.74 % (3971)Termination phase: Saturation
% 50.94/8.74
% 50.94/8.74 % (3971)Memory used [KB]: 10234
% 50.94/8.74 % (3971)Time elapsed: 0.715 s
% 50.94/8.74 % (3971)Instructions burned: 2341 (million)
% 50.94/8.74 % (3971)------------------------------
% 50.94/8.74 % (3971)------------------------------
% 50.94/8.75 % (3979)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3362 for (2927ds/474Mi)
% 51.88/8.84 % (3975)Instruction limit reached!
% 51.88/8.84 % (3975)------------------------------
% 51.88/8.84 % (3975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.88/8.84 % (3975)Termination reason: Unknown
% 51.88/8.84 % (3975)Termination phase: Saturation
% 51.88/8.84
% 51.88/8.84 % (3975)Memory used [KB]: 12409
% 51.88/8.84 % (3975)Time elapsed: 0.344 s
% 51.88/8.84 % (3975)Instructions burned: 1102 (million)
% 51.88/8.84 % (3975)------------------------------
% 51.88/8.84 % (3975)------------------------------
% 51.88/8.85 % (3980)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_3362 for (2926ds/3115Mi)
% 51.88/8.86 % (3979)Instruction limit reached!
% 51.88/8.86 % (3979)------------------------------
% 51.88/8.86 % (3979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.88/8.86 % (3979)Termination reason: Unknown
% 51.88/8.86 % (3979)Termination phase: Saturation
% 51.88/8.86
% 51.88/8.86 % (3979)Memory used [KB]: 10874
% 51.88/8.86 % (3979)Time elapsed: 0.118 s
% 51.88/8.86 % (3979)Instructions burned: 477 (million)
% 51.88/8.86 % (3979)------------------------------
% 51.88/8.86 % (3979)------------------------------
% 51.88/8.88 % (3981)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_3362 for (2926ds/831Mi)
% 55.24/9.08 % (3978)Instruction limit reached!
% 55.24/9.08 % (3978)------------------------------
% 55.24/9.08 % (3978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.24/9.08 % (3978)Termination reason: Unknown
% 55.24/9.08 % (3978)Termination phase: Saturation
% 55.24/9.08
% 55.24/9.08 % (3978)Memory used [KB]: 10746
% 55.24/9.08 % (3978)Time elapsed: 0.372 s
% 55.24/9.08 % (3978)Instructions burned: 1194 (million)
% 55.24/9.08 % (3978)------------------------------
% 55.24/9.08 % (3978)------------------------------
% 55.24/9.09 % (3982)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_3362 for (2924ds/1188Mi)
% 55.94/9.13 % (3981)Instruction limit reached!
% 55.94/9.13 % (3981)------------------------------
% 55.94/9.13 % (3981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.94/9.13 % (3981)Termination reason: Unknown
% 55.94/9.13 % (3981)Termination phase: Saturation
% 55.94/9.13
% 55.94/9.13 % (3981)Memory used [KB]: 8699
% 55.94/9.13 % (3981)Time elapsed: 0.257 s
% 55.94/9.13 % (3981)Instructions burned: 832 (million)
% 55.94/9.13 % (3981)------------------------------
% 55.94/9.13 % (3981)------------------------------
% 55.94/9.14 % (3983)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_3362 for (2923ds/2868Mi)
% 55.94/9.18 % (3977)Instruction limit reached!
% 55.94/9.18 % (3977)------------------------------
% 55.94/9.18 % (3977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.94/9.18 % (3977)Termination reason: Unknown
% 55.94/9.18 % (3977)Termination phase: Saturation
% 55.94/9.18
% 55.94/9.18 % (3977)Memory used [KB]: 16119
% 55.94/9.18 % (3977)Time elapsed: 0.581 s
% 55.94/9.18 % (3977)Instructions burned: 1872 (million)
% 55.94/9.18 % (3977)------------------------------
% 55.94/9.18 % (3977)------------------------------
% 55.94/9.19 % (3984)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_3362 for (2923ds/1516Mi)
% 56.31/9.20 % (3973)Instruction limit reached!
% 56.31/9.20 % (3973)------------------------------
% 56.31/9.20 % (3973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.31/9.20 % (3973)Termination reason: Unknown
% 56.31/9.20 % (3973)Termination phase: Saturation
% 56.31/9.20
% 56.31/9.20 % (3973)Memory used [KB]: 12920
% 56.31/9.20 % (3973)Time elapsed: 0.930 s
% 56.31/9.20 % (3973)Instructions burned: 3713 (million)
% 56.31/9.20 % (3973)------------------------------
% 56.31/9.20 % (3973)------------------------------
% 56.31/9.21 % (3985)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_3362 for (2923ds/2321Mi)
% 56.31/9.27 % (3962)Instruction limit reached!
% 56.31/9.27 % (3962)------------------------------
% 56.31/9.27 % (3962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.31/9.27 % (3962)Termination reason: Unknown
% 56.31/9.27 % (3962)Termination phase: Saturation
% 56.31/9.27
% 56.31/9.27 % (3962)Memory used [KB]: 16247
% 56.31/9.27 % (3962)Time elapsed: 2.318 s
% 56.31/9.27 % (3962)Instructions burned: 7680 (million)
% 56.31/9.27 % (3962)------------------------------
% 56.31/9.27 % (3962)------------------------------
% 56.31/9.28 % (3986)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_3362 for (2922ds/2812Mi)
% 56.62/9.39 % (3982)Instruction limit reached!
% 56.62/9.39 % (3982)------------------------------
% 56.62/9.39 % (3982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.62/9.39 % (3982)Termination reason: Unknown
% 56.62/9.39 % (3982)Termination phase: Saturation
% 56.62/9.39
% 56.62/9.39 % (3982)Memory used [KB]: 12025
% 56.62/9.39 % (3982)Time elapsed: 0.300 s
% 56.62/9.39 % (3982)Instructions burned: 1189 (million)
% 56.62/9.39 % (3982)------------------------------
% 56.62/9.39 % (3982)------------------------------
% 57.13/9.40 % (3987)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_3362 for (2921ds/4604Mi)
% 57.53/9.60 % (3980)Instruction limit reached!
% 57.53/9.60 % (3980)------------------------------
% 57.53/9.60 % (3980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.60 % (3980)Termination reason: Unknown
% 57.53/9.60 % (3980)Termination phase: Saturation
% 57.53/9.60
% 57.53/9.60 % (3980)Memory used [KB]: 11769
% 57.53/9.60 % (3980)Time elapsed: 0.756 s
% 57.53/9.60 % (3980)Instructions burned: 3119 (million)
% 57.53/9.60 % (3980)------------------------------
% 57.53/9.60 % (3980)------------------------------
% 57.53/9.61 % (3988)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_3362 for (2919ds/2678Mi)
% 57.53/9.64 % (3984)Instruction limit reached!
