%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU638^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:49 AM UTC 2026
% Result : Theorem 8.34s 2.43s
% Output : Refutation 8.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 3229 ( 908 equ; 0 cnn)
% Maximal formula atoms : 157 ( 55 avg)
% Number of connectives : 1758 ( 57 ~; 41 |; 497 &; 370 @)
% ( 4 <=>; 784 =>; 0 <=; 0 <~>)
% Maximal formula depth : 163 ( 25 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 362 ( 358 usr; 164 con; 0-4 aty)
% ( 0 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 185 ( 72 ^; 82 !; 31 ?; 185 :)
% 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_193,type,
sP1: $i > $o > $i > $i > $o ).
thf(func_def_194,type,
sP2: $i > $i > $i > $o ).
thf(func_def_199,type,
sP7: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_202,type,
sP10: $i > $i > $o ).
thf(func_def_208,type,
sP16: $i > ( $i > $i > $o ) > $o ).
thf(func_def_210,type,
sP18: $o > $i > $i > $o ).
thf(func_def_212,type,
sP20: $i > $o ).
thf(func_def_214,type,
sP22: ( $i > $o ) > $i > $o ).
thf(func_def_215,type,
sP23: $i > ( $i > $o ) > $o ).
thf(func_def_219,type,
sP27: $o > $i > $i > $o ).
thf(func_def_220,type,
sP28: $i > $i > $i > $o ).
thf(func_def_226,type,
sP34: $i > $i > $i > $o ).
thf(func_def_227,type,
sP35: $i > $i > $o ).
thf(func_def_228,type,
sP36: $i > $o ).
thf(func_def_229,type,
sP37: $i > $i > $o ).
thf(func_def_230,type,
sP38: $i > $i > $o ).
thf(func_def_237,type,
sK45: $i > $o ).
thf(func_def_240,type,
sK48: $i > $o ).
thf(func_def_241,type,
sK49: $i > $i ).
thf(func_def_242,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_243,type,
sK51: $i > $i > $i > $o ).
thf(func_def_259,type,
sK67: $i > $i > $i ).
thf(func_def_278,type,
sK86: $i > $i > $i ).
thf(func_def_286,type,
sK94: $i > $i ).
thf(func_def_305,type,
sK113: $i > $o ).
thf(func_def_306,type,
sK114: $i > $o ).
thf(func_def_307,type,
sK115: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_308,type,
sK116: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK117: $i > $o ).
thf(func_def_312,type,
sK120: $i > ( $i > $o ) > $i ).
thf(func_def_316,type,
sK124: $i > $i > $i ).
thf(func_def_325,type,
sK133: $i > $i ).
thf(func_def_327,type,
sK135: $i > $i ).
thf(func_def_339,type,
sK147: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_340,type,
sK148: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_343,type,
sK151: $i > $o ).
thf(func_def_344,type,
sK152: $i > $o ).
thf(func_def_349,type,
sK157: $i > $o ).
thf(func_def_356,type,
sK164: $i > $o ).
thf(func_def_357,type,
sK165: $i > $i ).
thf(func_def_358,type,
sK166: ( $i > $o ) > $i ).
thf(func_def_367,type,
sK175: $i > $o ).
thf(func_def_371,type,
sK179: $i > $i > $i ).
thf(func_def_372,type,
sK180: $i > $i > $i ).
thf(func_def_377,type,
sK185: $i > $o ).
thf(func_def_379,type,
sK187: $i > ( $i > $o ) > $i ).
thf(func_def_386,type,
sK194: $i > $i > $i ).
thf(func_def_411,type,
sK219: $i > $i ).
thf(func_def_413,type,
sK221: $i > $i ).
thf(func_def_416,type,
sK224: $i > $i > $i ).
thf(func_def_428,type,
sK236: $i > $i > $o ).
thf(func_def_430,type,
sK238: $i > ( $i > $i > $o ) > $i ).
thf(func_def_431,type,
sK239: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_432,type,
sK240: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_433,type,
sK241: $i > ( $i > $i > $o ) > $i ).
thf(func_def_434,type,
sK242: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_436,type,
sK244: $i > $o ).
thf(func_def_465,type,
sK273: $i > $o ).
thf(func_def_467,type,
sK275: $i > $i ).
thf(func_def_468,type,
sK276: $i > $i ).
thf(func_def_473,type,
sK281: $i > ( $i > $o ) > $i ).
thf(func_def_474,type,
sK282: $i > ( $i > $o ) > $i ).
thf(func_def_475,type,
sK283: ( $i > $o ) > $i > $i ).
thf(func_def_476,type,
sK284: $i > $o ).
thf(func_def_484,type,
sK292: $i > $o ).
thf(func_def_487,type,
sK295: $i > ( $i > $o ) > $i ).
thf(func_def_489,type,
sK297: $i > $o ).
thf(func_def_495,type,
sK303: $i > $i > $i > $i ).
thf(func_def_496,type,
sK304: $i > $i > $i > $i ).
thf(func_def_507,type,
sK315: $i > $o ).
thf(func_def_509,type,
sK317: ( $i > $o ) > $i > $i ).
thf(func_def_512,type,
sK320: $i > $i > $i > $o ).
thf(func_def_516,type,
sK324: $i > $o ).
thf(func_def_517,type,
sK325: ( $i > $o ) > $i ).
thf(func_def_518,type,
sK326: $i > $o ).
thf(func_def_520,type,
sK328: ( $i > $o ) > $i ).
thf(func_def_521,type,
sK329: ( $i > $o ) > $i ).
thf(func_def_523,type,
sK331: $i > $o ).
thf(func_def_525,type,
sK333: ( $i > $o ) > $i > $i ).
thf(func_def_526,type,
sK334: $i > $o ).
thf(func_def_537,type,
sK345: $i > $i > $i ).
thf(func_def_541,type,
sK349: $i > $i > $i ).
thf(func_def_546,type,
sK354: $i > $o ).
thf(func_def_548,type,
sK356: $i > $o ).
thf(func_def_550,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_559,type,
sK367: $i > $i ).
thf(func_def_560,type,
sK368: $i > $i ).
thf(func_def_561,type,
sK369: $i > $i ).
thf(func_def_562,type,
sK370: $i > $i > $i ).
thf(func_def_563,type,
sK371: $i > $i > $i ).
thf(func_def_564,type,
sK372: $i > $i > $i ).
thf(func_def_565,type,
sK373: $i > $i > $i ).
thf(func_def_566,type,
sK374: $i > $i > $i ).
thf(func_def_567,type,
sK375: $i > $i > $i > $i ).
thf(func_def_568,type,
sK376: $i > $i ).
thf(func_def_569,type,
sK377: $i > $i ).
thf(func_def_570,type,
sK378: $i > $i ).
thf(func_def_571,type,
sK379: $i > $i ).
thf(func_def_572,type,
sK380: $i > $i > $i ).
thf(func_def_573,type,
sK381: $i > $i > $i ).
thf(func_def_574,type,
sK382: $i > $i > $i ).
thf(func_def_575,type,
sK383: $i > $i > $i > $i ).
thf(func_def_576,type,
sK384: $i > $i > $i > $i ).
thf(func_def_581,type,
sK389: $i > $i > $i ).
thf(func_def_599,type,
sK407: $i > $o ).
thf(func_def_605,type,
sK413: $i > $i ).
thf(func_def_613,type,
sK421: $o > $i > $i > $i ).
thf(func_def_619,type,
sK427: $i > $o ).
thf(func_def_629,type,
sK437: $i > $o ).
thf(func_def_633,type,
sK441: $i > $o ).
thf(func_def_636,type,
sK444: $i > $o ).
thf(func_def_637,type,
sK445: $i > $o ).
thf(func_def_638,type,
sK446: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_639,type,
sK447: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_646,type,
sK454: $i > $o ).
thf(func_def_651,type,
sK459: $i > $o ).
thf(func_def_654,type,
sK462: $i > ( $i > $o ) > $i ).
thf(func_def_656,type,
sK464: $i > $o ).
thf(func_def_658,type,
sK466: ( $i > $o ) > $i > $i ).
thf(func_def_660,type,
sK468: $i > $i ).
thf(func_def_661,type,
sK469: $i > $i ).
thf(func_def_662,type,
sK470: $i > $i ).
thf(func_def_666,type,
sK474: ( $i > $o ) > $i ).
thf(func_def_667,type,
sK475: ( $i > $o ) > $i > $i ).
thf(func_def_668,type,
sK476: ( $i > $o ) > $i ).
thf(func_def_670,type,
sK478: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_671,type,
sK479: ( $i > $o ) > $i > $i ).
thf(func_def_672,type,
sK480: $i > ( $i > $o ) > $i ).
thf(func_def_673,type,
sK481: ( $i > $o ) > $i > $i ).
thf(func_def_674,type,
sK482: $i > $i > $i ).
thf(func_def_675,type,
sK483: $i > $i > $i ).
thf(func_def_676,type,
sK484: ( $i > $o ) > $i > $i ).
thf(func_def_677,type,
sK485: ( $i > $o ) > $i ).
thf(func_def_679,type,
sK487: ( $i > $o ) > $i ).
thf(func_def_680,type,
sK488: $i > $i ).
thf(func_def_681,type,
sK489: $i > ( $i > $o ) > $i ).
thf(func_def_682,type,
sK490: ( $i > $o ) > $i > $i ).
thf(func_def_683,type,
sK491: $i > ( $i > $o ) > $i ).
thf(func_def_684,type,
sK492: $i > ( $i > $o ) > $i ).
thf(func_def_685,type,
sK493: ( $i > $o ) > $i > $i ).
thf(func_def_686,type,
sK494: $i > $i ).
thf(func_def_688,type,
sK496: ( $i > $o ) > $i > $i ).
thf(func_def_689,type,
sK497: $i > ( $i > $o ) > $i ).
thf(func_def_690,type,
sK498: $i > ( $i > $o ) > $i ).
thf(func_def_691,type,
sK499: ( $i > $o ) > $i > $i ).
thf(func_def_692,type,
sK500: $i > ( $i > $o ) > $i ).
thf(func_def_693,type,
sK501: $i > ( $i > $o ) > $i ).
thf(func_def_694,type,
sK502: ( $i > $o ) > $i ).
thf(func_def_695,type,
sK503: ( $i > $o ) > $i > $i ).
thf(func_def_696,type,
sK504: ( $i > $o ) > $i > $i ).
thf(func_def_697,type,
sK505: ( $i > $o ) > $i > $i ).
thf(func_def_698,type,
sK506: ( $i > $o ) > $i > $i ).
thf(func_def_699,type,
sK507: ( $i > $o ) > $i ).
thf(func_def_700,type,
sK508: ( $i > $o ) > $i > $i ).
thf(func_def_701,type,
sK509: ( $i > $o ) > $i > $i ).
thf(func_def_702,type,
sK510: ( $i > $o ) > $i > $i ).
thf(func_def_703,type,
sK511: ( $i > $o ) > $i > $i ).
thf(func_def_704,type,
sK512: ( $i > $o ) > $i ).
thf(func_def_705,type,
sK513: ( $i > $o ) > $i ).
thf(func_def_707,type,
sK515: ( $i > $o ) > $i ).
thf(func_def_708,type,
sK516: ( $i > $o ) > $i ).
thf(func_def_709,type,
sK517: ( $i > $o ) > $i > $i ).
thf(func_def_710,type,
sK518: ( $i > $o ) > $i ).
thf(func_def_711,type,
sK519: ( $i > $o ) > $i > $i ).
thf(func_def_712,type,
sK520: ( $i > $o ) > $i > $i ).
thf(func_def_713,type,
sK521: $i > $i ).
thf(func_def_714,type,
sK522: $i > $i ).
thf(func_def_715,type,
sK523: ( $i > $o ) > $i > $i ).
thf(func_def_716,type,
sK524: $i > $i ).
thf(func_def_717,type,
sK525: $i > $i > $i ).
thf(func_def_718,type,
sK526: $i > $i > $i ).
thf(func_def_719,type,
sK527: ( $i > $o ) > $i > $i ).
thf(func_def_721,type,
sK529: $i > $i ).
thf(func_def_722,type,
ph530:
!>[X0: $tType] : X0 ).
thf(f5879,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f5876,f5807]) ).
thf(f5807,plain,
( ( sK175 @ sK528 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5803]) ).
thf(f5803,plain,
( ( ( sK175 @ sK528 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3137,f3538]) ).
thf(f3538,plain,
( $true
= ( in @ sK528 @ ( dsetconstr @ sK176 @ sK175 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3537]) ).
thf(f3537,plain,
( ( ( ( setadjoin @ sK528 @ emptyset )
= ( dsetconstr @ sK176 @ sK175 ) )
& ( in @ sK528 @ ( dsetconstr @ sK176 @ sK175 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3536]) ).
thf(f3536,plain,
( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK176 @ sK175 ) )
& ( in @ Y0 @ ( dsetconstr @ sK176 @ sK175 ) ) )
@ sK528 )
= $true ),
inference(sigma_clausification,[status(thm)],[f3535]) ).
thf(f3535,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ sK176 @ sK175 ) )
& ( in @ Y0 @ ( dsetconstr @ sK176 @ sK175 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2505]) ).
thf(f2505,plain,
( ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK176
@ ^ [Y0: $i] : ( sK175 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1736,f2350]) ).
thf(f2350,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)],[f1991,f2124]) ).
thf(f2124,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f447]) ).
thf(f447,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f446]) ).
thf(f446,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( ( setadjoin @ X1 @ emptyset )
= X0 ) ) ) ),
inference(rectify,[status(thm)],[f158]) ).
thf(f158,axiom,
( singleton
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( ( setadjoin @ X1 @ emptyset )
= X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',singleton) ).
thf(f1991,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
thf(f227,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f226]) ).
thf(f226,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[status(thm)],[f160]) ).
thf(f160,axiom,
( ( ^ [X3: $i,X0: $i > $o] :
( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',ex1) ).
thf(f1736,plain,
( ( ex1 @ sK176
@ ^ [Y0: $i] : ( sK175 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f982]) ).
thf(f982,plain,
( ( setminusI = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetE = $true )
& ( setminusSubset1 = $true )
& ( emptyE1 = $true )
& ( cartprodpairin = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( powersetE = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( bs114d = $true )
& ( powersetAx = $true )
& ( setunionsingleton = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( setminusER = $true )
& ( singletoninpowunion = $true )
& ( setadjoinSub = $true )
& ( sepSubset = $true )
& ( notequalI1 = $true )
& ( upairinpowunion = $true )
& ( eqimpsubset1 = $true )
& ( binunionE = $true )
& ( dsetconstrI = $true )
& ( setminusSubset2 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( setminusIRneg = $true )
& ( secondinupair = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( symdiffI2 = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset5 = $true )
& ( binintersectLsub = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyImpWitness = $true )
& ( inCongP = $true )
& ( setminusELneg = $true )
& ( uniqinunit = $true )
& ( singletonsubset = $true )
& ( setext = $true )
& ( symdiffIneg1 = $true )
& ( replAx = $true )
& ( binintersectSubset2 = $true )
& ( powersetI1 = $true )
& ( exuE3e = $true )
& ( kpairiskpair = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan3 = $true )
& ( setoftrueEq = $true )
& ( exu__Cong = $true )
& ( setunionI = $true )
& ( setunionsingleton2 = $true )
& ( singletonsswitch = $true )
& ( setminusEL = $true )
& ( notdallE = $true )
& ( powersetE1 = $true )
& ( omega__Cong = $true )
& ( binunionEcases = $true )
& ( setunionAx = $true )
& ( singletoninpowerset = $true )
& ( ubforcartprodlem2 = $true )
& ( notdexE = $true )
& ( emptyInPowerset = $true )
& ( subsetE = $true )
& ( setminusILneg = $true )
& ( descr__Cong = $true )
& ( upairsetE = $true )
& ( emptyI = $true )
& ( symdiffIneg2 = $true )
& ( prop2setE = $true )
& ( upairset2IR = $true )
& ( singletonprop = $true )
& ( subsetI2 = $true )
& ( setunionE2 = $true )
& ( emptyinunitempty = $true )
& ( setminusLsub = $true )
& ( emptysetimpfalse = $true )
& ( symdiffE = $true )
& ( setunionsingleton1 = $true )
& ( emptysetAx = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( cartprodmempair1 = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( setukpairIR = $true )
& ( binintersectSubset4 = $true )
& ( ubforcartprodlem1 = $true )
& ( setukpairIL = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( setbeta = $true )
& ( binintersectEL = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset3 = $true )
& ( disjointsetsI1 = $true )
& ( subsetRefl = $true )
& ( subsetTrans = $true )
& ( setadjoinOr = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( exuI1 = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( notsubsetI = $true )
& ( dsetconstrER = $true )
& ( kpairp = $true )
& ( setadjoinSub2 = $true )
& ( sepInPowerset = $true )
& ( exuE2 = $true )
& ( upairsetIR = $true )
& ( omegaIndAx = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ( binunionLsub = $true )
& ( setadjoinIR = $true )
& ( setunionE = $true )
& ( prop2set2propI = $true )
& ( vacuousDall = $true )
& ( powerset__Cong = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( powersetsubset = $true )
& ( exuI3 = $true )
& ( symdiffI1 = $true )
& ( nonemptyE1 = $true )
& ( upairset2E = $true )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK176 ) )
| ( ( sK175 @ X2 )
!= $true ) )
& ( ( ex1 @ sK176
@ ^ [Y0: $i] : ( sK175 @ Y0 ) )
= $true )
& ( quantDeMorgan2 = $true )
& ( omega0Ax = $true )
& ( powersetI = $true )
& ( binintersectRsub = $true )
& ( binunionIL = $true )
& ( upairsubunion = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( cartprodmempair = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( binintersectI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176])],[f543,f981]) ).
thf(f981,plain,
( ? [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
=> ( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK176 ) )
| ( ( sK175 @ X2 )
!= $true ) )
& ( ( ex1 @ sK176
@ ^ [Y0: $i] : ( sK175 @ Y0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f543,plain,
( ( setminusI = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetE = $true )
& ( setminusSubset1 = $true )
& ( emptyE1 = $true )
& ( cartprodpairin = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( powersetE = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( binintersectER = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( bs114d = $true )
& ( powersetAx = $true )
& ( setunionsingleton = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( setminusER = $true )
& ( singletoninpowunion = $true )
& ( setadjoinSub = $true )
& ( sepSubset = $true )
& ( notequalI1 = $true )
& ( upairinpowunion = $true )
& ( eqimpsubset1 = $true )
& ( binunionE = $true )
& ( dsetconstrI = $true )
& ( setminusSubset2 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( setminusIRneg = $true )
& ( secondinupair = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( symdiffI2 = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset5 = $true )
& ( binintersectLsub = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyImpWitness = $true )
& ( inCongP = $true )
& ( setminusELneg = $true )
& ( uniqinunit = $true )
& ( singletonsubset = $true )
& ( setext = $true )
& ( symdiffIneg1 = $true )
& ( replAx = $true )
& ( binintersectSubset2 = $true )
& ( powersetI1 = $true )
& ( exuE3e = $true )
& ( kpairiskpair = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan3 = $true )
& ( setoftrueEq = $true )
& ( exu__Cong = $true )
& ( setunionI = $true )
& ( setunionsingleton2 = $true )
& ( singletonsswitch = $true )
& ( setminusEL = $true )
& ( notdallE = $true )
& ( powersetE1 = $true )
& ( omega__Cong = $true )
& ( binunionEcases = $true )
& ( setunionAx = $true )
& ( singletoninpowerset = $true )
& ( ubforcartprodlem2 = $true )
& ( notdexE = $true )
& ( emptyInPowerset = $true )
& ( subsetE = $true )
& ( setminusILneg = $true )
& ( descr__Cong = $true )
& ( upairsetE = $true )
& ( emptyI = $true )
& ( symdiffIneg2 = $true )
& ( prop2setE = $true )
& ( upairset2IR = $true )
& ( singletonprop = $true )
& ( subsetI2 = $true )
& ( setunionE2 = $true )
& ( emptyinunitempty = $true )
& ( setminusLsub = $true )
& ( emptysetimpfalse = $true )
& ( symdiffE = $true )
& ( setunionsingleton1 = $true )
& ( emptysetAx = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( cartprodmempair1 = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( setukpairIR = $true )
& ( binintersectSubset4 = $true )
& ( ubforcartprodlem1 = $true )
& ( setukpairIL = $true )
& ( subPowSU = $true )
& ( inPowerset = $true )
& ( wellorderingAx = $true )
& ( setminusERneg = $true )
& ( setbeta = $true )
& ( binintersectEL = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset3 = $true )
& ( disjointsetsI1 = $true )
& ( subsetRefl = $true )
& ( subsetTrans = $true )
& ( setadjoinOr = $true )
& ( setadjoinIL = $true )
& ( setunion__Cong = $true )
& ( exuI1 = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoin__Cong = $true )
& ( in__Cong = $true )
& ( notsubsetI = $true )
& ( dsetconstrER = $true )
& ( kpairp = $true )
& ( setadjoinSub2 = $true )
& ( sepInPowerset = $true )
& ( exuE2 = $true )
& ( upairsetIR = $true )
& ( omegaIndAx = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ( binunionLsub = $true )
& ( setadjoinIR = $true )
& ( setunionE = $true )
& ( prop2set2propI = $true )
& ( vacuousDall = $true )
& ( powerset__Cong = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( powersetsubset = $true )
& ( exuI3 = $true )
& ( symdiffI1 = $true )
& ( nonemptyE1 = $true )
& ( upairset2E = $true )
& ? [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
& ( quantDeMorgan2 = $true )
& ( omega0Ax = $true )
& ( powersetI = $true )
& ( binintersectRsub = $true )
& ( binunionIL = $true )
& ( upairsubunion = $true )
& ( eqinunit = $true )
& ( omegaSAx = $true )
& ( cartprodmempair = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f542]) ).
thf(f542,plain,
( ? [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $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)],[f487]) ).
thf(f487,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 )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f225]) ).
thf(f225,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 )
=> ! [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( X0 @ X3 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f224]) ).
thf(f224,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
=> ! [X0: $i > $o,X1: $i] :
( ( ex1 @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X0 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f162]) ).
thf(f162,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
=> ! [X0: $i > $o,X3: $i] :
( ( ex1 @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f161]) ).
thf(f161,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
=> ! [X0: $i > $o,X3: $i] :
( ( ex1 @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',ex1E1) ).
thf(f3137,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X0 ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3136]) ).
thf(f3136,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2789]) ).
thf(f2789,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( ( X0 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2313,f1760]) ).
thf(f1760,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f982]) ).
thf(f2313,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f1486]) ).
thf(f1486,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( in @ sK443
@ ( dsetconstr @ sK442
@ ^ [Y0: $i] : ( sK441 @ Y0 ) ) )
= $true )
& ( $true
!= ( sK441 @ sK443 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK441,sK442,sK443])],[f1484,f1485]) ).
thf(f1485,plain,
( ? [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
& ( ( X3 @ X5 )
!= $true ) )
=> ( ( ( in @ sK443
@ ( dsetconstr @ sK442
@ ^ [Y0: $i] : ( sK441 @ Y0 ) ) )
= $true )
& ( $true
!= ( sK441 @ sK443 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1484,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i > $o,X4: $i,X5: $i] :
( ( ( in @ X5
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X3 @ Y0 ) ) )
= $true )
& ( ( X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1483]) ).
thf(f1483,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
& ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f618]) ).
thf(f618,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f421]) ).
thf(f421,plain,
( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f420]) ).
thf(f420,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X0: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',dsetconstrER) ).
thf(f5876,plain,
( ( sK175 @ sK528 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5874]) ).
thf(f5874,plain,
( ( ( sK175 @ sK528 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1737,f5806]) ).
thf(f5806,plain,
( ( in @ sK528 @ sK176 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5802]) ).
thf(f5802,plain,
( ( $true != $true )
| ( ( in @ sK528 @ sK176 )
= $true ) ),
inference(superposition,[status(thm)],[f3490,f3538]) ).
thf(f3490,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( in @ X3 @ ( dsetconstr @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3489]) ).
thf(f3489,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2699]) ).
thf(f2699,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( $true != $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2171,f1860]) ).
thf(f1860,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f982]) ).
thf(f2171,plain,
! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1318]) ).
thf(f1318,plain,
( ( ( dsetconstrEL = $true )
| ( ( ( in @ sK353 @ sK355 )
!= $true )
& ( ( in @ sK353
@ ( dsetconstr @ sK355
@ ^ [Y0: $i] : ( sK354 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK353,sK354,sK355])],[f1316,f1317]) ).
thf(f1317,plain,
( ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
=> ( ( ( in @ sK353 @ sK355 )
!= $true )
& ( ( in @ sK353
@ ( dsetconstr @ sK355
@ ^ [Y0: $i] : ( sK354 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1316,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
| ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(rectify,[status(thm)],[f1315]) ).
