%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU704^1 : 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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:31 AM UTC 2026
% Result : Theorem 17.76s 3.75s
% Output : Refutation 17.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 134 ( 10 unt; 0 typ; 9 def)
% Number of atoms : 5874 (1729 equ; 0 cnn)
% Maximal formula atoms : 225 ( 43 avg)
% Number of connectives : 3687 ( 477 ~; 524 |;1033 &; 727 @)
% ( 14 <=>; 912 =>; 0 <=; 0 <~>)
% Maximal formula depth : 234 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 421 ( 418 usr; 238 con; 0-4 aty)
% Number of variables : 321 ( 138 ^; 141 !; 42 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_274,type,
sP3: $i > $i > $o ).
thf(func_def_275,type,
sP4: $i > $o ).
thf(func_def_276,type,
sP5: $i > $i > $o ).
thf(func_def_277,type,
sP6: $i > $i > $o ).
thf(func_def_279,type,
sP8: $i > $i > $i > $o > $o ).
thf(func_def_280,type,
sP9: $i > $i > $i > $i > $o ).
thf(func_def_284,type,
sK13: $i > $i > $i ).
thf(func_def_313,type,
sK42: $i > $o ).
thf(func_def_315,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_316,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_331,type,
sK60: $i > $i > $i > $i > $i ).
thf(func_def_332,type,
sK61: $i > ( $i > $o ) > $i ).
thf(func_def_333,type,
sK62: $i > $o ).
thf(func_def_336,type,
sK65: $i > ( $i > $i ) > $i > $i ).
thf(func_def_338,type,
sK67: $i > $i ).
thf(func_def_344,type,
sK73: $i > $i ).
thf(func_def_346,type,
sK75: $i > $i > $i ).
thf(func_def_349,type,
sK78: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_350,type,
sK79: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_351,type,
sK80: $i > $o ).
thf(func_def_352,type,
sK81: $i > $o ).
thf(func_def_359,type,
sK88: $o > $i > $i > $i ).
thf(func_def_372,type,
sK101: $i > $i ).
thf(func_def_375,type,
sK104: $i > $i > ( $i > $i ) > $i ).
thf(func_def_381,type,
sK110: $i > $i > $o ).
thf(func_def_382,type,
sK111: $i > $i ).
thf(func_def_383,type,
sK112: $i > $i ).
thf(func_def_384,type,
sK113: ( $i > $i > $o ) > $i > $i ).
thf(func_def_385,type,
sK114: ( $i > $i > $o ) > $i > $i ).
thf(func_def_386,type,
sK115: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_390,type,
sK119: $i > $i > $o ).
thf(func_def_392,type,
sK121: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_393,type,
sK122: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_396,type,
sK125: $i > $o ).
thf(func_def_397,type,
sK126: $i > $o ).
thf(func_def_402,type,
sK131: $i > $i > $i > $i > $i ).
thf(func_def_420,type,
sK149: $i > $i ).
thf(func_def_423,type,
sK152: $i > $o ).
thf(func_def_439,type,
sK168: $i > $i > $o ).
thf(func_def_448,type,
sK177: $i > $i ).
thf(func_def_451,type,
sK180: $i > ( $i > $i ) > $i > $i ).
thf(func_def_468,type,
sK197: ( $i > $i ) > $i > $i > $i ).
thf(func_def_471,type,
sK200: $i > $i ).
thf(func_def_474,type,
sK203: $i > $i ).
thf(func_def_475,type,
sK204: $i > $i ).
thf(func_def_476,type,
sK205: $i > ( $i > $o ) > $i ).
thf(func_def_477,type,
sK206: $i > $o ).
thf(func_def_486,type,
sK215: $i > $i > $o ).
thf(func_def_491,type,
sK220: $i > $i > $i ).
thf(func_def_492,type,
sK221: $i > $i > $i ).
thf(func_def_493,type,
sK222: $i > $i > $i ).
thf(func_def_494,type,
sK223: $i > $i > $i ).
thf(func_def_495,type,
sK224: $i > $i > $i > $i ).
thf(func_def_496,type,
sK225: $i > $i ).
thf(func_def_497,type,
sK226: $i > $i ).
thf(func_def_498,type,
sK227: $i > $i ).
thf(func_def_499,type,
sK228: $i > $i ).
thf(func_def_500,type,
sK229: $i > $i > $i ).
thf(func_def_501,type,
sK230: $i > $i > $i > $i ).
thf(func_def_502,type,
sK231: $i > $i > $i > $i ).
thf(func_def_503,type,
sK232: $i > $i > $i ).
thf(func_def_504,type,
sK233: $i > $i > $i ).
thf(func_def_505,type,
sK234: $i > $i ).
thf(func_def_506,type,
sK235: $i > $i > $i ).
thf(func_def_508,type,
sK237: $i > $i ).
thf(func_def_509,type,
sK238: $i > $i ).
thf(func_def_516,type,
sK245: $i > $o ).
thf(func_def_517,type,
sK246: $i > $i > $i > $i ).
thf(func_def_518,type,
sK247: $i > $i > $i > $i ).
thf(func_def_527,type,
sK256: ( $i > $o ) > $i ).
thf(func_def_528,type,
sK257: $i > $o ).
thf(func_def_529,type,
sK258: $i > $i ).
thf(func_def_544,type,
sK273: $i > $i ).
thf(func_def_551,type,
sK280: $i > $i > $o ).
thf(func_def_570,type,
sK299: $i > $o ).
thf(func_def_583,type,
sK312: $i > $i > $o ).
thf(func_def_586,type,
sK315: $i > ( $i > $o ) > $i ).
thf(func_def_587,type,
sK316: $i > $o ).
thf(func_def_593,type,
sK322: $i > $i > $i > $i > $i ).
thf(func_def_609,type,
sK338: $i > $o ).
thf(func_def_612,type,
sK341: $i > ( $i > $o ) > $i ).
thf(func_def_613,type,
sK342: $i > ( $i > $o ) > $i ).
thf(func_def_616,type,
sK345: $i > $o ).
thf(func_def_622,type,
sK351: $i > $i > $i > $i > $i ).
thf(func_def_623,type,
sK352: $i > $i > $i > $i > $i ).
thf(func_def_630,type,
sK359: $i > $i ).
thf(func_def_643,type,
sK372: $i > ( $i > $o ) > $i ).
thf(func_def_644,type,
sK373: $i > $o ).
thf(func_def_665,type,
sK394: $i > $i > $i ).
thf(func_def_673,type,
sK402: $i > $i > $i ).
thf(func_def_686,type,
sK415: $i > $o ).
thf(func_def_694,type,
sK423: $i > $o ).
thf(func_def_699,type,
sK428: $i > $o ).
thf(func_def_701,type,
sK430: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_702,type,
sK431: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_707,type,
sK436: $i > $o ).
thf(func_def_709,type,
sK438: ( $i > $o ) > $i ).
thf(func_def_710,type,
sK439: ( $i > $o ) > $i ).
thf(func_def_715,type,
sK444: $i > $o ).
thf(func_def_718,type,
sK447: $i > ( $i > $o ) > $i ).
thf(func_def_725,type,
sK454: $i > $i > $i ).
thf(func_def_726,type,
sK455: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_727,type,
sK456: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_731,type,
sK460: $i > $o ).
thf(func_def_738,type,
sK467: $i > $o ).
thf(func_def_742,type,
sK471: $i > $i > $i ).
thf(func_def_771,type,
sK500: $i > $o ).
thf(func_def_774,type,
sK503: $i > $o ).
thf(func_def_804,type,
sK533: ( $i > $i ) > $i > $i > $i ).
thf(func_def_807,type,
sK536: $i > $i ).
thf(func_def_818,type,
sK547: $i > $o ).
thf(func_def_823,type,
sK552: $i > $o ).
thf(func_def_824,type,
sK553: $i > $i ).
thf(func_def_825,type,
sK554: ( $i > $o ) > $i ).
thf(func_def_826,type,
sK555: $i > $o ).
thf(func_def_829,type,
sK558: $i > ( $i > $o ) > $i ).
thf(func_def_833,type,
sK562: $i > $o ).
thf(func_def_841,type,
sK570: $i > $o ).
thf(func_def_843,type,
sK572: $i > $o ).
thf(func_def_845,type,
sK574: $i > ( $i > $o ) > $i ).
thf(func_def_846,type,
sK575: ( $i > $o ) > $i > $i ).
thf(func_def_848,type,
sK577: $i > $o ).
thf(func_def_859,type,
sK588: $i > $i > $i ).
thf(func_def_863,type,
sK592: $i > $o ).
thf(func_def_864,type,
sK593: ( $i > $o ) > $i ).
thf(func_def_865,type,
sK594: $i > $o ).
thf(func_def_868,type,
sK597: $i > ( $i > $o ) > $i ).
thf(func_def_883,type,
sK612: $i > $i > $o ).
thf(func_def_897,type,
sK626: $i > $i ).
thf(func_def_901,type,
sK630: $i > $i > $i ).
thf(func_def_902,type,
sK631: $i > $i > $i ).
thf(func_def_909,type,
sK638: $i > $i > $o ).
thf(func_def_915,type,
sK644: $i > $i > $i > $i > $i ).
thf(func_def_916,type,
sK645: $i > $i > $i > $i > $i ).
thf(func_def_917,type,
sK646: $i > $i > $i > $i > $i ).
thf(func_def_918,type,
sK647: $i > $i > $i > $i > $i ).
thf(func_def_928,type,
sK657: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_929,type,
sK658: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_930,type,
sK659: $i > $o ).
thf(func_def_931,type,
sK660: $i > $o ).
thf(func_def_932,type,
sK661: $i > $o ).
thf(func_def_935,type,
sK664: $i > $i ).
thf(func_def_939,type,
sK668: $i > $i > ( $i > $i ) > $i ).
thf(func_def_951,type,
sK680: $i > $i > $i ).
thf(func_def_953,type,
sK682: $i > $o ).
thf(func_def_955,type,
sK684: $i > ( $i > $o ) > $i > $i ).
thf(func_def_964,type,
ph693:
!>[X0: $tType] : X0 ).
thf(f4138,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3472,f3608,f3704,f3709,f3712,f3768,f3775,f3784,f3997,f4137]) ).
thf(f4137,plain,
( spl692_5
| spl692_1
| ~ spl692_4
| ~ spl692_7
| ~ spl692_10 ),
inference(avatar_split_clause,[status(thm)],[f4136,f3770,f3706,f3465,f3454,f3697]) ).
thf(f3697,definition,
( spl692_5
<=> ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321 != X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl692_5])],[avatar_definition]) ).
thf(f3454,definition,
( spl692_1
<=> ( $true = sK320 ) ),
introduced(definition,[new_symbols(naming,[spl692_1])],[avatar_definition]) ).
thf(f3465,definition,
( spl692_4
<=> ( $true = sP0 ) ),
introduced(definition,[new_symbols(naming,[spl692_4])],[avatar_definition]) ).
thf(f3706,definition,
( spl692_7
<=> ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ),
introduced(definition,[new_symbols(naming,[spl692_7])],[avatar_definition]) ).
thf(f3770,definition,
( spl692_10
<=> ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ),
introduced(definition,[new_symbols(naming,[spl692_10])],[avatar_definition]) ).
thf(f4136,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321 != X0 ) )
| spl692_1
| ~ spl692_4
| ~ spl692_7
| ~ spl692_10 ),
inference(subsumption_resolution,[status(thm)],[f4135,f3455]) ).
thf(f3455,plain,
( ( $true != sK320 )
| spl692_1 ),
inference(avatar_component_clause,[status(thm)],[f3454]) ).
thf(f4135,plain,
( ! [X0: $i] :
( ( $true = sK320 )
| ( sK321 != X0 )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| ~ spl692_4
| ~ spl692_7
| ~ spl692_10 ),
inference(subsumption_resolution,[status(thm)],[f4134,f2627]) ).
thf(f2627,plain,
( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1432]) ).
thf(f1432,plain,
( ( binunionE = $true )
& ( notsubsetI = $true )
& ( subsetTrans = $true )
& ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ sK321 @ sK318 )
= $true )
& ( ( in @ sK319 @ sK318 )
= $true )
& ( singletoninpowunion = $true )
& ( binintersectSubset5 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptysetimpfalse = $true )
& ( omega__Cong = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( kpairp = $true )
& ( setminusERneg = $true )
& ( lam2p = $true )
& ( emptyinunitempty = $true )
& ( binunionIL = $true )
& ( binunionRsub = $true )
& ( setunionE2 = $true )
& ( replAx = $true )
& ( powersetI1 = $true )
& ( setukpairIR = $true )
& ( subsetE2 = $true )
& ( emptyInPowerset = $true )
& ( setadjoin__Cong = $true )
& ( setminusLsub = $true )
& ( emptyE1 = $true )
& ( upairsetIL = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR = $true )
& ( cartprodfstpairEq = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( cartprodmempair1 = $true )
& ( ubforcartprodlem1 = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setext = $true )
& ( exuE1 = $true )
& ( binintersectI = $true )
& ( binintersectEL = $true )
& ( eqimpsubset1 = $true )
& ( binintersectSubset1 = $true )
& ( singletoninpowerset = $true )
& ( symdiffIneg1 = $true )
& ( setminusI = $true )
& ( dpsetconstrEL1 = $true )
& ( binintersectRsub = $true )
& ( funcext = $true )
& ( inCongP = $true )
& ( setadjoinAx = $true )
& ( cartprodsndin = $true )
& ( infuncsetfunc = $true )
& ( emptysetE = $true )
& ( powersetAx = $true )
& ( subbreln = $true )
& ( iftrueProp1 = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true )
& ( setunion__Cong = $true )
& ( setminusER = $true )
& ( quantDeMorgan4 = $true )
& ( bs114d = $true )
& ( cartprodpairmemER = $true )
& ( setunionAx = $true )
& ( setunionsingleton = $true )
& ( funcext2 = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetE = $true )
& ( funcGraphProp1 = $true )
& ( sepSubset = $true )
& ( cartprodfstin = $true )
& ( setunionsingleton2 = $true )
& ( kfstpairEq = $true )
& ( symdiffI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( subsetE = $true )
& ( symdiffE = $true )
& ( beta1 = $true )
& ( binunionEcases = $true )
& ( foundationAx = $true )
& ( secondinupair = $true )
& ( dpsetconstrERa = $true )
& ( exuE3e = $true )
& ( singletonsuniq = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset3 = $true )
& ( binintersectLsub = $true )
& ( cartprodmempair = $true )
& ( sepInPowerset = $true )
& ( subsetI1 = $true )
& ( binintersectSubset4 = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( lamp = $true )
& ( apProp = $true )
& ( brelnall1 = $true )
& ( setbeta = $true )
& ( disjointsetsI1 = $true )
& ( eta2 = $true )
& ( brelnall2 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( binintersectER = $true )
& ( funcGraphProp2 = $true )
& ( prop2setI = $true )
& ( emptyset__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( iftrueProp2 = $true )
& ( eqimpsubset2 = $true )
& ( iffalseProp1 = $true )
& ( powersetE1 = $true )
& ( cartprodpairin = $true )
& ( exuI3 = $true )
& ( setunionE = $true )
& ( binunionLsub = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( funcinfuncset = $true )
& ( noeltsimpempty = $true )
& ( ksndpairEq = $true )
& ( upairsubunion = $true )
& ( nonemptyI1 = $true )
& ( lam2lamEq = $true )
& ( descr__Cong = $true )
& ( symdiffI1 = $true )
& ( eqinunit = $true )
& ( eta1 = $true )
& ( setminusSubset2 = $true )
& ( inPowerset = $true )
& ( upairequniteq = $true )
& ( setukpairinjR12 = $true )
& ( exuEu = $true )
& ( funcGraphProp3 = $true )
& ( ex1I = $true )
& ( upairsetIR = $true )
& ( omegaSAx = $true )
& ( kpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( funcextLem = $true )
& ( ap2apEq1 = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( iffalseProp2 = $true )
& ( setminusSubset1 = $true )
& ( ap2p = $true )
& ( dpsetconstrSub = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( subsetemptysetimpeq = $true )
& ( powerset__Cong = $true )
& ( exu__Cong = $true )
& ( notdexE = $true )
& ( binunionIR = $true )
& ( exuE3u = $true )
& ( cartprodmempaircEq = $true )
& ( emptyinPowerset = $true )
& ( upairinpowunion = $true )
& ( dpsetconstrI = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusILneg = $true )
& ( ap2apEq2 = $true )
& ( setminusEL = $true )
& ( singletonprop = $true )
& ( setadjoinSub = $true )
& ( notinemptyset = $true )
& ( setoftrueEq = $true )
& ( ksndsingleton = $true )
& ( app = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR2 = $true )
& ( beta2 = $true )
& ( setukpairinjL2 = $true )
& ( setukpairIL = $true )
& ( setadjoinE = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( dsetconstr__Cong = $true )
& ( prop2set2propI = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( dsetconstrER = $true )
& ( subset2powerset = $true )
& ( vacuousDall = $true )
& ( notequalI1 = $true )
& ( upairsetE = $true )
& ( notequalI2 = $true )
& ( singletonsswitch = $true )
& ( ex1E2 = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( funcImageSingleton = $true )
& ( funcGraphProp4 = $true )
& ( upairset2E = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL2 = $true )
& ( descrp = $true )
& ( ex1I2 = $true )
& ( dpsetconstrER = $true )
& ( emptysetAx = $true )
& ( ex1E1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( setextsub = $true )
& ( lamProp = $true )
& ( setukpairinjR1 = $true )
& ( singletonsubset = $true )
& ( powersetI = $true )
& ( setadjoinOr = $true )
& ( eqbreln = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectSubset2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK318,sK319,sK320,sK321])],[f900,f1431,f1430]) ).