% 57.53/9.64 % (3984)------------------------------
% 57.53/9.64 % (3984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.64 % (3984)Termination reason: Unknown
% 57.53/9.64 % (3984)Termination phase: Saturation
% 57.53/9.64
% 57.53/9.64 % (3984)Memory used [KB]: 11385
% 57.53/9.64 % (3984)Time elapsed: 0.458 s
% 57.53/9.64 % (3984)Instructions burned: 1517 (million)
% 57.53/9.64 % (3984)------------------------------
% 57.53/9.64 % (3984)------------------------------
% 57.53/9.65 % (3989)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3362 for (2918ds/643Mi)
% 58.12/9.79 % (3985)Instruction limit reached!
% 58.12/9.79 % (3985)------------------------------
% 58.12/9.79 % (3985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.12/9.79 % (3985)Termination reason: Unknown
% 58.12/9.79 % (3985)Termination phase: Saturation
% 58.12/9.79
% 58.12/9.79 % (3985)Memory used [KB]: 11385
% 58.12/9.79 % (3985)Time elapsed: 0.577 s
% 58.12/9.79 % (3985)Instructions burned: 2321 (million)
% 58.12/9.79 % (3985)------------------------------
% 58.12/9.79 % (3985)------------------------------
% 58.81/9.80 % (3990)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_3362 for (2917ds/458Mi)
% 58.81/9.82 % (3989)Instruction limit reached!
% 58.81/9.82 % (3989)------------------------------
% 58.81/9.82 % (3989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.81/9.82 % (3989)Termination reason: Unknown
% 58.81/9.82 % (3989)Termination phase: Saturation
% 58.81/9.82
% 58.81/9.82 % (3989)Memory used [KB]: 10874
% 58.81/9.82 % (3989)Time elapsed: 0.187 s
% 58.81/9.82 % (3989)Instructions burned: 643 (million)
% 58.81/9.82 % (3989)------------------------------
% 58.81/9.82 % (3989)------------------------------
% 58.81/9.83 % (3991)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_3362 for (2916ds/2546Mi)
% 58.81/9.84 % (3983)Instruction limit reached!
% 58.81/9.84 % (3983)------------------------------
% 58.81/9.84 % (3983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.81/9.84 % (3983)Termination reason: Unknown
% 58.81/9.84 % (3983)Termination phase: Saturation
% 58.81/9.84
% 58.81/9.84 % (3983)Memory used [KB]: 7036
% 58.81/9.84 % (3983)Time elapsed: 0.701 s
% 58.81/9.84 % (3983)Instructions burned: 2868 (million)
% 58.81/9.84 % (3983)------------------------------
% 58.81/9.84 % (3983)------------------------------
% 58.81/9.85 % (3992)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_3362 for (2916ds/1432Mi)
% 59.78/9.91 % (3990)Instruction limit reached!
% 59.78/9.91 % (3990)------------------------------
% 59.78/9.91 % (3990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.78/9.91 % (3990)Termination reason: Unknown
% 59.78/9.91 % (3990)Termination phase: Saturation
% 59.78/9.91
% 59.78/9.91 % (3990)Memory used [KB]: 10746
% 59.78/9.91 % (3990)Time elapsed: 0.116 s
% 59.78/9.91 % (3990)Instructions burned: 461 (million)
% 59.78/9.91 % (3990)------------------------------
% 59.78/9.91 % (3990)------------------------------
% 59.78/9.92 % (3993)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_3362 for (2915ds/386Mi)
% 59.78/10.02 % (3993)Instruction limit reached!
% 59.78/10.02 % (3993)------------------------------
% 59.78/10.02 % (3993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.78/10.02 % (3993)Termination reason: Unknown
% 59.78/10.02 % (3993)Termination phase: Saturation
% 59.78/10.02
% 59.78/10.02 % (3993)Memory used [KB]: 6908
% 59.78/10.02 % (3993)Time elapsed: 0.097 s
% 59.78/10.02 % (3993)Instructions burned: 388 (million)
% 59.78/10.02 % (3993)------------------------------
% 59.78/10.02 % (3993)------------------------------
% 62.17/10.03 % (3994)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3362 for (2915ds/360Mi)
% 62.17/10.12 % (3994)Instruction limit reached!
% 62.17/10.12 % (3994)------------------------------
% 62.17/10.12 % (3994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.17/10.12 % (3994)Termination reason: Unknown
% 62.17/10.12 % (3994)Termination phase: Saturation
% 62.17/10.12
% 62.17/10.12 % (3994)Memory used [KB]: 6908
% 62.17/10.12 % (3994)Time elapsed: 0.089 s
% 62.17/10.12 % (3994)Instructions burned: 363 (million)
% 62.17/10.12 % (3994)------------------------------
% 62.17/10.12 % (3994)------------------------------
% 63.00/10.12 % (3995)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_3362 for (2913ds/5446Mi)
% 63.00/10.16 % (3986)Instruction limit reached!
% 63.00/10.16 % (3986)------------------------------
% 63.00/10.16 % (3986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.00/10.16 % (3986)Termination reason: Unknown
% 63.00/10.16 % (3986)Termination phase: Saturation
% 63.00/10.16
% 63.00/10.16 % (3986)Memory used [KB]: 10874
% 63.00/10.16 % (3986)Time elapsed: 0.903 s
% 63.00/10.16 % (3986)Instructions burned: 2814 (million)
% 63.00/10.16 % (3986)------------------------------
% 63.00/10.16 % (3986)------------------------------
% 63.00/10.17 % (3996)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_3362 for (2913ds/2573Mi)
% 63.00/10.19 % (3992)Instruction limit reached!
% 63.00/10.19 % (3992)------------------------------
% 63.00/10.19 % (3992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.00/10.19 % (3992)Termination reason: Unknown
% 63.00/10.19 % (3992)Termination phase: Saturation
% 63.00/10.19
% 63.00/10.19 % (3992)Memory used [KB]: 14711
% 63.00/10.19 % (3992)Time elapsed: 0.341 s
% 63.00/10.19 % (3992)Instructions burned: 1435 (million)
% 63.00/10.19 % (3992)------------------------------
% 63.00/10.19 % (3992)------------------------------
% 63.43/10.20 % (3997)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_3362 for (2913ds/2655Mi)
% 63.43/10.28 % (3988)Instruction limit reached!
% 63.43/10.28 % (3988)------------------------------
% 63.43/10.28 % (3988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.43/10.28 % (3988)Termination reason: Unknown
% 63.43/10.28 % (3988)Termination phase: Saturation
% 63.43/10.28
% 63.43/10.28 % (3988)Memory used [KB]: 15351
% 63.43/10.28 % (3988)Time elapsed: 0.693 s
% 63.43/10.28 % (3988)Instructions burned: 2679 (million)
% 63.43/10.28 % (3988)------------------------------
% 63.43/10.28 % (3988)------------------------------
% 63.43/10.29 % (3998)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_3362 for (2912ds/2781Mi)
% 64.12/10.42 % (3972)Instruction limit reached!
% 64.12/10.42 % (3972)------------------------------
% 64.12/10.42 % (3972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.12/10.42 % (3972)Termination reason: Unknown
% 64.12/10.42 % (3972)Termination phase: Saturation
% 64.12/10.42
% 64.12/10.42 % (3972)Memory used [KB]: 9466
% 64.12/10.42 % (3972)Time elapsed: 2.233 s
% 64.12/10.42 % (3972)Instructions burned: 7259 (million)
% 64.12/10.42 % (3972)------------------------------
% 64.12/10.42 % (3972)------------------------------
% 64.12/10.43 % (3999)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3362 for (2910ds/307Mi)
% 64.35/10.50 % (3999)Instruction limit reached!