thf(f1315,plain,
( ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f529]) ).
thf(f529,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f383]) ).
thf(f383,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(fool_elimination,[status(thm)],[f382]) ).
thf(f382,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X1: $i,X0: $i > $o,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',dsetconstrEL) ).
thf(f1737,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK176 ) )
| ( ( sK175 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f982]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU638^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU638^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Ordered Pairs - Singletons
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : (! A:i.! phi:i>o.ex1 A (^ x:i.phi x) -> (? x:i.in x A & phi x))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC140g [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 340 ( 160 unt; 179 typ; 160 def)
% 0.28/0.46 % Number of atoms : 846 ( 224 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 156 ( 5 avg)
% 0.28/0.46 % Number of connectives : 1457 ( 47 ~; 7 |; 36 &; 983 @)
% 0.28/0.46 % ( 14 <=>; 370 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 162 ( 2 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 182 ( 179 usr; 158 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 464 ( 39 ^; 388 !; 37 ?; 464 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=403
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx_type,type,
% 0.28/0.46 setextAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx,definition,
% 0.28/0.46 ( setextAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xx @ B ) )
% 0.28/0.46 => ( A = B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx_type,type,
% 0.28/0.46 emptysetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx,definition,
% 0.28/0.46 ( emptysetAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx_type,type,
% 0.28/0.46 setadjoinAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx,definition,
% 0.28/0.46 ( setadjoinAx
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 <=> ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx_type,type,
% 0.28/0.46 powersetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx,definition,
% 0.28/0.46 ( powersetAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 <=> ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion_type,type,
% 0.28/0.46 setunion: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx_type,type,
% 0.28/0.46 setunionAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx,definition,
% 0.28/0.46 ( setunionAx
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 <=> ? [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega_type,type,
% 0.28/0.46 omega: $i ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax_type,type,
% 0.28/0.46 omega0Ax: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax,definition,
% 0.28/0.46 ( omega0Ax
% 0.28/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx_type,type,
% 0.28/0.46 omegaSAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx,definition,
% 0.28/0.46 ( omegaSAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx_type,type,
% 0.28/0.46 omegaIndAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx,definition,
% 0.28/0.46 ( omegaIndAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( ( in @ emptyset @ A )
% 0.28/0.46 & ! [Xx: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ omega )
% 0.28/0.46 & ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(replAx_type,type,
% 0.28/0.46 replAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(replAx,definition,
% 0.28/0.46 ( replAx
% 0.28/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 <=> ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx_type,type,
% 0.28/0.46 foundationAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx,definition,
% 0.28/0.46 ( foundationAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ( ( in @ B @ A )
% 0.28/0.46 & ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx_type,type,
% 0.28/0.46 wellorderingAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx,definition,
% 0.28/0.46 ( wellorderingAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ? [B: $i] :
% 0.28/0.46 ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xy @ A ) )
% 0.28/0.46 => ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ( ( in @ Xx @ C )
% 0.28/0.46 <=> ( in @ Xy @ C ) ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 & ! [C: $i,D: $i] :
% 0.28/0.46 ( ( ( in @ C @ B )
% 0.28/0.46 & ( in @ D @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ D ) )
% 0.28/0.46 | ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ D )
% 0.28/0.46 => ( in @ Xx @ C ) ) ) )
% 0.28/0.46 & ! [C: $i] :
% 0.28/0.46 ( ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.46 => ? [D: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ D @ B )
% 0.28/0.46 & ( in @ Xx @ C )
% 0.28/0.46 & ~ ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ D )
% 0.28/0.46 & ( in @ Xy @ C ) )
% 0.28/0.46 & ! [E: $i] :
% 0.28/0.46 ( ( in @ E @ B )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ E )
% 0.28/0.46 => ( in @ Xy @ D ) )
% 0.28/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr_type,type,
% 0.28/0.46 descr: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(descrp_type,type,
% 0.28/0.46 descrp: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descrp,definition,
% 0.28/0.46 ( descrp
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( Xphi
% 0.28/0.46 @ ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set_type,type,
% 0.28/0.46 prop2set: $o > $i ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE_type,type,
% 0.28/0.46 prop2setE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE,definition,
% 0.28/0.46 ( prop2setE
% 0.28/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE_type,type,
% 0.28/0.47 emptysetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE,definition,
% 0.28/0.47 ( emptysetE
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse_type,type,
% 0.28/0.47 emptysetimpfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse,definition,
% 0.28/0.47 ( emptysetimpfalse
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => $false ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset_type,type,
% 0.28/0.47 notinemptyset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset,definition,
% 0.28/0.47 ( notinemptyset
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e_type,type,
% 0.28/0.47 exuE3e: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e,definition,
% 0.28/0.47 ( exuE3e
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setext_type,type,
% 0.28/0.47 setext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setext,definition,
% 0.28/0.47 ( setext
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI_type,type,
% 0.28/0.47 emptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI,definition,
% 0.28/0.47 ( emptyI
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty_type,type,
% 0.28/0.47 noeltsimpempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty,definition,
% 0.28/0.47 ( noeltsimpempty
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta_type,type,
% 0.28/0.47 setbeta: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta,definition,
% 0.28/0.47 ( setbeta
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty,definition,
% 0.28/0.47 ( nonempty
% 0.28/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1_type,type,
% 0.28/0.47 nonemptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1,definition,
% 0.28/0.47 ( nonemptyE1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI_type,type,
% 0.28/0.47 nonemptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI,definition,
% 0.28/0.47 ( nonemptyI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( nonempty
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1_type,type,
% 0.28/0.47 nonemptyI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1,definition,
% 0.28/0.47 ( nonemptyI1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL_type,type,
% 0.28/0.47 setadjoinIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL,definition,
% 0.28/0.47 ( setadjoinIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty_type,type,
% 0.28/0.47 emptyinunitempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty,definition,
% 0.28/0.47 ( emptyinunitempty
% 0.28/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR_type,type,
% 0.28/0.47 setadjoinIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR,definition,
% 0.28/0.47 ( setadjoinIR
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE_type,type,
% 0.28/0.47 setadjoinE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE,definition,
% 0.28/0.47 ( setadjoinE
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( Xy = Xx )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xy @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr_type,type,
% 0.28/0.47 setadjoinOr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr,definition,
% 0.28/0.47 ( setadjoinOr
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq_type,type,
% 0.28/0.47 setoftrueEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq,definition,
% 0.28/0.47 ( setoftrueEq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU_type,type,
% 0.28/0.47 subPowSU: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,definition,
% 0.28/0.47 ( subPowSU
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2_type,type,
% 0.28/0.47 exuE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2,definition,
% 0.28/0.47 ( exuE2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness_type,type,
% 0.28/0.47 nonemptyImpWitness: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness,definition,
% 0.28/0.47 ( nonemptyImpWitness
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton_type,type,
% 0.28/0.47 notinsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton,definition,
% 0.28/0.47 ( notinsingleton
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx != Xy )
% 0.28/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit_type,type,
% 0.28/0.47 eqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit,definition,
% 0.28/0.47 ( eqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch_type,type,
% 0.28/0.47 singletonsswitch: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch,definition,
% 0.28/0.47 ( singletonsswitch
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE_type,type,
% 0.28/0.47 upairsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE,definition,
% 0.28/0.47 ( upairsetE
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL_type,type,
% 0.28/0.47 upairsetIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL,definition,
% 0.28/0.47 ( upairsetIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR_type,type,
% 0.28/0.47 upairsetIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR,definition,
% 0.28/0.47 ( upairsetIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1_type,type,
% 0.28/0.47 emptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1,definition,
% 0.28/0.47 ( emptyE1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => $false ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall_type,type,
% 0.28/0.47 vacuousDall: $o ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall,definition,
% 0.28/0.47 ( vacuousDall
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1_type,type,
% 0.28/0.47 quantDeMorgan1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1,definition,
% 0.28/0.47 ( quantDeMorgan1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2_type,type,
% 0.28/0.47 quantDeMorgan2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2,definition,
% 0.28/0.47 ( quantDeMorgan2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3_type,type,
% 0.28/0.47 quantDeMorgan3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3,definition,
% 0.28/0.47 ( quantDeMorgan3
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4_type,type,
% 0.28/0.47 quantDeMorgan4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4,definition,
% 0.28/0.47 ( quantDeMorgan4
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI_type,type,
% 0.28/0.47 prop2setI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI,definition,
% 0.28/0.47 ( prop2setI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(set2prop_type,type,
% 0.28/0.47 set2prop: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI_type,type,
% 0.28/0.47 prop2set2propI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI,definition,
% 0.28/0.47 ( prop2set2propI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE_type,type,
% 0.28/0.47 notdexE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE,definition,
% 0.28/0.47 ( notdexE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE_type,type,
% 0.28/0.47 notdallE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE,definition,
% 0.28/0.47 ( notdallE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1_type,type,
% 0.28/0.47 exuI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1,definition,
% 0.28/0.47 ( exuI1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3_type,type,
% 0.28/0.47 exuI3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3,definition,
% 0.28/0.47 ( exuI3
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2_type,type,
% 0.28/0.47 exuI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2,definition,
% 0.28/0.47 ( exuI2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP_type,type,
% 0.28/0.47 inCongP: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP,definition,
% 0.28/0.47 ( inCongP
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u_type,type,
% 0.28/0.47 exuE3u: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u,definition,
% 0.28/0.47 ( exuE3u
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong_type,type,
% 0.28/0.47 exu__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong,definition,
% 0.28/0.47 ( exu__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 <=> ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong_type,type,
% 0.28/0.47 emptyset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong,definition,
% 0.28/0.47 ( emptyset__Cong
% 0.28/0.47 = ( emptyset = emptyset ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong_type,type,
% 0.28/0.47 setadjoin__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong,definition,
% 0.28/0.47 ( setadjoin__Cong
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ! [Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( Xz = Xu )
% 0.28/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong_type,type,
% 0.28/0.47 powerset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong,definition,
% 0.28/0.47 ( powerset__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( powerset @ A )
% 0.28/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong_type,type,
% 0.28/0.47 setunion__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong,definition,
% 0.28/0.47 ( setunion__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( setunion @ A )
% 0.28/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong_type,type,
% 0.28/0.47 omega__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong,definition,
% 0.28/0.47 ( omega__Cong
% 0.28/0.47 = ( omega = omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu_type,type,
% 0.28/0.47 exuEu: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu,definition,
% 0.28/0.47 ( exuEu
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong_type,type,
% 0.28/0.47 descr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong,definition,
% 0.28/0.47 ( descr__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.47 => ( ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong_type,type,
% 0.28/0.47 dsetconstr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong,definition,
% 0.28/0.47 ( dsetconstr__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset_type,type,
% 0.28/0.47 subset: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjoint_type,type,
% 0.28/0.47 disjoint: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setsmeet_type,type,
% 0.28/0.47 setsmeet: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1_type,type,
% 0.28/0.47 subsetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1,definition,
% 0.28/0.47 ( subsetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2_type,type,
% 0.28/0.47 eqimpsubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2,definition,
% 0.28/0.47 ( eqimpsubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1_type,type,
% 0.28/0.47 eqimpsubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1,definition,
% 0.28/0.47 ( eqimpsubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2_type,type,
% 0.28/0.47 subsetI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2,definition,
% 0.28/0.47 ( subsetI2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset_type,type,
% 0.28/0.47 emptysetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset,definition,
% 0.28/0.47 ( emptysetsubset
% 0.28/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE_type,type,
% 0.28/0.47 subsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE,definition,
% 0.28/0.47 ( subsetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2_type,type,
% 0.28/0.47 subsetE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2,definition,
% 0.28/0.47 ( subsetE2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI_type,type,
% 0.28/0.47 notsubsetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI,definition,
% 0.28/0.47 ( notsubsetI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1_type,type,
% 0.28/0.47 notequalI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1,definition,
% 0.28/0.47 ( notequalI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ( subset @ A @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2_type,type,
% 0.28/0.47 notequalI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2,definition,
% 0.28/0.47 ( notequalI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl_type,type,
% 0.28/0.47 subsetRefl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl,definition,
% 0.28/0.47 ( subsetRefl
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans_type,type,
% 0.28/0.47 subsetTrans: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans,definition,
% 0.28/0.47 ( subsetTrans
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ C )
% 0.28/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub_type,type,
% 0.28/0.47 setadjoinSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub,definition,
% 0.28/0.47 ( setadjoinSub
% 0.28/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2_type,type,
% 0.28/0.47 setadjoinSub2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2,definition,
% 0.28/0.47 ( setadjoinSub2
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset_type,type,
% 0.28/0.47 subset2powerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset,definition,
% 0.28/0.47 ( subset2powerset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub_type,type,
% 0.28/0.47 setextsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub,definition,
% 0.28/0.47 ( setextsub
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq_type,type,
% 0.28/0.47 subsetemptysetimpeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq,definition,
% 0.28/0.47 ( subsetemptysetimpeq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( subset @ A @ emptyset )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1_type,type,
% 0.28/0.47 powersetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1,definition,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1_type,type,
% 0.28/0.47 powersetE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1,definition,
% 0.28/0.47 ( powersetE1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset_type,type,
% 0.28/0.47 inPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset,definition,
% 0.28/0.47 ( inPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset_type,type,
% 0.28/0.47 powersetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset,definition,
% 0.28/0.47 ( powersetsubset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset_type,type,
% 0.28/0.47 sepInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset,definition,
% 0.28/0.47 ( sepInPowerset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( in
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset_type,type,
% 0.28/0.47 sepSubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset,definition,
% 0.28/0.47 ( sepSubset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunion_type,type,
% 0.28/0.47 binunion: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL_type,type,
% 0.28/0.47 binunionIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL,definition,
% 0.28/0.47 ( binunionIL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR_type,type,
% 0.28/0.47 upairset2IR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR,definition,
% 0.28/0.47 ( upairset2IR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR_type,type,
% 0.28/0.47 binunionIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR,definition,
% 0.28/0.47 ( binunionIR
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases_type,type,
% 0.28/0.47 binunionEcases: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases,definition,
% 0.28/0.47 ( binunionEcases
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( ( in @ Xx @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE_type,type,
% 0.28/0.47 binunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE,definition,
% 0.28/0.47 ( binunionE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub_type,type,
% 0.28/0.47 binunionLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub,definition,
% 0.28/0.47 ( binunionLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub_type,type,
% 0.28/0.47 binunionRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub,definition,
% 0.28/0.47 ( binunionRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect_type,type,
% 0.28/0.47 binintersect: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI_type,type,
% 0.28/0.47 binintersectI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI,definition,
% 0.28/0.47 ( binintersectI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5_type,type,
% 0.28/0.47 binintersectSubset5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5,definition,
% 0.28/0.47 ( binintersectSubset5
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ C @ A )
% 0.28/0.47 => ( ( subset @ C @ B )
% 0.28/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL_type,type,
% 0.28/0.47 binintersectEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL,definition,
% 0.28/0.47 ( binintersectEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub_type,type,
% 0.28/0.47 binintersectLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub,definition,
% 0.28/0.47 ( binintersectLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2_type,type,
% 0.28/0.47 binintersectSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2,definition,
% 0.28/0.47 ( binintersectSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3_type,type,
% 0.28/0.47 binintersectSubset3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3,definition,
% 0.28/0.47 ( binintersectSubset3
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER_type,type,
% 0.28/0.47 binintersectER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER,definition,
% 0.28/0.47 ( binintersectER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1_type,type,
% 0.28/0.47 disjointsetsI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1,definition,
% 0.28/0.47 ( disjointsetsI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xx @ B ) )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub_type,type,
% 0.28/0.47 binintersectRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub,definition,
% 0.28/0.47 ( binintersectRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4_type,type,
% 0.28/0.47 binintersectSubset4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4,definition,
% 0.28/0.47 ( binintersectSubset4
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1_type,type,
% 0.28/0.47 binintersectSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1,definition,
% 0.28/0.47 ( binintersectSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = A )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d_type,type,
% 0.28/0.47 bs114d: $o ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d,definition,
% 0.28/0.47 ( bs114d
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(regular_type,type,
% 0.28/0.47 regular: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminus_type,type,
% 0.28/0.47 setminus: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI_type,type,
% 0.28/0.47 setminusI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI,definition,
% 0.28/0.47 ( setminusI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL_type,type,
% 0.28/0.47 setminusEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL,definition,
% 0.28/0.47 ( setminusEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER_type,type,
% 0.28/0.47 setminusER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER,definition,
% 0.28/0.47 ( setminusER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2_type,type,
% 0.28/0.47 setminusSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2,definition,
% 0.28/0.47 ( setminusSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg_type,type,
% 0.28/0.47 setminusERneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg,definition,
% 0.28/0.47 ( setminusERneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg_type,type,
% 0.28/0.47 setminusELneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg,definition,
% 0.28/0.47 ( setminusELneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg_type,type,
% 0.28/0.47 setminusILneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg,definition,
% 0.28/0.47 ( setminusILneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg_type,type,
% 0.28/0.47 setminusIRneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg,definition,
% 0.28/0.47 ( setminusIRneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub_type,type,
% 0.28/0.47 setminusLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub,definition,
% 0.28/0.47 ( setminusLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1_type,type,
% 0.28/0.47 setminusSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1,definition,
% 0.28/0.47 ( setminusSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiff_type,type,
% 0.28/0.47 symdiff: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE_type,type,
% 0.28/0.47 symdiffE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE,definition,
% 0.28/0.47 ( symdiffE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1_type,type,
% 0.28/0.47 symdiffI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1,definition,
% 0.28/0.47 ( symdiffI1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2_type,type,
% 0.28/0.47 symdiffI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2,definition,
% 0.28/0.47 ( symdiffI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1_type,type,
% 0.28/0.47 symdiffIneg1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1,definition,
% 0.28/0.47 ( symdiffIneg1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2_type,type,
% 0.28/0.47 symdiffIneg2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2,definition,
% 0.28/0.47 ( symdiffIneg2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair,definition,
% 0.28/0.47 ( iskpair
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setunion @ A ) )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair_type,type,
% 0.28/0.47 secondinupair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair,definition,
% 0.28/0.47 ( secondinupair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL_type,type,
% 0.28/0.47 setukpairIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL,definition,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR_type,type,
% 0.28/0.47 setukpairIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR,definition,
% 0.28/0.47 ( setukpairIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair_type,type,
% 0.28/0.47 kpairiskpair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair,definition,
% 0.28/0.47 ( kpairiskpair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpair_type,type,
% 0.28/0.47 kpair: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kpair,definition,
% 0.28/0.47 ( kpair
% 0.28/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp_type,type,
% 0.28/0.47 kpairp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp,definition,
% 0.28/0.47 ( kpairp
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprod_type,type,
% 0.28/0.47 cartprod: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset_type,type,
% 0.28/0.47 singletonsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset,definition,
% 0.28/0.47 ( singletonsubset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset_type,type,
% 0.28/0.47 singletoninpowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset,definition,
% 0.28/0.47 ( singletoninpowerset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion_type,type,
% 0.28/0.47 singletoninpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion,definition,
% 0.28/0.47 ( singletoninpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E_type,type,
% 0.28/0.47 upairset2E: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E,definition,
% 0.28/0.47 ( upairset2E
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion_type,type,
% 0.28/0.47 upairsubunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion,definition,
% 0.28/0.47 ( upairsubunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion_type,type,
% 0.28/0.47 upairinpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion,definition,
% 0.28/0.47 ( upairinpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1_type,type,
% 0.28/0.47 ubforcartprodlem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1,definition,
% 0.28/0.47 ( ubforcartprodlem1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2_type,type,
% 0.28/0.47 ubforcartprodlem2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2,definition,
% 0.28/0.47 ( ubforcartprodlem2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3_type,type,
% 0.28/0.47 ubforcartprodlem3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3,definition,
% 0.28/0.47 ( ubforcartprodlem3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin_type,type,
% 0.28/0.47 cartprodpairin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin,definition,
% 0.28/0.47 ( cartprodpairin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1_type,type,
% 0.28/0.47 cartprodmempair1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1,definition,
% 0.28/0.47 ( cartprodmempair1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 & ( Xu
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair_type,type,
% 0.28/0.47 cartprodmempair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair,definition,
% 0.28/0.47 ( cartprodmempair
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2_type,type,
% 0.28/0.47 setunionE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2,definition,
% 0.28/0.47 ( setunionE2
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ? [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1_type,type,
% 0.28/0.47 setunionsingleton1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1,definition,
% 0.28/0.47 ( setunionsingleton1
% 0.28/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2_type,type,
% 0.28/0.47 setunionsingleton2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2,definition,
% 0.28/0.47 ( setunionsingleton2
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton_type,type,
% 0.28/0.47 setunionsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton,definition,
% 0.28/0.47 ( setunionsingleton
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singleton,definition,
% 0.28/0.47 ( singleton
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop_type,type,
% 0.28/0.47 singletonprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop,definition,
% 0.28/0.47 ( singletonprop
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1_type,type,
% 0.28/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1,definition,
% 0.28/0.47 ( ex1
% 0.28/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ( upairsetE
% 0.28/0.47 => ( upairsetIL
% 0.28/0.47 => ( upairsetIR
% 0.28/0.47 => ( emptyE1
% 0.28/0.47 => ( vacuousDall
% 0.28/0.47 => ( quantDeMorgan1
% 0.28/0.47 => ( quantDeMorgan2
% 0.28/0.47 => ( quantDeMorgan3
% 0.28/0.47 => ( quantDeMorgan4
% 0.28/0.47 => ( prop2setI
% 0.28/0.47 => ( prop2set2propI
% 0.28/0.47 => ( notdexE
% 0.28/0.47 => ( notdallE
% 0.28/0.47 => ( exuI1
% 0.28/0.47 => ( exuI3
% 0.28/0.47 => ( exuI2
% 0.28/0.47 => ( inCongP
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( exuE3u
% 0.28/0.47 => ( exu__Cong
% 0.28/0.47 => ( emptyset__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( powerset__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( omega__Cong
% 0.28/0.47 => ( exuEu
% 0.28/0.47 => ( descr__Cong
% 0.28/0.47 => ( dsetconstr__Cong
% 0.28/0.47 => ( subsetI1
% 0.28/0.47 => ( eqimpsubset2
% 0.28/0.47 => ( eqimpsubset1
% 0.28/0.47 => ( subsetI2
% 0.28/0.47 => ( emptysetsubset
% 0.28/0.47 => ( subsetE
% 0.28/0.47 => ( subsetE2
% 0.28/0.47 => ( notsubsetI
% 0.28/0.47 => ( notequalI1
% 0.28/0.47 => ( notequalI2
% 0.28/0.47 => ( subsetRefl
% 0.28/0.47 => ( subsetTrans
% 0.28/0.47 => ( setadjoinSub
% 0.28/0.47 => ( setadjoinSub2
% 0.28/0.47 => ( subset2powerset
% 0.28/0.47 => ( setextsub
% 0.28/0.47 => ( subsetemptysetimpeq
% 0.28/0.47 => ( powersetI1
% 0.28/0.47 => ( powersetE1
% 0.28/0.47 => ( inPowerset
% 0.28/0.47 => ( powersetsubset
% 0.28/0.47 => ( sepInPowerset
% 0.28/0.47 => ( sepSubset
% 0.28/0.47 => ( binunionIL
% 0.28/0.47 => ( upairset2IR
% 0.28/0.47 => ( binunionIR
% 0.28/0.47 => ( binunionEcases
% 0.28/0.47 => ( binunionE
% 0.28/0.47 => ( binunionLsub
% 0.28/0.47 => ( binunionRsub
% 0.28/0.47 => ( binintersectI
% 0.28/0.47 => ( binintersectSubset5
% 0.28/0.47 => ( binintersectEL
% 0.28/0.47 => ( binintersectLsub
% 0.28/0.47 => ( binintersectSubset2
% 0.28/0.47 => ( binintersectSubset3
% 0.28/0.47 => ( binintersectER
% 0.28/0.47 => ( disjointsetsI1
% 0.28/0.47 => ( binintersectRsub
% 0.28/0.47 => ( binintersectSubset4
% 0.28/0.47 => ( binintersectSubset1
% 0.28/0.47 => ( bs114d
% 0.28/0.47 => ( setminusI
% 0.28/0.47 => ( setminusEL
% 0.28/0.47 => ( setminusER
% 0.28/0.47 => ( setminusSubset2
% 0.28/0.47 => ( setminusERneg
% 0.28/0.47 => ( setminusELneg
% 0.28/0.47 => ( setminusILneg
% 0.28/0.47 => ( setminusIRneg
% 0.28/0.47 => ( setminusLsub
% 0.28/0.47 => ( setminusSubset1
% 0.28/0.47 => ( symdiffE
% 0.28/0.47 => ( symdiffI1
% 0.28/0.47 => ( symdiffI2
% 0.28/0.47 => ( symdiffIneg1
% 0.28/0.47 => ( symdiffIneg2
% 0.28/0.47 => ( secondinupair
% 0.28/0.47 => ( setukpairIL
% 0.28/0.47 => ( setukpairIR
% 0.28/0.47 => ( kpairiskpair
% 0.28/0.47 => ( kpairp
% 0.28/0.47 => ( singletonsubset
% 0.28/0.47 => ( singletoninpowerset
% 0.28/0.47 => ( singletoninpowunion
% 0.28/0.47 => ( upairset2E
% 0.28/0.47 => ( upairsubunion
% 0.28/0.47 => ( upairinpowunion
% 0.28/0.47 => ( ubforcartprodlem1
% 0.28/0.47 => ( ubforcartprodlem2
% 0.28/0.47 => ( ubforcartprodlem3
% 0.28/0.47 => ( cartprodpairin
% 0.28/0.47 => ( cartprodmempair1
% 0.28/0.47 => ( cartprodmempair
% 0.28/0.47 => ( setunionE2
% 0.28/0.47 => ( setunionsingleton1
% 0.28/0.47 => ( setunionsingleton2
% 0.28/0.47 => ( setunionsingleton
% 0.28/0.47 => ( singletonprop
% 0.28/0.47 => ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.30/1.45 ---- Embedded in THF ---
% 2.30/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.30/1.45 %%% Generated on Tue Feb 24 12:29:28 EST 2026
% 2.30/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.30/1.45 %%% Logic specification used:
% 2.30/1.45 %%% thf(spec, logic, $$dhol).