thf(f1430,plain,
( ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK318 ) ) )
& ( ( in @ sK319 @ sK318 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1431,plain,
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( $true
= ( in @ X3 @ sK318 ) ) )
=> ( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ sK321 @ sK318 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f900,plain,
( ( binunionE = $true )
& ( notsubsetI = $true )
& ( subsetTrans = $true )
& ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( singletoninpowunion = $true )
& ( binintersectSubset5 = $true )
& ( ubforcartprodlem3 = $true )
& ( emptysetimpfalse = $true )
& ( omega__Cong = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( kpairp = $true )
& ( setminusERneg = $true )
& ( lam2p = $true )
& ( emptyinunitempty = $true )
& ( binunionIL = $true )
& ( binunionRsub = $true )
& ( setunionE2 = $true )
& ( replAx = $true )
& ( powersetI1 = $true )
& ( setukpairIR = $true )
& ( subsetE2 = $true )
& ( emptyInPowerset = $true )
& ( setadjoin__Cong = $true )
& ( setminusLsub = $true )
& ( emptyE1 = $true )
& ( upairsetIL = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR = $true )
& ( cartprodfstpairEq = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( cartprodmempair1 = $true )
& ( ubforcartprodlem1 = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setext = $true )
& ( exuE1 = $true )
& ( binintersectI = $true )
& ( binintersectEL = $true )
& ( eqimpsubset1 = $true )
& ( binintersectSubset1 = $true )
& ( singletoninpowerset = $true )
& ( symdiffIneg1 = $true )
& ( setminusI = $true )
& ( dpsetconstrEL1 = $true )
& ( binintersectRsub = $true )
& ( funcext = $true )
& ( inCongP = $true )
& ( setadjoinAx = $true )
& ( cartprodsndin = $true )
& ( infuncsetfunc = $true )
& ( emptysetE = $true )
& ( powersetAx = $true )
& ( subbreln = $true )
& ( iftrueProp1 = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true )
& ( setunion__Cong = $true )
& ( setminusER = $true )
& ( quantDeMorgan4 = $true )
& ( bs114d = $true )
& ( cartprodpairmemER = $true )
& ( setunionAx = $true )
& ( setunionsingleton = $true )
& ( funcext2 = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetE = $true )
& ( funcGraphProp1 = $true )
& ( sepSubset = $true )
& ( cartprodfstin = $true )
& ( setunionsingleton2 = $true )
& ( kfstpairEq = $true )
& ( symdiffI2 = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( subsetE = $true )
& ( symdiffE = $true )
& ( beta1 = $true )
& ( binunionEcases = $true )
& ( foundationAx = $true )
& ( secondinupair = $true )
& ( dpsetconstrERa = $true )
& ( exuE3e = $true )
& ( singletonsuniq = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset3 = $true )
& ( binintersectLsub = $true )
& ( cartprodmempair = $true )
& ( sepInPowerset = $true )
& ( subsetI1 = $true )
& ( binintersectSubset4 = $true )
& ( in__Cong = $true )
& ( uniqinunit = $true )
& ( lamp = $true )
& ( apProp = $true )
& ( brelnall1 = $true )
& ( setbeta = $true )
& ( disjointsetsI1 = $true )
& ( eta2 = $true )
& ( brelnall2 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( binintersectER = $true )
& ( funcGraphProp2 = $true )
& ( prop2setI = $true )
& ( emptyset__Cong = $true )
& ( cartprodpairmemEL = $true )
& ( iftrueProp2 = $true )
& ( eqimpsubset2 = $true )
& ( iffalseProp1 = $true )
& ( powersetE1 = $true )
& ( cartprodpairin = $true )
& ( exuI3 = $true )
& ( setunionE = $true )
& ( binunionLsub = $true )
& ( symdiffIneg2 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( funcinfuncset = $true )
& ( noeltsimpempty = $true )
& ( ksndpairEq = $true )
& ( upairsubunion = $true )
& ( nonemptyI1 = $true )
& ( lam2lamEq = $true )
& ( descr__Cong = $true )
& ( symdiffI1 = $true )
& ( eqinunit = $true )
& ( eta1 = $true )
& ( setminusSubset2 = $true )
& ( inPowerset = $true )
& ( upairequniteq = $true )
& ( setukpairinjR12 = $true )
& ( exuEu = $true )
& ( funcGraphProp3 = $true )
& ( ex1I = $true )
& ( upairsetIR = $true )
& ( omegaSAx = $true )
& ( kpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( funcextLem = $true )
& ( ap2apEq1 = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( iffalseProp2 = $true )
& ( setminusSubset1 = $true )
& ( ap2p = $true )
& ( dpsetconstrSub = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( subsetemptysetimpeq = $true )
& ( powerset__Cong = $true )
& ( exu__Cong = $true )
& ( notdexE = $true )
& ( binunionIR = $true )
& ( exuE3u = $true )
& ( cartprodmempaircEq = $true )
& ( emptyinPowerset = $true )
& ( upairinpowunion = $true )
& ( dpsetconstrI = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusILneg = $true )
& ( ap2apEq2 = $true )
& ( setminusEL = $true )
& ( singletonprop = $true )
& ( setadjoinSub = $true )
& ( notinemptyset = $true )
& ( setoftrueEq = $true )
& ( ksndsingleton = $true )
& ( app = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR2 = $true )
& ( beta2 = $true )
& ( setukpairinjL2 = $true )
& ( setukpairIL = $true )
& ( setadjoinE = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( dsetconstr__Cong = $true )
& ( prop2set2propI = $true )
& ( emptyI = $true )
& ( nonemptyI = $true )
& ( dsetconstrER = $true )
& ( subset2powerset = $true )
& ( vacuousDall = $true )
& ( notequalI1 = $true )
& ( upairsetE = $true )
& ( notequalI2 = $true )
& ( singletonsswitch = $true )
& ( ex1E2 = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( funcImageSingleton = $true )
& ( funcGraphProp4 = $true )
& ( upairset2E = $true )
& ( prop2setE = $true )
& ( dpsetconstrEL2 = $true )
& ( descrp = $true )
& ( ex1I2 = $true )
& ( dpsetconstrER = $true )
& ( emptysetAx = $true )
& ( ex1E1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( setextsub = $true )
& ( lamProp = $true )
& ( setukpairinjR1 = $true )
& ( singletonsubset = $true )
& ( powersetI = $true )
& ( setadjoinOr = $true )
& ( eqbreln = $true )
& ( upairset2IR = $true )
& ( notinsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectSubset2 = $true ) ),
inference(flattening,[status(thm)],[f899]) ).
thf(f899,plain,
( ? [X0: $i,X1: $i,X2: $o] :
( ? [X3: $i] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X1 @ X0 )
= $true ) )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f456]) ).
thf(f456,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ! [X0: $i,X1: $i,X2: $o] :
( ( ( in @ X1 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( ( X2
& ( X1 = Y0 ) )
| ( ~ X2
& ( X3 = Y0 ) ) ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f455]) ).
thf(f455,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X0: $i,X1: $i,X2: $o] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X4: $i] :
( ( ( X3 = X4 )
& ~ X2 )
| ( ( X1 = X4 )
& X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f227]) ).
thf(f227,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X3: $i,X1: $i,X0: $o] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( singleton
@ ( dsetconstr @ X3
@ ^ [X8: $i] :
( ( ( X2 = X8 )
& ~ X0 )
| ( ( X1 = X8 )
& X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f226]) ).
thf(f226,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ! [X3: $i,X1: $i,X0: $o] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( singleton
@ ( dsetconstr @ X3
@ ^ [X8: $i] :
( ( ( X2 = X8 )
& ~ X0 )
| ( ( X1 = X8 )
& X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WuDOtMIMiy/DTF2THF_22813.p',ifSingleton) ).
thf(f4134,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( sK321 != X0 )
| ( $true = sK320 ) )
| ~ spl692_4
| ~ spl692_7
| ~ spl692_10 ),
inference(subsumption_resolution,[status(thm)],[f4133,f3771]) ).
thf(f3771,plain,
( ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ~ spl692_10 ),
inference(avatar_component_clause,[status(thm)],[f3770]) ).
thf(f4133,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $true = sK320 )
| ( sK321 != X0 ) )
| ~ spl692_4
| ~ spl692_7 ),
inference(subsumption_resolution,[status(thm)],[f4124,f3466]) ).
thf(f3466,plain,
( ( $true = sP0 )
| ~ spl692_4 ),
inference(avatar_component_clause,[status(thm)],[f3465]) ).
thf(f4124,plain,
( ! [X0: $i] :
( ( $true != sP0 )
| ( sK321 != X0 )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $true = sK320 )
| ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| ~ spl692_7 ),
inference(equality_proxy_clausification,[status(thm)],[f4123]) ).
thf(f4123,plain,
( ! [X0: $i] :
( ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true = sK320 )
| ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $false
= ( sK321 = X0 ) ) )
| ~ spl692_7 ),
inference(not_proxy_clausification,[status(thm)],[f4122]) ).
thf(f4122,plain,
( ! [X0: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( $false = ( ~ sK320 ) )
| ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $false
= ( sK321 = X0 ) ) )
| ~ spl692_7 ),
inference(binary_proxy_clausification,[status(thm)],[f4118]) ).
thf(f4118,plain,
( ! [X0: $i] :
( ( $true != sP0 )
| ( ( ~ sK320
& ( sK321 = X0 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ~ spl692_7 ),
inference(binary_proxy_clausification,[status(thm)],[f4117]) ).
thf(f4117,plain,
( ! [X0: $i] :
( ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 )
| ( ( ( sK320
& ( sK319 = X0 ) )
| ( ~ sK320
& ( sK321 = X0 ) ) )
!= $true )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| ~ spl692_7 ),
inference(beta_eta_normalization,[status(thm)],[f4114]) ).
thf(f4114,plain,
( ! [X0: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $true != sP0 )
| ( sK321
!= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true ) )
| ~ spl692_7 ),
inference(superposition,[status(thm)],[f3280,f3708]) ).
thf(f3708,plain,
( ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ~ spl692_7 ),
inference(avatar_component_clause,[status(thm)],[f3706]) ).
thf(f3280,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( sK44 @ X6 @ X5 )
!= ( sK45 @ X6 @ X5 ) )
| ( ( in @ X9 @ X5 )
!= $true )
| ( $true != sP0 )
| ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( ( X6 @ X9 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2055]) ).
thf(f2055,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( ( in @ X9 @ X5 )
!= $true )
| ( $true != sP0 )
| ( ( sK44 @ X6 @ X5 )
!= ( sK45 @ X6 @ X5 ) )
| ( ( X6 @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1027]) ).
thf(f1027,plain,
( ( ( $true = sP0 )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK41 )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( sK42 @ X2 ) )
| ( X2 = X3 )
| ( ( sK42 @ X3 )
!= $true )
| ( ( in @ X3 @ sK41 )
!= $true ) ) )
& ( ( sK42 @ sK43 )
= $true )
& ( ( in @ sK43 @ sK41 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK41
@ ^ [Y0: $i] : ( sK42 @ Y0 ) ) ) ) ) )
& ( ! [X5: $i,X6: $i > $o] :
( ( ( $true
= ( in @ ( sK44 @ X6 @ X5 ) @ X5 ) )
& ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
& ( ( sK44 @ X6 @ X5 )
!= ( sK45 @ X6 @ X5 ) )
& ( $true
= ( X6 @ ( sK45 @ X6 @ X5 ) ) )
& ( $true
= ( in @ ( sK45 @ X6 @ X5 ) @ X5 ) ) )
| ! [X9: $i] :
( ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true ) )
| ( $true != sP0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44,sK45])],[f1022,f1026,f1025,f1024,f1023]) ).
thf(f1023,plain,
( ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X1 @ X3 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK41 )
!= $true )
| ! [X3: $i] :
( ( $true
!= ( sK42 @ X2 ) )
| ( X2 = X3 )
| ( ( sK42 @ X3 )
!= $true )
| ( ( in @ X3 @ sK41 )
!= $true ) ) )
& ? [X4: $i] :
( ( ( sK42 @ X4 )
= $true )
& ( $true
= ( in @ X4 @ sK41 ) ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ sK41
@ ^ [Y0: $i] : ( sK42 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1024,plain,
( ? [X4: $i] :
( ( ( sK42 @ X4 )
= $true )
& ( $true
= ( in @ X4 @ sK41 ) ) )
=> ( ( ( sK42 @ sK43 )
= $true )
& ( ( in @ sK43 @ sK41 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1025,plain,
! [X5: $i,X6: $i > $o] :
( ? [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
& ? [X8: $i] :
( ( ( X6 @ X7 )
= $true )
& ( X7 != X8 )
& ( ( X6 @ X8 )
= $true )
& ( ( in @ X8 @ X5 )
= $true ) ) )
=> ( ( $true
= ( in @ ( sK44 @ X6 @ X5 ) @ X5 ) )
& ? [X8: $i] :
( ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
& ( ( sK44 @ X6 @ X5 )
!= X8 )
& ( ( X6 @ X8 )
= $true )
& ( ( in @ X8 @ X5 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1026,plain,
! [X5: $i,X6: $i > $o] :
( ? [X8: $i] :
( ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
& ( ( sK44 @ X6 @ X5 )
!= X8 )
& ( ( X6 @ X8 )
= $true )
& ( ( in @ X8 @ X5 )
= $true ) )
=> ( ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
& ( ( sK44 @ X6 @ X5 )
!= ( sK45 @ X6 @ X5 ) )
& ( $true
= ( X6 @ ( sK45 @ X6 @ X5 ) ) )
& ( $true
= ( in @ ( sK45 @ X6 @ X5 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1022,plain,
( ( ( $true = sP0 )
| ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X1 @ X3 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X5: $i,X6: $i > $o] :
( ? [X7: $i] :
( ( ( in @ X7 @ X5 )
= $true )
& ? [X8: $i] :
( ( ( X6 @ X7 )
= $true )
& ( X7 != X8 )
& ( ( X6 @ X8 )
= $true )
& ( ( in @ X8 @ X5 )
= $true ) ) )
| ! [X9: $i] :
( ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true ) )
| ( $true != sP0 ) ) ),
inference(rectify,[status(thm)],[f1021]) ).
thf(f1021,plain,
( ( ( $true = sP0 )
| ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ! [X3: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X1 @ X3 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( X1 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( X1 @ X3 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) )
| ( $true != sP0 ) ) ),
inference(nnf_transformation,[status(thm)],[f954]) ).
thf(f954,plain,
( ( $true = sP0 )
<=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( X1 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( X1 @ X3 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f3997,plain,
~ spl692_5,
inference(avatar_contradiction_clause,[status(thm)],[f3996]) ).
thf(f3996,plain,
( $false
| ~ spl692_5 ),
inference(trivial_inequality_removal,[status(thm)],[f3973]) ).
thf(f3973,plain,
( ( sK321 != sK321 )
| ( $true != $true )
| ~ spl692_5 ),
inference(superposition,[status(thm)],[f3698,f2626]) ).
thf(f2626,plain,
( ( in @ sK321 @ sK318 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1432]) ).
thf(f3698,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321 != X0 ) )
| ~ spl692_5 ),
inference(avatar_component_clause,[status(thm)],[f3697]) ).
thf(f3784,plain,
( spl692_10
| ~ spl692_4
| spl692_1
| spl692_5 ),
inference(avatar_split_clause,[status(thm)],[f3416,f3697,f3454,f3465,f3770]) ).
thf(f3416,plain,
! [X0: $i] :
( ( $true = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321 != X0 )
| ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f3415]) ).
thf(f3415,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true = sK320 )
| ( $true = sK320 )
| ( sK321 != X0 ) ),
inference(not_proxy_clausification,[status(thm)],[f3414]) ).
thf(f3414,plain,
! [X0: $i] :
( ( $false = ( ~ sK320 ) )
| ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 )
| ( sK321 != X0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true = sK320 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3412]) ).
thf(f3412,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321 != X0 )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( $false = ( ~ sK320 ) )
| ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f3411]) ).
thf(f3411,plain,
! [X0: $i] :
( ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $false
= ( sK321 = X0 ) )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( $false = ( ~ sK320 ) )
| ( $true != sP0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f3410]) ).
thf(f3410,plain,
! [X0: $i] :
( ( ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( $true != sP0 )
| ( $false
= ( sK321 = X0 ) )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = ( ~ sK320 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3396]) ).
thf(f3396,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( ~ sK320
& ( sK321 = X0 ) )
= $false )
| ( ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3395]) ).
thf(f3395,plain,
! [X0: $i] :
( ( ( ~ sK320
& ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( ~ sK320
& ( sK321 = X0 ) )
= $false )
| ( $true != sP0 )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3371]) ).
thf(f3371,plain,
! [X0: $i] :
( ( ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( ~ sK320
& ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( ( ~ sK320
& ( sK321 = X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f3370]) ).
thf(f3370,plain,
! [X0: $i] :
( ( ( ( sK320
& ( sK319 = X0 ) )
| ( ~ sK320
& ( sK321 = X0 ) ) )
!= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( ~ sK320
& ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
= $true )
| ( $true != sP0 ) ),
inference(beta_eta_normalization,[status(thm)],[f3369]) ).
thf(f3369,plain,
! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3304]) ).
thf(f3304,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f2627,f3243]) ).
thf(f3243,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
| ( $true != sP0 )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ X9 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2056]) ).
thf(f2056,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( X6 @ X9 )
!= $true )
| ( $true
= ( X6 @ ( sK44 @ X6 @ X5 ) ) )
| ( $true != sP0 )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1027]) ).
thf(f3775,plain,
( spl692_3
| spl692_2
| spl692_9
| ~ spl692_4 ),
inference(avatar_split_clause,[status(thm)],[f3386,f3465,f3765,f3458,f3461]) ).
thf(f3461,definition,
( spl692_3
<=> ( $false = sK320 ) ),
introduced(definition,[new_symbols(naming,[spl692_3])],[avatar_definition]) ).
thf(f3458,definition,
( spl692_2
<=> ! [X0: $i] :
( ( sK319 != X0 )
| ( ( in @ X0 @ sK318 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl692_2])],[avatar_definition]) ).
thf(f3765,definition,
( spl692_9
<=> ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
= sK319 ) ),
introduced(definition,[new_symbols(naming,[spl692_9])],[avatar_definition]) ).
thf(f3386,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
= sK319 )
| ( sK319 != X0 )
| ( $false = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f3385]) ).
thf(f3385,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
= sK319 )
| ( ( sK319 = X0 )
= $false )
| ( $false = sK320 ) ),
inference(duplicate_literal_removal,[status(thm)],[f3384]) ).
thf(f3384,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = sK320 )
| ( $true != sP0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
= sK319 )
| ( ( sK319 = X0 )
= $false )
| ( $false = sK320 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3383]) ).
thf(f3383,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = sK320 )
| ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
= sK319 )
| ( $true != sP0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f3382]) ).
thf(f3382,plain,
! [X0: $i] :
( ( ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( $true != sP0 )
| ( $false = sK320 ) ),
inference(not_proxy_clausification,[status(thm)],[f3376]) ).
thf(f3376,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ~ sK320 ) = $true )
| ( ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3375]) ).
thf(f3375,plain,
! [X0: $i] :
( ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( $true != sP0 )
| ( ( ~ sK320 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3373]) ).
thf(f3373,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( ~ sK320
& ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK320
& ( sK319 = X0 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f3372]) ).
thf(f3372,plain,
! [X0: $i] :
( ( ( ( sK320
& ( sK319
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( ~ sK320
& ( sK321
= ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
= $true )
| ( $true != sP0 )
| ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3370]) ).
thf(f3768,plain,
( ~ spl692_9
| spl692_2
| spl692_3
| ~ spl692_4
| ~ spl692_6 ),
inference(avatar_split_clause,[status(thm)],[f3739,f3701,f3465,f3461,f3458,f3765]) ).
thf(f3701,definition,
( spl692_6
<=> ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ),
introduced(definition,[new_symbols(naming,[spl692_6])],[avatar_definition]) ).
thf(f3739,plain,
( ! [X0: $i] :
( ( sK319 != X0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 ) )
| spl692_3
| ~ spl692_4
| ~ spl692_6 ),
inference(subsumption_resolution,[status(thm)],[f3738,f3466]) ).
thf(f3738,plain,
( ! [X0: $i] :
( ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK319 != X0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 ) )
| spl692_3
| ~ spl692_6 ),
inference(subsumption_resolution,[status(thm)],[f3737,f2627]) ).
thf(f3737,plain,
( ! [X0: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $true != sP0 )
| ( sK319 != X0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| spl692_3
| ~ spl692_6 ),
inference(subsumption_resolution,[status(thm)],[f3733,f3462]) ).
thf(f3462,plain,
( ( $false != sK320 )
| spl692_3 ),
inference(avatar_component_clause,[status(thm)],[f3461]) ).
thf(f3733,plain,
( ! [X0: $i] :
( ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( $true != sP0 )
| ( sK319 != X0 )
| ( $false = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| ~ spl692_6 ),
inference(equality_proxy_clausification,[status(thm)],[f3732]) ).
thf(f3732,plain,
( ! [X0: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( sK319 = X0 )
= $false )
| ( $false = sK320 )
| ( $true != sP0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 )
| ( ( in @ X0 @ sK318 )
!= $true ) )
| ~ spl692_6 ),
inference(binary_proxy_clausification,[status(thm)],[f3731]) ).
thf(f3731,plain,
( ! [X0: $i] :
( ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true ) )
| ~ spl692_6 ),
inference(binary_proxy_clausification,[status(thm)],[f3729]) ).
thf(f3729,plain,
( ! [X0: $i] :
( ( $true != sP0 )
| ( ( ( sK320
& ( sK319 = X0 ) )
| ( ~ sK320
& ( sK321 = X0 ) ) )
!= $true )
| ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 ) )
| ~ spl692_6 ),
inference(beta_eta_normalization,[status(thm)],[f3719]) ).
thf(f3719,plain,
( ! [X0: $i] :
( ( ( singleton
@ ( dsetconstr @ sK318
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( ( sK44
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 )
!= sK319 )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true ) )
| ~ spl692_6 ),
inference(superposition,[status(thm)],[f3280,f3703]) ).
thf(f3703,plain,
( ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ~ spl692_6 ),
inference(avatar_component_clause,[status(thm)],[f3701]) ).
thf(f3712,plain,
( ~ spl692_1
| ~ spl692_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f3711]) ).
thf(f3711,plain,
( $false
| ~ spl692_1
| ~ spl692_3 ),
inference(trivial_inequality_removal,[status(thm)],[f3710]) ).
thf(f3710,plain,
( ( $false = $true )
| ~ spl692_1
| ~ spl692_3 ),
inference(forward_demodulation,[status(thm)],[f3456,f3463]) ).
thf(f3463,plain,
( ( $false = sK320 )
| ~ spl692_3 ),
inference(avatar_component_clause,[status(thm)],[f3461]) ).