% 64.35/10.50 % (3999)------------------------------
% 64.35/10.50 % (3999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.35/10.50 % (3999)Termination reason: Unknown
% 64.35/10.50 % (3999)Termination phase: Saturation
% 64.35/10.50
% 64.35/10.50 % (3999)Memory used [KB]: 6908
% 64.35/10.50 % (3999)Time elapsed: 0.076 s
% 64.35/10.50 % (3999)Instructions burned: 307 (million)
% 64.35/10.50 % (3999)------------------------------
% 64.35/10.50 % (3999)------------------------------
% 64.35/10.51 % (4000)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_3362 for (2910ds/1548Mi)
% 64.35/10.60 % (3991)Instruction limit reached!
% 64.35/10.60 % (3991)------------------------------
% 64.35/10.60 % (3991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.35/10.60 % (3991)Termination reason: Unknown
% 64.64/10.60 % (3991)Termination phase: Saturation
% 64.64/10.60
% 64.64/10.60 % (3991)Memory used [KB]: 10618
% 64.64/10.60 % (3991)Time elapsed: 0.772 s
% 64.64/10.60 % (3991)Instructions burned: 2547 (million)
% 64.64/10.60 % (3991)------------------------------
% 64.64/10.60 % (3991)------------------------------
% 64.64/10.61 % (4001)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_3362 for (2909ds/5214Mi)
% 64.85/10.82 % (3996)Instruction limit reached!
% 64.85/10.82 % (3996)------------------------------
% 64.85/10.82 % (3996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.82 % (3996)Termination reason: Unknown
% 64.85/10.82 % (3996)Termination phase: Saturation
% 64.85/10.82
% 64.85/10.82 % (3996)Memory used [KB]: 12792
% 64.85/10.82 % (3996)Time elapsed: 0.652 s
% 64.85/10.82 % (3996)Instructions burned: 2574 (million)
% 64.85/10.82 % (3996)------------------------------
% 64.85/10.82 % (3996)------------------------------
% 64.85/10.83 % (3987)Instruction limit reached!
% 64.85/10.83 % (3987)------------------------------
% 64.85/10.83 % (3987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.83 % (3987)Termination reason: Unknown
% 64.85/10.83 % (3987)Termination phase: Saturation
% 64.85/10.83
% 64.85/10.83 % (3987)Memory used [KB]: 13176
% 64.85/10.83 % (3987)Time elapsed: 1.457 s
% 64.85/10.83 % (3987)Instructions burned: 4606 (million)
% 64.85/10.83 % (3987)------------------------------
% 64.85/10.83 % (3987)------------------------------
% 64.85/10.83 % (4002)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_3362 for (2906ds/3201Mi)
% 64.85/10.84 % (4003)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_3362 for (2906ds/454Mi)
% 64.85/10.87 % (3997)Instruction limit reached!
% 64.85/10.87 % (3997)------------------------------
% 64.85/10.87 % (3997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.85/10.87 % (3997)Termination reason: Unknown
% 64.85/10.87 % (3997)Termination phase: Saturation
% 64.85/10.87
% 64.85/10.87 % (3997)Memory used [KB]: 4733
% 64.85/10.87 % (3997)Time elapsed: 0.667 s
% 64.85/10.87 % (3997)Instructions burned: 2656 (million)
% 64.85/10.87 % (3997)------------------------------
% 64.85/10.87 % (3997)------------------------------
% 64.85/10.88 % (4004)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_3362 for (2906ds/3049Mi)
% 66.24/10.95 % (4003)Instruction limit reached!
% 66.24/10.95 % (4003)------------------------------
% 66.24/10.95 % (4003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.24/10.95 % (4003)Termination reason: Unknown
% 66.24/10.95 % (4003)Termination phase: Saturation
% 66.24/10.95
% 66.24/10.95 % (4003)Memory used [KB]: 15607
% 66.24/10.95 % (4003)Time elapsed: 0.114 s
% 66.24/10.95 % (4003)Instructions burned: 455 (million)
% 66.24/10.95 % (4003)------------------------------
% 66.24/10.95 % (4003)------------------------------
% 66.24/10.96 % (4005)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_3362 for (2905ds/7311Mi)
% 66.24/10.99 % (4000)Instruction limit reached!
% 66.24/10.99 % (4000)------------------------------
% 66.24/10.99 % (4000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.24/10.99 % (4000)Termination reason: Unknown
% 66.24/10.99 % (4000)Termination phase: Saturation
% 66.24/10.99
% 66.24/10.99 % (4000)Memory used [KB]: 9978
% 66.24/10.99 % (4000)Time elapsed: 0.477 s
% 66.24/10.99 % (4000)Instructions burned: 1550 (million)
% 66.24/10.99 % (4000)------------------------------
% 66.24/10.99 % (4000)------------------------------
% 66.24/11.00 % (4006)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_3362 for (2905ds/6804Mi)
% 69.28/11.08 % (3998)First to succeed.
% 69.28/11.09 % (3998)Refutation found. Thanks to Tanya!
% 69.28/11.09 % SZS status Theorem for DTF2THF_3362
% 69.28/11.09 % SZS output start Proof for DTF2THF_3362
% 69.28/11.09 thf(func_def_0, type, in: $i > $i > $o).
% 69.28/11.09 thf(func_def_1, type, exu: ($i > $o) > $o).
% 69.28/11.09 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 69.28/11.09 thf(func_def_8, type, powerset: $i > $i).
% 69.28/11.09 thf(func_def_10, type, setunion: $i > $i).
% 69.28/11.09 thf(func_def_19, type, descr: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_26, type, prop2set: $o > $i).
% 69.28/11.09 thf(func_def_36, type, nonempty: $i > $o).
% 69.28/11.09 thf(func_def_69, type, set2prop: $i > $o).
% 69.28/11.09 thf(func_def_88, type, subset: $i > $i > $o).
% 69.28/11.09 thf(func_def_89, type, disjoint: $i > $i > $o).
% 69.28/11.09 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 69.28/11.09 thf(func_def_114, type, binunion: $i > $i > $i).
% 69.28/11.09 thf(func_def_122, type, binintersect: $i > $i > $i).
% 69.28/11.09 thf(func_def_135, type, regular: $i > $o).
% 69.28/11.09 thf(func_def_136, type, setminus: $i > $i > $i).
% 69.28/11.09 thf(func_def_147, type, symdiff: $i > $i > $i).
% 69.28/11.09 thf(func_def_153, type, iskpair: $i > $o).
% 69.28/11.09 thf(func_def_158, type, kpair: $i > $i > $i).
% 69.28/11.09 thf(func_def_160, type, cartprod: $i > $i > $i).
% 69.28/11.09 thf(func_def_177, type, singleton: $i > $o).
% 69.28/11.09 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 69.28/11.09 thf(func_def_184, type, atmost1p: $i > $o).
% 69.28/11.09 thf(func_def_185, type, atleast2p: $i > $o).