% 2.30/1.45
% 2.30/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2DTF27992.p
% See solution above
% 2.30/1.45 ------------------------
% 2.30/1.47 ---- Cleaned THF ---
% 2.30/1.47 thf(in_type,type,
% 2.30/1.47 in: $i > $i > $o ).
% 2.30/1.47
% 2.30/1.47 thf(exu_type,type,
% 2.30/1.47 exu: ( $i > $o ) > $o ).
% 2.30/1.47
% 2.30/1.47 thf(exu,definition,
% 2.30/1.47 ( exu
% 2.30/1.47 = ( ^ [Xphi: $i > $o] :
% 2.30/1.47 ? [Xx: $i] :
% 2.30/1.47 ( ( Xphi @ Xx )
% 2.30/1.47 & ! [Xy: $i] :
% 2.30/1.47 ( ( Xphi @ Xy )
% 2.30/1.47 => ( Xx = Xy ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(setextAx_type,type,
% 2.30/1.47 setextAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(setextAx,definition,
% 2.30/1.47 ( setextAx
% 2.30/1.47 = ( ! [A: $i,B: $i] :
% 2.30/1.47 ( ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ A )
% 2.30/1.47 <=> ( in @ Xx @ B ) )
% 2.30/1.47 => ( A = B ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(emptyset_type,type,
% 2.30/1.47 emptyset: $i ).
% 2.30/1.47
% 2.30/1.47 thf(emptysetAx_type,type,
% 2.30/1.47 emptysetAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(emptysetAx,definition,
% 2.30/1.47 ( emptysetAx
% 2.30/1.47 = ( ! [Xx: $i] :
% 2.30/1.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(setadjoin_type,type,
% 2.30/1.47 setadjoin: $i > $i > $i ).
% 2.30/1.47
% 2.30/1.47 thf(setadjoinAx_type,type,
% 2.30/1.47 setadjoinAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(setadjoinAx,definition,
% 2.30/1.47 ( setadjoinAx
% 2.30/1.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.47 <=> ( ( Xy = Xx )
% 2.30/1.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(powerset_type,type,
% 2.30/1.47 powerset: $i > $i ).
% 2.30/1.47
% 2.30/1.47 thf(powersetAx_type,type,
% 2.30/1.47 powersetAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(powersetAx,definition,
% 2.30/1.47 ( powersetAx
% 2.30/1.47 = ( ! [A: $i,B: $i] :
% 2.30/1.47 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.47 <=> ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ B )
% 2.30/1.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(setunion_type,type,
% 2.30/1.47 setunion: $i > $i ).
% 2.30/1.47
% 2.30/1.47 thf(setunionAx_type,type,
% 2.30/1.47 setunionAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(setunionAx,definition,
% 2.30/1.47 ( setunionAx
% 2.30/1.47 = ( ! [A: $i,Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.47 <=> ? [B: $i] :
% 2.30/1.47 ( ( in @ Xx @ B )
% 2.30/1.47 & ( in @ B @ A ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(omega_type,type,
% 2.30/1.47 omega: $i ).
% 2.30/1.47
% 2.30/1.47 thf(omega0Ax_type,type,
% 2.30/1.47 omega0Ax: $o ).
% 2.30/1.47
% 2.30/1.47 thf(omega0Ax,definition,
% 2.30/1.47 ( omega0Ax
% 2.30/1.47 = ( in @ emptyset @ omega ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(omegaSAx_type,type,
% 2.30/1.47 omegaSAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(omegaSAx,definition,
% 2.30/1.47 ( omegaSAx
% 2.30/1.47 = ( ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ omega )
% 2.30/1.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(omegaIndAx_type,type,
% 2.30/1.47 omegaIndAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(omegaIndAx,definition,
% 2.30/1.47 ( omegaIndAx
% 2.30/1.47 = ( ! [A: $i] :
% 2.30/1.47 ( ( ( in @ emptyset @ A )
% 2.30/1.47 & ! [Xx: $i] :
% 2.30/1.47 ( ( ( in @ Xx @ omega )
% 2.30/1.47 & ( in @ Xx @ A ) )
% 2.30/1.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.30/1.47 => ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ omega )
% 2.30/1.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(replAx_type,type,
% 2.30/1.47 replAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(replAx,definition,
% 2.30/1.47 ( replAx
% 2.30/1.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.30/1.47 ( ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ A )
% 2.30/1.47 => ( exu
% 2.30/1.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.30/1.47 => ? [B: $i] :
% 2.30/1.47 ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ B )
% 2.30/1.47 <=> ? [Xy: $i] :
% 2.30/1.47 ( ( in @ Xy @ A )
% 2.30/1.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(foundationAx_type,type,
% 2.30/1.47 foundationAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(foundationAx,definition,
% 2.30/1.47 ( foundationAx
% 2.30/1.47 = ( ! [A: $i] :
% 2.30/1.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.30/1.47 => ? [B: $i] :
% 2.30/1.47 ( ( in @ B @ A )
% 2.30/1.47 & ~ ? [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ B )
% 2.30/1.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(wellorderingAx_type,type,
% 2.30/1.47 wellorderingAx: $o ).
% 2.30/1.47
% 2.30/1.47 thf(wellorderingAx,definition,
% 2.30/1.47 ( wellorderingAx
% 2.30/1.47 = ( ! [A: $i] :
% 2.30/1.47 ? [B: $i] :
% 2.30/1.47 ( ! [C: $i] :
% 2.30/1.47 ( ( in @ C @ B )
% 2.30/1.47 => ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ C )
% 2.30/1.47 => ( in @ Xx @ A ) ) )
% 2.30/1.47 & ! [Xx: $i,Xy: $i] :
% 2.30/1.47 ( ( ( in @ Xx @ A )
% 2.30/1.47 & ( in @ Xy @ A ) )
% 2.30/1.47 => ( ! [C: $i] :
% 2.30/1.47 ( ( in @ C @ B )
% 2.30/1.47 => ( ( in @ Xx @ C )
% 2.30/1.47 <=> ( in @ Xy @ C ) ) )
% 2.30/1.47 => ( Xx = Xy ) ) )
% 2.30/1.47 & ! [C: $i,D: $i] :
% 2.30/1.47 ( ( ( in @ C @ B )
% 2.30/1.47 & ( in @ D @ B ) )
% 2.30/1.47 => ( ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ C )
% 2.30/1.47 => ( in @ Xx @ D ) )
% 2.30/1.47 | ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ D )
% 2.30/1.47 => ( in @ Xx @ C ) ) ) )
% 2.30/1.47 & ! [C: $i] :
% 2.30/1.47 ( ( ! [Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ C )
% 2.30/1.47 => ( in @ Xx @ A ) )
% 2.30/1.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.30/1.47 => ? [D: $i,Xx: $i] :
% 2.30/1.47 ( ( in @ D @ B )
% 2.30/1.47 & ( in @ Xx @ C )
% 2.30/1.47 & ~ ? [Xy: $i] :
% 2.30/1.47 ( ( in @ Xy @ D )
% 2.30/1.47 & ( in @ Xy @ C ) )
% 2.30/1.47 & ! [E: $i] :
% 2.30/1.47 ( ( in @ E @ B )
% 2.30/1.47 => ( ! [Xy: $i] :
% 2.30/1.47 ( ( in @ Xy @ E )
% 2.30/1.47 => ( in @ Xy @ D ) )
% 2.30/1.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(descr_type,type,
% 2.30/1.47 descr: ( $i > $o ) > $i ).
% 2.30/1.47
% 2.30/1.47 thf(descrp_type,type,
% 2.30/1.47 descrp: $o ).
% 2.30/1.47
% 2.30/1.47 thf(descrp,definition,
% 2.30/1.47 ( descrp
% 2.30/1.47 = ( ! [Xphi: $i > $o] :
% 2.30/1.47 ( ( exu
% 2.30/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.47 => ( Xphi
% 2.30/1.47 @ ( descr
% 2.30/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstr_type,type,
% 2.30/1.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrI_type,type,
% 2.30/1.47 dsetconstrI: $o ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrI,definition,
% 2.30/1.47 ( dsetconstrI
% 2.30/1.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.47 ( ( in @ Xx @ A )
% 2.30/1.47 => ( ( Xphi @ Xx )
% 2.30/1.47 => ( in @ Xx
% 2.30/1.47 @ ( dsetconstr @ A
% 2.30/1.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrEL_type,type,
% 2.30/1.47 dsetconstrEL: $o ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrEL,definition,
% 2.30/1.47 ( dsetconstrEL
% 2.30/1.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.47 ( ( in @ Xx
% 2.30/1.47 @ ( dsetconstr @ A
% 2.30/1.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.47 => ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrER_type,type,
% 2.30/1.47 dsetconstrER: $o ).
% 2.30/1.47
% 2.30/1.47 thf(dsetconstrER,definition,
% 2.30/1.47 ( dsetconstrER
% 2.30/1.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.47 ( ( in @ Xx
% 2.30/1.47 @ ( dsetconstr @ A
% 2.30/1.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.47 => ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.47
% 2.30/1.47 thf(exuE1_type,type,
% 2.30/1.47 exuE1: $o ).
% 2.30/1.47
% 2.30/1.47 thf(exuE1,definition,
% 2.30/1.47 ( exuE1
% 2.30/1.47 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( Xphi @ Xx )
% 2.30/1.48 & ! [Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(prop2set_type,type,
% 2.30/1.48 prop2set: $o > $i ).
% 2.30/1.48
% 2.30/1.48 thf(prop2setE_type,type,
% 2.30/1.48 prop2setE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(prop2setE,definition,
% 2.30/1.48 ( prop2setE
% 2.30/1.48 = ( ! [Xphi: $o,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.30/1.48 => Xphi ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetE_type,type,
% 2.30/1.48 emptysetE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetE,definition,
% 2.30/1.48 ( emptysetE
% 2.30/1.48 = ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ emptyset )
% 2.30/1.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetimpfalse_type,type,
% 2.30/1.48 emptysetimpfalse: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetimpfalse,definition,
% 2.30/1.48 ( emptysetimpfalse
% 2.30/1.48 = ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ emptyset )
% 2.30/1.48 => $false ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notinemptyset_type,type,
% 2.30/1.48 notinemptyset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notinemptyset,definition,
% 2.30/1.48 ( notinemptyset
% 2.30/1.48 = ( ! [Xx: $i] :
% 2.30/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuE3e_type,type,
% 2.30/1.48 exuE3e: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuE3e,definition,
% 2.30/1.48 ( exuE3e
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setext_type,type,
% 2.30/1.48 setext: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setext,definition,
% 2.30/1.48 ( setext
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ B ) )
% 2.30/1.48 => ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ A ) )
% 2.30/1.48 => ( A = B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyI_type,type,
% 2.30/1.48 emptyI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyI,definition,
% 2.30/1.48 ( emptyI
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ~ ( in @ Xx @ A )
% 2.30/1.48 => ( A = emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(noeltsimpempty_type,type,
% 2.30/1.48 noeltsimpempty: $o ).
% 2.30/1.48
% 2.30/1.48 thf(noeltsimpempty,definition,
% 2.30/1.48 ( noeltsimpempty
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ~ ( in @ Xx @ A )
% 2.30/1.48 => ( A = emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setbeta_type,type,
% 2.30/1.48 setbeta: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setbeta,definition,
% 2.30/1.48 ( setbeta
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ( in @ Xx
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(nonempty_type,type,
% 2.30/1.48 nonempty: $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(nonempty,definition,
% 2.30/1.48 ( nonempty
% 2.30/1.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyE1_type,type,
% 2.30/1.48 nonemptyE1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyE1,definition,
% 2.30/1.48 ( nonemptyE1
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ( nonempty @ A )
% 2.30/1.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyI_type,type,
% 2.30/1.48 nonemptyI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyI,definition,
% 2.30/1.48 ( nonemptyI
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ( Xphi @ Xx )
% 2.30/1.48 => ( nonempty
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyI1_type,type,
% 2.30/1.48 nonemptyI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyI1,definition,
% 2.30/1.48 ( nonemptyI1
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.30/1.48 => ( nonempty @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinIL_type,type,
% 2.30/1.48 setadjoinIL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinIL,definition,
% 2.30/1.48 ( setadjoinIL
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyinunitempty_type,type,
% 2.30/1.48 emptyinunitempty: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyinunitempty,definition,
% 2.30/1.48 ( emptyinunitempty
% 2.30/1.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinIR_type,type,
% 2.30/1.48 setadjoinIR: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinIR,definition,
% 2.30/1.48 ( setadjoinIR
% 2.30/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ A )
% 2.30/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinE_type,type,
% 2.30/1.48 setadjoinE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinE,definition,
% 2.30/1.48 ( setadjoinE
% 2.30/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.48 => ! [Xphi: $o] :
% 2.30/1.48 ( ( ( Xy = Xx )
% 2.30/1.48 => Xphi )
% 2.30/1.48 => ( ( ( in @ Xy @ A )
% 2.30/1.48 => Xphi )
% 2.30/1.48 => Xphi ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinOr_type,type,
% 2.30/1.48 setadjoinOr: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinOr,definition,
% 2.30/1.48 ( setadjoinOr
% 2.30/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.48 => ( ( Xy = Xx )
% 2.30/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setoftrueEq_type,type,
% 2.30/1.48 setoftrueEq: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setoftrueEq,definition,
% 2.30/1.48 ( setoftrueEq
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : $true )
% 2.30/1.48 = A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powersetI_type,type,
% 2.30/1.48 powersetI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powersetI,definition,
% 2.30/1.48 ( powersetI
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ A ) )
% 2.30/1.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyinPowerset_type,type,
% 2.30/1.48 emptyinPowerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyinPowerset,definition,
% 2.30/1.48 ( emptyinPowerset
% 2.30/1.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyInPowerset_type,type,
% 2.30/1.48 emptyInPowerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyInPowerset,definition,
% 2.30/1.48 ( emptyInPowerset
% 2.30/1.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powersetE_type,type,
% 2.30/1.48 powersetE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powersetE,definition,
% 2.30/1.48 ( powersetE
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.48 => ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionI_type,type,
% 2.30/1.48 setunionI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionI,definition,
% 2.30/1.48 ( setunionI
% 2.30/1.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ( ( in @ B @ A )
% 2.30/1.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionE_type,type,
% 2.30/1.48 setunionE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionE,definition,
% 2.30/1.48 ( setunionE
% 2.30/1.48 = ( ! [A: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.48 => ! [Xphi: $o] :
% 2.30/1.48 ( ! [B: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ( ( in @ B @ A )
% 2.30/1.48 => Xphi ) )
% 2.30/1.48 => Xphi ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subPowSU_type,type,
% 2.30/1.48 subPowSU: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subPowSU,definition,
% 2.30/1.48 ( subPowSU
% 2.30/1.48 = ( ! [A: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuE2_type,type,
% 2.30/1.48 exuE2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuE2,definition,
% 2.30/1.48 ( exuE2
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ! [Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xy )
% 2.30/1.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyImpWitness_type,type,
% 2.30/1.48 nonemptyImpWitness: $o ).
% 2.30/1.48
% 2.30/1.48 thf(nonemptyImpWitness,definition,
% 2.30/1.48 ( nonemptyImpWitness
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ( nonempty @ A )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & $true ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(uniqinunit_type,type,
% 2.30/1.48 uniqinunit: $o ).
% 2.30/1.48
% 2.30/1.48 thf(uniqinunit,definition,
% 2.30/1.48 ( uniqinunit
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.30/1.48 => ( Xx = Xy ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notinsingleton_type,type,
% 2.30/1.48 notinsingleton: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notinsingleton,definition,
% 2.30/1.48 ( notinsingleton
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx != Xy )
% 2.30/1.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(eqinunit_type,type,
% 2.30/1.48 eqinunit: $o ).
% 2.30/1.48
% 2.30/1.48 thf(eqinunit,definition,
% 2.30/1.48 ( eqinunit
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(singletonsswitch_type,type,
% 2.30/1.48 singletonsswitch: $o ).
% 2.30/1.48
% 2.30/1.48 thf(singletonsswitch,definition,
% 2.30/1.48 ( singletonsswitch
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.30/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetE_type,type,
% 2.30/1.48 upairsetE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetE,definition,
% 2.30/1.48 ( upairsetE
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.30/1.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.30/1.48 => ( ( Xz = Xx )
% 2.30/1.48 | ( Xz = Xy ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetIL_type,type,
% 2.30/1.48 upairsetIL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetIL,definition,
% 2.30/1.48 ( upairsetIL
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetIR_type,type,
% 2.30/1.48 upairsetIR: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairsetIR,definition,
% 2.30/1.48 ( upairsetIR
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyE1_type,type,
% 2.30/1.48 emptyE1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyE1,definition,
% 2.30/1.48 ( emptyE1
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) )
% 2.30/1.48 => ( ( ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 = emptyset )
% 2.30/1.48 => $false ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(vacuousDall_type,type,
% 2.30/1.48 vacuousDall: $o ).
% 2.30/1.48
% 2.30/1.48 thf(vacuousDall,definition,
% 2.30/1.48 ( vacuousDall
% 2.30/1.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ emptyset )
% 2.30/1.48 => ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan1_type,type,
% 2.30/1.48 quantDeMorgan1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan1,definition,
% 2.30/1.48 ( quantDeMorgan1
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ~ ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan2_type,type,
% 2.30/1.48 quantDeMorgan2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan2,definition,
% 2.30/1.48 ( quantDeMorgan2
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ~ ( Xphi @ Xx ) )
% 2.30/1.48 => ~ ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan3_type,type,
% 2.30/1.48 quantDeMorgan3: $o ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan3,definition,
% 2.30/1.48 ( quantDeMorgan3
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ~ ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) )
% 2.30/1.48 => ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan4_type,type,
% 2.30/1.48 quantDeMorgan4: $o ).
% 2.30/1.48
% 2.30/1.48 thf(quantDeMorgan4,definition,
% 2.30/1.48 ( quantDeMorgan4
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ~ ( Xphi @ Xx ) )
% 2.30/1.48 => ~ ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(prop2setI_type,type,
% 2.30/1.48 prop2setI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(prop2setI,definition,
% 2.30/1.48 ( prop2setI
% 2.30/1.48 = ( ! [Xphi: $o] :
% 2.30/1.48 ( Xphi
% 2.30/1.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(set2prop_type,type,
% 2.30/1.48 set2prop: $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(prop2set2propI_type,type,
% 2.30/1.48 prop2set2propI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(prop2set2propI,definition,
% 2.30/1.48 ( prop2set2propI
% 2.30/1.48 = ( ! [Xphi: $o] :
% 2.30/1.48 ( Xphi
% 2.30/1.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notdexE_type,type,
% 2.30/1.48 notdexE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notdexE,definition,
% 2.30/1.48 ( notdexE
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ~ ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) )
% 2.30/1.48 => ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notdallE_type,type,
% 2.30/1.48 notdallE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notdallE,definition,
% 2.30/1.48 ( notdallE
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ~ ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuI1_type,type,
% 2.30/1.48 exuI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuI1,definition,
% 2.30/1.48 ( exuI1
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ? [Xx: $i] :
% 2.30/1.48 ( ( Xphi @ Xx )
% 2.30/1.48 & ! [Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) )
% 2.30/1.48 => ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuI3_type,type,
% 2.30/1.48 exuI3: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuI3,definition,
% 2.30/1.48 ( exuI3
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.30/1.48 => ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xx )
% 2.30/1.48 => ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) )
% 2.30/1.48 => ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuI2_type,type,
% 2.30/1.48 exuI2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuI2,definition,
% 2.30/1.48 ( exuI2
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ? [Xx: $i] :
% 2.30/1.48 ! [Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xy )
% 2.30/1.48 <=> ( Xy = Xx ) )
% 2.30/1.48 => ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(inCongP_type,type,
% 2.30/1.48 inCongP: $o ).
% 2.30/1.48
% 2.30/1.48 thf(inCongP,definition,
% 2.30/1.48 ( inCongP
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(in__Cong_type,type,
% 2.30/1.48 in__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(in__Cong,definition,
% 2.30/1.48 ( in__Cong
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ( ( in @ Xx @ A )
% 2.30/1.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuE3u_type,type,
% 2.30/1.48 exuE3u: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuE3u,definition,
% 2.30/1.48 ( exuE3u
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xx )
% 2.30/1.48 => ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exu__Cong_type,type,
% 2.30/1.48 exu__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exu__Cong,definition,
% 2.30/1.48 ( exu__Cong
% 2.30/1.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.48 ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ( ( Xphi @ Xx )
% 2.30/1.48 <=> ( Xpsi @ Xy ) ) )
% 2.30/1.48 => ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 <=> ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptyset__Cong_type,type,
% 2.30/1.48 emptyset__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptyset__Cong,definition,
% 2.30/1.48 ( emptyset__Cong
% 2.30/1.48 = ( emptyset = emptyset ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoin__Cong_type,type,
% 2.30/1.48 setadjoin__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoin__Cong,definition,
% 2.30/1.48 ( setadjoin__Cong
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ! [Xz: $i,Xu: $i] :
% 2.30/1.48 ( ( Xz = Xu )
% 2.30/1.48 => ( ( setadjoin @ Xx @ Xz )
% 2.30/1.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powerset__Cong_type,type,
% 2.30/1.48 powerset__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powerset__Cong,definition,
% 2.30/1.48 ( powerset__Cong
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ( ( powerset @ A )
% 2.30/1.48 = ( powerset @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunion__Cong_type,type,
% 2.30/1.48 setunion__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunion__Cong,definition,
% 2.30/1.48 ( setunion__Cong
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ( ( setunion @ A )
% 2.30/1.48 = ( setunion @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(omega__Cong_type,type,
% 2.30/1.48 omega__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(omega__Cong,definition,
% 2.30/1.48 ( omega__Cong
% 2.30/1.48 = ( omega = omega ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(exuEu_type,type,
% 2.30/1.48 exuEu: $o ).
% 2.30/1.48
% 2.30/1.48 thf(exuEu,definition,
% 2.30/1.48 ( exuEu
% 2.30/1.48 = ( ! [Xphi: $i > $o] :
% 2.30/1.48 ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xphi @ Xx )
% 2.30/1.48 => ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(descr__Cong_type,type,
% 2.30/1.48 descr__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(descr__Cong,definition,
% 2.30/1.48 ( descr__Cong
% 2.30/1.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.48 ( ! [Xx: $i,Xy: $i] :
% 2.30/1.48 ( ( Xx = Xy )
% 2.30/1.48 => ( ( Xphi @ Xx )
% 2.30/1.48 <=> ( Xpsi @ Xy ) ) )
% 2.30/1.48 => ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ( ( exu
% 2.30/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.30/1.48 => ( ( descr
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 = ( descr
% 2.30/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(dsetconstr__Cong_type,type,
% 2.30/1.48 dsetconstr__Cong: $o ).