thf(f3456,plain,
( ( $true = sK320 )
| ~ spl692_1 ),
inference(avatar_component_clause,[status(thm)],[f3454]) ).
thf(f3709,plain,
( spl692_7
| ~ spl692_4
| spl692_1
| spl692_5 ),
inference(avatar_split_clause,[status(thm)],[f3344,f3697,f3454,f3465,f3706]) ).
thf(f3344,plain,
! [X0: $i] :
( ( $true = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 )
| ( sK321 != X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f3343]) ).
thf(f3343,plain,
! [X0: $i] :
( ( $true = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true = sK320 )
| ( sK321 != X0 )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3341]) ).
thf(f3341,plain,
! [X0: $i] :
( ( sK321 != X0 )
| ( $true != sP0 )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f3340]) ).
thf(f3340,plain,
! [X0: $i] :
( ( sK321 != X0 )
| ( $true = sK320 )
| ( $true != sP0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f3339]) ).
thf(f3339,plain,
! [X0: $i] :
( ( sK321 != X0 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = ( ~ sK320 ) )
| ( $true != sP0 )
| ( ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f3338]) ).
thf(f3338,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( $false
= ( sK321 = X0 ) )
| ( ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( $false = ( ~ sK320 ) )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3327]) ).
thf(f3327,plain,
! [X0: $i] :
( ( ( ~ sK320
& ( sK321 = X0 ) )
= $false )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3309]) ).
thf(f3309,plain,
! [X0: $i] :
( ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( ~ sK320
& ( sK321 = X0 ) )
= $false )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3308]) ).
thf(f3308,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( ( ( sK320
& ( sK319 = X0 ) )
| ( ~ sK320
& ( sK321 = X0 ) ) )
!= $true )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3307]) ).
thf(f3307,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( $true
= ( ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
| ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) ) )
| ( ( ( sK320
& ( sK319 = X0 ) )
| ( ~ sK320
& ( sK321 = X0 ) ) )
!= $true )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f3306]) ).
thf(f3306,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3305]) ).
thf(f3305,plain,
! [X0: $i] :
( ( $true != sP0 )
| ( $true != $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f2627,f3227]) ).
thf(f3227,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( $true != sP0 )
| ( ( X6 @ X9 )
!= $true )
| ( $true
= ( X6 @ ( sK45 @ X6 @ X5 ) ) )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2054]) ).
thf(f2054,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( X6 @ X9 )
!= $true )
| ( $true != sP0 )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( $true
= ( X6 @ ( sK45 @ X6 @ X5 ) ) )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1027]) ).
thf(f3704,plain,
( spl692_6
| spl692_3
| spl692_2
| ~ spl692_4 ),
inference(avatar_split_clause,[status(thm)],[f3325,f3465,f3458,f3461,f3701]) ).
thf(f3325,plain,
! [X0: $i] :
( ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 )
| ( $false = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK319 != X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f3324]) ).
thf(f3324,plain,
! [X0: $i] :
( ( sK319 != X0 )
| ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 )
| ( $false = sK320 )
| ( $false = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f3323]) ).
thf(f3323,plain,
! [X0: $i] :
( ( sK319 != X0 )
| ( $false = sK320 )
| ( ( ~ sK320 ) = $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3321]) ).
thf(f3321,plain,
! [X0: $i] :
( ( sK319 != X0 )
| ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( $false = sK320 )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $true != sP0 )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f3320]) ).
thf(f3320,plain,
! [X0: $i] :
( ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = sK320 )
| ( ( sK319 = X0 )
= $false )
| ( $true != sP0 )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f3312]) ).
thf(f3312,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( $false = sK320 )
| ( ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) )
= $true )
| ( $true != sP0 )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( sK319 = X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f3311]) ).
thf(f3311,plain,
! [X0: $i] :
( ( $false = sK320 )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( $true != sP0 )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( sK319 = X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f3310]) ).
thf(f3310,plain,
! [X0: $i] :
( ( ( sK320
& ( sK319 = X0 ) )
= $false )
| ( $true
= ( sK320
& ( sK319
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) ) )
| ( ( in @ X0 @ sK318 )
!= $true )
| ( ( ~ sK320
& ( sK321
= ( sK45
@ ^ [Y0: $i] :
( ( sK320
& ( sK319 = Y0 ) )
| ( ~ sK320
& ( sK321 = Y0 ) ) )
@ sK318 ) ) )
= $true )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3308]) ).
thf(f3608,plain,
~ spl692_2,
inference(avatar_contradiction_clause,[status(thm)],[f3607]) ).
thf(f3607,plain,
( $false
| ~ spl692_2 ),
inference(trivial_inequality_removal,[status(thm)],[f3554]) ).
thf(f3554,plain,
( ( sK319 != sK319 )
| ( $true != $true )
| ~ spl692_2 ),
inference(superposition,[status(thm)],[f3459,f2625]) ).
thf(f2625,plain,
( ( in @ sK319 @ sK318 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1432]) ).
thf(f3459,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK318 )
!= $true )
| ( sK319 != X0 ) )
| ~ spl692_2 ),
inference(avatar_component_clause,[status(thm)],[f3458]) ).
thf(f3472,plain,
spl692_4,
inference(avatar_contradiction_clause,[status(thm)],[f3471]) ).
thf(f3471,plain,
( $false
| spl692_4 ),
inference(subsumption_resolution,[status(thm)],[f3470,f2460]) ).
thf(f2460,plain,
singletonprop = $true,
inference(cnf_transformation,[status(thm)],[f1432]) ).
thf(f3470,plain,
( ( singletonprop != $true )
| spl692_4 ),
inference(trivial_inequality_removal,[status(thm)],[f3469]) ).
thf(f3469,plain,
( ( $true != $true )
| ( singletonprop != $true )
| spl692_4 ),
inference(superposition,[status(thm)],[f3467,f2062]) ).
thf(f2062,plain,
( ( $true = sP0 )
| ( singletonprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f1028]) ).
thf(f1028,plain,
( ( ( singletonprop = $true )
| ( $true != sP0 ) )
& ( ( $true = sP0 )
| ( singletonprop != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f955]) ).
thf(f955,plain,
( ( singletonprop = $true )
<=> ( $true = sP0 ) ),
inference(definition_folding,[status(thm)],[f850,f954]) ).
thf(f850,plain,
( ( singletonprop = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( X1 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( X1 @ X3 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f849]) ).
thf(f849,plain,
( ! [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ( ( X1 @ X3 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) )
<=> ( singletonprop = $true ) ),
inference(ennf_transformation,[status(thm)],[f626]) ).
thf(f626,plain,
( ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( X1 @ X2 )
= $true )
=> ( ( ( X1 @ X3 )
= $true )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X1 @ X4 )
= $true ) )
=> ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) )
<=> ( singletonprop = $true ) ),
inference(fool_elimination,[status(thm)],[f625]) ).
thf(f625,plain,
( singletonprop
= ( ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( X1 @ X4 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f157]) ).
thf(f157,axiom,
( singletonprop
= ( ! [X3: $i,X0: $i > $o] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) )
=> ( ? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X0 @ X1 ) )
=> ( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WuDOtMIMiy/DTF2THF_22813.p',singletonprop) ).
thf(f3467,plain,
( ( $true != sP0 )
| spl692_4 ),
inference(avatar_component_clause,[status(thm)],[f3465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU704^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n028.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:31:27 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.39 ---- Original DTF file ---
% 0.14/0.39 thf(spec,logic,$$dhol).
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 % File : SEU704^1 : TPTP v9.2.1. Released v3.7.0.
% 0.14/0.39 % Domain : Set Theory
% 0.14/0.39 % Problem : Conditionals
% 0.14/0.39 % Version : Especial.
% 0.14/0.39 % English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A -> singleton
% 0.14/0.39 % (dsetconstr A (^ z:i.phi & z = x | ~phi & z = y))))
% 0.14/0.39
% 0.14/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.14/0.39 % Source : [Bro08]
% 0.14/0.39 % Names : ZFC206g [Bro08]
% 0.14/0.39
% 0.14/0.39 % Status : Theorem
% 0.14/0.39 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0, 1.00 v3.7.0
% 0.14/0.39 % Syntax : Number of formulae : 483 ( 225 unt; 257 typ; 225 def)
% 0.14/0.39 % Number of atoms : 1255 ( 347 equ; 0 cnn)
% 0.14/0.39 % Maximal formula atoms : 225 ( 5 avg)
% 0.14/0.39 % Number of connectives : 2422 ( 54 ~; 12 |; 45 &;1711 @)
% 0.14/0.39 % ( 14 <=>; 586 =>; 0 <=; 0 <~>)
% 0.14/0.39 % Maximal formula depth : 233 ( 2 avg)
% 0.14/0.39 % Number of types : 2 ( 0 usr)
% 0.14/0.39 % Number of type conns : 128 ( 128 >; 0 *; 0 +; 0 <<)
% 0.14/0.39 % Number of symbols : 260 ( 257 usr; 224 con; 0-4 aty)
% 0.14/0.39 % Number of variables : 756 ( 75 ^; 645 !; 36 ?; 756 :)
% 0.14/0.39 % SPC : TH0_THM_EQU_NAR
% 0.14/0.39
% 0.14/0.39 % Comments : http://mathgate.info/detsetitem.php?id=256
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 thf(in_type,type,
% 0.14/0.39 in: $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(exu_type,type,
% 0.14/0.39 exu: ( $i > $o ) > $o ).
% 0.14/0.39
% 0.14/0.39 thf(exu,definition,
% 0.14/0.39 ( exu
% 0.14/0.39 = ( ^ [Xphi: $i > $o] :
% 0.14/0.39 ? [Xx: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 & ! [Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setextAx_type,type,
% 0.14/0.39 setextAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setextAx,definition,
% 0.14/0.39 ( setextAx
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 <=> ( in @ Xx @ B ) )
% 0.14/0.39 => ( A = B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyset_type,type,
% 0.14/0.39 emptyset: $i ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetAx_type,type,
% 0.14/0.39 emptysetAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetAx,definition,
% 0.14/0.39 ( emptysetAx
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoin_type,type,
% 0.14/0.39 setadjoin: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinAx_type,type,
% 0.14/0.39 setadjoinAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinAx,definition,
% 0.14/0.39 ( setadjoinAx
% 0.14/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.14/0.39 <=> ( ( Xy = Xx )
% 0.14/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powerset_type,type,
% 0.14/0.39 powerset: $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(powersetAx_type,type,
% 0.14/0.39 powersetAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetAx,definition,
% 0.14/0.39 ( powersetAx
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.14/0.39 <=> ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunion_type,type,
% 0.14/0.39 setunion: $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(setunionAx_type,type,
% 0.14/0.39 setunionAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionAx,definition,
% 0.14/0.39 ( setunionAx
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.14/0.39 <=> ? [B: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(omega_type,type,
% 0.14/0.39 omega: $i ).
% 0.14/0.39
% 0.14/0.39 thf(omega0Ax_type,type,
% 0.14/0.39 omega0Ax: $o ).
% 0.14/0.39
% 0.14/0.39 thf(omega0Ax,definition,
% 0.14/0.39 ( omega0Ax
% 0.14/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(omegaSAx_type,type,
% 0.14/0.39 omegaSAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(omegaSAx,definition,
% 0.14/0.39 ( omegaSAx
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ omega )
% 0.14/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(omegaIndAx_type,type,
% 0.14/0.39 omegaIndAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(omegaIndAx,definition,
% 0.14/0.39 ( omegaIndAx
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ( ( in @ emptyset @ A )
% 0.14/0.39 & ! [Xx: $i] :
% 0.14/0.39 ( ( ( in @ Xx @ omega )
% 0.14/0.39 & ( in @ Xx @ A ) )
% 0.14/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ omega )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(replAx_type,type,
% 0.14/0.39 replAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(replAx,definition,
% 0.14/0.39 ( replAx
% 0.14/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( exu
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.14/0.39 => ? [B: $i] :
% 0.14/0.39 ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 <=> ? [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(foundationAx_type,type,
% 0.14/0.39 foundationAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(foundationAx,definition,
% 0.14/0.39 ( foundationAx
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.14/0.39 => ? [B: $i] :
% 0.14/0.39 ( ( in @ B @ A )
% 0.14/0.39 & ~ ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(wellorderingAx_type,type,
% 0.14/0.39 wellorderingAx: $o ).
% 0.14/0.39
% 0.14/0.39 thf(wellorderingAx,definition,
% 0.14/0.39 ( wellorderingAx
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ? [B: $i] :
% 0.14/0.39 ( ! [C: $i] :
% 0.14/0.39 ( ( in @ C @ B )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ C )
% 0.14/0.39 => ( in @ Xx @ A ) ) )
% 0.14/0.39 & ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( ( in @ Xx @ A )
% 0.14/0.39 & ( in @ Xy @ A ) )
% 0.14/0.39 => ( ! [C: $i] :
% 0.14/0.39 ( ( in @ C @ B )
% 0.14/0.39 => ( ( in @ Xx @ C )
% 0.14/0.39 <=> ( in @ Xy @ C ) ) )
% 0.14/0.39 => ( Xx = Xy ) ) )
% 0.14/0.39 & ! [C: $i,D: $i] :
% 0.14/0.39 ( ( ( in @ C @ B )
% 0.14/0.39 & ( in @ D @ B ) )
% 0.14/0.39 => ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ C )
% 0.14/0.39 => ( in @ Xx @ D ) )
% 0.14/0.39 | ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ D )
% 0.14/0.39 => ( in @ Xx @ C ) ) ) )
% 0.14/0.39 & ! [C: $i] :
% 0.14/0.39 ( ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ C )
% 0.14/0.39 => ( in @ Xx @ A ) )
% 0.14/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.14/0.39 => ? [D: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ D @ B )
% 0.14/0.39 & ( in @ Xx @ C )
% 0.14/0.39 & ~ ? [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ D )
% 0.14/0.39 & ( in @ Xy @ C ) )
% 0.14/0.39 & ! [E: $i] :
% 0.14/0.39 ( ( in @ E @ B )
% 0.14/0.39 => ( ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ E )
% 0.14/0.39 => ( in @ Xy @ D ) )
% 0.14/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(descr_type,type,
% 0.14/0.39 descr: ( $i > $o ) > $i ).
% 0.14/0.39
% 0.14/0.39 thf(descrp_type,type,
% 0.14/0.39 descrp: $o ).
% 0.14/0.39
% 0.14/0.39 thf(descrp,definition,
% 0.14/0.39 ( descrp
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ( Xphi
% 0.14/0.39 @ ( descr
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstr_type,type,
% 0.14/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrI_type,type,
% 0.14/0.39 dsetconstrI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrI,definition,
% 0.14/0.39 ( dsetconstrI
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( in @ Xx
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrEL_type,type,
% 0.14/0.39 dsetconstrEL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrEL,definition,
% 0.14/0.39 ( dsetconstrEL
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrER_type,type,
% 0.14/0.39 dsetconstrER: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstrER,definition,
% 0.14/0.39 ( dsetconstrER
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.14/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuE1_type,type,
% 0.14/0.39 exuE1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuE1,definition,
% 0.14/0.39 ( exuE1
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 & ! [Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(prop2set_type,type,
% 0.14/0.39 prop2set: $o > $i ).
% 0.14/0.39
% 0.14/0.39 thf(prop2setE_type,type,
% 0.14/0.39 prop2setE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(prop2setE,definition,
% 0.14/0.39 ( prop2setE
% 0.14/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.14/0.39 => Xphi ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetE_type,type,
% 0.14/0.39 emptysetE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetE,definition,
% 0.14/0.39 ( emptysetE
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ emptyset )
% 0.14/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetimpfalse_type,type,
% 0.14/0.39 emptysetimpfalse: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetimpfalse,definition,
% 0.14/0.39 ( emptysetimpfalse
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ emptyset )
% 0.14/0.39 => $false ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notinemptyset_type,type,
% 0.14/0.39 notinemptyset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notinemptyset,definition,
% 0.14/0.39 ( notinemptyset
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuE3e_type,type,
% 0.14/0.39 exuE3e: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuE3e,definition,
% 0.14/0.39 ( exuE3e
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setext_type,type,
% 0.14/0.39 setext: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setext,definition,
% 0.14/0.39 ( setext
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ B ) )
% 0.14/0.39 => ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ A ) )
% 0.14/0.39 => ( A = B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyI_type,type,
% 0.14/0.39 emptyI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyI,definition,
% 0.14/0.39 ( emptyI
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ~ ( in @ Xx @ A )
% 0.14/0.39 => ( A = emptyset ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(noeltsimpempty_type,type,
% 0.14/0.39 noeltsimpempty: $o ).
% 0.14/0.39
% 0.14/0.39 thf(noeltsimpempty,definition,
% 0.14/0.39 ( noeltsimpempty
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ~ ( in @ Xx @ A )
% 0.14/0.39 => ( A = emptyset ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setbeta_type,type,
% 0.14/0.39 setbeta: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setbeta,definition,
% 0.14/0.39 ( setbeta
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( in @ Xx
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.14/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nonempty_type,type,
% 0.14/0.39 nonempty: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(nonempty,definition,
% 0.14/0.39 ( nonempty
% 0.14/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyE1_type,type,
% 0.14/0.39 nonemptyE1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyE1,definition,
% 0.14/0.39 ( nonemptyE1
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ( nonempty @ A )
% 0.14/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyI_type,type,
% 0.14/0.39 nonemptyI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyI,definition,
% 0.14/0.39 ( nonemptyI
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( nonempty
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyI1_type,type,
% 0.14/0.39 nonemptyI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyI1,definition,
% 0.14/0.39 ( nonemptyI1
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.14/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinIL_type,type,
% 0.14/0.39 setadjoinIL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinIL,definition,
% 0.14/0.39 ( setadjoinIL
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyinunitempty_type,type,
% 0.14/0.39 emptyinunitempty: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyinunitempty,definition,
% 0.14/0.39 ( emptyinunitempty
% 0.14/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinIR_type,type,
% 0.14/0.39 setadjoinIR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinIR,definition,
% 0.14/0.39 ( setadjoinIR
% 0.14/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinE_type,type,
% 0.14/0.39 setadjoinE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinE,definition,
% 0.14/0.39 ( setadjoinE
% 0.14/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.14/0.39 => ! [Xphi: $o] :
% 0.14/0.39 ( ( ( Xy = Xx )
% 0.14/0.39 => Xphi )
% 0.14/0.39 => ( ( ( in @ Xy @ A )
% 0.14/0.39 => Xphi )
% 0.14/0.39 => Xphi ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinOr_type,type,
% 0.14/0.39 setadjoinOr: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinOr,definition,
% 0.14/0.39 ( setadjoinOr
% 0.14/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.14/0.39 => ( ( Xy = Xx )
% 0.14/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setoftrueEq_type,type,
% 0.14/0.39 setoftrueEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setoftrueEq,definition,
% 0.14/0.39 ( setoftrueEq
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : $true )
% 0.14/0.39 = A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powersetI_type,type,
% 0.14/0.39 powersetI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetI,definition,
% 0.14/0.39 ( powersetI
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ A ) )
% 0.14/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyinPowerset_type,type,
% 0.14/0.39 emptyinPowerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyinPowerset,definition,
% 0.14/0.39 ( emptyinPowerset
% 0.14/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyInPowerset_type,type,
% 0.14/0.39 emptyInPowerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyInPowerset,definition,
% 0.14/0.39 ( emptyInPowerset
% 0.14/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powersetE_type,type,
% 0.14/0.39 powersetE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetE,definition,
% 0.14/0.39 ( powersetE
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.14/0.39 => ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionI_type,type,
% 0.14/0.39 setunionI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionI,definition,
% 0.14/0.39 ( setunionI
% 0.14/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( ( in @ B @ A )
% 0.14/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionE_type,type,
% 0.14/0.39 setunionE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionE,definition,
% 0.14/0.39 ( setunionE
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.14/0.39 => ! [Xphi: $o] :
% 0.14/0.39 ( ! [B: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( ( in @ B @ A )
% 0.14/0.39 => Xphi ) )
% 0.14/0.39 => Xphi ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subPowSU_type,type,
% 0.14/0.39 subPowSU: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subPowSU,definition,
% 0.14/0.39 ( subPowSU
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuE2_type,type,
% 0.14/0.39 exuE2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuE2,definition,
% 0.14/0.39 ( exuE2
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ! [Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xy )
% 0.14/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyImpWitness_type,type,
% 0.14/0.39 nonemptyImpWitness: $o ).