% 69.28/11.09 thf(func_def_186, type, atmost2p: $i > $o).
% 69.28/11.09 thf(func_def_187, type, upairsetp: $i > $o).
% 69.28/11.09 thf(func_def_191, type, kfst: $i > $i).
% 69.28/11.09 thf(func_def_203, type, ksnd: $i > $i).
% 69.28/11.09 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 69.28/11.09 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 69.28/11.09 thf(func_def_222, type, func: $i > $i > $i > $o).
% 69.28/11.09 thf(func_def_223, type, funcSet: $i > $i > $i).
% 69.28/11.09 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_243, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 69.28/11.09 thf(func_def_244, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 69.28/11.09 thf(func_def_248, type, sK4: $i > $o).
% 69.28/11.09 thf(func_def_282, type, sK38: $i > $i > $o).
% 69.28/11.09 thf(func_def_286, type, sK42: $i > $i).
% 69.28/11.09 thf(func_def_288, type, sK44: $i > $i).
% 69.28/11.09 thf(func_def_291, type, sK47: $i > $o).
% 69.28/11.09 thf(func_def_305, type, sK61: $i > $o).
% 69.28/11.09 thf(func_def_318, type, sK74: $i > $i).
% 69.28/11.09 thf(func_def_319, type, sK75: $i > $i).
% 69.28/11.09 thf(func_def_320, type, sK76: $i > $i).
% 69.28/11.09 thf(func_def_321, type, sK77: $i > $i).
% 69.28/11.09 thf(func_def_322, type, sK78: $i > $i > $i).
% 69.28/11.09 thf(func_def_323, type, sK79: $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_324, type, sK80: $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_325, type, sK81: $i > $i).
% 69.28/11.09 thf(func_def_326, type, sK82: $i > $i).
% 69.28/11.09 thf(func_def_327, type, sK83: $i > $i).
% 69.28/11.09 thf(func_def_328, type, sK84: $i > $i).
% 69.28/11.09 thf(func_def_329, type, sK85: $i > $i).
% 69.28/11.09 thf(func_def_330, type, sK86: $i > $i).
% 69.28/11.09 thf(func_def_331, type, sK87: $i > $i).
% 69.28/11.09 thf(func_def_332, type, sK88: $i > $i > $i).
% 69.28/11.09 thf(func_def_333, type, sK89: $i > $i > $i).
% 69.28/11.09 thf(func_def_334, type, sK90: $i > $i > $i).
% 69.28/11.09 thf(func_def_335, type, sK91: $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_336, type, sK92: $i > $i > $i).
% 69.28/11.09 thf(func_def_347, type, sK103: $i > $i > $i).
% 69.28/11.09 thf(func_def_368, type, sK124: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_369, type, sK125: $i > $o).
% 69.28/11.09 thf(func_def_370, type, sK126: $i > $i).
% 69.28/11.09 thf(func_def_379, type, sK135: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_380, type, sK136: $i > $o).
% 69.28/11.09 thf(func_def_388, type, sK144: $i > $o).
% 69.28/11.09 thf(func_def_390, type, sK146: ($i > $o) > $i > $i).
% 69.28/11.09 thf(func_def_432, type, sK188: $i > $o).
% 69.28/11.09 thf(func_def_434, type, sK190: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_435, type, sK191: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_442, type, sK198: $i > $i > $i).
% 69.28/11.09 thf(func_def_447, type, sK203: $i > $o).
% 69.28/11.09 thf(func_def_454, type, sK210: $i > $i > $i).
% 69.28/11.09 thf(func_def_457, type, sK213: $i > $o).
% 69.28/11.09 thf(func_def_464, type, sK220: $i > $i > $o).
% 69.28/11.09 thf(func_def_471, type, sK227: $i > $i).
% 69.28/11.09 thf(func_def_474, type, sK230: $i > $o).
% 69.28/11.09 thf(func_def_495, type, sK251: $i > $i > $o).
% 69.28/11.09 thf(func_def_508, type, sK264: $i > $o).
% 69.28/11.09 thf(func_def_510, type, sK266: $i > $i > $o).
% 69.28/11.09 thf(func_def_515, type, sK271: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_516, type, sK272: $i > $o).
% 69.28/11.09 thf(func_def_519, type, sK275: ($i > $o) > $i > $i).
% 69.28/11.09 thf(func_def_520, type, sK276: ($i > $o) > $i > $i).
% 69.28/11.09 thf(func_def_522, type, sK278: $i > $o).
% 69.28/11.09 thf(func_def_525, type, sK281: $i > $i > $o).
% 69.28/11.09 thf(func_def_532, type, sK288: $i > $o).
% 69.28/11.09 thf(func_def_534, type, sK290: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_542, type, sK298: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_543, type, sK299: $i > $o).
% 69.28/11.09 thf(func_def_557, type, sK313: $i > $i > $i).
% 69.28/11.09 thf(func_def_570, type, sK326: $i > $i).
% 69.28/11.09 thf(func_def_574, type, sK330: $i > $o).
% 69.28/11.09 thf(func_def_575, type, sK331: $i > $o).
% 69.28/11.09 thf(func_def_576, type, sK332: ($i > $o) > ($i > $o) > $i > $i > $i).
% 69.28/11.09 thf(func_def_577, type, sK333: ($i > $o) > ($i > $o) > $i > $i > $i).
% 69.28/11.09 thf(func_def_581, type, sK337: $i > $o).
% 69.28/11.09 thf(func_def_582, type, sK338: $i > $i).
% 69.28/11.09 thf(func_def_583, type, sK339: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_584, type, sK340: $i > $i).
% 69.28/11.09 thf(func_def_604, type, sK360: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_605, type, sK361: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_606, type, sK362: $i > $o).
% 69.28/11.09 thf(func_def_613, type, sK369: $i > $o).
% 69.28/11.09 thf(func_def_614, type, sK370: ($i > $o) > $i).
% 69.28/11.09 thf(func_def_617, type, sK373: $i > $o).
% 69.28/11.09 thf(func_def_621, type, sK377: $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_622, type, sK378: $i > $i > $i > $i).
% 69.28/11.09 thf(func_def_633, type, sK389: $i > $i > $i).
% 69.28/11.09 thf(func_def_636, type, sK392: $i > $i > $i).
% 69.28/11.09 thf(func_def_637, type, sK393: $i > $i > $i).
% 69.28/11.09 thf(func_def_645, type, sK401: ($i > $o) > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_646, type, sK402: ($i > $o) > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_647, type, sK403: $i > $o).
% 69.28/11.09 thf(func_def_648, type, sK404: $i > $o).
% 69.28/11.09 thf(func_def_649, type, sK405: $i > $o).
% 69.28/11.09 thf(func_def_651, type, sK407: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_674, type, sK430: $i > $o).
% 69.28/11.09 thf(func_def_675, type, sK431: $i > $o).
% 69.28/11.09 thf(func_def_676, type, sK432: ($i > $o) > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_677, type, sK433: ($i > $o) > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_685, type, sK441: ($i > $o) > $i > $i).
% 69.28/11.09 thf(func_def_687, type, sK443: $i > $o).