% 2.30/1.48
% 2.30/1.48 thf(dsetconstr__Cong,definition,
% 2.30/1.48 ( dsetconstr__Cong
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( ( Xx = Xy )
% 2.30/1.48 => ( ( Xphi @ Xx )
% 2.30/1.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.30/1.48 => ( ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 = ( dsetconstr @ B
% 2.30/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subset_type,type,
% 2.30/1.48 subset: $i > $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(disjoint_type,type,
% 2.30/1.48 disjoint: $i > $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(setsmeet_type,type,
% 2.30/1.48 setsmeet: $i > $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetI1_type,type,
% 2.30/1.48 subsetI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetI1,definition,
% 2.30/1.48 ( subsetI1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ B ) )
% 2.30/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(eqimpsubset2_type,type,
% 2.30/1.48 eqimpsubset2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(eqimpsubset2,definition,
% 2.30/1.48 ( eqimpsubset2
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(eqimpsubset1_type,type,
% 2.30/1.48 eqimpsubset1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(eqimpsubset1,definition,
% 2.30/1.48 ( eqimpsubset1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( A = B )
% 2.30/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetI2_type,type,
% 2.30/1.48 subsetI2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetI2,definition,
% 2.30/1.48 ( subsetI2
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ B ) )
% 2.30/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetsubset_type,type,
% 2.30/1.48 emptysetsubset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(emptysetsubset,definition,
% 2.30/1.48 ( emptysetsubset
% 2.30/1.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetE_type,type,
% 2.30/1.48 subsetE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetE,definition,
% 2.30/1.48 ( subsetE
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetE2_type,type,
% 2.30/1.48 subsetE2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetE2,definition,
% 2.30/1.48 ( subsetE2
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notsubsetI_type,type,
% 2.30/1.48 notsubsetI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notsubsetI,definition,
% 2.30/1.48 ( notsubsetI
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notequalI1_type,type,
% 2.30/1.48 notequalI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notequalI1,definition,
% 2.30/1.48 ( notequalI1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ~ ( subset @ A @ B )
% 2.30/1.48 => ( A != B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(notequalI2_type,type,
% 2.30/1.48 notequalI2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(notequalI2,definition,
% 2.30/1.48 ( notequalI2
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ( A != B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetRefl_type,type,
% 2.30/1.48 subsetRefl: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetRefl,definition,
% 2.30/1.48 ( subsetRefl
% 2.30/1.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetTrans_type,type,
% 2.30/1.48 subsetTrans: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetTrans,definition,
% 2.30/1.48 ( subsetTrans
% 2.30/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ( subset @ B @ C )
% 2.30/1.48 => ( subset @ A @ C ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinSub_type,type,
% 2.30/1.48 setadjoinSub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinSub,definition,
% 2.30/1.48 ( setadjoinSub
% 2.30/1.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinSub2_type,type,
% 2.30/1.48 setadjoinSub2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setadjoinSub2,definition,
% 2.30/1.48 ( setadjoinSub2
% 2.30/1.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subset2powerset_type,type,
% 2.30/1.48 subset2powerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subset2powerset,definition,
% 2.30/1.48 ( subset2powerset
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setextsub_type,type,
% 2.30/1.48 setextsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setextsub,definition,
% 2.30/1.48 ( setextsub
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ( subset @ B @ A )
% 2.30/1.48 => ( A = B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(subsetemptysetimpeq_type,type,
% 2.30/1.48 subsetemptysetimpeq: $o ).
% 2.30/1.48
% 2.30/1.48 thf(subsetemptysetimpeq,definition,
% 2.30/1.48 ( subsetemptysetimpeq
% 2.30/1.48 = ( ! [A: $i] :
% 2.30/1.48 ( ( subset @ A @ emptyset )
% 2.30/1.48 => ( A = emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powersetI1_type,type,
% 2.30/1.48 powersetI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powersetI1,definition,
% 2.30/1.48 ( powersetI1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ B @ A )
% 2.30/1.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powersetE1_type,type,
% 2.30/1.48 powersetE1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powersetE1,definition,
% 2.30/1.48 ( powersetE1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(inPowerset_type,type,
% 2.30/1.48 inPowerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(inPowerset,definition,
% 2.30/1.48 ( inPowerset
% 2.30/1.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(powersetsubset_type,type,
% 2.30/1.48 powersetsubset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(powersetsubset,definition,
% 2.30/1.48 ( powersetsubset
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(sepInPowerset_type,type,
% 2.30/1.48 sepInPowerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(sepInPowerset,definition,
% 2.30/1.48 ( sepInPowerset
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( in
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 @ ( powerset @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(sepSubset_type,type,
% 2.30/1.48 sepSubset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(sepSubset,definition,
% 2.30/1.48 ( sepSubset
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( subset
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunion_type,type,
% 2.30/1.48 binunion: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(binunionIL_type,type,
% 2.30/1.48 binunionIL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionIL,definition,
% 2.30/1.48 ( binunionIL
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairset2IR_type,type,
% 2.30/1.48 upairset2IR: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairset2IR,definition,
% 2.30/1.48 ( upairset2IR
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunionIR_type,type,
% 2.30/1.48 binunionIR: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionIR,definition,
% 2.30/1.48 ( binunionIR
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunionEcases_type,type,
% 2.30/1.48 binunionEcases: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionEcases,definition,
% 2.30/1.48 ( binunionEcases
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.30/1.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.30/1.48 => ( ( ( in @ Xx @ A )
% 2.30/1.48 => Xphi )
% 2.30/1.48 => ( ( ( in @ Xx @ B )
% 2.30/1.48 => Xphi )
% 2.30/1.48 => Xphi ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunionE_type,type,
% 2.30/1.48 binunionE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionE,definition,
% 2.30/1.48 ( binunionE
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.30/1.48 => ( ( in @ Xx @ A )
% 2.30/1.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunionLsub_type,type,
% 2.30/1.48 binunionLsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionLsub,definition,
% 2.30/1.48 ( binunionLsub
% 2.30/1.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binunionRsub_type,type,
% 2.30/1.48 binunionRsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binunionRsub,definition,
% 2.30/1.48 ( binunionRsub
% 2.30/1.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersect_type,type,
% 2.30/1.48 binintersect: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectI_type,type,
% 2.30/1.48 binintersectI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectI,definition,
% 2.30/1.48 ( binintersectI
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset5_type,type,
% 2.30/1.48 binintersectSubset5: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset5,definition,
% 2.30/1.48 ( binintersectSubset5
% 2.30/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.30/1.48 ( ( subset @ C @ A )
% 2.30/1.48 => ( ( subset @ C @ B )
% 2.30/1.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectEL_type,type,
% 2.30/1.48 binintersectEL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectEL,definition,
% 2.30/1.48 ( binintersectEL
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.30/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectLsub_type,type,
% 2.30/1.48 binintersectLsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectLsub,definition,
% 2.30/1.48 ( binintersectLsub
% 2.30/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset2_type,type,
% 2.30/1.48 binintersectSubset2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset2,definition,
% 2.30/1.48 ( binintersectSubset2
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ( binintersect @ A @ B )
% 2.30/1.48 = A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset3_type,type,
% 2.30/1.48 binintersectSubset3: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset3,definition,
% 2.30/1.48 ( binintersectSubset3
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( ( binintersect @ A @ B )
% 2.30/1.48 = B )
% 2.30/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectER_type,type,
% 2.30/1.48 binintersectER: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectER,definition,
% 2.30/1.48 ( binintersectER
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.30/1.48 => ( in @ Xx @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(disjointsetsI1_type,type,
% 2.30/1.48 disjointsetsI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(disjointsetsI1,definition,
% 2.30/1.48 ( disjointsetsI1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ~ ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( in @ Xx @ B ) )
% 2.30/1.48 => ( ( binintersect @ A @ B )
% 2.30/1.48 = emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectRsub_type,type,
% 2.30/1.48 binintersectRsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectRsub,definition,
% 2.30/1.48 ( binintersectRsub
% 2.30/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset4_type,type,
% 2.30/1.48 binintersectSubset4: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset4,definition,
% 2.30/1.48 ( binintersectSubset4
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ B @ A )
% 2.30/1.48 => ( ( binintersect @ A @ B )
% 2.30/1.48 = B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset1_type,type,
% 2.30/1.48 binintersectSubset1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(binintersectSubset1,definition,
% 2.30/1.48 ( binintersectSubset1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( ( binintersect @ A @ B )
% 2.30/1.48 = A )
% 2.30/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(bs114d_type,type,
% 2.30/1.48 bs114d: $o ).
% 2.30/1.48
% 2.30/1.48 thf(bs114d,definition,
% 2.30/1.48 ( bs114d
% 2.30/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.30/1.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.30/1.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(regular_type,type,
% 2.30/1.48 regular: $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminus_type,type,
% 2.30/1.48 setminus: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(setminusI_type,type,
% 2.30/1.48 setminusI: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusI,definition,
% 2.30/1.48 ( setminusI
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusEL_type,type,
% 2.30/1.48 setminusEL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusEL,definition,
% 2.30/1.48 ( setminusEL
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.30/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusER_type,type,
% 2.30/1.48 setminusER: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusER,definition,
% 2.30/1.48 ( setminusER
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.30/1.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusSubset2_type,type,
% 2.30/1.48 setminusSubset2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusSubset2,definition,
% 2.30/1.48 ( setminusSubset2
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( subset @ A @ B )
% 2.30/1.48 => ( ( setminus @ A @ B )
% 2.30/1.48 = emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusERneg_type,type,
% 2.30/1.48 setminusERneg: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusERneg,definition,
% 2.30/1.48 ( setminusERneg
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.30/1.48 => ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusELneg_type,type,
% 2.30/1.48 setminusELneg: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusELneg,definition,
% 2.30/1.48 ( setminusELneg
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusILneg_type,type,
% 2.30/1.48 setminusILneg: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusILneg,definition,
% 2.30/1.48 ( setminusILneg
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ~ ( in @ Xx @ A )
% 2.30/1.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusIRneg_type,type,
% 2.30/1.48 setminusIRneg: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusIRneg,definition,
% 2.30/1.48 ( setminusIRneg
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ B )
% 2.30/1.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusLsub_type,type,
% 2.30/1.48 setminusLsub: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusLsub,definition,
% 2.30/1.48 ( setminusLsub
% 2.30/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setminusSubset1_type,type,
% 2.30/1.48 setminusSubset1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setminusSubset1,definition,
% 2.30/1.48 ( setminusSubset1
% 2.30/1.48 = ( ! [A: $i,B: $i] :
% 2.30/1.48 ( ( ( setminus @ A @ B )
% 2.30/1.48 = emptyset )
% 2.30/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(symdiff_type,type,
% 2.30/1.48 symdiff: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffE_type,type,
% 2.30/1.48 symdiffE: $o ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffE,definition,
% 2.30/1.48 ( symdiffE
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.30/1.48 => ! [Xphi: $o] :
% 2.30/1.48 ( ( ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => Xphi ) )
% 2.30/1.48 => ( ( ~ ( in @ Xx @ A )
% 2.30/1.48 => ( ( in @ Xx @ B )
% 2.30/1.48 => Xphi ) )
% 2.30/1.48 => Xphi ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffI1_type,type,
% 2.30/1.48 symdiffI1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffI1,definition,
% 2.30/1.48 ( symdiffI1
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffI2_type,type,
% 2.30/1.48 symdiffI2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffI2,definition,
% 2.30/1.48 ( symdiffI2
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ~ ( in @ Xx @ A )
% 2.30/1.48 => ( ( in @ Xx @ B )
% 2.30/1.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffIneg1_type,type,
% 2.30/1.48 symdiffIneg1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffIneg1,definition,
% 2.30/1.48 ( symdiffIneg1
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( ( in @ Xx @ B )
% 2.30/1.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffIneg2_type,type,
% 2.30/1.48 symdiffIneg2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(symdiffIneg2,definition,
% 2.30/1.48 ( symdiffIneg2
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ~ ( in @ Xx @ A )
% 2.30/1.48 => ( ~ ( in @ Xx @ B )
% 2.30/1.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(iskpair_type,type,
% 2.30/1.48 iskpair: $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(iskpair,definition,
% 2.30/1.48 ( iskpair
% 2.30/1.48 = ( ^ [A: $i] :
% 2.30/1.48 ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.48 & ? [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ ( setunion @ A ) )
% 2.30/1.48 & ( A
% 2.30/1.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(secondinupair_type,type,
% 2.30/1.48 secondinupair: $o ).
% 2.30/1.48
% 2.30/1.48 thf(secondinupair,definition,
% 2.30/1.48 ( secondinupair
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setukpairIL_type,type,
% 2.30/1.48 setukpairIL: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setukpairIL,definition,
% 2.30/1.48 ( setukpairIL
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setukpairIR_type,type,
% 2.30/1.48 setukpairIR: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setukpairIR,definition,
% 2.30/1.48 ( setukpairIR
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(kpairiskpair_type,type,
% 2.30/1.48 kpairiskpair: $o ).
% 2.30/1.48
% 2.30/1.48 thf(kpairiskpair,definition,
% 2.30/1.48 ( kpairiskpair
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(kpair_type,type,
% 2.30/1.48 kpair: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(kpair,definition,
% 2.30/1.48 ( kpair
% 2.30/1.48 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(kpairp_type,type,
% 2.30/1.48 kpairp: $o ).
% 2.30/1.48
% 2.30/1.48 thf(kpairp,definition,
% 2.30/1.48 ( kpairp
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(cartprod_type,type,
% 2.30/1.48 cartprod: $i > $i > $i ).
% 2.30/1.48
% 2.30/1.48 thf(singletonsubset_type,type,
% 2.30/1.48 singletonsubset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(singletonsubset,definition,
% 2.30/1.48 ( singletonsubset
% 2.30/1.48 = ( ! [A: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(singletoninpowerset_type,type,
% 2.30/1.48 singletoninpowerset: $o ).
% 2.30/1.48
% 2.30/1.48 thf(singletoninpowerset,definition,
% 2.30/1.48 ( singletoninpowerset
% 2.30/1.48 = ( ! [A: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(singletoninpowunion_type,type,
% 2.30/1.48 singletoninpowunion: $o ).
% 2.30/1.48
% 2.30/1.48 thf(singletoninpowunion,definition,
% 2.30/1.48 ( singletoninpowunion
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairset2E_type,type,
% 2.30/1.48 upairset2E: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairset2E,definition,
% 2.30/1.48 ( upairset2E
% 2.30/1.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.30/1.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.30/1.48 => ( ( Xz = Xx )
% 2.30/1.48 | ( Xz = Xy ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairsubunion_type,type,
% 2.30/1.48 upairsubunion: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairsubunion,definition,
% 2.30/1.48 ( upairsubunion
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(upairinpowunion_type,type,
% 2.30/1.48 upairinpowunion: $o ).
% 2.30/1.48
% 2.30/1.48 thf(upairinpowunion,definition,
% 2.30/1.48 ( upairinpowunion
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem1_type,type,
% 2.30/1.48 ubforcartprodlem1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem1,definition,
% 2.30/1.48 ( ubforcartprodlem1
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem2_type,type,
% 2.30/1.48 ubforcartprodlem2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem2,definition,
% 2.30/1.48 ( ubforcartprodlem2
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem3_type,type,
% 2.30/1.48 ubforcartprodlem3: $o ).
% 2.30/1.48
% 2.30/1.48 thf(ubforcartprodlem3,definition,
% 2.30/1.48 ( ubforcartprodlem3
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodpairin_type,type,
% 2.30/1.48 cartprodpairin: $o ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodpairin,definition,
% 2.30/1.48 ( cartprodpairin
% 2.30/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodmempair1_type,type,
% 2.30/1.48 cartprodmempair1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodmempair1,definition,
% 2.30/1.48 ( cartprodmempair1
% 2.30/1.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.30/1.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ? [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ B )
% 2.30/1.48 & ( Xu
% 2.30/1.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodmempair_type,type,
% 2.30/1.48 cartprodmempair: $o ).
% 2.30/1.48
% 2.30/1.48 thf(cartprodmempair,definition,
% 2.30/1.48 ( cartprodmempair
% 2.30/1.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.30/1.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.30/1.48 => ( iskpair @ Xu ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionE2_type,type,
% 2.30/1.48 setunionE2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionE2,definition,
% 2.30/1.48 ( setunionE2
% 2.30/1.48 = ( ! [A: $i,Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.48 => ? [X: $i] :
% 2.30/1.48 ( ( in @ X @ A )
% 2.30/1.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton1_type,type,
% 2.30/1.48 setunionsingleton1: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton1,definition,
% 2.30/1.48 ( setunionsingleton1
% 2.30/1.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton2_type,type,
% 2.30/1.48 setunionsingleton2: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton2,definition,
% 2.30/1.48 ( setunionsingleton2
% 2.30/1.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton_type,type,
% 2.30/1.48 setunionsingleton: $o ).
% 2.30/1.48
% 2.30/1.48 thf(setunionsingleton,definition,
% 2.30/1.48 ( setunionsingleton
% 2.30/1.48 = ( ! [Xx: $i] :
% 2.30/1.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.30/1.48 = Xx ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(singleton_type,type,
% 2.30/1.48 singleton: $i > $o ).
% 2.30/1.48
% 2.30/1.48 thf(singleton,definition,
% 2.30/1.48 ( singleton
% 2.30/1.48 = ( ^ [A: $i] :
% 2.30/1.48 ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( A
% 2.30/1.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(singletonprop_type,type,
% 2.30/1.48 singletonprop: $o ).
% 2.30/1.48
% 2.30/1.48 thf(singletonprop,definition,
% 2.30/1.48 ( singletonprop
% 2.30/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ! [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 => ! [Xy: $i] :
% 2.30/1.48 ( ( in @ Xy @ A )
% 2.30/1.48 => ( ( Xphi @ Xx )
% 2.30/1.48 => ( ( Xphi @ Xy )
% 2.30/1.48 => ( Xx = Xy ) ) ) ) )
% 2.30/1.48 => ( ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) )
% 2.30/1.48 => ( singleton
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(ex1_type,type,
% 2.30/1.48 ex1: $i > ( $i > $o ) > $o ).
% 2.30/1.48
% 2.30/1.48 thf(ex1,definition,
% 2.30/1.48 ( ex1
% 2.30/1.48 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( singleton
% 2.30/1.48 @ ( dsetconstr @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.48
% 2.30/1.48 thf(ex1E1,conjecture,
% 2.30/1.48 ( setextAx
% 2.30/1.48 => ( emptysetAx
% 2.30/1.48 => ( setadjoinAx
% 2.30/1.48 => ( powersetAx
% 2.30/1.48 => ( setunionAx
% 2.30/1.48 => ( omega0Ax
% 2.30/1.48 => ( omegaSAx
% 2.30/1.48 => ( omegaIndAx
% 2.30/1.48 => ( replAx
% 2.30/1.48 => ( foundationAx
% 2.30/1.48 => ( wellorderingAx
% 2.30/1.48 => ( descrp
% 2.30/1.48 => ( dsetconstrI
% 2.30/1.48 => ( dsetconstrEL
% 2.30/1.48 => ( dsetconstrER
% 2.30/1.48 => ( exuE1
% 2.30/1.48 => ( prop2setE
% 2.30/1.48 => ( emptysetE
% 2.30/1.48 => ( emptysetimpfalse
% 2.30/1.48 => ( notinemptyset
% 2.30/1.48 => ( exuE3e
% 2.30/1.48 => ( setext
% 2.30/1.48 => ( emptyI
% 2.30/1.48 => ( noeltsimpempty
% 2.30/1.48 => ( setbeta
% 2.30/1.48 => ( nonemptyE1
% 2.30/1.48 => ( nonemptyI
% 2.30/1.48 => ( nonemptyI1
% 2.30/1.48 => ( setadjoinIL
% 2.30/1.48 => ( emptyinunitempty
% 2.30/1.48 => ( setadjoinIR
% 2.30/1.48 => ( setadjoinE
% 2.30/1.48 => ( setadjoinOr
% 2.30/1.48 => ( setoftrueEq
% 2.30/1.48 => ( powersetI
% 2.30/1.48 => ( emptyinPowerset
% 2.30/1.48 => ( emptyInPowerset
% 2.30/1.48 => ( powersetE
% 2.30/1.48 => ( setunionI
% 2.30/1.48 => ( setunionE
% 2.30/1.48 => ( subPowSU
% 2.30/1.48 => ( exuE2
% 2.30/1.48 => ( nonemptyImpWitness
% 2.30/1.48 => ( uniqinunit
% 2.30/1.48 => ( notinsingleton
% 2.30/1.48 => ( eqinunit
% 2.30/1.48 => ( singletonsswitch
% 2.30/1.48 => ( upairsetE
% 2.30/1.48 => ( upairsetIL
% 2.30/1.48 => ( upairsetIR
% 2.30/1.48 => ( emptyE1
% 2.30/1.48 => ( vacuousDall
% 2.30/1.48 => ( quantDeMorgan1
% 2.30/1.48 => ( quantDeMorgan2
% 2.30/1.48 => ( quantDeMorgan3
% 2.30/1.48 => ( quantDeMorgan4
% 2.30/1.48 => ( prop2setI
% 2.30/1.48 => ( prop2set2propI
% 2.30/1.48 => ( notdexE
% 2.30/1.48 => ( notdallE
% 2.30/1.48 => ( exuI1
% 2.30/1.48 => ( exuI3
% 2.30/1.48 => ( exuI2
% 2.30/1.48 => ( inCongP
% 2.30/1.48 => ( in__Cong
% 2.30/1.48 => ( exuE3u
% 2.30/1.48 => ( exu__Cong
% 2.30/1.48 => ( emptyset__Cong
% 2.30/1.48 => ( setadjoin__Cong
% 2.30/1.48 => ( powerset__Cong
% 2.30/1.48 => ( setunion__Cong
% 2.30/1.48 => ( omega__Cong
% 2.30/1.48 => ( exuEu
% 2.30/1.48 => ( descr__Cong
% 2.30/1.48 => ( dsetconstr__Cong
% 2.30/1.48 => ( subsetI1
% 2.30/1.48 => ( eqimpsubset2
% 2.30/1.48 => ( eqimpsubset1
% 2.30/1.48 => ( subsetI2
% 2.30/1.48 => ( emptysetsubset
% 2.30/1.48 => ( subsetE
% 2.30/1.48 => ( subsetE2
% 2.30/1.48 => ( notsubsetI
% 2.30/1.48 => ( notequalI1
% 2.30/1.48 => ( notequalI2
% 2.30/1.48 => ( subsetRefl
% 2.30/1.48 => ( subsetTrans
% 2.30/1.48 => ( setadjoinSub
% 2.30/1.48 => ( setadjoinSub2
% 2.30/1.48 => ( subset2powerset
% 2.30/1.48 => ( setextsub
% 2.30/1.48 => ( subsetemptysetimpeq
% 2.30/1.48 => ( powersetI1
% 2.30/1.48 => ( powersetE1
% 2.30/1.48 => ( inPowerset
% 2.30/1.48 => ( powersetsubset
% 2.30/1.48 => ( sepInPowerset
% 2.30/1.48 => ( sepSubset
% 2.30/1.48 => ( binunionIL
% 2.30/1.48 => ( upairset2IR
% 2.30/1.48 => ( binunionIR
% 2.30/1.48 => ( binunionEcases
% 2.30/1.48 => ( binunionE
% 2.30/1.48 => ( binunionLsub
% 2.30/1.48 => ( binunionRsub
% 2.30/1.48 => ( binintersectI
% 2.30/1.48 => ( binintersectSubset5
% 2.30/1.48 => ( binintersectEL
% 2.30/1.48 => ( binintersectLsub
% 2.30/1.48 => ( binintersectSubset2
% 2.30/1.48 => ( binintersectSubset3
% 2.30/1.48 => ( binintersectER
% 2.30/1.48 => ( disjointsetsI1
% 2.30/1.48 => ( binintersectRsub
% 2.30/1.48 => ( binintersectSubset4
% 2.30/1.48 => ( binintersectSubset1
% 2.30/1.48 => ( bs114d
% 2.30/1.48 => ( setminusI
% 2.30/1.48 => ( setminusEL
% 2.30/1.48 => ( setminusER
% 2.30/1.48 => ( setminusSubset2
% 2.30/1.48 => ( setminusERneg
% 2.30/1.48 => ( setminusELneg
% 2.30/1.48 => ( setminusILneg
% 2.30/1.48 => ( setminusIRneg
% 2.30/1.48 => ( setminusLsub
% 2.30/1.48 => ( setminusSubset1
% 2.30/1.48 => ( symdiffE
% 2.30/1.48 => ( symdiffI1
% 2.30/1.48 => ( symdiffI2
% 2.30/1.48 => ( symdiffIneg1
% 2.30/1.48 => ( symdiffIneg2
% 2.30/1.48 => ( secondinupair
% 2.30/1.48 => ( setukpairIL
% 2.30/1.48 => ( setukpairIR
% 2.30/1.48 => ( kpairiskpair
% 2.30/1.48 => ( kpairp
% 2.30/1.48 => ( singletonsubset
% 2.30/1.48 => ( singletoninpowerset
% 2.30/1.48 => ( singletoninpowunion
% 2.30/1.48 => ( upairset2E
% 2.30/1.48 => ( upairsubunion
% 2.30/1.48 => ( upairinpowunion
% 2.30/1.48 => ( ubforcartprodlem1
% 2.30/1.48 => ( ubforcartprodlem2
% 2.30/1.48 => ( ubforcartprodlem3
% 2.30/1.48 => ( cartprodpairin
% 2.30/1.48 => ( cartprodmempair1
% 2.30/1.48 => ( cartprodmempair
% 2.30/1.48 => ( setunionE2
% 2.30/1.48 => ( setunionsingleton1
% 2.30/1.48 => ( setunionsingleton2
% 2.30/1.48 => ( setunionsingleton
% 2.30/1.48 => ( singletonprop
% 2.30/1.48 => ! [A: $i,Xphi: $i > $o] :
% 2.30/1.48 ( ( ex1 @ A
% 2.30/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.48 => ? [Xx: $i] :
% 2.30/1.48 ( ( in @ Xx @ A )
% 2.30/1.48 & ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.30/1.48 ------------------------
% 2.30/1.49 % (28099)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/18Mi)
% 2.30/1.49 % (28093)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/183Mi)
% 2.30/1.49 % (28095)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_27992 for (2999ds/27Mi)
% 2.30/1.50 % (28098)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_27992 for (2999ds/275Mi)
% 2.50/1.50 % (28099)Instruction limit reached!