% 0.14/0.39
% 0.14/0.39 thf(nonemptyImpWitness,definition,
% 0.14/0.39 ( nonemptyImpWitness
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ( nonempty @ A )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & $true ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(uniqinunit_type,type,
% 0.14/0.39 uniqinunit: $o ).
% 0.14/0.39
% 0.14/0.39 thf(uniqinunit,definition,
% 0.14/0.39 ( uniqinunit
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notinsingleton_type,type,
% 0.14/0.39 notinsingleton: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notinsingleton,definition,
% 0.14/0.39 ( notinsingleton
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx != Xy )
% 0.14/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(eqinunit_type,type,
% 0.14/0.39 eqinunit: $o ).
% 0.14/0.39
% 0.14/0.39 thf(eqinunit,definition,
% 0.14/0.39 ( eqinunit
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsswitch_type,type,
% 0.14/0.39 singletonsswitch: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsswitch,definition,
% 0.14/0.39 ( singletonsswitch
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetE_type,type,
% 0.14/0.39 upairsetE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetE,definition,
% 0.14/0.39 ( upairsetE
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.14/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.14/0.39 => ( ( Xz = Xx )
% 0.14/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetIL_type,type,
% 0.14/0.39 upairsetIL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetIL,definition,
% 0.14/0.39 ( upairsetIL
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetIR_type,type,
% 0.14/0.39 upairsetIR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetIR,definition,
% 0.14/0.39 ( upairsetIR
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyE1_type,type,
% 0.14/0.39 emptyE1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyE1,definition,
% 0.14/0.39 ( emptyE1
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) )
% 0.14/0.39 => ( ( ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 = emptyset )
% 0.14/0.39 => $false ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(vacuousDall_type,type,
% 0.14/0.39 vacuousDall: $o ).
% 0.14/0.39
% 0.14/0.39 thf(vacuousDall,definition,
% 0.14/0.39 ( vacuousDall
% 0.14/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ emptyset )
% 0.14/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan1_type,type,
% 0.14/0.39 quantDeMorgan1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan1,definition,
% 0.14/0.39 ( quantDeMorgan1
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ~ ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan2_type,type,
% 0.14/0.39 quantDeMorgan2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan2,definition,
% 0.14/0.39 ( quantDeMorgan2
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ~ ( Xphi @ Xx ) )
% 0.14/0.39 => ~ ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan3_type,type,
% 0.14/0.39 quantDeMorgan3: $o ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan3,definition,
% 0.14/0.39 ( quantDeMorgan3
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ~ ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan4_type,type,
% 0.14/0.39 quantDeMorgan4: $o ).
% 0.14/0.39
% 0.14/0.39 thf(quantDeMorgan4,definition,
% 0.14/0.39 ( quantDeMorgan4
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ~ ( Xphi @ Xx ) )
% 0.14/0.39 => ~ ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(prop2setI_type,type,
% 0.14/0.39 prop2setI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(prop2setI,definition,
% 0.14/0.39 ( prop2setI
% 0.14/0.39 = ( ! [Xphi: $o] :
% 0.14/0.39 ( Xphi
% 0.14/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(set2prop_type,type,
% 0.14/0.39 set2prop: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(prop2set2propI_type,type,
% 0.14/0.39 prop2set2propI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(prop2set2propI,definition,
% 0.14/0.39 ( prop2set2propI
% 0.14/0.39 = ( ! [Xphi: $o] :
% 0.14/0.39 ( Xphi
% 0.14/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notdexE_type,type,
% 0.14/0.39 notdexE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notdexE,definition,
% 0.14/0.39 ( notdexE
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ~ ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notdallE_type,type,
% 0.14/0.39 notdallE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notdallE,definition,
% 0.14/0.39 ( notdallE
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ~ ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuI1_type,type,
% 0.14/0.39 exuI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuI1,definition,
% 0.14/0.39 ( exuI1
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ? [Xx: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 & ! [Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) )
% 0.14/0.39 => ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuI3_type,type,
% 0.14/0.39 exuI3: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuI3,definition,
% 0.14/0.39 ( exuI3
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.14/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) )
% 0.14/0.39 => ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuI2_type,type,
% 0.14/0.39 exuI2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuI2,definition,
% 0.14/0.39 ( exuI2
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ? [Xx: $i] :
% 0.14/0.39 ! [Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xy )
% 0.14/0.39 <=> ( Xy = Xx ) )
% 0.14/0.39 => ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(inCongP_type,type,
% 0.14/0.39 inCongP: $o ).
% 0.14/0.39
% 0.14/0.39 thf(inCongP,definition,
% 0.14/0.39 ( inCongP
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(in__Cong_type,type,
% 0.14/0.39 in__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(in__Cong,definition,
% 0.14/0.39 ( in__Cong
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( in @ Xx @ A )
% 0.14/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuE3u_type,type,
% 0.14/0.39 exuE3u: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuE3u,definition,
% 0.14/0.39 ( exuE3u
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exu__Cong_type,type,
% 0.14/0.39 exu__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exu__Cong,definition,
% 0.14/0.39 ( exu__Cong
% 0.14/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.14/0.39 => ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 <=> ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptyset__Cong_type,type,
% 0.14/0.39 emptyset__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptyset__Cong,definition,
% 0.14/0.39 ( emptyset__Cong
% 0.14/0.39 = ( emptyset = emptyset ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoin__Cong_type,type,
% 0.14/0.39 setadjoin__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoin__Cong,definition,
% 0.14/0.39 ( setadjoin__Cong
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ! [Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( Xz = Xu )
% 0.14/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.14/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powerset__Cong_type,type,
% 0.14/0.39 powerset__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powerset__Cong,definition,
% 0.14/0.39 ( powerset__Cong
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ( ( powerset @ A )
% 0.14/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunion__Cong_type,type,
% 0.14/0.39 setunion__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunion__Cong,definition,
% 0.14/0.39 ( setunion__Cong
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ( ( setunion @ A )
% 0.14/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(omega__Cong_type,type,
% 0.14/0.39 omega__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(omega__Cong,definition,
% 0.14/0.39 ( omega__Cong
% 0.14/0.39 = ( omega = omega ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(exuEu_type,type,
% 0.14/0.39 exuEu: $o ).
% 0.14/0.39
% 0.14/0.39 thf(exuEu,definition,
% 0.14/0.39 ( exuEu
% 0.14/0.39 = ( ! [Xphi: $i > $o] :
% 0.14/0.39 ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(descr__Cong_type,type,
% 0.14/0.39 descr__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(descr__Cong,definition,
% 0.14/0.39 ( descr__Cong
% 0.14/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.14/0.39 => ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ( ( exu
% 0.14/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.14/0.39 => ( ( descr
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 = ( descr
% 0.14/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstr__Cong_type,type,
% 0.14/0.39 dsetconstr__Cong: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dsetconstr__Cong,definition,
% 0.14/0.39 ( dsetconstr__Cong
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( Xx = Xy )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.14/0.39 => ( ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 = ( dsetconstr @ B
% 0.14/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subset_type,type,
% 0.14/0.39 subset: $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(disjoint_type,type,
% 0.14/0.39 disjoint: $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(setsmeet_type,type,
% 0.14/0.39 setsmeet: $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetI1_type,type,
% 0.14/0.39 subsetI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetI1,definition,
% 0.14/0.39 ( subsetI1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ B ) )
% 0.14/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(eqimpsubset2_type,type,
% 0.14/0.39 eqimpsubset2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(eqimpsubset2,definition,
% 0.14/0.39 ( eqimpsubset2
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(eqimpsubset1_type,type,
% 0.14/0.39 eqimpsubset1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(eqimpsubset1,definition,
% 0.14/0.39 ( eqimpsubset1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( A = B )
% 0.14/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetI2_type,type,
% 0.14/0.39 subsetI2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetI2,definition,
% 0.14/0.39 ( subsetI2
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ B ) )
% 0.14/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetsubset_type,type,
% 0.14/0.39 emptysetsubset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(emptysetsubset,definition,
% 0.14/0.39 ( emptysetsubset
% 0.14/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetE_type,type,
% 0.14/0.39 subsetE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetE,definition,
% 0.14/0.39 ( subsetE
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetE2_type,type,
% 0.14/0.39 subsetE2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetE2,definition,
% 0.14/0.39 ( subsetE2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notsubsetI_type,type,
% 0.14/0.39 notsubsetI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notsubsetI,definition,
% 0.14/0.39 ( notsubsetI
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notequalI1_type,type,
% 0.14/0.39 notequalI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notequalI1,definition,
% 0.14/0.39 ( notequalI1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ~ ( subset @ A @ B )
% 0.14/0.39 => ( A != B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(notequalI2_type,type,
% 0.14/0.39 notequalI2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(notequalI2,definition,
% 0.14/0.39 ( notequalI2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ( A != B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetRefl_type,type,
% 0.14/0.39 subsetRefl: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetRefl,definition,
% 0.14/0.39 ( subsetRefl
% 0.14/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetTrans_type,type,
% 0.14/0.39 subsetTrans: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetTrans,definition,
% 0.14/0.39 ( subsetTrans
% 0.14/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ( subset @ B @ C )
% 0.14/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinSub_type,type,
% 0.14/0.39 setadjoinSub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinSub,definition,
% 0.14/0.39 ( setadjoinSub
% 0.14/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinSub2_type,type,
% 0.14/0.39 setadjoinSub2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setadjoinSub2,definition,
% 0.14/0.39 ( setadjoinSub2
% 0.14/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subset2powerset_type,type,
% 0.14/0.39 subset2powerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subset2powerset,definition,
% 0.14/0.39 ( subset2powerset
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setextsub_type,type,
% 0.14/0.39 setextsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setextsub,definition,
% 0.14/0.39 ( setextsub
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ( subset @ B @ A )
% 0.14/0.39 => ( A = B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subsetemptysetimpeq_type,type,
% 0.14/0.39 subsetemptysetimpeq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subsetemptysetimpeq,definition,
% 0.14/0.39 ( subsetemptysetimpeq
% 0.14/0.39 = ( ! [A: $i] :
% 0.14/0.39 ( ( subset @ A @ emptyset )
% 0.14/0.39 => ( A = emptyset ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powersetI1_type,type,
% 0.14/0.39 powersetI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetI1,definition,
% 0.14/0.39 ( powersetI1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ B @ A )
% 0.14/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powersetE1_type,type,
% 0.14/0.39 powersetE1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetE1,definition,
% 0.14/0.39 ( powersetE1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.14/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(inPowerset_type,type,
% 0.14/0.39 inPowerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(inPowerset,definition,
% 0.14/0.39 ( inPowerset
% 0.14/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(powersetsubset_type,type,
% 0.14/0.39 powersetsubset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(powersetsubset,definition,
% 0.14/0.39 ( powersetsubset
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sepInPowerset_type,type,
% 0.14/0.39 sepInPowerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(sepInPowerset,definition,
% 0.14/0.39 ( sepInPowerset
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( in
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sepSubset_type,type,
% 0.14/0.39 sepSubset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(sepSubset,definition,
% 0.14/0.39 ( sepSubset
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( subset
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunion_type,type,
% 0.14/0.39 binunion: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(binunionIL_type,type,
% 0.14/0.39 binunionIL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionIL,definition,
% 0.14/0.39 ( binunionIL
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairset2IR_type,type,
% 0.14/0.39 upairset2IR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairset2IR,definition,
% 0.14/0.39 ( upairset2IR
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunionIR_type,type,
% 0.14/0.39 binunionIR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionIR,definition,
% 0.14/0.39 ( binunionIR
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunionEcases_type,type,
% 0.14/0.39 binunionEcases: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionEcases,definition,
% 0.14/0.39 ( binunionEcases
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.14/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.14/0.39 => ( ( ( in @ Xx @ A )
% 0.14/0.39 => Xphi )
% 0.14/0.39 => ( ( ( in @ Xx @ B )
% 0.14/0.39 => Xphi )
% 0.14/0.39 => Xphi ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunionE_type,type,
% 0.14/0.39 binunionE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionE,definition,
% 0.14/0.39 ( binunionE
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.14/0.39 => ( ( in @ Xx @ A )
% 0.14/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunionLsub_type,type,
% 0.14/0.39 binunionLsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionLsub,definition,
% 0.14/0.39 ( binunionLsub
% 0.14/0.39 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binunionRsub_type,type,
% 0.14/0.39 binunionRsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binunionRsub,definition,
% 0.14/0.39 ( binunionRsub
% 0.14/0.39 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersect_type,type,
% 0.14/0.39 binintersect: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectI_type,type,
% 0.14/0.39 binintersectI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectI,definition,
% 0.14/0.39 ( binintersectI
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset5_type,type,
% 0.14/0.39 binintersectSubset5: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset5,definition,
% 0.14/0.39 ( binintersectSubset5
% 0.14/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.14/0.39 ( ( subset @ C @ A )
% 0.14/0.39 => ( ( subset @ C @ B )
% 0.14/0.39 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectEL_type,type,
% 0.14/0.39 binintersectEL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectEL,definition,
% 0.14/0.39 ( binintersectEL
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectLsub_type,type,
% 0.14/0.39 binintersectLsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectLsub,definition,
% 0.14/0.39 ( binintersectLsub
% 0.14/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset2_type,type,
% 0.14/0.39 binintersectSubset2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset2,definition,
% 0.14/0.39 ( binintersectSubset2
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ( binintersect @ A @ B )
% 0.14/0.39 = A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset3_type,type,
% 0.14/0.39 binintersectSubset3: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset3,definition,
% 0.14/0.39 ( binintersectSubset3
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( ( binintersect @ A @ B )
% 0.14/0.39 = B )
% 0.14/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectER_type,type,
% 0.14/0.39 binintersectER: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectER,definition,
% 0.14/0.39 ( binintersectER
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.14/0.39 => ( in @ Xx @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(disjointsetsI1_type,type,
% 0.14/0.39 disjointsetsI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(disjointsetsI1,definition,
% 0.14/0.39 ( disjointsetsI1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ~ ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( in @ Xx @ B ) )
% 0.14/0.39 => ( ( binintersect @ A @ B )
% 0.14/0.39 = emptyset ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectRsub_type,type,
% 0.14/0.39 binintersectRsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectRsub,definition,
% 0.14/0.39 ( binintersectRsub
% 0.14/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset4_type,type,
% 0.14/0.39 binintersectSubset4: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset4,definition,
% 0.14/0.39 ( binintersectSubset4
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ B @ A )
% 0.14/0.39 => ( ( binintersect @ A @ B )
% 0.14/0.39 = B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset1_type,type,
% 0.14/0.39 binintersectSubset1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(binintersectSubset1,definition,
% 0.14/0.39 ( binintersectSubset1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( ( binintersect @ A @ B )
% 0.14/0.39 = A )
% 0.14/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(bs114d_type,type,
% 0.14/0.39 bs114d: $o ).
% 0.14/0.39
% 0.14/0.39 thf(bs114d,definition,
% 0.14/0.39 ( bs114d
% 0.14/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.14/0.39 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.14/0.39 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(regular_type,type,
% 0.14/0.39 regular: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminus_type,type,
% 0.14/0.39 setminus: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(setminusI_type,type,
% 0.14/0.39 setminusI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusI,definition,
% 0.14/0.39 ( setminusI
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusEL_type,type,
% 0.14/0.39 setminusEL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusEL,definition,
% 0.14/0.39 ( setminusEL
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusER_type,type,
% 0.14/0.39 setminusER: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusER,definition,
% 0.14/0.39 ( setminusER
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.14/0.39 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusSubset2_type,type,
% 0.14/0.39 setminusSubset2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusSubset2,definition,
% 0.14/0.39 ( setminusSubset2
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( subset @ A @ B )
% 0.14/0.39 => ( ( setminus @ A @ B )
% 0.14/0.39 = emptyset ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusERneg_type,type,
% 0.14/0.39 setminusERneg: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusERneg,definition,
% 0.14/0.39 ( setminusERneg
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.14/0.39 => ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusELneg_type,type,
% 0.14/0.39 setminusELneg: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusELneg,definition,
% 0.14/0.39 ( setminusELneg
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusILneg_type,type,
% 0.14/0.39 setminusILneg: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusILneg,definition,
% 0.14/0.39 ( setminusILneg
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ~ ( in @ Xx @ A )
% 0.14/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusIRneg_type,type,
% 0.14/0.39 setminusIRneg: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusIRneg,definition,
% 0.14/0.39 ( setminusIRneg
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ B )
% 0.14/0.39 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusLsub_type,type,
% 0.14/0.39 setminusLsub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusLsub,definition,
% 0.14/0.39 ( setminusLsub
% 0.14/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setminusSubset1_type,type,
% 0.14/0.39 setminusSubset1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setminusSubset1,definition,
% 0.14/0.39 ( setminusSubset1
% 0.14/0.39 = ( ! [A: $i,B: $i] :
% 0.14/0.39 ( ( ( setminus @ A @ B )
% 0.14/0.39 = emptyset )
% 0.14/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(symdiff_type,type,
% 0.14/0.39 symdiff: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffE_type,type,
% 0.14/0.39 symdiffE: $o ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffE,definition,
% 0.14/0.39 ( symdiffE
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.14/0.39 => ! [Xphi: $o] :
% 0.14/0.39 ( ( ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => Xphi ) )
% 0.14/0.39 => ( ( ~ ( in @ Xx @ A )
% 0.14/0.39 => ( ( in @ Xx @ B )
% 0.14/0.39 => Xphi ) )
% 0.14/0.39 => Xphi ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffI1_type,type,
% 0.14/0.39 symdiffI1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffI1,definition,
% 0.14/0.39 ( symdiffI1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffI2_type,type,
% 0.14/0.39 symdiffI2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffI2,definition,
% 0.14/0.39 ( symdiffI2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ~ ( in @ Xx @ A )
% 0.14/0.39 => ( ( in @ Xx @ B )
% 0.14/0.39 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffIneg1_type,type,
% 0.14/0.39 symdiffIneg1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffIneg1,definition,
% 0.14/0.39 ( symdiffIneg1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( in @ Xx @ B )
% 0.14/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffIneg2_type,type,
% 0.14/0.39 symdiffIneg2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(symdiffIneg2,definition,
% 0.14/0.39 ( symdiffIneg2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ~ ( in @ Xx @ A )
% 0.14/0.39 => ( ~ ( in @ Xx @ B )
% 0.14/0.39 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(iskpair_type,type,
% 0.14/0.39 iskpair: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(secondinupair_type,type,
% 0.14/0.39 secondinupair: $o ).
% 0.14/0.39
% 0.14/0.39 thf(secondinupair,definition,
% 0.14/0.39 ( secondinupair
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairIL_type,type,
% 0.14/0.39 setukpairIL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairIL,definition,
% 0.14/0.39 ( setukpairIL
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairIR_type,type,
% 0.14/0.39 setukpairIR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairIR,definition,
% 0.14/0.39 ( setukpairIR
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(kpairiskpair_type,type,
% 0.14/0.39 kpairiskpair: $o ).
% 0.14/0.39
% 0.14/0.39 thf(kpairiskpair,definition,
% 0.14/0.39 ( kpairiskpair
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(kpair_type,type,
% 0.14/0.39 kpair: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(kpairp_type,type,
% 0.14/0.39 kpairp: $o ).