% 69.28/11.09 thf(func_def_707, type, sK463: $i > $o).
% 69.28/11.09 thf(func_def_709, type, sK465: ($i > $o) > $i > $i).
% 69.28/11.09 thf(func_def_710, type, sK466: $i > $i > $o).
% 69.28/11.09 thf(func_def_712, type, sK468: $i > $i).
% 69.28/11.09 thf(func_def_713, type, sK469: $i > $i).
% 69.28/11.09 thf(func_def_714, type, sK470: $i > ($i > $i > $o) > $i).
% 69.28/11.09 thf(func_def_715, type, sK471: $i > ($i > $i > $o) > $i).
% 69.28/11.09 thf(func_def_716, type, sK472: $i > $i > ($i > $i > $o) > $i).
% 69.28/11.09 thf(func_def_717, type, sK473: $i > $o).
% 69.28/11.09 thf(func_def_724, type, sK480: $i > $o).
% 69.28/11.09 thf(func_def_730, type, sK486: $i > ($i > $o) > $i).
% 69.28/11.09 thf(func_def_731, type, sK487: $i > $o).
% 69.28/11.09 thf(func_def_735, type, sK491: $i > $i > $i).
% 69.28/11.09 thf(func_def_742, type, sK498: $i > $i).
% 69.28/11.09 thf(func_def_744, type, sK500: $o > $i > $i > $i).
% 69.28/11.09 thf(func_def_749, type, sK505: $i > $i > $o).
% 69.28/11.09 thf(func_def_753, type, sK509: ($i > $o) > $i > $i > $i).
% 69.28/11.09 thf(func_def_756, type, sK512: $i > $o).
% 69.28/11.09 thf(func_def_770, type, sK526: $i > $o).
% 69.28/11.09 thf(func_def_772, type, sK528: $i > $i > $o).
% 69.28/11.09 thf(func_def_777, type, sK533: $i > $o).
% 69.28/11.09 thf(func_def_780, type, sK536: $i > $i).
% 69.28/11.09 thf(func_def_782, type, sK538: $i > $i > $i).
% 69.28/11.09 thf(func_def_801, type, ph556: !>[X0: $tType]:(X0)).
% 69.28/11.09 thf(f9451,plain,(
% 69.28/11.09 $false),
% 69.28/11.09 inference(subsumption_resolution,[status(thm)],[f9449,f8291])).
% 69.28/11.09 thf(f8291,plain,(
% 69.28/11.09 ((subset @ sK242 @ (cartprod @ sK243 @ sK241)) = $true)),
% 69.28/11.09 inference(trivial_inequality_removal,[status(thm)],[f8287])).
% 69.28/11.09 thf(f8287,plain,(
% 69.28/11.09 ((subset @ sK242 @ (cartprod @ sK243 @ sK241)) = $true) | ($false = $true)),
% 69.28/11.09 inference(superposition,[status(thm)],[f617,f5039])).
% 69.28/11.09 thf(f5039,plain,(
% 69.28/11.09 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK243) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK241 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK242)))) & (in @ Y1 @ (dsetconstr @ sK241 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK242)))))))))) & (subset @ sK242 @ (cartprod @ sK243 @ sK241))) = $true)),
% 69.28/11.09 inference(beta_eta_normalization,[status(thm)],[f4370])).
% 69.28/11.09 thf(f4370,plain,(
% 69.28/11.09 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))) @ sK243 @ sK241 @ sK242) = $true)),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f2779,f3354])).
% 69.28/11.09 thf(f3354,plain,(
% 69.28/11.09 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: (((setadjoin @ Y7 @ emptyset) = Y6) & (in @ Y7 @ Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))))),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f3002,f3353,f3007])).
% 69.28/11.09 thf(f3007,plain,(
% 69.28/11.09 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f549])).
% 69.28/11.09 thf(f549,plain,(
% 69.28/11.09 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f548])).
% 69.28/11.09 thf(f548,plain,(
% 69.28/11.09 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f186])).
% 69.28/11.09 thf(f186,axiom,(
% 69.28/11.09 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',breln)).
% 69.28/11.09 thf(f3353,plain,(
% 69.28/11.09 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f3319,f3138])).
% 69.28/11.09 thf(f3138,plain,(
% 69.28/11.09 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f421])).
% 69.28/11.09 thf(f421,plain,(
% 69.28/11.09 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f420])).
% 69.28/11.09 thf(f420,plain,(
% 69.28/11.09 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f156])).
% 69.28/11.09 thf(f156,axiom,(
% 69.28/11.09 (singleton = (^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ X3) & ((setadjoin @ X1 @ emptyset) = X3)))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',singleton)).
% 69.28/11.09 thf(f3319,plain,(
% 69.28/11.09 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f277])).
% 69.28/11.09 thf(f277,plain,(
% 69.28/11.09 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f276])).
% 69.28/11.09 thf(f276,plain,(
% 69.28/11.09 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f158])).
% 69.28/11.09 thf(f158,axiom,(
% 69.28/11.09 (ex1 = (^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',ex1)).
% 69.28/11.09 thf(f3002,plain,(
% 69.28/11.09 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f307])).
% 69.28/11.09 thf(f307,plain,(
% 69.28/11.09 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f306])).
% 69.28/11.09 thf(f306,plain,(
% 69.28/11.09 (func = (^[X0 : $i, X1 : $i, X2 : $i] : ((breln @ X0 @ X1 @ X2) & ! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f194])).
% 69.28/11.09 thf(f194,axiom,(
% 69.28/11.09 (func = (^[X3 : $i, X4 : $i, X12 : $i] : ((breln @ X3 @ X4 @ X12) & ! [X1 : $i] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',func)).
% 69.28/11.09 thf(f2779,plain,(
% 69.28/11.09 ((func @ sK243 @ sK241 @ sK242) = $true)),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1225])).