% 2.50/1.50 % (28099)------------------------------
% 2.50/1.50 % (28099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.50 % (28099)Termination reason: Unknown
% 2.50/1.50 % (28099)Termination phase: Property scanning
% 2.50/1.50
% 2.50/1.50 % (28099)Memory used [KB]: 1535
% 2.50/1.50 % (28099)Time elapsed: 0.007 s
% 2.50/1.50 % (28099)Instructions burned: 19 (million)
% 2.50/1.50 % (28099)------------------------------
% 2.50/1.50 % (28099)------------------------------
% 2.50/1.50 % (28096)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/2Mi)
% 2.50/1.50 % (28097)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_27992 for (2999ds/2Mi)
% 2.50/1.50 % (28095)Instruction limit reached!
% 2.50/1.50 % (28095)------------------------------
% 2.50/1.50 % (28095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.50 % (28094)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_27992 for (2999ds/4Mi)
% 2.50/1.50 % (28095)Termination reason: Unknown
% 2.50/1.50 % (28095)Termination phase: Property scanning
% 2.50/1.50
% 2.50/1.50 % (28095)Memory used [KB]: 1663
% 2.50/1.50 % (28095)Time elapsed: 0.009 s
% 2.50/1.50 % (28095)Instructions burned: 27 (million)
% 2.50/1.50 % (28095)------------------------------
% 2.50/1.50 % (28095)------------------------------
% 2.50/1.50 % (28096)Instruction limit reached!
% 2.50/1.50 % (28096)------------------------------
% 2.50/1.50 % (28096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.50 % (28096)Termination reason: Unknown
% 2.50/1.50 % (28097)Instruction limit reached!
% 2.50/1.50 % (28097)------------------------------
% 2.50/1.50 % (28097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.50 % (28096)Termination phase: shuffling
% 2.50/1.50
% 2.50/1.50 % (28096)Memory used [KB]: 1279
% 2.50/1.50 % (28096)Time elapsed: 0.004 s
% 2.50/1.50 % (28096)Instructions burned: 3 (million)
% 2.50/1.50 % (28096)------------------------------
% 2.50/1.50 % (28096)------------------------------
% 2.50/1.50 % (28097)Termination reason: Unknown
% 2.50/1.50 % (28097)Termination phase: shuffling
% 2.50/1.50
% 2.50/1.50 % (28097)Memory used [KB]: 1279
% 2.50/1.50 % (28097)Time elapsed: 0.004 s
% 2.50/1.50 % (28097)Instructions burned: 3 (million)
% 2.50/1.50 % (28097)------------------------------
% 2.50/1.50 % (28097)------------------------------
% 2.50/1.50 % (28094)Instruction limit reached!
% 2.50/1.50 % (28094)------------------------------
% 2.50/1.50 % (28094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.50 % (28094)Termination reason: Unknown
% 2.50/1.50 % (28094)Termination phase: shuffling
% 2.50/1.50
% 2.50/1.50 % (28094)Memory used [KB]: 1279
% 2.50/1.50 % (28094)Time elapsed: 0.004 s
% 2.50/1.50 % (28094)Instructions burned: 4 (million)
% 2.50/1.51 % (28094)------------------------------
% 2.50/1.51 % (28094)------------------------------
% 2.50/1.51 % (28100)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/3Mi)
% 2.50/1.51 % (28100)Instruction limit reached!
% 2.50/1.51 % (28100)------------------------------
% 2.50/1.51 % (28100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.51 % (28100)Termination reason: Unknown
% 2.50/1.51 % (28100)Termination phase: shuffling
% 2.50/1.51
% 2.50/1.51 % (28100)Memory used [KB]: 1279
% 2.50/1.51 % (28100)Time elapsed: 0.002 s
% 2.50/1.51 % (28100)Instructions burned: 4 (million)
% 2.50/1.51 % (28100)------------------------------
% 2.50/1.51 % (28100)------------------------------
% 2.50/1.51 % (28101)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_27992 for (2999ds/37Mi)
% 2.50/1.52 % (28106)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/7Mi)
% 2.50/1.52 % (28102)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_27992 for (2999ds/15Mi)
% 2.50/1.52 % (28103)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_27992 for (2999ds/3Mi)
% 2.50/1.52 % (28106)Instruction limit reached!
% 2.50/1.52 % (28106)------------------------------
% 2.50/1.52 % (28106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.52 % (28106)Termination reason: Unknown
% 2.50/1.52 % (28106)Termination phase: shuffling
% 2.50/1.52
% 2.50/1.52 % (28106)Memory used [KB]: 1407
% 2.50/1.52 % (28106)Time elapsed: 0.003 s
% 2.50/1.52 % (28106)Instructions burned: 7 (million)
% 2.50/1.52 % (28106)------------------------------
% 2.50/1.52 % (28106)------------------------------
% 2.50/1.52 % (28105)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_27992 for (2999ds/1041Mi)
% 2.50/1.52 % (28101)Instruction limit reached!
% 2.50/1.52 % (28101)------------------------------
% 2.50/1.52 % (28101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.52 % (28101)Termination reason: Unknown
% 2.50/1.52 % (28101)Termination phase: Property scanning
% 2.50/1.52
% 2.50/1.52 % (28101)Memory used [KB]: 1663
% 2.50/1.52 % (28101)Time elapsed: 0.012 s
% 2.50/1.52 % (28101)Instructions burned: 37 (million)
% 2.50/1.52 % (28101)------------------------------
% 2.50/1.52 % (28101)------------------------------
% 2.50/1.52 % (28103)Instruction limit reached!
% 2.50/1.52 % (28103)------------------------------
% 2.50/1.52 % (28103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.52 % (28103)Termination reason: Unknown
% 2.50/1.52 % (28103)Termination phase: shuffling
% 2.50/1.52
% 2.50/1.52 % (28103)Memory used [KB]: 1279
% 2.50/1.52 % (28103)Time elapsed: 0.004 s
% 2.50/1.52 % (28103)Instructions burned: 4 (million)
% 2.50/1.52 % (28103)------------------------------
% 2.50/1.52 % (28103)------------------------------
% 2.50/1.53 % (28102)Instruction limit reached!
% 2.50/1.53 % (28102)------------------------------
% 2.50/1.53 % (28102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.53 % (28102)Termination reason: Unknown
% 2.50/1.53 % (28102)Termination phase: Property scanning
% 2.50/1.53
% 2.50/1.53 % (28102)Memory used [KB]: 1535
% 2.50/1.53 % (28102)Time elapsed: 0.011 s
% 2.50/1.53 % (28102)Instructions burned: 15 (million)
% 2.50/1.53 % (28102)------------------------------
% 2.50/1.53 % (28102)------------------------------
% 2.50/1.53 % (28107)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/16Mi)
% 2.50/1.53 % (28108)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_27992 for (2999ds/3Mi)
% 2.50/1.53 % (28108)Instruction limit reached!
% 2.50/1.53 % (28108)------------------------------
% 2.50/1.53 % (28108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.53 % (28108)Termination reason: Unknown
% 2.50/1.53 % (28108)Termination phase: shuffling
% 2.50/1.53
% 2.50/1.53 % (28108)Memory used [KB]: 1279
% 2.50/1.53 % (28108)Time elapsed: 0.003 s
% 2.50/1.53 % (28108)Instructions burned: 4 (million)
% 2.50/1.53 % (28108)------------------------------
% 2.50/1.53 % (28108)------------------------------
% 2.50/1.54 % (28107)Instruction limit reached!
% 2.50/1.54 % (28107)------------------------------
% 2.50/1.54 % (28107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.54 % (28107)Termination reason: Unknown
% 2.50/1.54 % (28107)Termination phase: shuffling
% 2.50/1.54
% 2.50/1.54 % (28107)Memory used [KB]: 1663
% 2.50/1.54 % (28107)Time elapsed: 0.006 s
% 2.50/1.54 % (28107)Instructions burned: 19 (million)
% 2.50/1.54 % (28107)------------------------------
% 2.50/1.54 % (28107)------------------------------
% 2.50/1.54 % (28109)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_27992 for (2999ds/3Mi)
% 2.50/1.54 % (28109)Instruction limit reached!
% 2.50/1.54 % (28109)------------------------------
% 2.50/1.54 % (28109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.54 % (28109)Termination reason: Unknown
% 2.50/1.54 % (28109)Termination phase: shuffling
% 2.50/1.54
% 2.50/1.54 % (28109)Memory used [KB]: 1279
% 2.50/1.54 % (28109)Time elapsed: 0.004 s
% 2.50/1.54 % (28109)Instructions burned: 4 (million)
% 2.50/1.54 % (28109)------------------------------
% 2.50/1.54 % (28109)------------------------------
% 2.50/1.54 % (28111)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/3Mi)
% 2.50/1.55 % (28112)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/4Mi)
% 2.50/1.55 % (28111)Instruction limit reached!
% 2.50/1.55 % (28111)------------------------------
% 2.50/1.55 % (28111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.55 % (28111)Termination reason: Unknown
% 2.50/1.55 % (28111)Termination phase: shuffling
% 2.50/1.55
% 2.50/1.55 % (28111)Memory used [KB]: 1279
% 2.50/1.55 % (28111)Time elapsed: 0.003 s
% 2.50/1.55 % (28111)Instructions burned: 4 (million)
% 2.50/1.55 % (28111)------------------------------
% 2.50/1.55 % (28111)------------------------------
% 2.50/1.55 % (28112)Instruction limit reached!
% 2.50/1.55 % (28112)------------------------------
% 2.50/1.55 % (28112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.55 % (28112)Termination reason: Unknown
% 2.50/1.55 % (28112)Termination phase: shuffling
% 2.50/1.55
% 2.50/1.55 % (28112)Memory used [KB]: 1279
% 2.50/1.55 % (28112)Time elapsed: 0.002 s
% 2.50/1.55 % (28112)Instructions burned: 4 (million)
% 2.50/1.55 % (28112)------------------------------
% 2.50/1.55 % (28112)------------------------------
% 2.50/1.55 % (28110)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/7Mi)
% 2.50/1.55 % (28093)Instruction limit reached!
% 2.50/1.55 % (28093)------------------------------
% 2.50/1.55 % (28093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.55 % (28093)Termination reason: Unknown
% 2.50/1.55 % (28093)Termination phase: Saturation
% 2.50/1.55
% 2.50/1.55 % (28093)Memory used [KB]: 7419
% 2.50/1.55 % (28093)Time elapsed: 0.055 s
% 2.50/1.55 % (28093)Instructions burned: 183 (million)
% 2.50/1.55 % (28093)------------------------------
% 2.50/1.55 % (28093)------------------------------
% 2.50/1.55 % (28110)Instruction limit reached!
% 2.50/1.55 % (28110)------------------------------
% 2.50/1.55 % (28110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.55 % (28110)Termination reason: Unknown
% 2.50/1.55 % (28110)Termination phase: shuffling
% 2.50/1.55
% 2.50/1.55 % (28110)Memory used [KB]: 1407
% 2.50/1.55 % (28110)Time elapsed: 0.006 s
% 2.50/1.55 % (28110)Instructions burned: 8 (million)
% 2.50/1.55 % (28110)------------------------------
% 2.50/1.55 % (28110)------------------------------
% 2.50/1.56 % (28115)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/6Mi)
% 2.50/1.56 % (28114)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/710Mi)
% 2.50/1.56 % (28115)Instruction limit reached!
% 2.50/1.56 % (28115)------------------------------
% 2.50/1.56 % (28115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.56 % (28115)Termination reason: Unknown
% 2.50/1.56 % (28115)Termination phase: shuffling
% 2.50/1.56
% 2.50/1.56 % (28115)Memory used [KB]: 1407
% 2.50/1.56 % (28115)Time elapsed: 0.003 s
% 2.50/1.56 % (28115)Instructions burned: 8 (million)
% 2.50/1.56 % (28115)------------------------------
% 2.50/1.56 % (28115)------------------------------
% 2.50/1.56 % (28116)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_27992 for (2999ds/902Mi)
% 2.50/1.56 % (28113)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/18Mi)
% 2.50/1.57 % (28118)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/5Mi)
% 2.50/1.57 % (28118)Instruction limit reached!
% 2.50/1.57 % (28118)------------------------------
% 2.50/1.57 % (28118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.57 % (28118)Termination reason: Unknown
% 2.50/1.57 % (28118)Termination phase: shuffling
% 2.50/1.57
% 2.50/1.57 % (28118)Memory used [KB]: 1407
% 2.50/1.57 % (28118)Time elapsed: 0.003 s
% 2.50/1.57 % (28118)Instructions burned: 7 (million)
% 2.50/1.57 % (28118)------------------------------
% 2.50/1.57 % (28118)------------------------------
% 2.50/1.57 % (28113)Instruction limit reached!
% 2.50/1.57 % (28113)------------------------------
% 2.50/1.57 % (28113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.57 % (28113)Termination reason: Unknown
% 2.50/1.57 % (28113)Termination phase: shuffling
% 2.50/1.57
% 2.50/1.57 % (28117)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_27992 for (2999ds/21Mi)
% 2.50/1.57 % (28113)Memory used [KB]: 1535
% 2.50/1.57 % (28113)Time elapsed: 0.011 s
% 2.50/1.57 % (28113)Instructions burned: 18 (million)
% 2.50/1.57 % (28113)------------------------------
% 2.50/1.57 % (28113)------------------------------
% 2.50/1.58 % (28119)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_27992 for (2999ds/6Mi)
% 2.50/1.58 % (28119)Instruction limit reached!
% 2.50/1.58 % (28119)------------------------------
% 2.50/1.58 % (28119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.58 % (28119)Termination reason: Unknown
% 2.50/1.58 % (28119)Termination phase: shuffling
% 2.50/1.58
% 2.50/1.58 % (28119)Memory used [KB]: 1407
% 2.50/1.58 % (28119)Time elapsed: 0.003 s
% 2.50/1.58 % (28119)Instructions burned: 8 (million)
% 2.50/1.58 % (28117)Instruction limit reached!
% 2.50/1.58 % (28117)------------------------------
% 2.50/1.58 % (28117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.58 % (28117)Termination reason: Unknown
% 2.50/1.58 % (28117)Termination phase: shuffling
% 2.50/1.58
% 2.50/1.58 % (28117)Memory used [KB]: 1791
% 2.50/1.58 % (28117)Time elapsed: 0.013 s
% 2.50/1.58 % (28117)Instructions burned: 22 (million)
% 2.50/1.58 % (28117)------------------------------
% 2.50/1.58 % (28117)------------------------------
% 2.50/1.58 % (28119)------------------------------
% 2.50/1.58 % (28119)------------------------------
% 2.50/1.58 % (28120)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27992 for (2999ds/377Mi)
% 2.50/1.59 % (28098)Instruction limit reached!
% 2.50/1.59 % (28098)------------------------------
% 2.50/1.59 % (28098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.59 % (28098)Termination reason: Unknown
% 2.50/1.59 % (28098)Termination phase: Saturation
% 2.50/1.59
% 2.50/1.59 % (28098)Memory used [KB]: 8187
% 2.50/1.59 % (28098)Time elapsed: 0.091 s
% 2.50/1.59 % (28098)Instructions burned: 275 (million)
% 2.50/1.59 % (28098)------------------------------
% 2.50/1.59 % (28098)------------------------------
% 2.50/1.59 % (28121)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_27992 for (2999ds/779Mi)
% 2.50/1.59 % (28123)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27992 for (2998ds/879Mi)
% 2.50/1.60 % (28122)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_27992 for (2999ds/19Mi)
% 2.50/1.60 % (28122)Instruction limit reached!
% 2.50/1.60 % (28122)------------------------------
% 2.50/1.60 % (28122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.60 % (28122)Termination reason: Unknown
% 2.50/1.60 % (28122)Termination phase: shuffling
% 2.50/1.60
% 2.50/1.60 % (28122)Memory used [KB]: 1663
% 2.50/1.60 % (28122)Time elapsed: 0.008 s
% 2.50/1.60 % (28122)Instructions burned: 21 (million)
% 2.50/1.60 % (28122)------------------------------
% 2.50/1.60 % (28122)------------------------------
% 2.50/1.61 % (28124)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27992 for (2998ds/17Mi)
% 2.50/1.62 % (28124)Instruction limit reached!
% 2.50/1.62 % (28124)------------------------------
% 2.50/1.62 % (28124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.62 % (28124)Termination reason: Unknown
% 2.50/1.62 % (28124)Termination phase: shuffling
% 2.50/1.62
% 2.50/1.62 % (28124)Memory used [KB]: 1535
% 2.50/1.62 % (28124)Time elapsed: 0.006 s
% 2.50/1.62 % (28124)Instructions burned: 17 (million)
% 2.50/1.62 % (28124)------------------------------
% 2.50/1.62 % (28124)------------------------------
% 2.50/1.63 % (28125)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27992 for (2998ds/3Mi)
% 2.50/1.63 % (28125)Instruction limit reached!
% 2.50/1.63 % (28125)------------------------------
% 2.50/1.63 % (28125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.63 % (28125)Termination reason: Unknown
% 2.50/1.63 % (28125)Termination phase: shuffling
% 2.50/1.63
% 2.50/1.63 % (28125)Memory used [KB]: 1279
% 2.50/1.63 % (28125)Time elapsed: 0.003 s
% 2.50/1.63 % (28125)Instructions burned: 4 (million)
% 2.50/1.63 % (28125)------------------------------
% 2.50/1.63 % (28125)------------------------------
% 2.50/1.64 % (28126)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27992 for (2998ds/30Mi)
% 2.50/1.65 % (28126)Instruction limit reached!
% 2.50/1.65 % (28126)------------------------------
% 2.50/1.65 % (28126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.65 % (28126)Termination reason: Unknown
% 2.50/1.65 % (28126)Termination phase: Property scanning
% 2.50/1.65
% 2.50/1.65 % (28126)Memory used [KB]: 1791
% 2.50/1.65 % (28126)Time elapsed: 0.011 s
% 2.50/1.65 % (28126)Instructions burned: 31 (million)
% 2.50/1.65 % (28126)------------------------------
% 2.50/1.65 % (28126)------------------------------
% 2.50/1.66 % (28127)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27992 for (2998ds/127Mi)
% 2.50/1.70 % (28127)Instruction limit reached!
% 2.50/1.70 % (28127)------------------------------
% 2.50/1.70 % (28127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.70 % (28127)Termination reason: Unknown
% 2.50/1.70 % (28127)Termination phase: Saturation
% 2.50/1.70
% 2.50/1.70 % (28127)Memory used [KB]: 6908
% 2.50/1.70 % (28127)Time elapsed: 0.038 s
% 2.50/1.70 % (28127)Instructions burned: 127 (million)
% 2.50/1.70 % (28127)------------------------------
% 2.50/1.70 % (28127)------------------------------
% 2.50/1.71 % (28128)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27992 for (2997ds/100Mi)
% 2.50/1.71 % (28120)Instruction limit reached!
% 2.50/1.71 % (28120)------------------------------
% 2.50/1.71 % (28120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.71 % (28120)Termination reason: Unknown
% 2.50/1.71 % (28120)Termination phase: Saturation
% 2.50/1.71
% 2.50/1.71 % (28120)Memory used [KB]: 7931
% 2.50/1.71 % (28120)Time elapsed: 0.123 s
% 2.50/1.71 % (28120)Instructions burned: 377 (million)
% 2.50/1.71 % (28120)------------------------------
% 2.50/1.71 % (28120)------------------------------
% 2.50/1.72 % (28129)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_27992 for (2997ds/3Mi)
% 2.50/1.72 % (28129)Instruction limit reached!
% 2.50/1.72 % (28129)------------------------------
% 2.50/1.72 % (28129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.72 % (28129)Termination reason: Unknown
% 2.50/1.72 % (28129)Termination phase: shuffling
% 2.50/1.72
% 2.50/1.72 % (28129)Memory used [KB]: 1279
% 2.50/1.72 % (28129)Time elapsed: 0.002 s
% 2.50/1.72 % (28129)Instructions burned: 3 (million)
% 2.50/1.72 % (28129)------------------------------
% 2.50/1.72 % (28129)------------------------------
% 2.50/1.73 % (28130)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_27992 for (2997ds/20Mi)
% 2.50/1.74 % (28128)Instruction limit reached!
% 2.50/1.74 % (28128)------------------------------
% 2.50/1.74 % (28128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.74 % (28128)Termination reason: Unknown
% 2.50/1.74 % (28128)Termination phase: Saturation
% 2.50/1.74
% 2.50/1.74 % (28128)Memory used [KB]: 6652
% 2.50/1.74 % (28128)Time elapsed: 0.030 s
% 2.50/1.74 % (28128)Instructions burned: 102 (million)
% 2.50/1.74 % (28128)------------------------------
% 2.50/1.74 % (28128)------------------------------
% 2.50/1.74 % (28130)Instruction limit reached!
% 2.50/1.74 % (28130)------------------------------
% 2.50/1.74 % (28130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.74 % (28130)Termination reason: Unknown
% 2.50/1.74 % (28130)Termination phase: SInE selection
% 2.50/1.74
% 2.50/1.74 % (28130)Memory used [KB]: 1535
% 2.50/1.74 % (28130)Time elapsed: 0.009 s
% 2.50/1.74 % (28130)Instructions burned: 22 (million)
% 2.50/1.74 % (28130)------------------------------
% 2.50/1.74 % (28130)------------------------------
% 2.50/1.75 % (28132)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_27992 for (2997ds/107Mi)
% 2.50/1.75 % (28131)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_27992 for (2997ds/86Mi)
% 2.50/1.77 % (28121)Instruction limit reached!
% 2.50/1.77 % (28121)------------------------------
% 2.50/1.77 % (28121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.77 % (28121)Termination reason: Unknown
% 2.50/1.77 % (28121)Termination phase: Saturation
% 2.50/1.77
% 2.50/1.77 % (28121)Memory used [KB]: 6652
% 2.50/1.77 % (28121)Time elapsed: 0.180 s
% 2.50/1.77 % (28121)Instructions burned: 781 (million)
% 2.50/1.77 % (28121)------------------------------
% 2.50/1.77 % (28121)------------------------------
% 2.50/1.77 % (28131)Instruction limit reached!
% 2.50/1.77 % (28131)------------------------------
% 2.50/1.77 % (28131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.77 % (28131)Termination reason: Unknown
% 2.50/1.77 % (28131)Termination phase: Saturation
% 2.50/1.77
% 2.50/1.77 % (28131)Memory used [KB]: 6524
% 2.50/1.77 % (28131)Time elapsed: 0.026 s
% 2.50/1.77 % (28131)Instructions burned: 89 (million)
% 2.50/1.77 % (28131)------------------------------
% 2.50/1.77 % (28131)------------------------------
% 2.50/1.78 % (28132)Instruction limit reached!
% 2.50/1.78 % (28132)------------------------------
% 2.50/1.78 % (28132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.78 % (28132)Termination reason: Unknown
% 2.50/1.78 % (28132)Termination phase: Saturation
% 2.50/1.78
% 2.50/1.78 % (28132)Memory used [KB]: 6780
% 2.50/1.78 % (28132)Time elapsed: 0.032 s
% 2.50/1.78 % (28132)Instructions burned: 108 (million)
% 2.50/1.78 % (28132)------------------------------
% 2.50/1.78 % (28132)------------------------------
% 2.50/1.78 % (28133)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_27992 for (2997ds/39Mi)
% 2.50/1.78 % (28134)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_27992 for (2997ds/448Mi)
% 2.50/1.79 % (28135)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_27992 for (2997ds/46Mi)
% 2.50/1.79 % (28133)Instruction limit reached!