% 0.14/0.39
% 0.14/0.39 thf(kpairp,definition,
% 0.14/0.39 ( kpairp
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprod_type,type,
% 0.14/0.39 cartprod: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsubset_type,type,
% 0.14/0.39 singletonsubset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsubset,definition,
% 0.14/0.39 ( singletonsubset
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singletoninpowerset_type,type,
% 0.14/0.39 singletoninpowerset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletoninpowerset,definition,
% 0.14/0.39 ( singletoninpowerset
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singletoninpowunion_type,type,
% 0.14/0.39 singletoninpowunion: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletoninpowunion,definition,
% 0.14/0.39 ( singletoninpowunion
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairset2E_type,type,
% 0.14/0.39 upairset2E: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairset2E,definition,
% 0.14/0.39 ( upairset2E
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.14/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.14/0.39 => ( ( Xz = Xx )
% 0.14/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairsubunion_type,type,
% 0.14/0.39 upairsubunion: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairsubunion,definition,
% 0.14/0.39 ( upairsubunion
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairinpowunion_type,type,
% 0.14/0.39 upairinpowunion: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairinpowunion,definition,
% 0.14/0.39 ( upairinpowunion
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem1_type,type,
% 0.14/0.39 ubforcartprodlem1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem1,definition,
% 0.14/0.39 ( ubforcartprodlem1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem2_type,type,
% 0.14/0.39 ubforcartprodlem2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem2,definition,
% 0.14/0.39 ( ubforcartprodlem2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem3_type,type,
% 0.14/0.39 ubforcartprodlem3: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ubforcartprodlem3,definition,
% 0.14/0.39 ( ubforcartprodlem3
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairin_type,type,
% 0.14/0.39 cartprodpairin: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairin,definition,
% 0.14/0.39 ( cartprodpairin
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempair1_type,type,
% 0.14/0.39 cartprodmempair1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempair1,definition,
% 0.14/0.39 ( cartprodmempair1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.14/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ? [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 & ( Xu
% 0.14/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempair_type,type,
% 0.14/0.39 cartprodmempair: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempair,definition,
% 0.14/0.39 ( cartprodmempair
% 0.14/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.14/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( iskpair @ Xu ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionE2_type,type,
% 0.14/0.39 setunionE2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionE2,definition,
% 0.14/0.39 ( setunionE2
% 0.14/0.39 = ( ! [A: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.14/0.39 => ? [X: $i] :
% 0.14/0.39 ( ( in @ X @ A )
% 0.14/0.39 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton1_type,type,
% 0.14/0.39 setunionsingleton1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton1,definition,
% 0.14/0.39 ( setunionsingleton1
% 0.14/0.39 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton2_type,type,
% 0.14/0.39 setunionsingleton2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton2,definition,
% 0.14/0.39 ( setunionsingleton2
% 0.14/0.39 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton_type,type,
% 0.14/0.39 setunionsingleton: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setunionsingleton,definition,
% 0.14/0.39 ( setunionsingleton
% 0.14/0.39 = ( ! [Xx: $i] :
% 0.14/0.39 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.14/0.39 = Xx ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singleton_type,type,
% 0.14/0.39 singleton: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(singleton,definition,
% 0.14/0.39 ( singleton
% 0.14/0.39 = ( ^ [A: $i] :
% 0.14/0.39 ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( A
% 0.14/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singletonprop_type,type,
% 0.14/0.39 singletonprop: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletonprop,definition,
% 0.14/0.39 ( singletonprop
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) )
% 0.14/0.39 => ( ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) )
% 0.14/0.39 => ( singleton
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ex1_type,type,
% 0.14/0.39 ex1: $i > ( $i > $o ) > $o ).
% 0.14/0.39
% 0.14/0.39 thf(ex1,definition,
% 0.14/0.39 ( ex1
% 0.14/0.39 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( singleton
% 0.14/0.39 @ ( dsetconstr @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ex1E1_type,type,
% 0.14/0.39 ex1E1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ex1E1,definition,
% 0.14/0.39 ( ex1E1
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ( ex1 @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ex1I_type,type,
% 0.14/0.39 ex1I: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ex1I,definition,
% 0.14/0.39 ( ex1I
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xy = Xx ) ) )
% 0.14/0.39 => ( ex1 @ A
% 0.14/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ex1I2_type,type,
% 0.14/0.39 ex1I2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ex1I2,definition,
% 0.14/0.39 ( ex1I2
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) )
% 0.14/0.39 => ( ? [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 & ( Xphi @ Xx ) )
% 0.14/0.39 => ( ex1 @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsuniq_type,type,
% 0.14/0.39 singletonsuniq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(singletonsuniq,definition,
% 0.14/0.39 ( singletonsuniq
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( ( setadjoin @ Xx @ emptyset )
% 0.14/0.39 = ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(atmost1p_type,type,
% 0.14/0.39 atmost1p: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(atleast2p_type,type,
% 0.14/0.39 atleast2p: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(atmost2p_type,type,
% 0.14/0.39 atmost2p: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairsetp_type,type,
% 0.14/0.39 upairsetp: $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL1_type,type,
% 0.14/0.39 setukpairinjL1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL1,definition,
% 0.14/0.39 ( setukpairinjL1
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.14/0.39 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.14/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(kfstsingleton_type,type,
% 0.14/0.39 kfstsingleton: $o ).
% 0.14/0.39
% 0.14/0.39 thf(kfstsingleton,definition,
% 0.14/0.39 ( kfstsingleton
% 0.14/0.39 = ( ! [Xu: $i] :
% 0.14/0.39 ( ( iskpair @ Xu )
% 0.14/0.39 => ( singleton
% 0.14/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.14/0.39 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(theprop_type,type,
% 0.14/0.39 theprop: $o ).
% 0.14/0.39
% 0.14/0.39 thf(theprop,definition,
% 0.14/0.39 ( theprop
% 0.14/0.39 = ( ! [X: $i] :
% 0.14/0.39 ( ( singleton @ X )
% 0.14/0.39 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(kfst_type,type,
% 0.14/0.39 kfst: $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(kfstpairEq_type,type,
% 0.14/0.39 kfstpairEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(kfstpairEq,definition,
% 0.14/0.39 ( kfstpairEq
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.14/0.39 = Xx ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodfstin_type,type,
% 0.14/0.39 cartprodfstin: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodfstin,definition,
% 0.14/0.39 ( cartprodfstin
% 0.14/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.14/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL2_type,type,
% 0.14/0.39 setukpairinjL2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL2,definition,
% 0.14/0.39 ( setukpairinjL2
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.14/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL_type,type,
% 0.14/0.39 setukpairinjL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjL,definition,
% 0.14/0.39 ( setukpairinjL
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.14/0.39 = ( kpair @ Xz @ Xu ) )
% 0.14/0.39 => ( Xx = Xz ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR11_type,type,
% 0.14/0.39 setukpairinjR11: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR11,definition,
% 0.14/0.39 ( setukpairinjR11
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR12_type,type,
% 0.14/0.39 setukpairinjR12: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR12,definition,
% 0.14/0.39 ( setukpairinjR12
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xx = Xy )
% 0.14/0.39 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR1_type,type,
% 0.14/0.39 setukpairinjR1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR1,definition,
% 0.14/0.39 ( setukpairinjR1
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.14/0.39 => ( ( Xz = Xu )
% 0.14/0.39 => ( Xy = Xu ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(upairequniteq_type,type,
% 0.14/0.39 upairequniteq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(upairequniteq,definition,
% 0.14/0.39 ( upairequniteq
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.14/0.39 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ Xz @ emptyset ) )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR2_type,type,
% 0.14/0.39 setukpairinjR2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR2,definition,
% 0.14/0.39 ( setukpairinjR2
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.14/0.39 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.14/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR_type,type,
% 0.14/0.39 setukpairinjR: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setukpairinjR,definition,
% 0.14/0.39 ( setukpairinjR
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.14/0.39 ( ( ( kpair @ Xx @ Xy )
% 0.14/0.39 = ( kpair @ Xz @ Xu ) )
% 0.14/0.39 => ( Xy = Xu ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ksndsingleton_type,type,
% 0.14/0.39 ksndsingleton: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ksndsingleton,definition,
% 0.14/0.39 ( ksndsingleton
% 0.14/0.39 = ( ! [Xu: $i] :
% 0.14/0.39 ( ( iskpair @ Xu )
% 0.14/0.39 => ( singleton
% 0.14/0.39 @ ( dsetconstr @ ( setunion @ Xu )
% 0.14/0.39 @ ^ [Xx: $i] :
% 0.14/0.39 ( Xu
% 0.14/0.39 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ksnd_type,type,
% 0.14/0.39 ksnd: $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(ksndpairEq_type,type,
% 0.14/0.39 ksndpairEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ksndpairEq,definition,
% 0.14/0.39 ( ksndpairEq
% 0.14/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.14/0.39 = Xy ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(kpairsurjEq_type,type,
% 0.14/0.39 kpairsurjEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(kpairsurjEq,definition,
% 0.14/0.39 ( kpairsurjEq
% 0.14/0.39 = ( ! [Xu: $i] :
% 0.14/0.39 ( ( iskpair @ Xu )
% 0.14/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.14/0.39 = Xu ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodsndin_type,type,
% 0.14/0.39 cartprodsndin: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodsndin,definition,
% 0.14/0.39 ( cartprodsndin
% 0.14/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.14/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairmemEL_type,type,
% 0.14/0.39 cartprodpairmemEL: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairmemEL,definition,
% 0.14/0.39 ( cartprodpairmemEL
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairmemER_type,type,
% 0.14/0.39 cartprodpairmemER: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairmemER,definition,
% 0.14/0.39 ( cartprodpairmemER
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempaircEq_type,type,
% 0.14/0.39 cartprodmempaircEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodmempaircEq,definition,
% 0.14/0.39 ( cartprodmempaircEq
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( kpair @ Xx @ Xy )
% 0.14/0.39 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodfstpairEq_type,type,
% 0.14/0.39 cartprodfstpairEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodfstpairEq,definition,
% 0.14/0.39 ( cartprodfstpairEq
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.14/0.39 = Xx ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodsndpairEq_type,type,
% 0.14/0.39 cartprodsndpairEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodsndpairEq,definition,
% 0.14/0.39 ( cartprodsndpairEq
% 0.14/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.14/0.39 = Xy ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairsurjEq_type,type,
% 0.14/0.39 cartprodpairsurjEq: $o ).
% 0.14/0.39
% 0.14/0.39 thf(cartprodpairsurjEq,definition,
% 0.14/0.39 ( cartprodpairsurjEq
% 0.14/0.39 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.14/0.39 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.14/0.39 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.14/0.39 = Xu ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(breln_type,type,
% 0.14/0.39 breln: $i > $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(breln,definition,
% 0.14/0.39 ( breln
% 0.14/0.39 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstr_type,type,
% 0.14/0.39 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrI_type,type,
% 0.14/0.39 dpsetconstrI: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrI,definition,
% 0.14/0.39 ( dpsetconstrI
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( Xphi @ Xx @ Xy )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ Xy )
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrSub_type,type,
% 0.14/0.39 dpsetconstrSub: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrSub,definition,
% 0.14/0.39 ( dpsetconstrSub
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.14/0.39 ( subset
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.14/0.39 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(setOfPairsIsBReln_type,type,
% 0.14/0.39 setOfPairsIsBReln: $o ).
% 0.14/0.39
% 0.14/0.39 thf(setOfPairsIsBReln,definition,
% 0.14/0.39 ( setOfPairsIsBReln
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.14/0.39 ( breln @ A @ B
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrERa_type,type,
% 0.14/0.39 dpsetconstrERa: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrERa,definition,
% 0.14/0.39 ( dpsetconstrERa
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.14/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrEL1_type,type,
% 0.14/0.39 dpsetconstrEL1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrEL1,definition,
% 0.14/0.39 ( dpsetconstrEL1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.14/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrEL2_type,type,
% 0.14/0.39 dpsetconstrEL2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrEL2,definition,
% 0.14/0.39 ( dpsetconstrEL2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.14/0.39 => ( in @ Xy @ B ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrER_type,type,
% 0.14/0.39 dpsetconstrER: $o ).
% 0.14/0.39
% 0.14/0.39 thf(dpsetconstrER,definition,
% 0.14/0.39 ( dpsetconstrER
% 0.14/0.39 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( in @ ( kpair @ Xx @ Xy )
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.14/0.39 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(func_type,type,
% 0.14/0.39 func: $i > $i > $i > $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcSet_type,type,
% 0.14/0.39 funcSet: $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(funcImageSingleton_type,type,
% 0.14/0.39 funcImageSingleton: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcImageSingleton,definition,
% 0.14/0.39 ( funcImageSingleton
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( singleton
% 0.14/0.39 @ ( dsetconstr @ B
% 0.14/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(apProp_type,type,
% 0.14/0.39 apProp: $o ).
% 0.14/0.39
% 0.14/0.39 thf(apProp,definition,
% 0.14/0.39 ( apProp
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in
% 0.14/0.39 @ ( setunion
% 0.14/0.39 @ ( dsetconstr @ B
% 0.14/0.39 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.14/0.39 @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ap_type,type,
% 0.14/0.39 ap: $i > $i > $i > $i > $i ).
% 0.14/0.39
% 0.14/0.39 thf(app_type,type,
% 0.14/0.39 app: $o ).
% 0.14/0.39
% 0.14/0.39 thf(app,definition,
% 0.14/0.39 ( app
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(infuncsetfunc_type,type,
% 0.14/0.39 infuncsetfunc: $o ).
% 0.14/0.39
% 0.14/0.39 thf(infuncsetfunc,definition,
% 0.14/0.39 ( infuncsetfunc
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.39 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ap2p_type,type,
% 0.14/0.39 ap2p: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ap2p,definition,
% 0.14/0.39 ( ap2p
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcinfuncset_type,type,
% 0.14/0.39 funcinfuncset: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcinfuncset,definition,
% 0.14/0.39 ( funcinfuncset
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(lamProp_type,type,
% 0.14/0.39 lamProp: $o ).
% 0.14/0.39
% 0.14/0.39 thf(lamProp,definition,
% 0.14/0.39 ( lamProp
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.39 => ( func @ A @ B
% 0.14/0.39 @ ( dpsetconstr @ A @ B
% 0.14/0.39 @ ^ [Xx: $i,Xy: $i] :
% 0.14/0.39 ( ( Xf @ Xx )
% 0.14/0.39 = Xy ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(lam_type,type,
% 0.14/0.39 lam: $i > $i > ( $i > $i ) > $i ).
% 0.14/0.39
% 0.14/0.39 thf(lamp_type,type,
% 0.14/0.39 lamp: $o ).
% 0.14/0.39
% 0.14/0.39 thf(lamp,definition,
% 0.14/0.39 ( lamp
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.39 => ( func @ A @ B
% 0.14/0.39 @ ( lam @ A @ B
% 0.14/0.39 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(lam2p_type,type,
% 0.14/0.39 lam2p: $o ).
% 0.14/0.39
% 0.14/0.39 thf(lam2p,definition,
% 0.14/0.39 ( lam2p
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.39 => ( in
% 0.14/0.39 @ ( lam @ A @ B
% 0.14/0.39 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.14/0.39 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(brelnall1_type,type,
% 0.14/0.39 brelnall1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(brelnall1,definition,
% 0.14/0.39 ( brelnall1
% 0.14/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.14/0.39 ( ( breln @ A @ B @ R )
% 0.14/0.39 => ! [Xphi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.14/0.39 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ R )
% 0.14/0.39 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(brelnall2_type,type,
% 0.14/0.39 brelnall2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(brelnall2,definition,
% 0.14/0.39 ( brelnall2
% 0.14/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.14/0.39 ( ( breln @ A @ B @ R )
% 0.14/0.39 => ! [Xphi: $i > $o] :
% 0.14/0.39 ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.14/0.39 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ R )
% 0.14/0.39 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(ex1E2_type,type,
% 0.14/0.39 ex1E2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(ex1E2,definition,
% 0.14/0.39 ( ex1E2
% 0.14/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.14/0.39 ( ( ex1 @ A
% 0.14/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ A )
% 0.14/0.39 => ( ( Xphi @ Xx )
% 0.14/0.39 => ( ( Xphi @ Xy )
% 0.14/0.39 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp1_type,type,
% 0.14/0.39 funcGraphProp1: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp1,definition,
% 0.14/0.39 ( funcGraphProp1
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp3_type,type,
% 0.14/0.39 funcGraphProp3: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp3,definition,
% 0.14/0.39 ( funcGraphProp3
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp2_type,type,
% 0.14/0.39 funcGraphProp2: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp2,definition,
% 0.14/0.39 ( funcGraphProp2
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.14/0.39 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.39 = Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcextLem_type,type,
% 0.14/0.39 funcextLem: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcextLem,definition,
% 0.14/0.39 ( funcextLem
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xf )
% 0.14/0.39 => ! [Xg: $i] :
% 0.14/0.39 ( ( func @ A @ B @ Xg )
% 0.14/0.39 => ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.39 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp4_type,type,
% 0.14/0.39 funcGraphProp4: $o ).
% 0.14/0.39
% 0.14/0.39 thf(funcGraphProp4,definition,
% 0.14/0.39 ( funcGraphProp4
% 0.14/0.39 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.39 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.39 => ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.14/0.39 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.39 = Xy ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(subbreln_type,type,
% 0.14/0.39 subbreln: $o ).
% 0.14/0.39
% 0.14/0.39 thf(subbreln,definition,
% 0.14/0.39 ( subbreln
% 0.14/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.14/0.39 ( ( breln @ A @ B @ R )
% 0.14/0.39 => ! [S: $i] :
% 0.14/0.39 ( ( breln @ A @ B @ S )
% 0.14/0.39 => ( ! [Xx: $i] :
% 0.14/0.39 ( ( in @ Xx @ A )
% 0.14/0.39 => ! [Xy: $i] :
% 0.14/0.39 ( ( in @ Xy @ B )
% 0.14/0.39 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.14/0.39 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.14/0.39 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(eqbreln_type,type,
% 0.14/0.39 eqbreln: $o ).
% 0.14/0.39
% 0.14/0.39 thf(eqbreln,definition,
% 0.14/0.39 ( eqbreln
% 0.14/0.39 = ( ! [A: $i,B: $i,R: $i] :
% 0.14/0.40 ( ( breln @ A @ B @ R )
% 0.14/0.40 => ! [S: $i] :
% 0.14/0.40 ( ( breln @ A @ B @ S )
% 0.14/0.40 => ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ B )
% 0.14/0.40 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.14/0.40 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.14/0.40 => ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ B )
% 0.14/0.40 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.14/0.40 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.14/0.40 => ( R = S ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(funcext_type,type,
% 0.14/0.40 funcext: $o ).
% 0.14/0.40
% 0.14/0.40 thf(funcext,definition,
% 0.14/0.40 ( funcext
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( func @ A @ B @ Xf )
% 0.14/0.40 => ! [Xg: $i] :
% 0.14/0.40 ( ( func @ A @ B @ Xg )
% 0.14/0.40 => ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.40 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.14/0.40 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(funcext2_type,type,
% 0.14/0.40 funcext2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(funcext2,definition,
% 0.14/0.40 ( funcext2
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.40 => ! [Xg: $i] :
% 0.14/0.40 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.14/0.40 => ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.40 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.14/0.40 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(ap2apEq1_type,type,
% 0.14/0.40 ap2apEq1: $o ).
% 0.14/0.40
% 0.14/0.40 thf(ap2apEq1,definition,
% 0.14/0.40 ( ap2apEq1
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.40 => ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.40 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(ap2apEq2_type,type,
% 0.14/0.40 ap2apEq2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(ap2apEq2,definition,
% 0.14/0.40 ( ap2apEq2
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( func @ A @ B @ Xf )
% 0.14/0.40 => ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.14/0.40 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(beta1_type,type,
% 0.14/0.40 beta1: $o ).
% 0.14/0.40
% 0.14/0.40 thf(beta1,definition,
% 0.14/0.40 ( beta1
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.40 ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.40 => ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B
% 0.14/0.40 @ ( lam @ A @ B
% 0.14/0.40 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.14/0.40 @ Xx )
% 0.14/0.40 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(eta1_type,type,
% 0.14/0.40 eta1: $o ).
% 0.14/0.40
% 0.14/0.40 thf(eta1,definition,
% 0.14/0.40 ( eta1
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( func @ A @ B @ Xf )
% 0.14/0.40 => ( ( lam @ A @ B
% 0.14/0.40 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.14/0.40 = Xf ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(lam2lamEq_type,type,
% 0.14/0.40 lam2lamEq: $o ).
% 0.14/0.40
% 0.14/0.40 thf(lam2lamEq,definition,
% 0.14/0.40 ( lam2lamEq
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.40 ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.40 => ( ( lam @ A @ B
% 0.14/0.40 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.14/0.40 = ( lam @ A @ B
% 0.14/0.40 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(beta2_type,type,
% 0.14/0.40 beta2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(beta2,definition,
% 0.14/0.40 ( beta2
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.14/0.40 ( ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.14/0.40 => ! [Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ( ( ap @ A @ B
% 0.14/0.40 @ ( lam @ A @ B
% 0.14/0.40 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.14/0.40 @ Xx )
% 0.14/0.40 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(eta2_type,type,
% 0.14/0.40 eta2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(eta2,definition,
% 0.14/0.40 ( eta2
% 0.14/0.40 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.14/0.40 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.14/0.40 => ( ( lam @ A @ B
% 0.14/0.40 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.14/0.40 = Xf ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(iffalseProp1_type,type,
% 0.14/0.40 iffalseProp1: $o ).