% 69.28/11.09 thf(f1225,plain,(
% 69.28/11.09 (binintersectI = $true) & (ksndpairEq = $true) & (emptyinunitempty = $true) & (apProp = $true) & (powersetI = $true) & (powersetsubset = $true) & (dpsetconstrER = $true) & (binunionRsub = $true) & (setadjoinIR = $true) & (notsubsetI = $true) & (kfstpairEq = $true) & (exuI1 = $true) & (prop2setI = $true) & (kpairsurjEq = $true) & (notdallE = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (setminusI = $true) & (setukpairinjL = $true) & (binintersectRsub = $true) & (setminusELneg = $true) & (nonemptyImpWitness = $true) & (foundationAx = $true) & (binunionLsub = $true) & (setminusILneg = $true) & (setbeta = $true) & (setukpairIL = $true) & (emptyE1 = $true) & (setadjoinOr = $true) & (exuE3u = $true) & (sepInPowerset = $true) & (symdiffE = $true) & (descrp = $true) & (cartprodmempaircEq = $true) & (setunionsingleton1 = $true) & (setukpairinjR11 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (powersetAx = $true) & (singletonsubset = $true) & (setunionI = $true) & (vacuousDall = $true) & (powersetE1 = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dpsetconstrEL1 = $true) & (replAx = $true) & (upairequniteq = $true) & (setminusEL = $true) & (emptysetAx = $true) & (subsetemptysetimpeq = $true) & (emptyset__Cong = $true) & (setminusSubset1 = $true) & (exuE3e = $true) & (setminusSubset2 = $true) & (eqimpsubset2 = $true) & (binintersectER = $true) & (dpsetconstrEL2 = $true) & (cartprodpairsurjEq = $true) & (setminusERneg = $true) & (prop2set2propI = $true) & (setukpairinjR12 = $true) & (subset2powerset = $true) & (binunionE = $true) & (setunionE = $true) & (singletoninpowunion = $true) & (exuI3 = $true) & (binintersectSubset1 = $true) & (powerset__Cong = $true) & (omegaIndAx = $true) & (setminusER = $true) & (cartprodsndin = $true) & (binunionEcases = $true) & (quantDeMorgan3 = $true) & (setukpairinjR2 = $true) & (setadjoin__Cong = $true) & (exuE2 = $true) & (descr__Cong = $true) & (subPowSU = $true) & (inPowerset = $true) & (symdiffIneg2 = $true) & (singletonprop = $true) & (nonemptyI = $true) & (infuncsetfunc = $true) & (quantDeMorgan4 = $true) & (setextsub = $true) & (setadjoinE = $true) & (inCongP = $true) & (notequalI2 = $true) & (cartprodmempair1 = $true) & (in__Cong = $true) & (setunionE2 = $true) & (dsetconstr__Cong = $true) & (subsetE2 = $true) & (symdiffI2 = $true) & (binunionIR = $true) & (exuI2 = $true) & (quantDeMorgan2 = $true) & (setadjoinAx = $true) & (notdexE = $true) & (ex1E1 = $true) & (dsetconstrI = $true) & (eqinunit = $true) & (upairsetIL = $true) & (ex1I = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (setukpairinjL2 = $true) & (singletoninpowerset = $true) & (subsetTrans = $true) & (kpairp = $true) & (binintersectSubset5 = $true) & (app = $true) & (emptyInPowerset = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (kfstsingleton = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (setadjoinSub = $true) & (disjointsetsI1 = $true) & (exu__Cong = $true) & (setminusLsub = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (binintersectEL = $true) & (cartprodpairmemEL = $true) & (prop2setE = $true) & (emptysetimpfalse = $true) & (symdiffIneg1 = $true) & (ap2p = $true) & (funcImageSingleton = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (emptyinPowerset = $true) & (subsetI1 = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (setextAx = $true) & (bs114d = $true) & (cartprodsndpairEq = $true) & (ex1I2 = $true) & (ksndsingleton = $true) & (subsetE = $true) & (cartprodfstin = $true) & (binintersectSubset3 = $true) & (setukpairIR = $true) & (omegaSAx = $true) & (dpsetconstrSub = $true) & (upairsubunion = $true) & (eqimpsubset1 = $true) & (exuEu = $true) & (setext = $true) & (upairset2IR = $true) & (secondinupair = $true) & (((func @ sK243 @ sK241 @ sK242) = $true) & ((in @ sK242 @ (funcSet @ sK243 @ sK241)) != $true)) & (upairset2E = $true) & (noeltsimpempty = $true) & (notinemptyset = $true) & (omega0Ax = $true) & (setunionsingleton = $true) & (cartprodpairmemER = $true) & (dpsetconstrI = $true) & (sepSubset = $true) & (subsetI2 = $true) & (setoftrueEq = $true) & (powersetE = $true) & (subsetRefl = $true) & (emptyI = $true) & (binintersectSubset4 = $true) & (upairsetE = $true) & (cartprodfstpairEq = $true) & (binunionIL = $true) & (singletonsswitch = $true) & (setunionsingleton2 = $true) & (cartprodmempair = $true) & (setOfPairsIsBReln = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrERa = $true) & (binintersectSubset2 = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (ubforcartprodlem2 = $true) & (notequalI1 = $true) & (singletonsuniq = $true) & (setukpairinjR1 = $true) & (upairsetIR = $true) & (setminusIRneg = $true) & (setukpairinjR = $true) & (upairinpowunion = $true) & (symdiffI1 = $true) & (powersetI1 = $true) & (binintersectLsub = $true) & (kpairiskpair = $true)),
% 69.28/11.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK241,sK242,sK243])],[f774,f1224])).
% 69.28/11.09 thf(f1224,plain,(
% 69.28/11.09 ? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) & ((in @ X1 @ (funcSet @ X2 @ X0)) != $true)) => (((func @ sK243 @ sK241 @ sK242) = $true) & ((in @ sK242 @ (funcSet @ sK243 @ sK241)) != $true))),
% 69.28/11.09 introduced(definition,[],[choice_axiom])).
% 69.28/11.09 thf(f774,plain,(
% 69.28/11.09 (binintersectI = $true) & (ksndpairEq = $true) & (emptyinunitempty = $true) & (apProp = $true) & (powersetI = $true) & (powersetsubset = $true) & (dpsetconstrER = $true) & (binunionRsub = $true) & (setadjoinIR = $true) & (notsubsetI = $true) & (kfstpairEq = $true) & (exuI1 = $true) & (prop2setI = $true) & (kpairsurjEq = $true) & (notdallE = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (setminusI = $true) & (setukpairinjL = $true) & (binintersectRsub = $true) & (setminusELneg = $true) & (nonemptyImpWitness = $true) & (foundationAx = $true) & (binunionLsub = $true) & (setminusILneg = $true) & (setbeta = $true) & (setukpairIL = $true) & (emptyE1 = $true) & (setadjoinOr = $true) & (exuE3u = $true) & (sepInPowerset = $true) & (symdiffE = $true) & (descrp = $true) & (cartprodmempaircEq = $true) & (setunionsingleton1 = $true) & (setukpairinjR11 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (powersetAx = $true) & (singletonsubset = $true) & (setunionI = $true) & (vacuousDall = $true) & (powersetE1 = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dpsetconstrEL1 = $true) & (replAx = $true) & (upairequniteq = $true) & (setminusEL = $true) & (emptysetAx = $true) & (subsetemptysetimpeq = $true) & (emptyset__Cong = $true) & (setminusSubset1 = $true) & (exuE3e = $true) & (setminusSubset2 = $true) & (eqimpsubset2 = $true) & (binintersectER = $true) & (dpsetconstrEL2 = $true) & (cartprodpairsurjEq = $true) & (setminusERneg = $true) & (prop2set2propI = $true) & (setukpairinjR12 = $true) & (subset2powerset = $true) & (binunionE = $true) & (setunionE = $true) & (singletoninpowunion = $true) & (exuI3 = $true) & (binintersectSubset1 = $true) & (powerset__Cong = $true) & (omegaIndAx = $true) & (setminusER = $true) & (cartprodsndin = $true) & (binunionEcases = $true) & (quantDeMorgan3 = $true) & (setukpairinjR2 = $true) & (setadjoin__Cong = $true) & (exuE2 = $true) & (descr__Cong = $true) & (subPowSU = $true) & (inPowerset = $true) & (symdiffIneg2 = $true) & (singletonprop = $true) & (nonemptyI = $true) & (infuncsetfunc = $true) & (quantDeMorgan4 = $true) & (setextsub = $true) & (setadjoinE = $true) & (inCongP = $true) & (notequalI2 = $true) & (cartprodmempair1 = $true) & (in__Cong = $true) & (setunionE2 = $true) & (dsetconstr__Cong = $true) & (subsetE2 = $true) & (symdiffI2 = $true) & (binunionIR = $true) & (exuI2 = $true) & (quantDeMorgan2 = $true) & (setadjoinAx = $true) & (notdexE = $true) & (ex1E1 = $true) & (dsetconstrI = $true) & (eqinunit = $true) & (upairsetIL = $true) & (ex1I = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (setukpairinjL2 = $true) & (singletoninpowerset = $true) & (subsetTrans = $true) & (kpairp = $true) & (binintersectSubset5 = $true) & (app = $true) & (emptyInPowerset = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (kfstsingleton = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (setadjoinSub = $true) & (disjointsetsI1 = $true) & (exu__Cong = $true) & (setminusLsub = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (binintersectEL = $true) & (cartprodpairmemEL = $true) & (prop2setE = $true) & (emptysetimpfalse = $true) & (symdiffIneg1 = $true) & (ap2p = $true) & (funcImageSingleton = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (emptyinPowerset = $true) & (subsetI1 = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (setextAx = $true) & (bs114d = $true) & (cartprodsndpairEq = $true) & (ex1I2 = $true) & (ksndsingleton = $true) & (subsetE = $true) & (cartprodfstin = $true) & (binintersectSubset3 = $true) & (setukpairIR = $true) & (omegaSAx = $true) & (dpsetconstrSub = $true) & (upairsubunion = $true) & (eqimpsubset1 = $true) & (exuEu = $true) & (setext = $true) & (upairset2IR = $true) & (secondinupair = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) & ((in @ X1 @ (funcSet @ X2 @ X0)) != $true)) & (upairset2E = $true) & (noeltsimpempty = $true) & (notinemptyset = $true) & (omega0Ax = $true) & (setunionsingleton = $true) & (cartprodpairmemER = $true) & (dpsetconstrI = $true) & (sepSubset = $true) & (subsetI2 = $true) & (setoftrueEq = $true) & (powersetE = $true) & (subsetRefl = $true) & (emptyI = $true) & (binintersectSubset4 = $true) & (upairsetE = $true) & (cartprodfstpairEq = $true) & (binunionIL = $true) & (singletonsswitch = $true) & (setunionsingleton2 = $true) & (cartprodmempair = $true) & (setOfPairsIsBReln = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrERa = $true) & (binintersectSubset2 = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (ubforcartprodlem2 = $true) & (notequalI1 = $true) & (singletonsuniq = $true) & (setukpairinjR1 = $true) & (upairsetIR = $true) & (setminusIRneg = $true) & (setukpairinjR = $true) & (upairinpowunion = $true) & (symdiffI1 = $true) & (powersetI1 = $true) & (binintersectLsub = $true) & (kpairiskpair = $true)),
% 69.28/11.09 inference(flattening,[status(thm)],[f773])).
% 69.28/11.09 thf(f773,plain,(
% 69.28/11.09 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) & ((in @ X1 @ (funcSet @ X2 @ X0)) != $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 69.28/11.09 inference(ennf_transformation,[status(thm)],[f399])).
% 69.28/11.09 thf(f399,plain,(
% 69.28/11.09 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((func @ X2 @ X0 @ X1) = $true) => ((in @ X1 @ (funcSet @ X2 @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f398])).
% 69.28/11.09 thf(f398,plain,(
% 69.28/11.09 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X0 @ X1) => (in @ X1 @ (funcSet @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f203])).
% 69.28/11.09 thf(f203,negated_conjecture,(
% 69.28/11.09 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => ! [X4 : $i,X13 : $i,X3 : $i] : ((func @ X3 @ X4 @ X13) => (in @ X13 @ (funcSet @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 69.28/11.09 inference(negated_conjecture,[status(cth)],[f202])).
% 69.28/11.09 thf(f202,conjecture,(
% 69.28/11.09 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => ! [X4 : $i,X13 : $i,X3 : $i] : ((func @ X3 @ X4 @ X13) => (in @ X13 @ (funcSet @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',funcinfuncset)).
% 69.28/11.09 thf(f617,plain,(
% 69.28/11.09 ( ! [X2 : $o,X1 : $o] : (($false = (X1 & X2)) | ($true = X2)) )),
% 69.28/11.09 introduced(definition,[],[logical_and_proxy_axiom])).
% 69.28/11.09 thf(f9449,plain,(
% 69.28/11.09 ((subset @ sK242 @ (cartprod @ sK243 @ sK241)) != $true)),
% 69.28/11.09 inference(trivial_inequality_removal,[status(thm)],[f9447])).
% 69.28/11.09 thf(f9447,plain,(
% 69.28/11.09 ($true != $true) | ((subset @ sK242 @ (cartprod @ sK243 @ sK241)) != $true)),
% 69.28/11.09 inference(superposition,[status(thm)],[f8305,f4865])).
% 69.28/11.09 thf(f4865,plain,(
% 69.28/11.09 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) )),
% 69.28/11.09 inference(trivial_inequality_removal,[status(thm)],[f4267])).
% 69.28/11.09 thf(f4267,plain,(
% 69.28/11.09 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true) | ($true != $true)) )),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f2639,f2742])).
% 69.28/11.09 thf(f2742,plain,(
% 69.28/11.09 (powersetI1 = $true)),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1225])).
% 69.28/11.09 thf(f2639,plain,(
% 69.28/11.09 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true) | (powersetI1 != $true)) )),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1096])).
% 69.28/11.09 thf(f1096,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | (((subset @ sK162 @ sK161) = $true) & ((in @ sK162 @ (powerset @ sK161)) != $true)))),
% 69.28/11.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK161,sK162])],[f1094,f1095])).
% 69.28/11.09 thf(f1095,plain,(
% 69.28/11.09 ? [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) & ((in @ X3 @ (powerset @ X2)) != $true)) => (((subset @ sK162 @ sK161) = $true) & ((in @ sK162 @ (powerset @ sK161)) != $true))),
% 69.28/11.09 introduced(definition,[],[choice_axiom])).
% 69.28/11.09 thf(f1094,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) & ((in @ X3 @ (powerset @ X2)) != $true)))),
% 69.28/11.09 inference(rectify,[status(thm)],[f1093])).
% 69.28/11.09 thf(f1093,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ((in @ X1 @ (powerset @ X0)) != $true)))),
% 69.28/11.09 inference(nnf_transformation,[status(thm)],[f839])).
% 69.28/11.09 thf(f839,plain,(
% 69.28/11.09 ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true)) <=> (powersetI1 = $true)),
% 69.28/11.09 inference(ennf_transformation,[status(thm)],[f559])).
% 69.28/11.09 thf(f559,plain,(
% 69.28/11.09 (powersetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => ((in @ X1 @ (powerset @ X0)) = $true))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f558])).
% 69.28/11.09 thf(f558,plain,(
% 69.28/11.09 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f95])).