% 2.50/1.79 % (28133)------------------------------
% 2.50/1.79 % (28133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.79 % (28133)Termination reason: Unknown
% 2.50/1.79 % (28133)Termination phase: Unused predicate definition removal
% 2.50/1.79
% 2.50/1.79 % (28133)Memory used [KB]: 1791
% 2.50/1.79 % (28133)Time elapsed: 0.011 s
% 2.50/1.79 % (28133)Instructions burned: 39 (million)
% 2.50/1.79 % (28133)------------------------------
% 2.50/1.79 % (28133)------------------------------
% 2.50/1.79 % (28114)Instruction limit reached!
% 2.50/1.79 % (28114)------------------------------
% 2.50/1.79 % (28114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.79 % (28114)Termination reason: Unknown
% 2.50/1.79 % (28114)Termination phase: Saturation
% 2.50/1.79
% 2.50/1.79 % (28105)Instruction limit reached!
% 2.50/1.79 % (28105)------------------------------
% 2.50/1.79 % (28105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.79 % (28114)Memory used [KB]: 9210
% 2.50/1.79 % (28114)Time elapsed: 0.238 s
% 2.50/1.79 % (28114)Instructions burned: 710 (million)
% 2.50/1.79 % (28114)------------------------------
% 2.50/1.79 % (28114)------------------------------
% 2.50/1.79 % (28105)Termination reason: Unknown
% 2.50/1.79 % (28105)Termination phase: Saturation
% 2.50/1.79
% 2.50/1.79 % (28105)Memory used [KB]: 9210
% 2.50/1.79 % (28105)Time elapsed: 0.272 s
% 2.50/1.79 % (28105)Instructions burned: 1042 (million)
% 2.50/1.79 % (28105)------------------------------
% 2.50/1.79 % (28105)------------------------------
% 2.50/1.80 % (28136)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_27992 for (2996ds/98Mi)
% 2.50/1.80 % (28135)Instruction limit reached!
% 2.50/1.80 % (28135)------------------------------
% 2.50/1.80 % (28135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.80 % (28135)Termination reason: Unknown
% 2.50/1.80 % (28135)Termination phase: Preprocessing 2
% 2.50/1.80
% 2.50/1.80 % (28135)Memory used [KB]: 1791
% 2.50/1.80 % (28135)Time elapsed: 0.014 s
% 2.50/1.80 % (28135)Instructions burned: 47 (million)
% 2.50/1.80 % (28135)------------------------------
% 2.50/1.80 % (28135)------------------------------
% 2.50/1.80 % (28137)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_27992 for (2996ds/507Mi)
% 2.50/1.80 % (28138)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_27992 for (2996ds/149Mi)
% 2.50/1.81 % (28139)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27992 for (2996ds/39Mi)
% 2.50/1.82 % (28139)Instruction limit reached!
% 2.50/1.82 % (28139)------------------------------
% 2.50/1.82 % (28139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.82 % (28139)Termination reason: Unknown
% 2.50/1.82 % (28139)Termination phase: Preprocessing 3
% 2.50/1.82
% 2.50/1.82 % (28139)Memory used [KB]: 1791
% 2.50/1.82 % (28139)Time elapsed: 0.012 s
% 2.50/1.82 % (28139)Instructions burned: 39 (million)
% 2.50/1.82 % (28139)------------------------------
% 2.50/1.82 % (28139)------------------------------
% 2.50/1.82 % (28136)Instruction limit reached!
% 2.50/1.82 % (28136)------------------------------
% 2.50/1.82 % (28136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.82 % (28136)Termination reason: Unknown
% 2.50/1.82 % (28136)Termination phase: Saturation
% 2.50/1.82
% 2.50/1.82 % (28136)Memory used [KB]: 2046
% 2.50/1.82 % (28136)Time elapsed: 0.026 s
% 2.50/1.82 % (28136)Instructions burned: 101 (million)
% 2.50/1.82 % (28136)------------------------------
% 2.50/1.82 % (28136)------------------------------
% 2.50/1.83 % (28116)Instruction limit reached!
% 2.50/1.83 % (28116)------------------------------
% 2.50/1.83 % (28116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.83 % (28116)Termination reason: Unknown
% 2.50/1.83 % (28116)Termination phase: Saturation
% 2.50/1.83
% 2.50/1.83 % (28116)Memory used [KB]: 10362
% 2.50/1.83 % (28116)Time elapsed: 0.268 s
% 2.50/1.83 % (28116)Instructions burned: 903 (million)
% 2.50/1.83 % (28116)------------------------------
% 2.50/1.83 % (28116)------------------------------
% 2.50/1.83 % (28140)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_27992 for (2996ds/6Mi)
% 2.50/1.83 % (28141)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_27992 for (2996ds/1087Mi)
% 2.50/1.83 % (28140)Instruction limit reached!
% 2.50/1.83 % (28140)------------------------------
% 2.50/1.83 % (28140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.83 % (28140)Termination reason: Unknown
% 2.50/1.83 % (28140)Termination phase: shuffling
% 2.50/1.83
% 2.50/1.83 % (28140)Memory used [KB]: 1407
% 2.50/1.83 % (28140)Time elapsed: 0.004 s
% 2.50/1.83 % (28140)Instructions burned: 8 (million)
% 2.50/1.83 % (28140)------------------------------
% 2.50/1.83 % (28140)------------------------------
% 2.50/1.84 % (28142)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27992 for (2996ds/47Mi)
% 2.50/1.84 % (28143)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_27992 for (2996ds/44Mi)
% 2.50/1.85 % (28138)Instruction limit reached!
% 2.50/1.85 % (28138)------------------------------
% 2.50/1.85 % (28138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.85 % (28138)Termination reason: Unknown
% 2.50/1.85 % (28138)Termination phase: Saturation
% 2.50/1.85
% 2.50/1.85 % (28138)Memory used [KB]: 7164
% 2.50/1.85 % (28138)Time elapsed: 0.043 s
% 2.50/1.85 % (28138)Instructions burned: 149 (million)
% 2.50/1.85 % (28138)------------------------------
% 2.50/1.85 % (28138)------------------------------
% 2.50/1.85 % (28142)Instruction limit reached!
% 2.50/1.85 % (28142)------------------------------
% 2.50/1.85 % (28142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.85 % (28142)Termination reason: Unknown
% 2.50/1.85 % (28142)Termination phase: Property scanning
% 2.50/1.85
% 2.50/1.85 % (28142)Memory used [KB]: 1791
% 2.50/1.85 % (28142)Time elapsed: 0.013 s
% 2.50/1.85 % (28142)Instructions burned: 47 (million)
% 2.50/1.85 % (28142)------------------------------
% 2.50/1.85 % (28142)------------------------------
% 2.50/1.85 % (28144)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_27992 for (2996ds/432Mi)
% 2.50/1.86 % (28143)Instruction limit reached!
% 2.50/1.86 % (28143)------------------------------
% 2.50/1.86 % (28143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.86 % (28143)Termination reason: Unknown
% 2.50/1.86 % (28143)Termination phase: SInE selection
% 2.50/1.86
% 2.50/1.86 % (28143)Memory used [KB]: 1791
% 2.50/1.86 % (28143)Time elapsed: 0.013 s
% 2.50/1.86 % (28143)Instructions burned: 45 (million)
% 2.50/1.86 % (28143)------------------------------
% 2.50/1.86 % (28143)------------------------------
% 2.50/1.86 % (28145)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27992 for (2996ds/62Mi)
% 2.50/1.86 % (28123)Instruction limit reached!
% 2.50/1.86 % (28123)------------------------------
% 2.50/1.86 % (28123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.86 % (28123)Termination reason: Unknown
% 2.50/1.86 % (28123)Termination phase: Saturation
% 2.50/1.86
% 2.50/1.86 % (28123)Memory used [KB]: 8315
% 2.50/1.86 % (28123)Time elapsed: 0.269 s
% 2.50/1.86 % (28123)Instructions burned: 879 (million)
% 2.50/1.86 % (28123)------------------------------
% 2.50/1.86 % (28123)------------------------------
% 2.50/1.87 % (28146)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_27992 for (2996ds/31Mi)
% 2.50/1.87 % (28147)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27992 for (2996ds/96Mi)
% 2.50/1.87 % (28145)Instruction limit reached!
% 2.50/1.87 % (28145)------------------------------
% 2.50/1.87 % (28145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.87 % (28145)Termination reason: Unknown
% 2.50/1.87 % (28145)Termination phase: Property scanning
% 2.50/1.87
% 2.50/1.87 % (28145)Memory used [KB]: 1791
% 2.50/1.87 % (28145)Time elapsed: 0.017 s
% 2.50/1.87 % (28145)Instructions burned: 65 (million)
% 2.50/1.87 % (28145)------------------------------
% 2.50/1.87 % (28145)------------------------------
% 2.50/1.88 % (28146)Instruction limit reached!
% 2.50/1.88 % (28146)------------------------------
% 2.50/1.88 % (28146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.88 % (28146)Termination reason: Unknown
% 2.50/1.88 % (28146)Termination phase: Property scanning
% 2.50/1.88
% 2.50/1.88 % (28146)Memory used [KB]: 1791
% 2.50/1.88 % (28146)Time elapsed: 0.010 s
% 2.50/1.88 % (28146)Instructions burned: 32 (million)
% 2.50/1.88 % (28146)------------------------------
% 2.50/1.88 % (28146)------------------------------
% 2.50/1.88 % (28148)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_27992 for (2996ds/453Mi)
% 2.50/1.89 % (28149)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_27992 for (2996ds/71Mi)
% 2.50/1.90 % (28134)Instruction limit reached!
% 2.50/1.90 % (28134)------------------------------
% 2.50/1.90 % (28134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.90 % (28134)Termination reason: Unknown
% 2.50/1.90 % (28134)Termination phase: Saturation
% 2.50/1.90
% 2.50/1.90 % (28134)Memory used [KB]: 6652
% 2.50/1.90 % (28134)Time elapsed: 0.116 s
% 2.50/1.90 % (28134)Instructions burned: 448 (million)
% 2.50/1.90 % (28134)------------------------------
% 2.50/1.90 % (28134)------------------------------
% 2.50/1.90 % (28147)Instruction limit reached!
% 2.50/1.90 % (28147)------------------------------
% 2.50/1.90 % (28147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.90 % (28147)Termination reason: Unknown
% 2.50/1.90 % (28147)Termination phase: Saturation
% 2.50/1.90
% 2.50/1.90 % (28147)Memory used [KB]: 6652
% 2.50/1.90 % (28147)Time elapsed: 0.026 s
% 2.50/1.90 % (28147)Instructions burned: 97 (million)
% 2.50/1.90 % (28147)------------------------------
% 2.50/1.90 % (28147)------------------------------
% 2.50/1.91 % (28149)Instruction limit reached!
% 2.50/1.91 % (28149)------------------------------
% 2.50/1.91 % (28149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.91 % (28149)Termination reason: Unknown
% 2.50/1.91 % (28149)Termination phase: Property scanning
% 2.50/1.91
% 2.50/1.91 % (28149)Memory used [KB]: 1918
% 2.50/1.91 % (28149)Time elapsed: 0.022 s
% 2.50/1.91 % (28149)Instructions burned: 73 (million)
% 2.50/1.91 % (28149)------------------------------
% 2.50/1.91 % (28149)------------------------------
% 2.50/1.91 % (28150)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/83Mi)
% 2.50/1.91 % (28151)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/11Mi)
% 2.50/1.91 % (28151)Instruction limit reached!
% 2.50/1.91 % (28151)------------------------------
% 2.50/1.91 % (28151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.91 % (28151)Termination reason: Unknown
% 2.50/1.91 % (28151)Termination phase: shuffling
% 2.50/1.91
% 2.50/1.91 % (28151)Memory used [KB]: 1407
% 2.50/1.91 % (28151)Time elapsed: 0.004 s
% 2.50/1.91 % (28151)Instructions burned: 12 (million)
% 2.50/1.91 % (28151)------------------------------
% 2.50/1.91 % (28151)------------------------------
% 2.50/1.92 % (28152)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_27992 for (2995ds/41Mi)
% 2.50/1.92 % (28153)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/6Mi)
% 2.50/1.92 % (28153)Instruction limit reached!
% 2.50/1.92 % (28153)------------------------------
% 2.50/1.92 % (28153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.92 % (28153)Termination reason: Unknown
% 2.50/1.92 % (28153)Termination phase: shuffling
% 2.50/1.92
% 2.50/1.92 % (28153)Memory used [KB]: 1407
% 2.50/1.92 % (28153)Time elapsed: 0.003 s
% 2.50/1.92 % (28153)Instructions burned: 7 (million)
% 2.50/1.92 % (28153)------------------------------
% 2.50/1.92 % (28153)------------------------------
% 2.50/1.93 % (28152)Instruction limit reached!
% 2.50/1.93 % (28152)------------------------------
% 2.50/1.93 % (28152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.93 % (28152)Termination reason: Unknown
% 2.50/1.93 % (28152)Termination phase: Property scanning
% 2.50/1.93
% 2.50/1.93 % (28152)Memory used [KB]: 1791
% 2.50/1.93 % (28152)Time elapsed: 0.013 s
% 2.50/1.93 % (28152)Instructions burned: 41 (million)
% 2.50/1.93 % (28152)------------------------------
% 2.50/1.93 % (28152)------------------------------
% 2.50/1.93 % (28150)Instruction limit reached!
% 2.50/1.93 % (28150)------------------------------
% 2.50/1.93 % (28150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.93 % (28150)Termination reason: Unknown
% 2.50/1.93 % (28150)Termination phase: Property scanning
% 2.50/1.93
% 2.50/1.93 % (28150)Memory used [KB]: 1918
% 2.50/1.93 % (28150)Time elapsed: 0.024 s
% 2.50/1.93 % (28150)Instructions burned: 86 (million)
% 2.50/1.93 % (28150)------------------------------
% 2.50/1.93 % (28150)------------------------------
% 2.50/1.93 % (28154)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/150Mi)
% 2.50/1.94 % (28155)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/343Mi)
% 2.50/1.94 % (28156)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_27992 for (2995ds/109Mi)
% 2.50/1.95 % (28137)Instruction limit reached!
% 2.50/1.95 % (28137)------------------------------
% 2.50/1.95 % (28137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.95 % (28137)Termination reason: Unknown
% 2.50/1.95 % (28137)Termination phase: Saturation
% 2.50/1.95
% 2.50/1.95 % (28137)Memory used [KB]: 7419
% 2.50/1.95 % (28137)Time elapsed: 0.148 s
% 2.50/1.95 % (28137)Instructions burned: 507 (million)
% 2.50/1.95 % (28137)------------------------------
% 2.50/1.95 % (28137)------------------------------
% 2.50/1.96 % (28157)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_27992 for (2995ds/253Mi)
% 2.50/1.96 % (28144)Instruction limit reached!
% 2.50/1.96 % (28144)------------------------------
% 2.50/1.96 % (28144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.96 % (28144)Termination reason: Unknown
% 2.50/1.96 % (28144)Termination phase: Saturation
% 2.50/1.96
% 2.50/1.96 % (28144)Memory used [KB]: 2942
% 2.50/1.96 % (28144)Time elapsed: 0.106 s
% 2.50/1.96 % (28144)Instructions burned: 435 (million)
% 2.50/1.96 % (28144)------------------------------
% 2.50/1.96 % (28144)------------------------------
% 2.50/1.97 % (28158)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27992 for (2995ds/140Mi)
% 2.50/1.97 % (28156)Instruction limit reached!
% 2.50/1.97 % (28156)------------------------------
% 2.50/1.97 % (28156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.97 % (28156)Termination reason: Unknown
% 2.50/1.97 % (28156)Termination phase: Saturation
% 2.50/1.97
% 2.50/1.97 % (28156)Memory used [KB]: 6780
% 2.50/1.97 % (28156)Time elapsed: 0.032 s
% 2.50/1.97 % (28156)Instructions burned: 111 (million)
% 2.50/1.97 % (28156)------------------------------
% 2.50/1.97 % (28156)------------------------------
% 2.50/1.97 % (28154)Instruction limit reached!
% 2.50/1.97 % (28154)------------------------------
% 2.50/1.97 % (28154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.97 % (28154)Termination reason: Unknown
% 2.50/1.97 % (28154)Termination phase: Saturation
% 2.50/1.97
% 2.50/1.97 % (28154)Memory used [KB]: 7803
% 2.50/1.97 % (28154)Time elapsed: 0.044 s
% 2.50/1.97 % (28154)Instructions burned: 150 (million)
% 2.50/1.97 % (28154)------------------------------
% 2.50/1.97 % (28154)------------------------------
% 2.50/1.98 % (28159)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_27992 for (2995ds/614Mi)
% 2.50/1.98 % (28160)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_27992 for (2995ds/202Mi)
% 2.50/1.99 % (28148)Instruction limit reached!
% 2.50/1.99 % (28148)------------------------------
% 2.50/1.99 % (28148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.50/1.99 % (28148)Termination reason: Unknown
% 2.50/1.99 % (28148)Termination phase: Saturation
% 2.50/1.99
% 2.50/1.99 % (28148)Memory used [KB]: 6652
% 2.50/1.99 % (28148)Time elapsed: 0.108 s
% 2.50/1.99 % (28148)Instructions burned: 454 (million)
% 2.50/1.99 % (28148)------------------------------
% 2.50/1.99 % (28148)------------------------------
% 2.50/2.00 % (28161)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_27992 for (2994ds/339Mi)
% 6.10/2.02 % (28158)Instruction limit reached!
% 6.10/2.02 % (28158)------------------------------
% 6.10/2.02 % (28158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.02 % (28158)Termination reason: Unknown
% 6.10/2.02 % (28158)Termination phase: Saturation
% 6.10/2.02
% 6.10/2.02 % (28158)Memory used [KB]: 6524
% 6.10/2.02 % (28158)Time elapsed: 0.039 s
% 6.10/2.02 % (28158)Instructions burned: 141 (million)
% 6.10/2.02 % (28158)------------------------------
% 6.10/2.02 % (28158)------------------------------
% 6.10/2.03 % (28162)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_27992 for (2994ds/283Mi)
% 6.10/2.04 % (28155)Instruction limit reached!
% 6.10/2.04 % (28155)------------------------------
% 6.10/2.04 % (28155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.04 % (28155)Termination reason: Unknown
% 6.10/2.04 % (28155)Termination phase: Saturation
% 6.10/2.04
% 6.10/2.04 % (28155)Memory used [KB]: 7803
% 6.10/2.04 % (28155)Time elapsed: 0.101 s
% 6.10/2.04 % (28155)Instructions burned: 345 (million)
% 6.10/2.04 % (28155)------------------------------
% 6.10/2.04 % (28155)------------------------------
% 6.10/2.04 % (28160)Instruction limit reached!
% 6.10/2.04 % (28160)------------------------------
% 6.10/2.04 % (28160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.04 % (28160)Termination reason: Unknown
% 6.10/2.04 % (28160)Termination phase: Saturation
% 6.10/2.04
% 6.10/2.04 % (28160)Memory used [KB]: 8443
% 6.10/2.04 % (28160)Time elapsed: 0.061 s
% 6.10/2.04 % (28160)Instructions burned: 204 (million)
% 6.10/2.04 % (28160)------------------------------
% 6.10/2.04 % (28160)------------------------------
% 6.10/2.04 % (28157)Instruction limit reached!
% 6.10/2.04 % (28157)------------------------------
% 6.10/2.04 % (28157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.04 % (28157)Termination reason: Unknown
% 6.10/2.04 % (28157)Termination phase: Saturation
% 6.10/2.04
% 6.10/2.04 % (28157)Memory used [KB]: 8187
% 6.10/2.04 % (28157)Time elapsed: 0.078 s
% 6.10/2.04 % (28157)Instructions burned: 253 (million)
% 6.10/2.04 % (28157)------------------------------
% 6.10/2.04 % (28157)------------------------------
% 6.10/2.05 % (28163)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27992 for (2994ds/134Mi)
% 6.10/2.05 % (28164)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27992 for (2994ds/298Mi)
% 6.10/2.05 % (28165)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27992 for (2994ds/192Mi)
% 6.10/2.08 % (28163)Instruction limit reached!
% 6.10/2.08 % (28163)------------------------------
% 6.10/2.08 % (28163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.08 % (28163)Termination reason: Unknown
% 6.10/2.08 % (28163)Termination phase: Saturation
% 6.10/2.08
% 6.10/2.08 % (28163)Memory used [KB]: 7036
% 6.10/2.08 % (28163)Time elapsed: 0.036 s
% 6.10/2.08 % (28163)Instructions burned: 134 (million)
% 6.10/2.08 % (28163)------------------------------
% 6.10/2.08 % (28163)------------------------------
% 6.10/2.09 % (28166)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_27992 for (2993ds/258Mi)
% 6.10/2.09 % (28161)Instruction limit reached!
% 6.10/2.09 % (28161)------------------------------
% 6.10/2.09 % (28161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.09 % (28161)Termination reason: Unknown
% 6.10/2.09 % (28161)Termination phase: Saturation
% 6.10/2.09
% 6.10/2.09 % (28161)Memory used [KB]: 7803
% 6.10/2.09 % (28161)Time elapsed: 0.097 s
% 6.10/2.09 % (28161)Instructions burned: 340 (million)
% 6.10/2.09 % (28161)------------------------------
% 6.10/2.09 % (28161)------------------------------
% 6.10/2.10 % (28162)Instruction limit reached!
% 6.10/2.10 % (28162)------------------------------
% 6.10/2.10 % (28162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.10 % (28162)Termination reason: Unknown
% 6.10/2.10 % (28162)Termination phase: Saturation
% 6.10/2.10
% 6.10/2.10 % (28162)Memory used [KB]: 9083
% 6.10/2.10 % (28162)Time elapsed: 0.070 s
% 6.10/2.10 % (28162)Instructions burned: 285 (million)
% 6.10/2.10 % (28162)------------------------------
% 6.10/2.10 % (28162)------------------------------
% 6.10/2.10 % (28167)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_27992 for (2993ds/90Mi)
% 6.10/2.11 % (28165)Instruction limit reached!
% 6.10/2.11 % (28165)------------------------------
% 6.10/2.11 % (28165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.10/2.11 % (28165)Termination reason: Unknown
% 6.10/2.11 % (28165)Termination phase: Saturation
% 6.10/2.11
% 6.10/2.11 % (28165)Memory used [KB]: 7419
% 6.10/2.11 % (28165)Time elapsed: 0.054 s
% 6.10/2.11 % (28165)Instructions burned: 194 (million)
% 6.10/2.11 % (28165)------------------------------
% 6.10/2.11 % (28165)------------------------------
% 6.10/2.11 % (28168)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_27992 for (2993ds/231Mi)
% 6.70/2.12 % (28169)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_27992 for (2993ds/458Mi)
% 6.70/2.13 % (28164)Instruction limit reached!
% 6.70/2.13 % (28164)------------------------------
% 6.70/2.13 % (28164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.13 % (28164)Termination reason: Unknown
% 6.70/2.13 % (28164)Termination phase: Saturation
% 6.70/2.13
% 6.70/2.13 % (28164)Memory used [KB]: 6652
% 6.70/2.13 % (28164)Time elapsed: 0.075 s
% 6.70/2.13 % (28164)Instructions burned: 300 (million)
% 6.70/2.13 % (28164)------------------------------
% 6.70/2.13 % (28164)------------------------------
% 6.70/2.13 % (28167)Instruction limit reached!
% 6.70/2.13 % (28167)------------------------------
% 6.70/2.13 % (28167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.13 % (28167)Termination reason: Unknown
% 6.70/2.13 % (28167)Termination phase: Saturation
% 6.70/2.13
% 6.70/2.13 % (28167)Memory used [KB]: 6908
% 6.70/2.13 % (28167)Time elapsed: 0.024 s
% 6.70/2.13 % (28167)Instructions burned: 90 (million)
% 6.70/2.13 % (28167)------------------------------
% 6.70/2.13 % (28167)------------------------------
% 6.70/2.14 % (28170)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_27992 for (2993ds/31Mi)
% 6.70/2.14 % (28171)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_27992 for (2993ds/297Mi)
% 6.70/2.14 % (28170)Instruction limit reached!
% 6.70/2.14 % (28170)------------------------------
% 6.70/2.14 % (28170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.14 % (28170)Termination reason: Unknown
% 6.70/2.14 % (28170)Termination phase: Property scanning
% 6.70/2.14
% 6.70/2.14 % (28170)Memory used [KB]: 1663
% 6.70/2.14 % (28170)Time elapsed: 0.009 s
% 6.70/2.14 % (28170)Instructions burned: 31 (million)
% 6.70/2.14 % (28170)------------------------------
% 6.70/2.14 % (28170)------------------------------
% 6.70/2.15 % (28172)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_27992 for (2993ds/987Mi)
% 6.70/2.16 % (28166)Instruction limit reached!