% 0.14/0.40
% 0.14/0.40 thf(iffalseProp1,definition,
% 0.14/0.40 ( iffalseProp1
% 0.14/0.40 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ A )
% 0.14/0.40 => ( ~ Xphi
% 0.14/0.40 => ( in @ Xy
% 0.14/0.40 @ ( dsetconstr @ A
% 0.14/0.40 @ ^ [Xz: $i] :
% 0.14/0.40 ( ( Xphi
% 0.14/0.40 & ( Xz = Xx ) )
% 0.14/0.40 | ( ~ Xphi
% 0.14/0.40 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(iffalseProp2_type,type,
% 0.14/0.40 iffalseProp2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(iffalseProp2,definition,
% 0.14/0.40 ( iffalseProp2
% 0.14/0.40 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ A )
% 0.14/0.40 => ( ~ Xphi
% 0.14/0.40 => ( ( dsetconstr @ A
% 0.14/0.40 @ ^ [Xz: $i] :
% 0.14/0.40 ( ( Xphi
% 0.14/0.40 & ( Xz = Xx ) )
% 0.14/0.40 | ( ~ Xphi
% 0.14/0.40 & ( Xz = Xy ) ) ) )
% 0.14/0.40 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(iftrueProp1_type,type,
% 0.14/0.40 iftrueProp1: $o ).
% 0.14/0.40
% 0.14/0.40 thf(iftrueProp1,definition,
% 0.14/0.40 ( iftrueProp1
% 0.14/0.40 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ A )
% 0.14/0.40 => ( Xphi
% 0.14/0.40 => ( in @ Xx
% 0.14/0.40 @ ( dsetconstr @ A
% 0.14/0.40 @ ^ [Xz: $i] :
% 0.14/0.40 ( ( Xphi
% 0.14/0.40 & ( Xz = Xx ) )
% 0.14/0.40 | ( ~ Xphi
% 0.14/0.40 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(iftrueProp2_type,type,
% 0.14/0.40 iftrueProp2: $o ).
% 0.14/0.40
% 0.14/0.40 thf(iftrueProp2,definition,
% 0.14/0.40 ( iftrueProp2
% 0.14/0.40 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ A )
% 0.14/0.40 => ( Xphi
% 0.14/0.40 => ( ( dsetconstr @ A
% 0.14/0.40 @ ^ [Xz: $i] :
% 0.14/0.40 ( ( Xphi
% 0.14/0.40 & ( Xz = Xx ) )
% 0.14/0.40 | ( ~ Xphi
% 0.14/0.40 & ( Xz = Xy ) ) ) )
% 0.14/0.40 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 thf(ifSingleton,conjecture,
% 0.14/0.40 ( setextAx
% 0.14/0.40 => ( emptysetAx
% 0.14/0.40 => ( setadjoinAx
% 0.14/0.40 => ( powersetAx
% 0.14/0.40 => ( setunionAx
% 0.14/0.40 => ( omega0Ax
% 0.14/0.40 => ( omegaSAx
% 0.14/0.40 => ( omegaIndAx
% 0.14/0.40 => ( replAx
% 0.14/0.40 => ( foundationAx
% 0.14/0.40 => ( wellorderingAx
% 0.14/0.40 => ( descrp
% 0.14/0.40 => ( dsetconstrI
% 0.14/0.40 => ( dsetconstrEL
% 0.14/0.40 => ( dsetconstrER
% 0.14/0.40 => ( exuE1
% 0.14/0.40 => ( prop2setE
% 0.14/0.40 => ( emptysetE
% 0.14/0.40 => ( emptysetimpfalse
% 0.14/0.40 => ( notinemptyset
% 0.14/0.40 => ( exuE3e
% 0.14/0.40 => ( setext
% 0.14/0.40 => ( emptyI
% 0.14/0.40 => ( noeltsimpempty
% 0.14/0.40 => ( setbeta
% 0.14/0.40 => ( nonemptyE1
% 0.14/0.40 => ( nonemptyI
% 0.14/0.40 => ( nonemptyI1
% 0.14/0.40 => ( setadjoinIL
% 0.14/0.40 => ( emptyinunitempty
% 0.14/0.40 => ( setadjoinIR
% 0.14/0.40 => ( setadjoinE
% 0.14/0.40 => ( setadjoinOr
% 0.14/0.40 => ( setoftrueEq
% 0.14/0.40 => ( powersetI
% 0.14/0.40 => ( emptyinPowerset
% 0.14/0.40 => ( emptyInPowerset
% 0.14/0.40 => ( powersetE
% 0.14/0.40 => ( setunionI
% 0.14/0.40 => ( setunionE
% 0.14/0.40 => ( subPowSU
% 0.14/0.40 => ( exuE2
% 0.14/0.40 => ( nonemptyImpWitness
% 0.14/0.40 => ( uniqinunit
% 0.14/0.40 => ( notinsingleton
% 0.14/0.40 => ( eqinunit
% 0.14/0.40 => ( singletonsswitch
% 0.14/0.40 => ( upairsetE
% 0.14/0.40 => ( upairsetIL
% 0.14/0.40 => ( upairsetIR
% 0.14/0.40 => ( emptyE1
% 0.14/0.40 => ( vacuousDall
% 0.14/0.40 => ( quantDeMorgan1
% 0.14/0.40 => ( quantDeMorgan2
% 0.14/0.40 => ( quantDeMorgan3
% 0.14/0.40 => ( quantDeMorgan4
% 0.14/0.40 => ( prop2setI
% 0.14/0.40 => ( prop2set2propI
% 0.14/0.40 => ( notdexE
% 0.14/0.40 => ( notdallE
% 0.14/0.40 => ( exuI1
% 0.14/0.40 => ( exuI3
% 0.14/0.40 => ( exuI2
% 0.14/0.40 => ( inCongP
% 0.14/0.40 => ( in__Cong
% 0.14/0.40 => ( exuE3u
% 0.14/0.40 => ( exu__Cong
% 0.14/0.40 => ( emptyset__Cong
% 0.14/0.40 => ( setadjoin__Cong
% 0.14/0.40 => ( powerset__Cong
% 0.14/0.40 => ( setunion__Cong
% 0.14/0.40 => ( omega__Cong
% 0.14/0.40 => ( exuEu
% 0.14/0.40 => ( descr__Cong
% 0.14/0.40 => ( dsetconstr__Cong
% 0.14/0.40 => ( subsetI1
% 0.14/0.40 => ( eqimpsubset2
% 0.14/0.40 => ( eqimpsubset1
% 0.14/0.40 => ( subsetI2
% 0.14/0.40 => ( emptysetsubset
% 0.14/0.40 => ( subsetE
% 0.14/0.40 => ( subsetE2
% 0.14/0.40 => ( notsubsetI
% 0.14/0.40 => ( notequalI1
% 0.14/0.40 => ( notequalI2
% 0.14/0.40 => ( subsetRefl
% 0.14/0.40 => ( subsetTrans
% 0.14/0.40 => ( setadjoinSub
% 0.14/0.40 => ( setadjoinSub2
% 0.14/0.40 => ( subset2powerset
% 0.14/0.40 => ( setextsub
% 0.14/0.40 => ( subsetemptysetimpeq
% 0.14/0.40 => ( powersetI1
% 0.14/0.40 => ( powersetE1
% 0.14/0.40 => ( inPowerset
% 0.14/0.40 => ( powersetsubset
% 0.14/0.40 => ( sepInPowerset
% 0.14/0.40 => ( sepSubset
% 0.14/0.40 => ( binunionIL
% 0.14/0.40 => ( upairset2IR
% 0.14/0.40 => ( binunionIR
% 0.14/0.40 => ( binunionEcases
% 0.14/0.40 => ( binunionE
% 0.14/0.40 => ( binunionLsub
% 0.14/0.40 => ( binunionRsub
% 0.14/0.40 => ( binintersectI
% 0.14/0.40 => ( binintersectSubset5
% 0.14/0.40 => ( binintersectEL
% 0.14/0.40 => ( binintersectLsub
% 0.14/0.40 => ( binintersectSubset2
% 0.14/0.40 => ( binintersectSubset3
% 0.14/0.40 => ( binintersectER
% 0.14/0.40 => ( disjointsetsI1
% 0.14/0.40 => ( binintersectRsub
% 0.14/0.40 => ( binintersectSubset4
% 0.14/0.40 => ( binintersectSubset1
% 0.14/0.40 => ( bs114d
% 0.14/0.40 => ( setminusI
% 0.14/0.40 => ( setminusEL
% 0.14/0.40 => ( setminusER
% 0.14/0.40 => ( setminusSubset2
% 0.14/0.40 => ( setminusERneg
% 0.14/0.40 => ( setminusELneg
% 0.14/0.40 => ( setminusILneg
% 0.14/0.40 => ( setminusIRneg
% 0.14/0.40 => ( setminusLsub
% 0.14/0.40 => ( setminusSubset1
% 0.14/0.40 => ( symdiffE
% 0.14/0.40 => ( symdiffI1
% 0.14/0.40 => ( symdiffI2
% 0.14/0.40 => ( symdiffIneg1
% 0.14/0.40 => ( symdiffIneg2
% 0.14/0.40 => ( secondinupair
% 0.14/0.40 => ( setukpairIL
% 0.14/0.40 => ( setukpairIR
% 0.14/0.40 => ( kpairiskpair
% 0.14/0.40 => ( kpairp
% 0.14/0.40 => ( singletonsubset
% 0.14/0.40 => ( singletoninpowerset
% 0.14/0.40 => ( singletoninpowunion
% 0.14/0.40 => ( upairset2E
% 0.14/0.40 => ( upairsubunion
% 0.14/0.40 => ( upairinpowunion
% 0.14/0.40 => ( ubforcartprodlem1
% 0.14/0.40 => ( ubforcartprodlem2
% 0.14/0.40 => ( ubforcartprodlem3
% 0.14/0.40 => ( cartprodpairin
% 0.14/0.40 => ( cartprodmempair1
% 0.14/0.40 => ( cartprodmempair
% 0.14/0.40 => ( setunionE2
% 0.14/0.40 => ( setunionsingleton1
% 0.14/0.40 => ( setunionsingleton2
% 0.14/0.40 => ( setunionsingleton
% 0.14/0.40 => ( singletonprop
% 0.14/0.40 => ( ex1E1
% 0.14/0.40 => ( ex1I
% 0.14/0.40 => ( ex1I2
% 0.14/0.40 => ( singletonsuniq
% 0.14/0.40 => ( setukpairinjL1
% 0.14/0.40 => ( kfstsingleton
% 0.14/0.40 => ( theprop
% 0.14/0.40 => ( kfstpairEq
% 0.14/0.40 => ( cartprodfstin
% 0.14/0.40 => ( setukpairinjL2
% 0.14/0.40 => ( setukpairinjL
% 0.14/0.40 => ( setukpairinjR11
% 0.14/0.40 => ( setukpairinjR12
% 0.14/0.40 => ( setukpairinjR1
% 0.14/0.40 => ( upairequniteq
% 0.14/0.40 => ( setukpairinjR2
% 0.14/0.40 => ( setukpairinjR
% 0.14/0.40 => ( ksndsingleton
% 0.14/0.40 => ( ksndpairEq
% 0.14/0.40 => ( kpairsurjEq
% 0.14/0.40 => ( cartprodsndin
% 0.14/0.40 => ( cartprodpairmemEL
% 0.14/0.40 => ( cartprodpairmemER
% 0.14/0.40 => ( cartprodmempaircEq
% 0.14/0.40 => ( cartprodfstpairEq
% 0.14/0.40 => ( cartprodsndpairEq
% 0.14/0.40 => ( cartprodpairsurjEq
% 0.14/0.40 => ( dpsetconstrI
% 0.14/0.40 => ( dpsetconstrSub
% 0.14/0.40 => ( setOfPairsIsBReln
% 0.14/0.40 => ( dpsetconstrERa
% 0.14/0.40 => ( dpsetconstrEL1
% 0.14/0.40 => ( dpsetconstrEL2
% 0.14/0.40 => ( dpsetconstrER
% 0.14/0.40 => ( funcImageSingleton
% 0.14/0.40 => ( apProp
% 0.14/0.40 => ( app
% 0.14/0.40 => ( infuncsetfunc
% 0.14/0.40 => ( ap2p
% 0.14/0.40 => ( funcinfuncset
% 0.14/0.40 => ( lamProp
% 0.14/0.40 => ( lamp
% 0.14/0.40 => ( lam2p
% 0.14/0.40 => ( brelnall1
% 0.14/0.40 => ( brelnall2
% 0.14/0.40 => ( ex1E2
% 0.14/0.40 => ( funcGraphProp1
% 0.14/0.40 => ( funcGraphProp3
% 0.14/0.40 => ( funcGraphProp2
% 0.14/0.40 => ( funcextLem
% 0.14/0.40 => ( funcGraphProp4
% 0.14/0.40 => ( subbreln
% 0.14/0.40 => ( eqbreln
% 0.14/0.40 => ( funcext
% 0.14/0.40 => ( funcext2
% 0.14/0.40 => ( ap2apEq1
% 0.14/0.40 => ( ap2apEq2
% 0.14/0.40 => ( beta1
% 0.14/0.40 => ( eta1
% 0.14/0.40 => ( lam2lamEq
% 0.14/0.40 => ( beta2
% 0.14/0.40 => ( eta2
% 0.14/0.40 => ( iffalseProp1
% 0.14/0.40 => ( iffalseProp2
% 0.14/0.40 => ( iftrueProp1
% 0.14/0.40 => ( iftrueProp2
% 0.14/0.40 => ! [A: $i,Xphi: $o,Xx: $i] :
% 0.14/0.40 ( ( in @ Xx @ A )
% 0.14/0.40 => ! [Xy: $i] :
% 0.14/0.40 ( ( in @ Xy @ A )
% 0.14/0.40 => ( singleton
% 0.14/0.40 @ ( dsetconstr @ A
% 0.14/0.40 @ ^ [Xz: $i] :
% 0.14/0.40 ( ( Xphi
% 0.14/0.40 & ( Xz = Xx ) )
% 0.14/0.40 | ( ~ Xphi
% 0.14/0.40 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.14/0.40
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 ------------------------
% 2.27/1.37 ---- Embedded in THF ---
% 2.27/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.27/1.37 %%% Generated on Tue Feb 24 12:31:27 EST 2026
% 2.27/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 2.27/1.37 %%% Logic specification used:
% 2.27/1.37 %%% thf(spec, logic, $$dhol).
% 2.27/1.37
% 2.27/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WuDOtMIMiy/DTF2DTF22813.p
% See solution above
% 2.27/1.37 ------------------------
% 2.49/1.41 ---- Cleaned THF ---
% 2.49/1.41 thf(in_type,type,
% 2.49/1.41 in: $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(exu_type,type,
% 2.49/1.41 exu: ( $i > $o ) > $o ).
% 2.49/1.41
% 2.49/1.41 thf(exu,definition,
% 2.49/1.41 ( exu
% 2.49/1.41 = ( ^ [Xphi: $i > $o] :
% 2.49/1.41 ? [Xx: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 & ! [Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setextAx_type,type,
% 2.49/1.41 setextAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setextAx,definition,
% 2.49/1.41 ( setextAx
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 <=> ( in @ Xx @ B ) )
% 2.49/1.41 => ( A = B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyset_type,type,
% 2.49/1.41 emptyset: $i ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetAx_type,type,
% 2.49/1.41 emptysetAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetAx,definition,
% 2.49/1.41 ( emptysetAx
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoin_type,type,
% 2.49/1.41 setadjoin: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinAx_type,type,
% 2.49/1.41 setadjoinAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinAx,definition,
% 2.49/1.41 ( setadjoinAx
% 2.49/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.49/1.41 <=> ( ( Xy = Xx )
% 2.49/1.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powerset_type,type,
% 2.49/1.41 powerset: $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(powersetAx_type,type,
% 2.49/1.41 powersetAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetAx,definition,
% 2.49/1.41 ( powersetAx
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( in @ B @ ( powerset @ A ) )
% 2.49/1.41 <=> ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunion_type,type,
% 2.49/1.41 setunion: $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(setunionAx_type,type,
% 2.49/1.41 setunionAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionAx,definition,
% 2.49/1.41 ( setunionAx
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setunion @ A ) )
% 2.49/1.41 <=> ? [B: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 & ( in @ B @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(omega_type,type,
% 2.49/1.41 omega: $i ).
% 2.49/1.41
% 2.49/1.41 thf(omega0Ax_type,type,
% 2.49/1.41 omega0Ax: $o ).
% 2.49/1.41
% 2.49/1.41 thf(omega0Ax,definition,
% 2.49/1.41 ( omega0Ax
% 2.49/1.41 = ( in @ emptyset @ omega ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(omegaSAx_type,type,
% 2.49/1.41 omegaSAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(omegaSAx,definition,
% 2.49/1.41 ( omegaSAx
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ omega )
% 2.49/1.41 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(omegaIndAx_type,type,
% 2.49/1.41 omegaIndAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(omegaIndAx,definition,
% 2.49/1.41 ( omegaIndAx
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ( ( in @ emptyset @ A )
% 2.49/1.41 & ! [Xx: $i] :
% 2.49/1.41 ( ( ( in @ Xx @ omega )
% 2.49/1.41 & ( in @ Xx @ A ) )
% 2.49/1.41 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ omega )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(replAx_type,type,
% 2.49/1.41 replAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(replAx,definition,
% 2.49/1.41 ( replAx
% 2.49/1.41 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( exu
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.49/1.41 => ? [B: $i] :
% 2.49/1.41 ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 <=> ? [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(foundationAx_type,type,
% 2.49/1.41 foundationAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(foundationAx,definition,
% 2.49/1.41 ( foundationAx
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.49/1.41 => ? [B: $i] :
% 2.49/1.41 ( ( in @ B @ A )
% 2.49/1.41 & ~ ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(wellorderingAx_type,type,
% 2.49/1.41 wellorderingAx: $o ).
% 2.49/1.41
% 2.49/1.41 thf(wellorderingAx,definition,
% 2.49/1.41 ( wellorderingAx
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ? [B: $i] :
% 2.49/1.41 ( ! [C: $i] :
% 2.49/1.41 ( ( in @ C @ B )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ C )
% 2.49/1.41 => ( in @ Xx @ A ) ) )
% 2.49/1.41 & ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( ( in @ Xx @ A )
% 2.49/1.41 & ( in @ Xy @ A ) )
% 2.49/1.41 => ( ! [C: $i] :
% 2.49/1.41 ( ( in @ C @ B )
% 2.49/1.41 => ( ( in @ Xx @ C )
% 2.49/1.41 <=> ( in @ Xy @ C ) ) )
% 2.49/1.41 => ( Xx = Xy ) ) )
% 2.49/1.41 & ! [C: $i,D: $i] :
% 2.49/1.41 ( ( ( in @ C @ B )
% 2.49/1.41 & ( in @ D @ B ) )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ C )
% 2.49/1.41 => ( in @ Xx @ D ) )
% 2.49/1.41 | ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ D )
% 2.49/1.41 => ( in @ Xx @ C ) ) ) )
% 2.49/1.41 & ! [C: $i] :
% 2.49/1.41 ( ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ C )
% 2.49/1.41 => ( in @ Xx @ A ) )
% 2.49/1.41 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.49/1.41 => ? [D: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ D @ B )
% 2.49/1.41 & ( in @ Xx @ C )
% 2.49/1.41 & ~ ? [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ D )
% 2.49/1.41 & ( in @ Xy @ C ) )
% 2.49/1.41 & ! [E: $i] :
% 2.49/1.41 ( ( in @ E @ B )
% 2.49/1.41 => ( ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ E )
% 2.49/1.41 => ( in @ Xy @ D ) )
% 2.49/1.41 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(descr_type,type,
% 2.49/1.41 descr: ( $i > $o ) > $i ).