% 69.28/11.09 thf(f95,axiom,(
% 69.28/11.09 (powersetI1 = ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => (in @ X4 @ (powerset @ X3))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',powersetI1)).
% 69.28/11.09 thf(f8305,plain,(
% 69.28/11.09 ((in @ sK242 @ (powerset @ (cartprod @ sK243 @ sK241))) != $true)),
% 69.28/11.09 inference(subsumption_resolution,[status(thm)],[f8304,f5039])).
% 69.28/11.09 thf(f8304,plain,(
% 69.28/11.09 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK243) => (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = (dsetconstr @ sK241 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK242)))) & (in @ Y1 @ (dsetconstr @ sK241 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ sK242)))))))))) & (subset @ sK242 @ (cartprod @ sK243 @ sK241))) != $true) | ((in @ sK242 @ (powerset @ (cartprod @ sK243 @ sK241))) != $true)),
% 69.28/11.09 inference(beta_eta_normalization,[status(thm)],[f8297])).
% 69.28/11.09 thf(f8297,plain,(
% 69.28/11.09 ((in @ sK242 @ (powerset @ (cartprod @ sK243 @ sK241))) != $true) | (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK243) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK241 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK241 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK243 @ sK241)))) @ sK242) != $true)),
% 69.28/11.09 inference(superposition,[status(thm)],[f5055,f4863])).
% 69.28/11.09 thf(f4863,plain,(
% 69.28/11.09 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ X1))) | ((in @ X2 @ X0) != $true)) )),
% 69.28/11.09 inference(beta_eta_normalization,[status(thm)],[f4862])).
% 69.28/11.09 thf(f4862,plain,(
% 69.28/11.09 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) )),
% 69.28/11.09 inference(trivial_inequality_removal,[status(thm)],[f4395])).
% 69.28/11.09 thf(f4395,plain,(
% 69.28/11.09 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != $true) | ((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) )),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f2961,f2909])).
% 69.28/11.09 thf(f2909,plain,(
% 69.28/11.09 (setbeta = $true)),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1225])).
% 69.28/11.09 thf(f2961,plain,(
% 69.28/11.09 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) | (setbeta != $true)) )),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1261])).
% 69.28/11.09 thf(f1261,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (setbeta != $true)) & ((setbeta = $true) | (((in @ sK265 @ sK263) = $true) & ((sK264 @ sK265) != (in @ sK265 @ (dsetconstr @ sK263 @ (^[Y0 : $i]: (sK264 @ Y0)))))))),
% 69.28/11.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK263,sK264,sK265])],[f1259,f1260])).
% 69.28/11.09 thf(f1260,plain,(
% 69.28/11.09 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X3) = $true) & ((X4 @ X5) != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) => (((in @ sK265 @ sK263) = $true) & ((sK264 @ sK265) != (in @ sK265 @ (dsetconstr @ sK263 @ (^[Y0 : $i]: (sK264 @ Y0))))))),
% 69.28/11.09 introduced(definition,[],[choice_axiom])).
% 69.28/11.09 thf(f1259,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (setbeta != $true)) & ((setbeta = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X3) = $true) & ((X4 @ X5) != (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f1258])).
% 69.28/11.09 thf(f1258,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (setbeta != $true)) & ((setbeta = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 69.28/11.09 inference(nnf_transformation,[status(thm)],[f699])).
% 69.28/11.09 thf(f699,plain,(
% 69.28/11.09 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) != $true) | ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) <=> (setbeta = $true)),
% 69.28/11.09 inference(ennf_transformation,[status(thm)],[f295])).
% 69.28/11.09 thf(f295,plain,(
% 69.28/11.09 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ X0) = $true) => ((X1 @ X2) = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) <=> (setbeta = $true)),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f294])).
% 69.28/11.09 thf(f294,plain,(
% 69.28/11.09 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) <=> (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = setbeta)),
% 69.28/11.09 inference(rectify,[status(thm)],[f26])).
% 69.28/11.09 thf(f26,axiom,(
% 69.28/11.09 (! [X3 : $i,X0 : $i > $o,X1 : $i] : ((in @ X1 @ X3) => ((X0 @ X1) <=> (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = setbeta)),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',setbeta)).
% 69.28/11.09 thf(f5055,plain,(
% 69.28/11.09 ((in @ sK242 @ (dsetconstr @ (powerset @ (cartprod @ sK243 @ sK241)) @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK243) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ sK241 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))) & (in @ Y2 @ (dsetconstr @ sK241 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ Y0)))))))))) & (subset @ Y0 @ (cartprod @ sK243 @ sK241)))))) != $true)),
% 69.28/11.09 inference(beta_eta_normalization,[status(thm)],[f4371])).
% 69.28/11.09 thf(f4371,plain,(
% 69.28/11.09 ((in @ sK242 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))) @ sK243 @ sK241)) != $true)),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f2778,f3355])).
% 69.28/11.09 thf(f3355,plain,(
% 69.28/11.09 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: (((setadjoin @ Y10 @ emptyset) = Y9) & (in @ Y10 @ Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2)))))))),
% 69.28/11.09 inference(definition_unfolding,[status(thm)],[f2986,f3354])).
% 69.28/11.09 thf(f2986,plain,(
% 69.28/11.09 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f432])).
% 69.28/11.09 thf(f432,plain,(
% 69.28/11.09 (funcSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (cartprod @ Y0 @ Y1)) @ (^[Y2 : $i]: (func @ Y0 @ Y1 @ Y2)))))))),
% 69.28/11.09 inference(fool_elimination,[status(thm)],[f431])).
% 69.28/11.09 thf(f431,plain,(
% 69.28/11.09 (funcSet = (^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (cartprod @ X0 @ X1)) @ (^[X2 : $i] : (func @ X0 @ X1 @ X2)))))),
% 69.28/11.09 inference(rectify,[status(thm)],[f195])).
% 69.28/11.09 thf(f195,axiom,(
% 69.28/11.09 (funcSet = (^[X3 : $i, X4 : $i] : (dsetconstr @ (powerset @ (cartprod @ X3 @ X4)) @ (^[X13 : $i] : (func @ X3 @ X4 @ X13)))))),
% 69.28/11.09 file('/export/starexec/sandbox2/tmp/tmp.yp4agTpS9m/DTF2THF_3362.p',funcSet)).
% 69.28/11.09 thf(f2778,plain,(
% 69.28/11.09 ((in @ sK242 @ (funcSet @ sK243 @ sK241)) != $true)),
% 69.28/11.09 inference(cnf_transformation,[status(thm)],[f1225])).
% 69.28/11.09 % SZS output end Proof for DTF2THF_3362
% 69.28/11.09 % (3998)------------------------------
% 69.28/11.09 % (3998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.28/11.09 % (3998)Termination reason: Refutation
% 69.28/11.09
% 69.28/11.09 % (3998)Memory used [KB]: 7675
% 69.28/11.09 % (3998)Time elapsed: 0.793 s
% 69.28/11.09 % (3998)Instructions burned: 2617 (million)
% 69.28/11.09 % (3998)------------------------------
% 69.28/11.09 % (3998)------------------------------
% 69.28/11.09 % (3588)Success in time 9.565 s
%------------------------------------------------------------------------------