% 6.70/2.16 % (28166)------------------------------
% 6.70/2.16 % (28166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.16 % (28166)Termination reason: Unknown
% 6.70/2.16 % (28166)Termination phase: Saturation
% 6.70/2.16
% 6.70/2.16 % (28166)Memory used [KB]: 7547
% 6.70/2.16 % (28166)Time elapsed: 0.073 s
% 6.70/2.16 % (28166)Instructions burned: 260 (million)
% 6.70/2.16 % (28166)------------------------------
% 6.70/2.16 % (28166)------------------------------
% 6.70/2.16 % (28159)Instruction limit reached!
% 6.70/2.16 % (28159)------------------------------
% 6.70/2.16 % (28159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.16 % (28159)Termination reason: Unknown
% 6.70/2.16 % (28159)Termination phase: Saturation
% 6.70/2.16
% 6.70/2.16 % (28159)Memory used [KB]: 8315
% 6.70/2.16 % (28159)Time elapsed: 0.184 s
% 6.70/2.16 % (28159)Instructions burned: 615 (million)
% 6.70/2.16 % (28159)------------------------------
% 6.70/2.16 % (28159)------------------------------
% 6.70/2.17 % (28168)Instruction limit reached!
% 6.70/2.17 % (28168)------------------------------
% 6.70/2.17 % (28168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.17 % (28168)Termination reason: Unknown
% 6.70/2.17 % (28168)Termination phase: Saturation
% 6.70/2.17
% 6.70/2.17 % (28168)Memory used [KB]: 10618
% 6.70/2.17 % (28168)Time elapsed: 0.065 s
% 6.70/2.17 % (28168)Instructions burned: 233 (million)
% 6.70/2.17 % (28168)------------------------------
% 6.70/2.17 % (28168)------------------------------
% 6.70/2.17 % (28173)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_27992 for (2993ds/182Mi)
% 6.70/2.17 % (28141)Instruction limit reached!
% 6.70/2.17 % (28141)------------------------------
% 6.70/2.17 % (28141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.17 % (28141)Termination reason: Unknown
% 6.70/2.17 % (28141)Termination phase: Saturation
% 6.70/2.17
% 6.70/2.17 % (28141)Memory used [KB]: 10106
% 6.70/2.17 % (28141)Time elapsed: 0.341 s
% 6.70/2.17 % (28141)Instructions burned: 1089 (million)
% 6.70/2.17 % (28141)------------------------------
% 6.70/2.17 % (28141)------------------------------
% 6.70/2.17 % (28174)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_27992 for (2993ds/182Mi)
% 6.70/2.18 % (28175)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_27992 for (2993ds/154Mi)
% 6.70/2.18 % (28176)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_27992 for (2993ds/79Mi)
% 7.12/2.20 % (28176)Instruction limit reached!
% 7.12/2.20 % (28176)------------------------------
% 7.12/2.20 % (28176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.20 % (28176)Termination reason: Unknown
% 7.12/2.20 % (28176)Termination phase: Saturation
% 7.12/2.20
% 7.12/2.20 % (28176)Memory used [KB]: 6524
% 7.12/2.20 % (28176)Time elapsed: 0.022 s
% 7.12/2.20 % (28176)Instructions burned: 81 (million)
% 7.12/2.20 % (28176)------------------------------
% 7.12/2.20 % (28176)------------------------------
% 7.12/2.21 % (28171)Instruction limit reached!
% 7.12/2.21 % (28171)------------------------------
% 7.12/2.21 % (28171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.21 % (28171)Termination reason: Unknown
% 7.12/2.21 % (28171)Termination phase: Saturation
% 7.12/2.21
% 7.12/2.21 % (28171)Memory used [KB]: 8187
% 7.12/2.21 % (28171)Time elapsed: 0.073 s
% 7.12/2.21 % (28171)Instructions burned: 297 (million)
% 7.12/2.21 % (28171)------------------------------
% 7.12/2.21 % (28171)------------------------------
% 7.12/2.21 % (28177)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_27992 for (2992ds/216Mi)
% 7.12/2.22 % (28178)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_27992 for (2992ds/114Mi)
% 7.12/2.22 % (28175)Instruction limit reached!
% 7.12/2.22 % (28175)------------------------------
% 7.12/2.22 % (28175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.22 % (28175)Termination reason: Unknown
% 7.12/2.22 % (28175)Termination phase: Saturation
% 7.12/2.22
% 7.12/2.22 % (28175)Memory used [KB]: 6524
% 7.12/2.22 % (28175)Time elapsed: 0.039 s
% 7.12/2.22 % (28175)Instructions burned: 155 (million)
% 7.12/2.22 % (28175)------------------------------
% 7.12/2.22 % (28175)------------------------------
% 7.12/2.22 % (28173)Instruction limit reached!
% 7.12/2.22 % (28173)------------------------------
% 7.12/2.22 % (28173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.22 % (28173)Termination reason: Unknown
% 7.12/2.22 % (28173)Termination phase: Saturation
% 7.12/2.22
% 7.12/2.22 % (28173)Memory used [KB]: 7419
% 7.12/2.22 % (28173)Time elapsed: 0.050 s
% 7.12/2.22 % (28173)Instructions burned: 183 (million)
% 7.12/2.22 % (28173)------------------------------
% 7.12/2.22 % (28173)------------------------------
% 7.12/2.23 % (28174)Instruction limit reached!
% 7.12/2.23 % (28174)------------------------------
% 7.12/2.23 % (28174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.23 % (28174)Termination reason: Unknown
% 7.12/2.23 % (28174)Termination phase: Saturation
% 7.12/2.23
% 7.12/2.23 % (28174)Memory used [KB]: 9466
% 7.12/2.23 % (28174)Time elapsed: 0.054 s
% 7.12/2.23 % (28174)Instructions burned: 182 (million)
% 7.12/2.23 % (28174)------------------------------
% 7.12/2.23 % (28174)------------------------------
% 7.12/2.23 % (28179)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_27992 for (2992ds/922Mi)
% 7.12/2.23 % (28180)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_27992 for (2992ds/182Mi)
% 7.12/2.24 % (28181)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_27992 for (2992ds/164Mi)
% 7.12/2.25 % (28178)Instruction limit reached!
% 7.12/2.25 % (28178)------------------------------
% 7.12/2.25 % (28178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.25 % (28178)Termination reason: Unknown
% 7.12/2.25 % (28178)Termination phase: Saturation
% 7.12/2.25
% 7.12/2.25 % (28178)Memory used [KB]: 6780
% 7.12/2.25 % (28178)Time elapsed: 0.031 s
% 7.12/2.25 % (28178)Instructions burned: 116 (million)
% 7.12/2.25 % (28178)------------------------------
% 7.12/2.25 % (28178)------------------------------
% 7.12/2.26 % (28182)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_27992 for (2992ds/50Mi)
% 7.12/2.26 % (28169)Instruction limit reached!
% 7.12/2.26 % (28169)------------------------------
% 7.12/2.26 % (28169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.26 % (28169)Termination reason: Unknown
% 7.12/2.26 % (28169)Termination phase: Saturation
% 7.12/2.26
% 7.12/2.26 % (28169)Memory used [KB]: 7931
% 7.12/2.26 % (28169)Time elapsed: 0.147 s
% 7.12/2.26 % (28169)Instructions burned: 458 (million)
% 7.12/2.26 % (28169)------------------------------
% 7.12/2.26 % (28169)------------------------------
% 7.12/2.26 % (28177)Instruction limit reached!
% 7.12/2.26 % (28177)------------------------------
% 7.12/2.26 % (28177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.26 % (28177)Termination reason: Unknown
% 7.12/2.26 % (28177)Termination phase: Saturation
% 7.12/2.26
% 7.12/2.26 % (28177)Memory used [KB]: 6652
% 7.12/2.26 % (28177)Time elapsed: 0.053 s
% 7.12/2.26 % (28177)Instructions burned: 217 (million)
% 7.12/2.26 % (28177)------------------------------
% 7.12/2.26 % (28177)------------------------------
% 7.12/2.27 % (28182)Instruction limit reached!
% 7.12/2.27 % (28182)------------------------------
% 7.12/2.27 % (28182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.27 % (28182)Termination reason: Unknown
% 7.12/2.27 % (28182)Termination phase: Property scanning
% 7.12/2.27
% 7.12/2.27 % (28182)Memory used [KB]: 1791
% 7.12/2.27 % (28182)Time elapsed: 0.014 s
% 7.12/2.27 % (28182)Instructions burned: 51 (million)
% 7.12/2.27 % (28182)------------------------------
% 7.12/2.27 % (28182)------------------------------
% 7.12/2.27 % (28183)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_27992 for (2992ds/368Mi)
% 7.12/2.27 % (28184)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_27992 for (2992ds/1021Mi)
% 7.12/2.28 % (28180)Instruction limit reached!
% 7.12/2.28 % (28180)------------------------------
% 7.12/2.28 % (28180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.28 % (28180)Termination reason: Unknown
% 7.12/2.28 % (28180)Termination phase: Saturation
% 7.12/2.28
% 7.12/2.28 % (28180)Memory used [KB]: 6524
% 7.12/2.28 % (28180)Time elapsed: 0.046 s
% 7.12/2.28 % (28180)Instructions burned: 187 (million)
% 7.12/2.28 % (28180)------------------------------
% 7.12/2.28 % (28180)------------------------------
% 7.12/2.28 % (28185)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_27992 for (2992ds/267Mi)
% 7.12/2.28 % (28181)Instruction limit reached!
% 7.12/2.28 % (28181)------------------------------
% 7.12/2.28 % (28181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.28 % (28181)Termination reason: Unknown
% 7.12/2.28 % (28181)Termination phase: Saturation
% 7.12/2.28
% 7.12/2.28 % (28181)Memory used [KB]: 2302
% 7.12/2.28 % (28181)Time elapsed: 0.046 s
% 7.12/2.28 % (28181)Instructions burned: 167 (million)
% 7.12/2.28 % (28181)------------------------------
% 7.12/2.28 % (28181)------------------------------
% 7.12/2.29 % (28186)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_27992 for (2992ds/204Mi)
% 7.12/2.29 % (28187)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_27992 for (2992ds/26Mi)
% 7.80/2.30 % (28187)Instruction limit reached!
% 7.80/2.30 % (28187)------------------------------
% 7.80/2.30 % (28187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.30 % (28187)Termination reason: Unknown
% 7.80/2.30 % (28187)Termination phase: Property scanning
% 7.80/2.30
% 7.80/2.30 % (28187)Memory used [KB]: 1663
% 7.80/2.30 % (28187)Time elapsed: 0.008 s
% 7.80/2.30 % (28187)Instructions burned: 26 (million)
% 7.80/2.30 % (28187)------------------------------
% 7.80/2.30 % (28187)------------------------------
% 7.80/2.31 % (28188)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_27992 for (2991ds/53Mi)
% 7.80/2.32 % (28188)Instruction limit reached!
% 7.80/2.32 % (28188)------------------------------
% 7.80/2.32 % (28188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.32 % (28188)Termination reason: Unknown
% 7.80/2.32 % (28188)Termination phase: Function definition elimination
% 7.80/2.32
% 7.80/2.32 % (28188)Memory used [KB]: 1791
% 7.80/2.32 % (28188)Time elapsed: 0.015 s
% 7.80/2.32 % (28188)Instructions burned: 55 (million)
% 7.80/2.32 % (28188)------------------------------
% 7.80/2.32 % (28188)------------------------------
% 7.80/2.33 % (28189)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_27992 for (2991ds/4436Mi)
% 7.80/2.34 % (28186)Instruction limit reached!
% 7.80/2.34 % (28186)------------------------------
% 7.80/2.34 % (28186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.34 % (28186)Termination reason: Unknown
% 7.80/2.34 % (28186)Termination phase: Saturation
% 7.80/2.34
% 7.80/2.34 % (28186)Memory used [KB]: 7419
% 7.80/2.34 % (28186)Time elapsed: 0.055 s
% 7.80/2.34 % (28186)Instructions burned: 204 (million)
% 7.80/2.34 % (28186)------------------------------
% 7.80/2.34 % (28186)------------------------------
% 7.80/2.35 % (28185)Instruction limit reached!
% 7.80/2.35 % (28185)------------------------------
% 7.80/2.35 % (28185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.35 % (28185)Termination reason: Unknown
% 7.80/2.35 % (28185)Termination phase: Saturation
% 7.80/2.35
% 7.80/2.35 % (28185)Memory used [KB]: 9083
% 7.80/2.35 % (28185)Time elapsed: 0.066 s
% 7.80/2.35 % (28185)Instructions burned: 267 (million)
% 7.80/2.35 % (28185)------------------------------
% 7.80/2.35 % (28185)------------------------------
% 7.80/2.35 % (28190)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_27992 for (2991ds/1539Mi)
% 7.80/2.35 % (28191)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_27992 for (2991ds/408Mi)
% 7.80/2.38 % (28183)Instruction limit reached!
% 7.80/2.38 % (28183)------------------------------
% 7.80/2.38 % (28183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.38 % (28183)Termination reason: Unknown
% 7.80/2.38 % (28183)Termination phase: Saturation
% 7.80/2.38
% 7.80/2.38 % (28183)Memory used [KB]: 7803
% 7.80/2.38 % (28183)Time elapsed: 0.110 s
% 7.80/2.38 % (28183)Instructions burned: 369 (million)
% 7.80/2.38 % (28183)------------------------------
% 7.80/2.38 % (28183)------------------------------
% 7.80/2.39 % (28172)Instruction limit reached!
% 7.80/2.39 % (28172)------------------------------
% 7.80/2.39 % (28172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.80/2.39 % (28172)Termination reason: Unknown
% 7.80/2.39 % (28172)Termination phase: Saturation
% 7.80/2.39
% 7.80/2.39 % (28172)Memory used [KB]: 9594
% 7.80/2.39 % (28172)Time elapsed: 0.235 s
% 7.80/2.39 % (28172)Instructions burned: 988 (million)
% 7.80/2.39 % (28172)------------------------------
% 7.80/2.39 % (28172)------------------------------
% 7.80/2.39 % (28192)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_27992 for (2991ds/5205Mi)
% 8.34/2.40 % (28193)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_27992 for (2991ds/1913Mi)
% 8.34/2.43 % (28184)First to succeed.
% 8.34/2.43 % (28184)Refutation found. Thanks to Tanya!
% 8.34/2.43 % SZS status Theorem for DTF2THF_27992
% 8.34/2.43 % SZS output start Proof for DTF2THF_27992
% 8.34/2.43 thf(func_def_0, type, in: $i > $i > $o).
% 8.34/2.43 thf(func_def_1, type, exu: ($i > $o) > $o).
% 8.34/2.43 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 8.34/2.43 thf(func_def_8, type, powerset: $i > $i).
% 8.34/2.43 thf(func_def_10, type, setunion: $i > $i).
% 8.34/2.43 thf(func_def_19, type, descr: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_26, type, prop2set: $o > $i).
% 8.34/2.43 thf(func_def_36, type, nonempty: $i > $o).
% 8.34/2.43 thf(func_def_69, type, set2prop: $i > $o).
% 8.34/2.43 thf(func_def_88, type, subset: $i > $i > $o).
% 8.34/2.43 thf(func_def_89, type, disjoint: $i > $i > $o).
% 8.34/2.43 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 8.34/2.43 thf(func_def_114, type, binunion: $i > $i > $i).
% 8.34/2.43 thf(func_def_122, type, binintersect: $i > $i > $i).
% 8.34/2.43 thf(func_def_135, type, regular: $i > $o).
% 8.34/2.43 thf(func_def_136, type, setminus: $i > $i > $i).
% 8.34/2.43 thf(func_def_147, type, symdiff: $i > $i > $i).
% 8.34/2.43 thf(func_def_153, type, iskpair: $i > $o).
% 8.34/2.43 thf(func_def_158, type, kpair: $i > $i > $i).
% 8.34/2.43 thf(func_def_160, type, cartprod: $i > $i > $i).
% 8.34/2.43 thf(func_def_177, type, singleton: $i > $o).
% 8.34/2.43 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 8.34/2.43 thf(func_def_193, type, sP1: $i > $o > $i > $i > $o).
% 8.34/2.43 thf(func_def_194, type, sP2: $i > $i > $i > $o).
% 8.34/2.43 thf(func_def_199, type, sP7: $i > ($i > $o) > ($i > $o) > $i > $o).
% 8.34/2.43 thf(func_def_202, type, sP10: $i > $i > $o).
% 8.34/2.43 thf(func_def_208, type, sP16: $i > ($i > $i > $o) > $o).
% 8.34/2.43 thf(func_def_210, type, sP18: $o > $i > $i > $o).
% 8.34/2.43 thf(func_def_212, type, sP20: $i > $o).
% 8.34/2.43 thf(func_def_214, type, sP22: ($i > $o) > $i > $o).
% 8.34/2.43 thf(func_def_215, type, sP23: $i > ($i > $o) > $o).
% 8.34/2.43 thf(func_def_219, type, sP27: $o > $i > $i > $o).
% 8.34/2.43 thf(func_def_220, type, sP28: $i > $i > $i > $o).
% 8.34/2.43 thf(func_def_226, type, sP34: $i > $i > $i > $o).
% 8.34/2.43 thf(func_def_227, type, sP35: $i > $i > $o).
% 8.34/2.43 thf(func_def_228, type, sP36: $i > $o).
% 8.34/2.43 thf(func_def_229, type, sP37: $i > $i > $o).
% 8.34/2.43 thf(func_def_230, type, sP38: $i > $i > $o).
% 8.34/2.43 thf(func_def_237, type, sK45: $i > $o).
% 8.34/2.43 thf(func_def_240, type, sK48: $i > $o).
% 8.34/2.43 thf(func_def_241, type, sK49: $i > $i).
% 8.34/2.43 thf(func_def_242, type, sK50: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_243, type, sK51: $i > $i > $i > $o).
% 8.34/2.43 thf(func_def_259, type, sK67: $i > $i > $i).
% 8.34/2.43 thf(func_def_278, type, sK86: $i > $i > $i).
% 8.34/2.43 thf(func_def_286, type, sK94: $i > $i).
% 8.34/2.43 thf(func_def_305, type, sK113: $i > $o).
% 8.34/2.43 thf(func_def_306, type, sK114: $i > $o).
% 8.34/2.43 thf(func_def_307, type, sK115: ($i > $o) > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_308, type, sK116: ($i > $o) > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_309, type, sK117: $i > $o).
% 8.34/2.43 thf(func_def_312, type, sK120: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_316, type, sK124: $i > $i > $i).
% 8.34/2.43 thf(func_def_325, type, sK133: $i > $i).
% 8.34/2.43 thf(func_def_327, type, sK135: $i > $i).
% 8.34/2.43 thf(func_def_339, type, sK147: $i > ($i > $o) > ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_340, type, sK148: $i > ($i > $o) > ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_343, type, sK151: $i > $o).
% 8.34/2.43 thf(func_def_344, type, sK152: $i > $o).
% 8.34/2.43 thf(func_def_349, type, sK157: $i > $o).
% 8.34/2.43 thf(func_def_356, type, sK164: $i > $o).
% 8.34/2.43 thf(func_def_357, type, sK165: $i > $i).
% 8.34/2.43 thf(func_def_358, type, sK166: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_367, type, sK175: $i > $o).
% 8.34/2.43 thf(func_def_371, type, sK179: $i > $i > $i).
% 8.34/2.43 thf(func_def_372, type, sK180: $i > $i > $i).
% 8.34/2.43 thf(func_def_377, type, sK185: $i > $o).
% 8.34/2.43 thf(func_def_379, type, sK187: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_386, type, sK194: $i > $i > $i).
% 8.34/2.43 thf(func_def_411, type, sK219: $i > $i).
% 8.34/2.43 thf(func_def_413, type, sK221: $i > $i).
% 8.34/2.43 thf(func_def_416, type, sK224: $i > $i > $i).
% 8.34/2.43 thf(func_def_428, type, sK236: $i > $i > $o).
% 8.34/2.43 thf(func_def_430, type, sK238: $i > ($i > $i > $o) > $i).
% 8.34/2.43 thf(func_def_431, type, sK239: $i > $i > ($i > $i > $o) > $i).
% 8.34/2.43 thf(func_def_432, type, sK240: $i > $i > ($i > $i > $o) > $i).
% 8.34/2.43 thf(func_def_433, type, sK241: $i > ($i > $i > $o) > $i).
% 8.34/2.43 thf(func_def_434, type, sK242: $i > $i > ($i > $i > $o) > $i).
% 8.34/2.43 thf(func_def_436, type, sK244: $i > $o).
% 8.34/2.43 thf(func_def_465, type, sK273: $i > $o).
% 8.34/2.43 thf(func_def_467, type, sK275: $i > $i).
% 8.34/2.43 thf(func_def_468, type, sK276: $i > $i).
% 8.34/2.43 thf(func_def_473, type, sK281: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_474, type, sK282: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_475, type, sK283: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_476, type, sK284: $i > $o).
% 8.34/2.43 thf(func_def_484, type, sK292: $i > $o).
% 8.34/2.43 thf(func_def_487, type, sK295: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_489, type, sK297: $i > $o).
% 8.34/2.43 thf(func_def_495, type, sK303: $i > $i > $i > $i).
% 8.34/2.43 thf(func_def_496, type, sK304: $i > $i > $i > $i).
% 8.34/2.43 thf(func_def_507, type, sK315: $i > $o).
% 8.34/2.43 thf(func_def_509, type, sK317: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_512, type, sK320: $i > $i > $i > $o).
% 8.34/2.43 thf(func_def_516, type, sK324: $i > $o).
% 8.34/2.43 thf(func_def_517, type, sK325: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_518, type, sK326: $i > $o).
% 8.34/2.43 thf(func_def_520, type, sK328: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_521, type, sK329: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_523, type, sK331: $i > $o).
% 8.34/2.43 thf(func_def_525, type, sK333: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_526, type, sK334: $i > $o).
% 8.34/2.43 thf(func_def_537, type, sK345: $i > $i > $i).
% 8.34/2.43 thf(func_def_541, type, sK349: $i > $i > $i).
% 8.34/2.43 thf(func_def_546, type, sK354: $i > $o).
% 8.34/2.43 thf(func_def_548, type, sK356: $i > $o).
% 8.34/2.43 thf(func_def_550, type, sK358: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_559, type, sK367: $i > $i).
% 8.34/2.43 thf(func_def_560, type, sK368: $i > $i).
% 8.34/2.43 thf(func_def_561, type, sK369: $i > $i).
% 8.34/2.43 thf(func_def_562, type, sK370: $i > $i > $i).
% 8.34/2.43 thf(func_def_563, type, sK371: $i > $i > $i).
% 8.34/2.43 thf(func_def_564, type, sK372: $i > $i > $i).
% 8.34/2.43 thf(func_def_565, type, sK373: $i > $i > $i).
% 8.34/2.43 thf(func_def_566, type, sK374: $i > $i > $i).
% 8.34/2.43 thf(func_def_567, type, sK375: $i > $i > $i > $i).
% 8.34/2.43 thf(func_def_568, type, sK376: $i > $i).
% 8.34/2.43 thf(func_def_569, type, sK377: $i > $i).
% 8.34/2.43 thf(func_def_570, type, sK378: $i > $i).
% 8.34/2.43 thf(func_def_571, type, sK379: $i > $i).
% 8.34/2.43 thf(func_def_572, type, sK380: $i > $i > $i).
% 8.34/2.43 thf(func_def_573, type, sK381: $i > $i > $i).
% 8.34/2.43 thf(func_def_574, type, sK382: $i > $i > $i).
% 8.34/2.43 thf(func_def_575, type, sK383: $i > $i > $i > $i).
% 8.34/2.43 thf(func_def_576, type, sK384: $i > $i > $i > $i).
% 8.34/2.43 thf(func_def_581, type, sK389: $i > $i > $i).
% 8.34/2.43 thf(func_def_599, type, sK407: $i > $o).
% 8.34/2.43 thf(func_def_605, type, sK413: $i > $i).
% 8.34/2.43 thf(func_def_613, type, sK421: $o > $i > $i > $i).
% 8.34/2.43 thf(func_def_619, type, sK427: $i > $o).
% 8.34/2.43 thf(func_def_629, type, sK437: $i > $o).
% 8.34/2.43 thf(func_def_633, type, sK441: $i > $o).
% 8.34/2.43 thf(func_def_636, type, sK444: $i > $o).
% 8.34/2.43 thf(func_def_637, type, sK445: $i > $o).
% 8.34/2.43 thf(func_def_638, type, sK446: ($i > $o) > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_639, type, sK447: ($i > $o) > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_646, type, sK454: $i > $o).
% 8.34/2.43 thf(func_def_651, type, sK459: $i > $o).