% 2.49/1.41
% 2.49/1.41 thf(descrp_type,type,
% 2.49/1.41 descrp: $o ).
% 2.49/1.41
% 2.49/1.41 thf(descrp,definition,
% 2.49/1.41 ( descrp
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ( Xphi
% 2.49/1.41 @ ( descr
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstr_type,type,
% 2.49/1.41 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrI_type,type,
% 2.49/1.41 dsetconstrI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrI,definition,
% 2.49/1.41 ( dsetconstrI
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( in @ Xx
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrEL_type,type,
% 2.49/1.41 dsetconstrEL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrEL,definition,
% 2.49/1.41 ( dsetconstrEL
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrER_type,type,
% 2.49/1.41 dsetconstrER: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstrER,definition,
% 2.49/1.41 ( dsetconstrER
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.49/1.41 => ( Xphi @ Xx ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuE1_type,type,
% 2.49/1.41 exuE1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuE1,definition,
% 2.49/1.41 ( exuE1
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 & ! [Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(prop2set_type,type,
% 2.49/1.41 prop2set: $o > $i ).
% 2.49/1.41
% 2.49/1.41 thf(prop2setE_type,type,
% 2.49/1.41 prop2setE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(prop2setE,definition,
% 2.49/1.41 ( prop2setE
% 2.49/1.41 = ( ! [Xphi: $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.49/1.41 => Xphi ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetE_type,type,
% 2.49/1.41 emptysetE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetE,definition,
% 2.49/1.41 ( emptysetE
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ emptyset )
% 2.49/1.41 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetimpfalse_type,type,
% 2.49/1.41 emptysetimpfalse: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetimpfalse,definition,
% 2.49/1.41 ( emptysetimpfalse
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ emptyset )
% 2.49/1.41 => $false ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notinemptyset_type,type,
% 2.49/1.41 notinemptyset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notinemptyset,definition,
% 2.49/1.41 ( notinemptyset
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuE3e_type,type,
% 2.49/1.41 exuE3e: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuE3e,definition,
% 2.49/1.41 ( exuE3e
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setext_type,type,
% 2.49/1.41 setext: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setext,definition,
% 2.49/1.41 ( setext
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ B ) )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ A ) )
% 2.49/1.41 => ( A = B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyI_type,type,
% 2.49/1.41 emptyI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyI,definition,
% 2.49/1.41 ( emptyI
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ~ ( in @ Xx @ A )
% 2.49/1.41 => ( A = emptyset ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(noeltsimpempty_type,type,
% 2.49/1.41 noeltsimpempty: $o ).
% 2.49/1.41
% 2.49/1.41 thf(noeltsimpempty,definition,
% 2.49/1.41 ( noeltsimpempty
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ~ ( in @ Xx @ A )
% 2.49/1.41 => ( A = emptyset ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setbeta_type,type,
% 2.49/1.41 setbeta: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setbeta,definition,
% 2.49/1.41 ( setbeta
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( in @ Xx
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.49/1.41 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(nonempty_type,type,
% 2.49/1.41 nonempty: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(nonempty,definition,
% 2.49/1.41 ( nonempty
% 2.49/1.41 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyE1_type,type,
% 2.49/1.41 nonemptyE1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyE1,definition,
% 2.49/1.41 ( nonemptyE1
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ( nonempty @ A )
% 2.49/1.41 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyI_type,type,
% 2.49/1.41 nonemptyI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyI,definition,
% 2.49/1.41 ( nonemptyI
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( nonempty
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyI1_type,type,
% 2.49/1.41 nonemptyI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyI1,definition,
% 2.49/1.41 ( nonemptyI1
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.49/1.41 => ( nonempty @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinIL_type,type,
% 2.49/1.41 setadjoinIL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinIL,definition,
% 2.49/1.41 ( setadjoinIL
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyinunitempty_type,type,
% 2.49/1.41 emptyinunitempty: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyinunitempty,definition,
% 2.49/1.41 ( emptyinunitempty
% 2.49/1.41 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinIR_type,type,
% 2.49/1.41 setadjoinIR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinIR,definition,
% 2.49/1.41 ( setadjoinIR
% 2.49/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinE_type,type,
% 2.49/1.41 setadjoinE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinE,definition,
% 2.49/1.41 ( setadjoinE
% 2.49/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.49/1.41 => ! [Xphi: $o] :
% 2.49/1.41 ( ( ( Xy = Xx )
% 2.49/1.41 => Xphi )
% 2.49/1.41 => ( ( ( in @ Xy @ A )
% 2.49/1.41 => Xphi )
% 2.49/1.41 => Xphi ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinOr_type,type,
% 2.49/1.41 setadjoinOr: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinOr,definition,
% 2.49/1.41 ( setadjoinOr
% 2.49/1.41 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.49/1.41 => ( ( Xy = Xx )
% 2.49/1.41 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setoftrueEq_type,type,
% 2.49/1.41 setoftrueEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setoftrueEq,definition,
% 2.49/1.41 ( setoftrueEq
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : $true )
% 2.49/1.41 = A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powersetI_type,type,
% 2.49/1.41 powersetI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetI,definition,
% 2.49/1.41 ( powersetI
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ A ) )
% 2.49/1.41 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyinPowerset_type,type,
% 2.49/1.41 emptyinPowerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyinPowerset,definition,
% 2.49/1.41 ( emptyinPowerset
% 2.49/1.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyInPowerset_type,type,
% 2.49/1.41 emptyInPowerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyInPowerset,definition,
% 2.49/1.41 ( emptyInPowerset
% 2.49/1.41 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powersetE_type,type,
% 2.49/1.41 powersetE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetE,definition,
% 2.49/1.41 ( powersetE
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ B @ ( powerset @ A ) )
% 2.49/1.41 => ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionI_type,type,
% 2.49/1.41 setunionI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionI,definition,
% 2.49/1.41 ( setunionI
% 2.49/1.41 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( ( in @ B @ A )
% 2.49/1.41 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionE_type,type,
% 2.49/1.41 setunionE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionE,definition,
% 2.49/1.41 ( setunionE
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setunion @ A ) )
% 2.49/1.41 => ! [Xphi: $o] :
% 2.49/1.41 ( ! [B: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( ( in @ B @ A )
% 2.49/1.41 => Xphi ) )
% 2.49/1.41 => Xphi ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subPowSU_type,type,
% 2.49/1.41 subPowSU: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subPowSU,definition,
% 2.49/1.41 ( subPowSU
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuE2_type,type,
% 2.49/1.41 exuE2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuE2,definition,
% 2.49/1.41 ( exuE2
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ! [Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xy )
% 2.49/1.41 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyImpWitness_type,type,
% 2.49/1.41 nonemptyImpWitness: $o ).
% 2.49/1.41
% 2.49/1.41 thf(nonemptyImpWitness,definition,
% 2.49/1.41 ( nonemptyImpWitness
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ( nonempty @ A )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & $true ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(uniqinunit_type,type,
% 2.49/1.41 uniqinunit: $o ).
% 2.49/1.41
% 2.49/1.41 thf(uniqinunit,definition,
% 2.49/1.41 ( uniqinunit
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notinsingleton_type,type,
% 2.49/1.41 notinsingleton: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notinsingleton,definition,
% 2.49/1.41 ( notinsingleton
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx != Xy )
% 2.49/1.41 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eqinunit_type,type,
% 2.49/1.41 eqinunit: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eqinunit,definition,
% 2.49/1.41 ( eqinunit
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsswitch_type,type,
% 2.49/1.41 singletonsswitch: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsswitch,definition,
% 2.49/1.41 ( singletonsswitch
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.49/1.41 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetE_type,type,
% 2.49/1.41 upairsetE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetE,definition,
% 2.49/1.41 ( upairsetE
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.49/1.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.49/1.41 => ( ( Xz = Xx )
% 2.49/1.41 | ( Xz = Xy ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetIL_type,type,
% 2.49/1.41 upairsetIL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetIL,definition,
% 2.49/1.41 ( upairsetIL
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetIR_type,type,
% 2.49/1.41 upairsetIR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetIR,definition,
% 2.49/1.41 ( upairsetIR
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyE1_type,type,
% 2.49/1.41 emptyE1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyE1,definition,
% 2.49/1.41 ( emptyE1
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) )
% 2.49/1.41 => ( ( ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 = emptyset )
% 2.49/1.41 => $false ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(vacuousDall_type,type,
% 2.49/1.41 vacuousDall: $o ).
% 2.49/1.41
% 2.49/1.41 thf(vacuousDall,definition,
% 2.49/1.41 ( vacuousDall
% 2.49/1.41 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ emptyset )
% 2.49/1.41 => ( Xphi @ Xx ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan1_type,type,
% 2.49/1.41 quantDeMorgan1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan1,definition,
% 2.49/1.41 ( quantDeMorgan1
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ~ ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan2_type,type,
% 2.49/1.41 quantDeMorgan2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan2,definition,
% 2.49/1.41 ( quantDeMorgan2
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ~ ( Xphi @ Xx ) )
% 2.49/1.41 => ~ ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan3_type,type,
% 2.49/1.41 quantDeMorgan3: $o ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan3,definition,
% 2.49/1.41 ( quantDeMorgan3
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ~ ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan4_type,type,
% 2.49/1.41 quantDeMorgan4: $o ).
% 2.49/1.41
% 2.49/1.41 thf(quantDeMorgan4,definition,
% 2.49/1.41 ( quantDeMorgan4
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ~ ( Xphi @ Xx ) )
% 2.49/1.41 => ~ ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(prop2setI_type,type,
% 2.49/1.41 prop2setI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(prop2setI,definition,
% 2.49/1.41 ( prop2setI
% 2.49/1.41 = ( ! [Xphi: $o] :
% 2.49/1.41 ( Xphi
% 2.49/1.41 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(set2prop_type,type,
% 2.49/1.41 set2prop: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(prop2set2propI_type,type,
% 2.49/1.41 prop2set2propI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(prop2set2propI,definition,
% 2.49/1.41 ( prop2set2propI
% 2.49/1.41 = ( ! [Xphi: $o] :
% 2.49/1.41 ( Xphi
% 2.49/1.41 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notdexE_type,type,
% 2.49/1.41 notdexE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notdexE,definition,
% 2.49/1.41 ( notdexE
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ~ ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notdallE_type,type,
% 2.49/1.41 notdallE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notdallE,definition,
% 2.49/1.41 ( notdallE
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ~ ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuI1_type,type,
% 2.49/1.41 exuI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuI1,definition,
% 2.49/1.41 ( exuI1
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ? [Xx: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 & ! [Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) )
% 2.49/1.41 => ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuI3_type,type,
% 2.49/1.41 exuI3: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuI3,definition,
% 2.49/1.41 ( exuI3
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.49/1.41 => ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) )
% 2.49/1.41 => ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuI2_type,type,
% 2.49/1.41 exuI2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuI2,definition,
% 2.49/1.41 ( exuI2
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ? [Xx: $i] :
% 2.49/1.41 ! [Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xy )
% 2.49/1.41 <=> ( Xy = Xx ) )
% 2.49/1.41 => ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(inCongP_type,type,
% 2.49/1.41 inCongP: $o ).
% 2.49/1.41
% 2.49/1.41 thf(inCongP,definition,
% 2.49/1.41 ( inCongP
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(in__Cong_type,type,
% 2.49/1.41 in__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(in__Cong,definition,
% 2.49/1.41 ( in__Cong
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( in @ Xx @ A )
% 2.49/1.41 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuE3u_type,type,
% 2.49/1.41 exuE3u: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuE3u,definition,
% 2.49/1.41 ( exuE3u
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exu__Cong_type,type,
% 2.49/1.41 exu__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exu__Cong,definition,
% 2.49/1.41 ( exu__Cong
% 2.49/1.41 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 <=> ( Xpsi @ Xy ) ) )
% 2.49/1.41 => ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 <=> ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptyset__Cong_type,type,
% 2.49/1.41 emptyset__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptyset__Cong,definition,
% 2.49/1.41 ( emptyset__Cong
% 2.49/1.41 = ( emptyset = emptyset ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoin__Cong_type,type,
% 2.49/1.41 setadjoin__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoin__Cong,definition,
% 2.49/1.41 ( setadjoin__Cong
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ! [Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( Xz = Xu )
% 2.49/1.41 => ( ( setadjoin @ Xx @ Xz )
% 2.49/1.41 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powerset__Cong_type,type,
% 2.49/1.41 powerset__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powerset__Cong,definition,
% 2.49/1.41 ( powerset__Cong
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ( ( powerset @ A )
% 2.49/1.41 = ( powerset @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunion__Cong_type,type,
% 2.49/1.41 setunion__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunion__Cong,definition,
% 2.49/1.41 ( setunion__Cong
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ( ( setunion @ A )
% 2.49/1.41 = ( setunion @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(omega__Cong_type,type,
% 2.49/1.41 omega__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(omega__Cong,definition,
% 2.49/1.41 ( omega__Cong
% 2.49/1.41 = ( omega = omega ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(exuEu_type,type,
% 2.49/1.41 exuEu: $o ).
% 2.49/1.41
% 2.49/1.41 thf(exuEu,definition,
% 2.49/1.41 ( exuEu
% 2.49/1.41 = ( ! [Xphi: $i > $o] :
% 2.49/1.41 ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(descr__Cong_type,type,
% 2.49/1.41 descr__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(descr__Cong,definition,
% 2.49/1.41 ( descr__Cong
% 2.49/1.41 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 <=> ( Xpsi @ Xy ) ) )
% 2.49/1.41 => ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ( ( exu
% 2.49/1.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.49/1.41 => ( ( descr
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 = ( descr
% 2.49/1.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstr__Cong_type,type,
% 2.49/1.41 dsetconstr__Cong: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dsetconstr__Cong,definition,
% 2.49/1.41 ( dsetconstr__Cong
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( Xx = Xy )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.49/1.41 => ( ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 = ( dsetconstr @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subset_type,type,
% 2.49/1.41 subset: $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(disjoint_type,type,
% 2.49/1.41 disjoint: $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(setsmeet_type,type,
% 2.49/1.41 setsmeet: $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetI1_type,type,
% 2.49/1.41 subsetI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetI1,definition,
% 2.49/1.41 ( subsetI1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ B ) )
% 2.49/1.41 => ( subset @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eqimpsubset2_type,type,
% 2.49/1.41 eqimpsubset2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eqimpsubset2,definition,
% 2.49/1.41 ( eqimpsubset2
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ( subset @ B @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eqimpsubset1_type,type,
% 2.49/1.41 eqimpsubset1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eqimpsubset1,definition,
% 2.49/1.41 ( eqimpsubset1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( A = B )
% 2.49/1.41 => ( subset @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetI2_type,type,
% 2.49/1.41 subsetI2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetI2,definition,
% 2.49/1.41 ( subsetI2
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ B ) )
% 2.49/1.41 => ( subset @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetsubset_type,type,
% 2.49/1.41 emptysetsubset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(emptysetsubset,definition,
% 2.49/1.41 ( emptysetsubset
% 2.49/1.41 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetE_type,type,
% 2.49/1.41 subsetE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetE,definition,
% 2.49/1.41 ( subsetE
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetE2_type,type,
% 2.49/1.41 subsetE2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetE2,definition,
% 2.49/1.41 ( subsetE2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notsubsetI_type,type,
% 2.49/1.41 notsubsetI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notsubsetI,definition,
% 2.49/1.41 ( notsubsetI
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notequalI1_type,type,
% 2.49/1.41 notequalI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notequalI1,definition,
% 2.49/1.41 ( notequalI1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ~ ( subset @ A @ B )
% 2.49/1.41 => ( A != B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(notequalI2_type,type,
% 2.49/1.41 notequalI2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(notequalI2,definition,
% 2.49/1.41 ( notequalI2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ( A != B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetRefl_type,type,
% 2.49/1.41 subsetRefl: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetRefl,definition,
% 2.49/1.41 ( subsetRefl
% 2.49/1.41 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetTrans_type,type,
% 2.49/1.41 subsetTrans: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetTrans,definition,
% 2.49/1.41 ( subsetTrans
% 2.49/1.41 = ( ! [A: $i,B: $i,C: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ( subset @ B @ C )
% 2.49/1.41 => ( subset @ A @ C ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinSub_type,type,
% 2.49/1.41 setadjoinSub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinSub,definition,
% 2.49/1.41 ( setadjoinSub
% 2.49/1.41 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinSub2_type,type,
% 2.49/1.41 setadjoinSub2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setadjoinSub2,definition,
% 2.49/1.41 ( setadjoinSub2
% 2.49/1.41 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subset2powerset_type,type,
% 2.49/1.41 subset2powerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subset2powerset,definition,
% 2.49/1.41 ( subset2powerset
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setextsub_type,type,
% 2.49/1.41 setextsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setextsub,definition,
% 2.49/1.41 ( setextsub
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ( subset @ B @ A )
% 2.49/1.41 => ( A = B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subsetemptysetimpeq_type,type,
% 2.49/1.41 subsetemptysetimpeq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subsetemptysetimpeq,definition,
% 2.49/1.41 ( subsetemptysetimpeq
% 2.49/1.41 = ( ! [A: $i] :
% 2.49/1.41 ( ( subset @ A @ emptyset )
% 2.49/1.41 => ( A = emptyset ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powersetI1_type,type,
% 2.49/1.41 powersetI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetI1,definition,
% 2.49/1.41 ( powersetI1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ B @ A )
% 2.49/1.41 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powersetE1_type,type,
% 2.49/1.41 powersetE1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetE1,definition,
% 2.49/1.41 ( powersetE1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( in @ B @ ( powerset @ A ) )
% 2.49/1.41 => ( subset @ B @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(inPowerset_type,type,
% 2.49/1.41 inPowerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(inPowerset,definition,
% 2.49/1.41 ( inPowerset
% 2.49/1.41 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(powersetsubset_type,type,
% 2.49/1.41 powersetsubset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(powersetsubset,definition,
% 2.49/1.41 ( powersetsubset
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(sepInPowerset_type,type,
% 2.49/1.41 sepInPowerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(sepInPowerset,definition,
% 2.49/1.41 ( sepInPowerset
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( in
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 @ ( powerset @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(sepSubset_type,type,
% 2.49/1.41 sepSubset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(sepSubset,definition,
% 2.49/1.41 ( sepSubset
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( subset
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunion_type,type,
% 2.49/1.41 binunion: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(binunionIL_type,type,
% 2.49/1.41 binunionIL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionIL,definition,
% 2.49/1.41 ( binunionIL
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairset2IR_type,type,
% 2.49/1.41 upairset2IR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairset2IR,definition,
% 2.49/1.41 ( upairset2IR
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunionIR_type,type,
% 2.49/1.41 binunionIR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionIR,definition,
% 2.49/1.41 ( binunionIR
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunionEcases_type,type,
% 2.49/1.41 binunionEcases: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionEcases,definition,
% 2.49/1.41 ( binunionEcases
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.49/1.41 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.49/1.41 => ( ( ( in @ Xx @ A )
% 2.49/1.41 => Xphi )
% 2.49/1.41 => ( ( ( in @ Xx @ B )
% 2.49/1.41 => Xphi )
% 2.49/1.41 => Xphi ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunionE_type,type,
% 2.49/1.41 binunionE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionE,definition,
% 2.49/1.41 ( binunionE
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.49/1.41 => ( ( in @ Xx @ A )
% 2.49/1.41 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunionLsub_type,type,
% 2.49/1.41 binunionLsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionLsub,definition,
% 2.49/1.41 ( binunionLsub
% 2.49/1.41 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binunionRsub_type,type,
% 2.49/1.41 binunionRsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binunionRsub,definition,
% 2.49/1.41 ( binunionRsub
% 2.49/1.41 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersect_type,type,
% 2.49/1.41 binintersect: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectI_type,type,
% 2.49/1.41 binintersectI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectI,definition,
% 2.49/1.41 ( binintersectI
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset5_type,type,
% 2.49/1.41 binintersectSubset5: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset5,definition,
% 2.49/1.41 ( binintersectSubset5
% 2.49/1.41 = ( ! [A: $i,B: $i,C: $i] :
% 2.49/1.41 ( ( subset @ C @ A )
% 2.49/1.41 => ( ( subset @ C @ B )
% 2.49/1.41 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectEL_type,type,
% 2.49/1.41 binintersectEL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectEL,definition,
% 2.49/1.41 ( binintersectEL
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectLsub_type,type,
% 2.49/1.41 binintersectLsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectLsub,definition,
% 2.49/1.41 ( binintersectLsub
% 2.49/1.41 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset2_type,type,
% 2.49/1.41 binintersectSubset2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset2,definition,
% 2.49/1.41 ( binintersectSubset2
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ( binintersect @ A @ B )
% 2.49/1.41 = A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset3_type,type,
% 2.49/1.41 binintersectSubset3: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset3,definition,
% 2.49/1.41 ( binintersectSubset3
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( ( binintersect @ A @ B )
% 2.49/1.41 = B )
% 2.49/1.41 => ( subset @ B @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectER_type,type,
% 2.49/1.41 binintersectER: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectER,definition,
% 2.49/1.41 ( binintersectER
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.49/1.41 => ( in @ Xx @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(disjointsetsI1_type,type,
% 2.49/1.41 disjointsetsI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(disjointsetsI1,definition,
% 2.49/1.41 ( disjointsetsI1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ~ ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( in @ Xx @ B ) )
% 2.49/1.41 => ( ( binintersect @ A @ B )
% 2.49/1.41 = emptyset ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectRsub_type,type,
% 2.49/1.41 binintersectRsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectRsub,definition,
% 2.49/1.41 ( binintersectRsub
% 2.49/1.41 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset4_type,type,
% 2.49/1.41 binintersectSubset4: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset4,definition,
% 2.49/1.41 ( binintersectSubset4
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ B @ A )
% 2.49/1.41 => ( ( binintersect @ A @ B )
% 2.49/1.41 = B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset1_type,type,
% 2.49/1.41 binintersectSubset1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(binintersectSubset1,definition,
% 2.49/1.41 ( binintersectSubset1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( ( binintersect @ A @ B )
% 2.49/1.41 = A )
% 2.49/1.41 => ( subset @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(bs114d_type,type,
% 2.49/1.41 bs114d: $o ).