% 8.34/2.43 thf(func_def_654, type, sK462: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_656, type, sK464: $i > $o).
% 8.34/2.43 thf(func_def_658, type, sK466: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_660, type, sK468: $i > $i).
% 8.34/2.43 thf(func_def_661, type, sK469: $i > $i).
% 8.34/2.43 thf(func_def_662, type, sK470: $i > $i).
% 8.34/2.43 thf(func_def_666, type, sK474: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_667, type, sK475: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_668, type, sK476: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_670, type, sK478: ($i > $i > $o) > $i > $i > $i).
% 8.34/2.43 thf(func_def_671, type, sK479: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_672, type, sK480: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_673, type, sK481: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_674, type, sK482: $i > $i > $i).
% 8.34/2.43 thf(func_def_675, type, sK483: $i > $i > $i).
% 8.34/2.43 thf(func_def_676, type, sK484: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_677, type, sK485: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_679, type, sK487: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_680, type, sK488: $i > $i).
% 8.34/2.43 thf(func_def_681, type, sK489: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_682, type, sK490: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_683, type, sK491: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_684, type, sK492: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_685, type, sK493: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_686, type, sK494: $i > $i).
% 8.34/2.43 thf(func_def_688, type, sK496: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_689, type, sK497: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_690, type, sK498: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_691, type, sK499: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_692, type, sK500: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_693, type, sK501: $i > ($i > $o) > $i).
% 8.34/2.43 thf(func_def_694, type, sK502: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_695, type, sK503: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_696, type, sK504: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_697, type, sK505: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_698, type, sK506: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_699, type, sK507: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_700, type, sK508: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_701, type, sK509: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_702, type, sK510: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_703, type, sK511: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_704, type, sK512: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_705, type, sK513: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_707, type, sK515: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_708, type, sK516: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_709, type, sK517: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_710, type, sK518: ($i > $o) > $i).
% 8.34/2.43 thf(func_def_711, type, sK519: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_712, type, sK520: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_713, type, sK521: $i > $i).
% 8.34/2.43 thf(func_def_714, type, sK522: $i > $i).
% 8.34/2.43 thf(func_def_715, type, sK523: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_716, type, sK524: $i > $i).
% 8.34/2.43 thf(func_def_717, type, sK525: $i > $i > $i).
% 8.34/2.43 thf(func_def_718, type, sK526: $i > $i > $i).
% 8.34/2.43 thf(func_def_719, type, sK527: ($i > $o) > $i > $i).
% 8.34/2.43 thf(func_def_721, type, sK529: $i > $i).
% 8.34/2.43 thf(func_def_722, type, ph530: !>[X0: $tType]:(X0)).
% 8.34/2.43 thf(f5879,plain,(
% 8.34/2.43 $false),
% 8.34/2.43 inference(subsumption_resolution,[status(thm)],[f5876,f5807])).
% 8.34/2.43 thf(f5807,plain,(
% 8.34/2.43 ((sK175 @ sK528) = $true)),
% 8.34/2.43 inference(trivial_inequality_removal,[status(thm)],[f5803])).
% 8.34/2.43 thf(f5803,plain,(
% 8.34/2.43 ((sK175 @ sK528) = $true) | ($true != $true)),
% 8.34/2.43 inference(superposition,[status(thm)],[f3137,f3538])).
% 8.34/2.43 thf(f3538,plain,(
% 8.34/2.43 ($true = (in @ sK528 @ (dsetconstr @ sK176 @ sK175)))),
% 8.34/2.43 inference(binary_proxy_clausification,[status(thm)],[f3537])).
% 8.34/2.43 thf(f3537,plain,(
% 8.34/2.43 ((((setadjoin @ sK528 @ emptyset) = (dsetconstr @ sK176 @ sK175)) & (in @ sK528 @ (dsetconstr @ sK176 @ sK175))) = $true)),
% 8.34/2.43 inference(beta_eta_normalization,[status(thm)],[f3536])).
% 8.34/2.43 thf(f3536,plain,(
% 8.34/2.43 (((^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK176 @ sK175)) & (in @ Y0 @ (dsetconstr @ sK176 @ sK175)))) @ sK528) = $true)),
% 8.34/2.43 inference(sigma_clausification,[status(thm)],[f3535])).
% 8.34/2.43 thf(f3535,plain,(
% 8.34/2.43 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ Y0 @ emptyset) = (dsetconstr @ sK176 @ sK175)) & (in @ Y0 @ (dsetconstr @ sK176 @ sK175))))) = $true)),
% 8.34/2.43 inference(beta_eta_normalization,[status(thm)],[f2505])).
% 8.34/2.43 thf(f2505,plain,(
% 8.34/2.43 (((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK176 @ (^[Y0 : $i]: (sK175 @ Y0))) = $true)),
% 8.34/2.43 inference(definition_unfolding,[status(thm)],[f1736,f2350])).
% 8.34/2.43 thf(f2350,plain,(
% 8.34/2.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.34/2.43 inference(definition_unfolding,[status(thm)],[f1991,f2124])).
% 8.34/2.43 thf(f2124,plain,(
% 8.34/2.43 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f447])).
% 8.34/2.43 thf(f447,plain,(
% 8.34/2.43 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))),
% 8.34/2.43 inference(fool_elimination,[status(thm)],[f446])).
% 8.34/2.43 thf(f446,plain,(
% 8.34/2.43 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))))),
% 8.34/2.43 inference(rectify,[status(thm)],[f158])).
% 8.34/2.43 thf(f158,axiom,(
% 8.34/2.43 (singleton = (^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ X3) & ((setadjoin @ X1 @ emptyset) = X3)))))),
% 8.34/2.43 file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',singleton)).
% 8.34/2.43 thf(f1991,plain,(
% 8.34/2.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f227])).
% 8.34/2.43 thf(f227,plain,(
% 8.34/2.43 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.34/2.43 inference(fool_elimination,[status(thm)],[f226])).
% 8.34/2.43 thf(f226,plain,(
% 8.34/2.43 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)),
% 8.34/2.43 inference(rectify,[status(thm)],[f160])).
% 8.34/2.43 thf(f160,axiom,(
% 8.34/2.43 ((^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1)),
% 8.34/2.43 file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',ex1)).
% 8.34/2.43 thf(f1736,plain,(
% 8.34/2.43 ((ex1 @ sK176 @ (^[Y0 : $i]: (sK175 @ Y0))) = $true)),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f982])).
% 8.34/2.43 thf(f982,plain,(
% 8.34/2.43 (setminusI = $true) & (subsetemptysetimpeq = $true) & (quantDeMorgan4 = $true) & (emptysetE = $true) & (setminusSubset1 = $true) & (emptyE1 = $true) & (cartprodpairin = $true) & (exuE1 = $true) & (exuEu = $true) & (prop2setI = $true) & (powersetE = $true) & (setextsub = $true) & (subset2powerset = $true) & (binintersectER = $true) & (nonemptyI = $true) & (binunionRsub = $true) & (bs114d = $true) & (powersetAx = $true) & (setunionsingleton = $true) & (dsetconstrEL = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (setminusER = $true) & (singletoninpowunion = $true) & (setadjoinSub = $true) & (sepSubset = $true) & (notequalI1 = $true) & (upairinpowunion = $true) & (eqimpsubset1 = $true) & (binunionE = $true) & (dsetconstrI = $true) & (setminusSubset2 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (binunionIR = $true) & (setminusIRneg = $true) & (secondinupair = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (notinemptyset = $true) & (symdiffI2 = $true) & (setadjoinAx = $true) & (binintersectSubset5 = $true) & (binintersectLsub = $true) & (ubforcartprodlem3 = $true) & (nonemptyImpWitness = $true) & (inCongP = $true) & (setminusELneg = $true) & (uniqinunit = $true) & (singletonsubset = $true) & (setext = $true) & (symdiffIneg1 = $true) & (replAx = $true) & (binintersectSubset2 = $true) & (powersetI1 = $true) & (exuE3e = $true) & (kpairiskpair = $true) & (nonemptyI1 = $true) & (quantDeMorgan3 = $true) & (setoftrueEq = $true) & (exu__Cong = $true) & (setunionI = $true) & (setunionsingleton2 = $true) & (singletonsswitch = $true) & (setminusEL = $true) & (notdallE = $true) & (powersetE1 = $true) & (omega__Cong = $true) & (binunionEcases = $true) & (setunionAx = $true) & (singletoninpowerset = $true) & (ubforcartprodlem2 = $true) & (notdexE = $true) & (emptyInPowerset = $true) & (subsetE = $true) & (setminusILneg = $true) & (descr__Cong = $true) & (upairsetE = $true) & (emptyI = $true) & (symdiffIneg2 = $true) & (prop2setE = $true) & (upairset2IR = $true) & (singletonprop = $true) & (subsetI2 = $true) & (setunionE2 = $true) & (emptyinunitempty = $true) & (setminusLsub = $true) & (emptysetimpfalse = $true) & (symdiffE = $true) & (setunionsingleton1 = $true) & (emptysetAx = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (cartprodmempair1 = $true) & (subsetE2 = $true) & (exuE3u = $true) & (setukpairIR = $true) & (binintersectSubset4 = $true) & (ubforcartprodlem1 = $true) & (setukpairIL = $true) & (subPowSU = $true) & (inPowerset = $true) & (wellorderingAx = $true) & (setminusERneg = $true) & (setbeta = $true) & (binintersectEL = $true) & (binintersectSubset1 = $true) & (binintersectSubset3 = $true) & (disjointsetsI1 = $true) & (subsetRefl = $true) & (subsetTrans = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (setunion__Cong = $true) & (exuI1 = $true) & (dsetconstr__Cong = $true) & (setadjoin__Cong = $true) & (in__Cong = $true) & (notsubsetI = $true) & (dsetconstrER = $true) & (kpairp = $true) & (setadjoinSub2 = $true) & (sepInPowerset = $true) & (exuE2 = $true) & (upairsetIR = $true) & (omegaIndAx = $true) & (notequalI2 = $true) & (exuI2 = $true) & (binunionLsub = $true) & (setadjoinIR = $true) & (setunionE = $true) & (prop2set2propI = $true) & (vacuousDall = $true) & (powerset__Cong = $true) & (upairsetIL = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (powersetsubset = $true) & (exuI3 = $true) & (symdiffI1 = $true) & (nonemptyE1 = $true) & (upairset2E = $true) & (! [X2 : $i] : (($true != (in @ X2 @ sK176)) | ((sK175 @ X2) != $true)) & ((ex1 @ sK176 @ (^[Y0 : $i]: (sK175 @ Y0))) = $true)) & (quantDeMorgan2 = $true) & (omega0Ax = $true) & (powersetI = $true) & (binintersectRsub = $true) & (binunionIL = $true) & (upairsubunion = $true) & (eqinunit = $true) & (omegaSAx = $true) & (cartprodmempair = $true) & (setadjoinE = $true) & (descrp = $true) & (binintersectI = $true)),
% 8.34/2.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176])],[f543,f981])).
% 8.34/2.43 thf(f981,plain,(
% 8.34/2.43 ? [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true)) & ((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) => (! [X2 : $i] : (($true != (in @ X2 @ sK176)) | ((sK175 @ X2) != $true)) & ((ex1 @ sK176 @ (^[Y0 : $i]: (sK175 @ Y0))) = $true))),
% 8.34/2.43 introduced(definition,[],[choice_axiom])).
% 8.34/2.43 thf(f543,plain,(
% 8.34/2.43 (setminusI = $true) & (subsetemptysetimpeq = $true) & (quantDeMorgan4 = $true) & (emptysetE = $true) & (setminusSubset1 = $true) & (emptyE1 = $true) & (cartprodpairin = $true) & (exuE1 = $true) & (exuEu = $true) & (prop2setI = $true) & (powersetE = $true) & (setextsub = $true) & (subset2powerset = $true) & (binintersectER = $true) & (nonemptyI = $true) & (binunionRsub = $true) & (bs114d = $true) & (powersetAx = $true) & (setunionsingleton = $true) & (dsetconstrEL = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (setminusER = $true) & (singletoninpowunion = $true) & (setadjoinSub = $true) & (sepSubset = $true) & (notequalI1 = $true) & (upairinpowunion = $true) & (eqimpsubset1 = $true) & (binunionE = $true) & (dsetconstrI = $true) & (setminusSubset2 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (binunionIR = $true) & (setminusIRneg = $true) & (secondinupair = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (notinemptyset = $true) & (symdiffI2 = $true) & (setadjoinAx = $true) & (binintersectSubset5 = $true) & (binintersectLsub = $true) & (ubforcartprodlem3 = $true) & (nonemptyImpWitness = $true) & (inCongP = $true) & (setminusELneg = $true) & (uniqinunit = $true) & (singletonsubset = $true) & (setext = $true) & (symdiffIneg1 = $true) & (replAx = $true) & (binintersectSubset2 = $true) & (powersetI1 = $true) & (exuE3e = $true) & (kpairiskpair = $true) & (nonemptyI1 = $true) & (quantDeMorgan3 = $true) & (setoftrueEq = $true) & (exu__Cong = $true) & (setunionI = $true) & (setunionsingleton2 = $true) & (singletonsswitch = $true) & (setminusEL = $true) & (notdallE = $true) & (powersetE1 = $true) & (omega__Cong = $true) & (binunionEcases = $true) & (setunionAx = $true) & (singletoninpowerset = $true) & (ubforcartprodlem2 = $true) & (notdexE = $true) & (emptyInPowerset = $true) & (subsetE = $true) & (setminusILneg = $true) & (descr__Cong = $true) & (upairsetE = $true) & (emptyI = $true) & (symdiffIneg2 = $true) & (prop2setE = $true) & (upairset2IR = $true) & (singletonprop = $true) & (subsetI2 = $true) & (setunionE2 = $true) & (emptyinunitempty = $true) & (setminusLsub = $true) & (emptysetimpfalse = $true) & (symdiffE = $true) & (setunionsingleton1 = $true) & (emptysetAx = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (cartprodmempair1 = $true) & (subsetE2 = $true) & (exuE3u = $true) & (setukpairIR = $true) & (binintersectSubset4 = $true) & (ubforcartprodlem1 = $true) & (setukpairIL = $true) & (subPowSU = $true) & (inPowerset = $true) & (wellorderingAx = $true) & (setminusERneg = $true) & (setbeta = $true) & (binintersectEL = $true) & (binintersectSubset1 = $true) & (binintersectSubset3 = $true) & (disjointsetsI1 = $true) & (subsetRefl = $true) & (subsetTrans = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (setunion__Cong = $true) & (exuI1 = $true) & (dsetconstr__Cong = $true) & (setadjoin__Cong = $true) & (in__Cong = $true) & (notsubsetI = $true) & (dsetconstrER = $true) & (kpairp = $true) & (setadjoinSub2 = $true) & (sepInPowerset = $true) & (exuE2 = $true) & (upairsetIR = $true) & (omegaIndAx = $true) & (notequalI2 = $true) & (exuI2 = $true) & (binunionLsub = $true) & (setadjoinIR = $true) & (setunionE = $true) & (prop2set2propI = $true) & (vacuousDall = $true) & (powerset__Cong = $true) & (upairsetIL = $true) & (foundationAx = $true) & (noeltsimpempty = $true) & (powersetsubset = $true) & (exuI3 = $true) & (symdiffI1 = $true) & (nonemptyE1 = $true) & (upairset2E = $true) & ? [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true)) & ((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) & (quantDeMorgan2 = $true) & (omega0Ax = $true) & (powersetI = $true) & (binintersectRsub = $true) & (binunionIL = $true) & (upairsubunion = $true) & (eqinunit = $true) & (omegaSAx = $true) & (cartprodmempair = $true) & (setadjoinE = $true) & (descrp = $true) & (binintersectI = $true)),
% 8.34/2.43 inference(flattening,[status(thm)],[f542])).
% 8.34/2.43 thf(f542,plain,(
% 8.34/2.43 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((X0 @ X2) != $true)) & ((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $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)),
% 8.34/2.43 inference(ennf_transformation,[status(thm)],[f487])).
% 8.34/2.43 thf(f487,plain,(
% 8.34/2.43 ~((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) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : (((X0 @ X2) = $true) & ((in @ X2 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.34/2.43 inference(rectify,[status(thm)],[f225])).
% 8.34/2.43 thf(f225,plain,(
% 8.34/2.43 ~((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) => ! [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ((X0 @ X3) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.34/2.43 inference(fool_elimination,[status(thm)],[f224])).
% 8.34/2.43 thf(f224,plain,(
% 8.34/2.43 ~(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 => ! [X0 : $i > $o,X1 : $i] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3 : $i] : ((in @ X3 @ X1) & (X0 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.34/2.43 inference(rectify,[status(thm)],[f162])).
% 8.34/2.43 thf(f162,negated_conjecture,(
% 8.34/2.43 ~(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 => ! [X0 : $i > $o,X3 : $i] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ((in @ X1 @ X3) & (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.34/2.43 inference(negated_conjecture,[status(cth)],[f161])).
% 8.34/2.43 thf(f161,conjecture,(
% 8.34/2.43 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 => ! [X0 : $i > $o,X3 : $i] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ((in @ X1 @ X3) & (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.34/2.43 file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',ex1E1)).
% 8.34/2.43 thf(f3137,plain,(
% 8.34/2.43 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X0)) != $true) | ((X0 @ X2) = $true)) )),
% 8.34/2.43 inference(beta_eta_normalization,[status(thm)],[f3136])).
% 8.34/2.43 thf(f3136,plain,(
% 8.34/2.43 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) )),
% 8.34/2.43 inference(trivial_inequality_removal,[status(thm)],[f2789])).
% 8.34/2.43 thf(f2789,plain,(
% 8.34/2.43 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != $true) | ((X0 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) )),
% 8.34/2.43 inference(definition_unfolding,[status(thm)],[f2313,f1760])).
% 8.34/2.43 thf(f1760,plain,(
% 8.34/2.43 (dsetconstrER = $true)),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f982])).
% 8.34/2.43 thf(f2313,plain,(
% 8.34/2.43 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true) | (dsetconstrER != $true)) )),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f1486])).
% 8.34/2.43 thf(f1486,plain,(
% 8.34/2.43 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((in @ sK443 @ (dsetconstr @ sK442 @ (^[Y0 : $i]: (sK441 @ Y0)))) = $true) & ($true != (sK441 @ sK443))))),
% 8.34/2.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK441,sK442,sK443])],[f1484,f1485])).
% 8.34/2.43 thf(f1485,plain,(
% 8.34/2.43 ? [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true) & ((X3 @ X5) != $true)) => (((in @ sK443 @ (dsetconstr @ sK442 @ (^[Y0 : $i]: (sK441 @ Y0)))) = $true) & ($true != (sK441 @ sK443)))),
% 8.34/2.43 introduced(definition,[],[choice_axiom])).
% 8.34/2.43 thf(f1484,plain,(
% 8.34/2.43 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) = $true) & ((X3 @ X5) != $true)))),
% 8.34/2.43 inference(rectify,[status(thm)],[f1483])).
% 8.34/2.43 thf(f1483,plain,(
% 8.34/2.43 (! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ((X0 @ X2) != $true)))),
% 8.34/2.43 inference(nnf_transformation,[status(thm)],[f618])).
% 8.34/2.43 thf(f618,plain,(
% 8.34/2.43 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ((X0 @ X2) = $true)) <=> (dsetconstrER = $true)),
% 8.34/2.43 inference(ennf_transformation,[status(thm)],[f421])).
% 8.34/2.43 thf(f421,plain,(
% 8.34/2.43 ! [X0 : $i > $o,X1 : $i,X2 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ((X0 @ X2) = $true)) <=> (dsetconstrER = $true)),
% 8.34/2.43 inference(fool_elimination,[status(thm)],[f420])).
% 8.34/2.43 thf(f420,plain,(
% 8.34/2.43 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 8.34/2.43 inference(rectify,[status(thm)],[f16])).
% 8.34/2.43 thf(f16,axiom,(
% 8.34/2.43 (! [X0 : $i > $o,X3 : $i,X1 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 8.34/2.43 file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',dsetconstrER)).
% 8.34/2.43 thf(f5876,plain,(
% 8.34/2.43 ((sK175 @ sK528) != $true)),
% 8.34/2.43 inference(trivial_inequality_removal,[status(thm)],[f5874])).
% 8.34/2.43 thf(f5874,plain,(
% 8.34/2.43 ((sK175 @ sK528) != $true) | ($true != $true)),
% 8.34/2.43 inference(superposition,[status(thm)],[f1737,f5806])).
% 8.34/2.43 thf(f5806,plain,(
% 8.34/2.43 ((in @ sK528 @ sK176) = $true)),
% 8.34/2.43 inference(trivial_inequality_removal,[status(thm)],[f5802])).
% 8.34/2.43 thf(f5802,plain,(
% 8.34/2.43 ($true != $true) | ((in @ sK528 @ sK176) = $true)),
% 8.34/2.43 inference(superposition,[status(thm)],[f3490,f3538])).
% 8.34/2.43 thf(f3490,plain,(
% 8.34/2.43 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != (in @ X3 @ (dsetconstr @ X5 @ X4))) | ((in @ X3 @ X5) = $true)) )),
% 8.34/2.43 inference(beta_eta_normalization,[status(thm)],[f3489])).
% 8.34/2.43 thf(f3489,plain,(
% 8.34/2.43 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | ((in @ X3 @ X5) = $true)) )),
% 8.34/2.43 inference(trivial_inequality_removal,[status(thm)],[f2699])).
% 8.34/2.43 thf(f2699,plain,(
% 8.34/2.43 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ($true != $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) )),
% 8.34/2.43 inference(definition_unfolding,[status(thm)],[f2171,f1860])).
% 8.34/2.43 thf(f1860,plain,(
% 8.34/2.43 (dsetconstrEL = $true)),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f982])).
% 8.34/2.43 thf(f2171,plain,(
% 8.34/2.43 ( ! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true) | (dsetconstrEL != $true)) )),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f1318])).
% 8.34/2.43 thf(f1318,plain,(
% 8.34/2.43 ((dsetconstrEL = $true) | (((in @ sK353 @ sK355) != $true) & ((in @ sK353 @ (dsetconstr @ sK355 @ (^[Y0 : $i]: (sK354 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 8.34/2.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK353,sK354,sK355])],[f1316,f1317])).
% 8.34/2.43 thf(f1317,plain,(
% 8.34/2.43 ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)) => (((in @ sK353 @ sK355) != $true) & ((in @ sK353 @ (dsetconstr @ sK355 @ (^[Y0 : $i]: (sK354 @ Y0)))) = $true))),
% 8.34/2.43 introduced(definition,[],[choice_axiom])).
% 8.34/2.43 thf(f1316,plain,(
% 8.34/2.43 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 8.34/2.43 inference(rectify,[status(thm)],[f1315])).
% 8.34/2.43 thf(f1315,plain,(
% 8.34/2.43 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) & (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrEL != $true))),
% 8.34/2.43 inference(nnf_transformation,[status(thm)],[f529])).
% 8.34/2.43 thf(f529,plain,(
% 8.34/2.43 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true))),
% 8.34/2.43 inference(ennf_transformation,[status(thm)],[f383])).
% 8.34/2.43 thf(f383,plain,(
% 8.34/2.43 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((in @ X0 @ X2) = $true)) <=> (dsetconstrEL = $true)),
% 8.34/2.43 inference(fool_elimination,[status(thm)],[f382])).
% 8.34/2.43 thf(f382,plain,(
% 8.34/2.43 (dsetconstrEL = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)))),
% 8.34/2.43 inference(rectify,[status(thm)],[f15])).
% 8.34/2.43 thf(f15,axiom,(
% 8.34/2.43 (dsetconstrEL = ! [X1 : $i,X0 : $i > $o,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)))),
% 8.34/2.43 file('/export/starexec/sandbox/tmp/tmp.M6BPAvB2Ss/DTF2THF_27992.p',dsetconstrEL)).
% 8.34/2.43 thf(f1737,plain,(
% 8.34/2.43 ( ! [X2 : $i] : (($true != (in @ X2 @ sK176)) | ((sK175 @ X2) != $true)) )),
% 8.34/2.43 inference(cnf_transformation,[status(thm)],[f982])).
% 8.34/2.43 % SZS output end Proof for DTF2THF_27992
% 8.34/2.43 % (28184)------------------------------
% 8.34/2.43 % (28184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.43 % (28184)Termination reason: Refutation
% 8.34/2.43
% 8.34/2.43 % (28184)Memory used [KB]: 9466
% 8.34/2.43 % (28184)Time elapsed: 0.157 s
% 8.34/2.43 % (28184)Instructions burned: 498 (million)
% 8.34/2.43 % (28184)------------------------------
% 8.34/2.43 % (28184)------------------------------
% 8.34/2.43 % (28092)Success in time 0.94 s
%------------------------------------------------------------------------------