% 2.49/1.41
% 2.49/1.41 thf(bs114d,definition,
% 2.49/1.41 ( bs114d
% 2.49/1.41 = ( ! [A: $i,B: $i,C: $i] :
% 2.49/1.41 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.49/1.41 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(regular_type,type,
% 2.49/1.41 regular: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminus_type,type,
% 2.49/1.41 setminus: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(setminusI_type,type,
% 2.49/1.41 setminusI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusI,definition,
% 2.49/1.41 ( setminusI
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusEL_type,type,
% 2.49/1.41 setminusEL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusEL,definition,
% 2.49/1.41 ( setminusEL
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusER_type,type,
% 2.49/1.41 setminusER: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusER,definition,
% 2.49/1.41 ( setminusER
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.49/1.41 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusSubset2_type,type,
% 2.49/1.41 setminusSubset2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusSubset2,definition,
% 2.49/1.41 ( setminusSubset2
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( subset @ A @ B )
% 2.49/1.41 => ( ( setminus @ A @ B )
% 2.49/1.41 = emptyset ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusERneg_type,type,
% 2.49/1.41 setminusERneg: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusERneg,definition,
% 2.49/1.41 ( setminusERneg
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.49/1.41 => ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusELneg_type,type,
% 2.49/1.41 setminusELneg: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusELneg,definition,
% 2.49/1.41 ( setminusELneg
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusILneg_type,type,
% 2.49/1.41 setminusILneg: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusILneg,definition,
% 2.49/1.41 ( setminusILneg
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ~ ( in @ Xx @ A )
% 2.49/1.41 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusIRneg_type,type,
% 2.49/1.41 setminusIRneg: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusIRneg,definition,
% 2.49/1.41 ( setminusIRneg
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ B )
% 2.49/1.41 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusLsub_type,type,
% 2.49/1.41 setminusLsub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusLsub,definition,
% 2.49/1.41 ( setminusLsub
% 2.49/1.41 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setminusSubset1_type,type,
% 2.49/1.41 setminusSubset1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setminusSubset1,definition,
% 2.49/1.41 ( setminusSubset1
% 2.49/1.41 = ( ! [A: $i,B: $i] :
% 2.49/1.41 ( ( ( setminus @ A @ B )
% 2.49/1.41 = emptyset )
% 2.49/1.41 => ( subset @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(symdiff_type,type,
% 2.49/1.41 symdiff: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffE_type,type,
% 2.49/1.41 symdiffE: $o ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffE,definition,
% 2.49/1.41 ( symdiffE
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.49/1.41 => ! [Xphi: $o] :
% 2.49/1.41 ( ( ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => Xphi ) )
% 2.49/1.41 => ( ( ~ ( in @ Xx @ A )
% 2.49/1.41 => ( ( in @ Xx @ B )
% 2.49/1.41 => Xphi ) )
% 2.49/1.41 => Xphi ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffI1_type,type,
% 2.49/1.41 symdiffI1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffI1,definition,
% 2.49/1.41 ( symdiffI1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffI2_type,type,
% 2.49/1.41 symdiffI2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffI2,definition,
% 2.49/1.41 ( symdiffI2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ~ ( in @ Xx @ A )
% 2.49/1.41 => ( ( in @ Xx @ B )
% 2.49/1.41 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffIneg1_type,type,
% 2.49/1.41 symdiffIneg1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffIneg1,definition,
% 2.49/1.41 ( symdiffIneg1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( in @ Xx @ B )
% 2.49/1.41 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffIneg2_type,type,
% 2.49/1.41 symdiffIneg2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(symdiffIneg2,definition,
% 2.49/1.41 ( symdiffIneg2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ~ ( in @ Xx @ A )
% 2.49/1.41 => ( ~ ( in @ Xx @ B )
% 2.49/1.41 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(iskpair_type,type,
% 2.49/1.41 iskpair: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(secondinupair_type,type,
% 2.49/1.41 secondinupair: $o ).
% 2.49/1.41
% 2.49/1.41 thf(secondinupair,definition,
% 2.49/1.41 ( secondinupair
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairIL_type,type,
% 2.49/1.41 setukpairIL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairIL,definition,
% 2.49/1.41 ( setukpairIL
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairIR_type,type,
% 2.49/1.41 setukpairIR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairIR,definition,
% 2.49/1.41 ( setukpairIR
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(kpairiskpair_type,type,
% 2.49/1.41 kpairiskpair: $o ).
% 2.49/1.41
% 2.49/1.41 thf(kpairiskpair,definition,
% 2.49/1.41 ( kpairiskpair
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(kpair_type,type,
% 2.49/1.41 kpair: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(kpairp_type,type,
% 2.49/1.41 kpairp: $o ).
% 2.49/1.41
% 2.49/1.41 thf(kpairp,definition,
% 2.49/1.41 ( kpairp
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprod_type,type,
% 2.49/1.41 cartprod: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsubset_type,type,
% 2.49/1.41 singletonsubset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsubset,definition,
% 2.49/1.41 ( singletonsubset
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singletoninpowerset_type,type,
% 2.49/1.41 singletoninpowerset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletoninpowerset,definition,
% 2.49/1.41 ( singletoninpowerset
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singletoninpowunion_type,type,
% 2.49/1.41 singletoninpowunion: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletoninpowunion,definition,
% 2.49/1.41 ( singletoninpowunion
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairset2E_type,type,
% 2.49/1.41 upairset2E: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairset2E,definition,
% 2.49/1.41 ( upairset2E
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.49/1.41 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.49/1.41 => ( ( Xz = Xx )
% 2.49/1.41 | ( Xz = Xy ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairsubunion_type,type,
% 2.49/1.41 upairsubunion: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairsubunion,definition,
% 2.49/1.41 ( upairsubunion
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairinpowunion_type,type,
% 2.49/1.41 upairinpowunion: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairinpowunion,definition,
% 2.49/1.41 ( upairinpowunion
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem1_type,type,
% 2.49/1.41 ubforcartprodlem1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem1,definition,
% 2.49/1.41 ( ubforcartprodlem1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem2_type,type,
% 2.49/1.41 ubforcartprodlem2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem2,definition,
% 2.49/1.41 ( ubforcartprodlem2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem3_type,type,
% 2.49/1.41 ubforcartprodlem3: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ubforcartprodlem3,definition,
% 2.49/1.41 ( ubforcartprodlem3
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairin_type,type,
% 2.49/1.41 cartprodpairin: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairin,definition,
% 2.49/1.41 ( cartprodpairin
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempair1_type,type,
% 2.49/1.41 cartprodmempair1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempair1,definition,
% 2.49/1.41 ( cartprodmempair1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.49/1.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ? [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 & ( Xu
% 2.49/1.41 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempair_type,type,
% 2.49/1.41 cartprodmempair: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempair,definition,
% 2.49/1.41 ( cartprodmempair
% 2.49/1.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.49/1.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( iskpair @ Xu ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionE2_type,type,
% 2.49/1.41 setunionE2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionE2,definition,
% 2.49/1.41 ( setunionE2
% 2.49/1.41 = ( ! [A: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ ( setunion @ A ) )
% 2.49/1.41 => ? [X: $i] :
% 2.49/1.41 ( ( in @ X @ A )
% 2.49/1.41 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton1_type,type,
% 2.49/1.41 setunionsingleton1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton1,definition,
% 2.49/1.41 ( setunionsingleton1
% 2.49/1.41 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton2_type,type,
% 2.49/1.41 setunionsingleton2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton2,definition,
% 2.49/1.41 ( setunionsingleton2
% 2.49/1.41 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton_type,type,
% 2.49/1.41 setunionsingleton: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setunionsingleton,definition,
% 2.49/1.41 ( setunionsingleton
% 2.49/1.41 = ( ! [Xx: $i] :
% 2.49/1.41 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.49/1.41 = Xx ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singleton_type,type,
% 2.49/1.41 singleton: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(singleton,definition,
% 2.49/1.41 ( singleton
% 2.49/1.41 = ( ^ [A: $i] :
% 2.49/1.41 ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( A
% 2.49/1.41 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singletonprop_type,type,
% 2.49/1.41 singletonprop: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletonprop,definition,
% 2.49/1.41 ( singletonprop
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) )
% 2.49/1.41 => ( ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) )
% 2.49/1.41 => ( singleton
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ex1_type,type,
% 2.49/1.41 ex1: $i > ( $i > $o ) > $o ).
% 2.49/1.41
% 2.49/1.41 thf(ex1,definition,
% 2.49/1.41 ( ex1
% 2.49/1.41 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( singleton
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ex1E1_type,type,
% 2.49/1.41 ex1E1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ex1E1,definition,
% 2.49/1.41 ( ex1E1
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ( ex1 @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ex1I_type,type,
% 2.49/1.41 ex1I: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ex1I,definition,
% 2.49/1.41 ( ex1I
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xy = Xx ) ) )
% 2.49/1.41 => ( ex1 @ A
% 2.49/1.41 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ex1I2_type,type,
% 2.49/1.41 ex1I2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ex1I2,definition,
% 2.49/1.41 ( ex1I2
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) )
% 2.49/1.41 => ( ? [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 & ( Xphi @ Xx ) )
% 2.49/1.41 => ( ex1 @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsuniq_type,type,
% 2.49/1.41 singletonsuniq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(singletonsuniq,definition,
% 2.49/1.41 ( singletonsuniq
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( ( setadjoin @ Xx @ emptyset )
% 2.49/1.41 = ( setadjoin @ Xy @ emptyset ) )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(atmost1p_type,type,
% 2.49/1.41 atmost1p: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(atleast2p_type,type,
% 2.49/1.41 atleast2p: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(atmost2p_type,type,
% 2.49/1.41 atmost2p: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairsetp_type,type,
% 2.49/1.41 upairsetp: $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL1_type,type,
% 2.49/1.41 setukpairinjL1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL1,definition,
% 2.49/1.41 ( setukpairinjL1
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.49/1.41 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.49/1.41 => ( Xx = Xz ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(kfstsingleton_type,type,
% 2.49/1.41 kfstsingleton: $o ).
% 2.49/1.41
% 2.49/1.41 thf(kfstsingleton,definition,
% 2.49/1.41 ( kfstsingleton
% 2.49/1.41 = ( ! [Xu: $i] :
% 2.49/1.41 ( ( iskpair @ Xu )
% 2.49/1.41 => ( singleton
% 2.49/1.41 @ ( dsetconstr @ ( setunion @ Xu )
% 2.49/1.41 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(theprop_type,type,
% 2.49/1.41 theprop: $o ).
% 2.49/1.41
% 2.49/1.41 thf(theprop,definition,
% 2.49/1.41 ( theprop
% 2.49/1.41 = ( ! [X: $i] :
% 2.49/1.41 ( ( singleton @ X )
% 2.49/1.41 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(kfst_type,type,
% 2.49/1.41 kfst: $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(kfstpairEq_type,type,
% 2.49/1.41 kfstpairEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(kfstpairEq,definition,
% 2.49/1.41 ( kfstpairEq
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.49/1.41 = Xx ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodfstin_type,type,
% 2.49/1.41 cartprodfstin: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodfstin,definition,
% 2.49/1.41 ( cartprodfstin
% 2.49/1.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.49/1.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL2_type,type,
% 2.49/1.41 setukpairinjL2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL2,definition,
% 2.49/1.41 ( setukpairinjL2
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.49/1.41 => ( Xx = Xz ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL_type,type,
% 2.49/1.41 setukpairinjL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjL,definition,
% 2.49/1.41 ( setukpairinjL
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( ( kpair @ Xx @ Xy )
% 2.49/1.41 = ( kpair @ Xz @ Xu ) )
% 2.49/1.41 => ( Xx = Xz ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR11_type,type,
% 2.49/1.41 setukpairinjR11: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR11,definition,
% 2.49/1.41 ( setukpairinjR11
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR12_type,type,
% 2.49/1.41 setukpairinjR12: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR12,definition,
% 2.49/1.41 ( setukpairinjR12
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xx = Xy )
% 2.49/1.41 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR1_type,type,
% 2.49/1.41 setukpairinjR1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR1,definition,
% 2.49/1.41 ( setukpairinjR1
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.49/1.41 => ( ( Xz = Xu )
% 2.49/1.41 => ( Xy = Xu ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(upairequniteq_type,type,
% 2.49/1.41 upairequniteq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(upairequniteq,definition,
% 2.49/1.41 ( upairequniteq
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.49/1.41 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ Xz @ emptyset ) )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR2_type,type,
% 2.49/1.41 setukpairinjR2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR2,definition,
% 2.49/1.41 ( setukpairinjR2
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.49/1.41 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.49/1.41 => ( Xy = Xu ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR_type,type,
% 2.49/1.41 setukpairinjR: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setukpairinjR,definition,
% 2.49/1.41 ( setukpairinjR
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.49/1.41 ( ( ( kpair @ Xx @ Xy )
% 2.49/1.41 = ( kpair @ Xz @ Xu ) )
% 2.49/1.41 => ( Xy = Xu ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ksndsingleton_type,type,
% 2.49/1.41 ksndsingleton: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ksndsingleton,definition,
% 2.49/1.41 ( ksndsingleton
% 2.49/1.41 = ( ! [Xu: $i] :
% 2.49/1.41 ( ( iskpair @ Xu )
% 2.49/1.41 => ( singleton
% 2.49/1.41 @ ( dsetconstr @ ( setunion @ Xu )
% 2.49/1.41 @ ^ [Xx: $i] :
% 2.49/1.41 ( Xu
% 2.49/1.41 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ksnd_type,type,
% 2.49/1.41 ksnd: $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(ksndpairEq_type,type,
% 2.49/1.41 ksndpairEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ksndpairEq,definition,
% 2.49/1.41 ( ksndpairEq
% 2.49/1.41 = ( ! [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.49/1.41 = Xy ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(kpairsurjEq_type,type,
% 2.49/1.41 kpairsurjEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(kpairsurjEq,definition,
% 2.49/1.41 ( kpairsurjEq
% 2.49/1.41 = ( ! [Xu: $i] :
% 2.49/1.41 ( ( iskpair @ Xu )
% 2.49/1.41 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.49/1.41 = Xu ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodsndin_type,type,
% 2.49/1.41 cartprodsndin: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodsndin,definition,
% 2.49/1.41 ( cartprodsndin
% 2.49/1.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.49/1.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairmemEL_type,type,
% 2.49/1.41 cartprodpairmemEL: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairmemEL,definition,
% 2.49/1.41 ( cartprodpairmemEL
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairmemER_type,type,
% 2.49/1.41 cartprodpairmemER: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairmemER,definition,
% 2.49/1.41 ( cartprodpairmemER
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( in @ Xy @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempaircEq_type,type,
% 2.49/1.41 cartprodmempaircEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodmempaircEq,definition,
% 2.49/1.41 ( cartprodmempaircEq
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( kpair @ Xx @ Xy )
% 2.49/1.41 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodfstpairEq_type,type,
% 2.49/1.41 cartprodfstpairEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodfstpairEq,definition,
% 2.49/1.41 ( cartprodfstpairEq
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.49/1.41 = Xx ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodsndpairEq_type,type,
% 2.49/1.41 cartprodsndpairEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodsndpairEq,definition,
% 2.49/1.41 ( cartprodsndpairEq
% 2.49/1.41 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.49/1.41 = Xy ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairsurjEq_type,type,
% 2.49/1.41 cartprodpairsurjEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(cartprodpairsurjEq,definition,
% 2.49/1.41 ( cartprodpairsurjEq
% 2.49/1.41 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.49/1.41 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.49/1.41 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.49/1.41 = Xu ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(breln_type,type,
% 2.49/1.41 breln: $i > $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(breln,definition,
% 2.49/1.41 ( breln
% 2.49/1.41 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstr_type,type,
% 2.49/1.41 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrI_type,type,
% 2.49/1.41 dpsetconstrI: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrI,definition,
% 2.49/1.41 ( dpsetconstrI
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( Xphi @ Xx @ Xy )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy )
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrSub_type,type,
% 2.49/1.41 dpsetconstrSub: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrSub,definition,
% 2.49/1.41 ( dpsetconstrSub
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.49/1.41 ( subset
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.49/1.41 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(setOfPairsIsBReln_type,type,
% 2.49/1.41 setOfPairsIsBReln: $o ).
% 2.49/1.41
% 2.49/1.41 thf(setOfPairsIsBReln,definition,
% 2.49/1.41 ( setOfPairsIsBReln
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.49/1.41 ( breln @ A @ B
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrERa_type,type,
% 2.49/1.41 dpsetconstrERa: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrERa,definition,
% 2.49/1.41 ( dpsetconstrERa
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.49/1.41 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrEL1_type,type,
% 2.49/1.41 dpsetconstrEL1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrEL1,definition,
% 2.49/1.41 ( dpsetconstrEL1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ ( kpair @ Xx @ Xy )
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.49/1.41 => ( in @ Xx @ A ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrEL2_type,type,
% 2.49/1.41 dpsetconstrEL2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrEL2,definition,
% 2.49/1.41 ( dpsetconstrEL2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ ( kpair @ Xx @ Xy )
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.49/1.41 => ( in @ Xy @ B ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrER_type,type,
% 2.49/1.41 dpsetconstrER: $o ).
% 2.49/1.41
% 2.49/1.41 thf(dpsetconstrER,definition,
% 2.49/1.41 ( dpsetconstrER
% 2.49/1.41 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( in @ ( kpair @ Xx @ Xy )
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.49/1.41 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(func_type,type,
% 2.49/1.41 func: $i > $i > $i > $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcSet_type,type,
% 2.49/1.41 funcSet: $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(funcImageSingleton_type,type,
% 2.49/1.41 funcImageSingleton: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcImageSingleton,definition,
% 2.49/1.41 ( funcImageSingleton
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( singleton
% 2.49/1.41 @ ( dsetconstr @ B
% 2.49/1.41 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(apProp_type,type,
% 2.49/1.41 apProp: $o ).
% 2.49/1.41
% 2.49/1.41 thf(apProp,definition,
% 2.49/1.41 ( apProp
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in
% 2.49/1.41 @ ( setunion
% 2.49/1.41 @ ( dsetconstr @ B
% 2.49/1.41 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.49/1.41 @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ap_type,type,
% 2.49/1.41 ap: $i > $i > $i > $i > $i ).
% 2.49/1.41
% 2.49/1.41 thf(app_type,type,
% 2.49/1.41 app: $o ).
% 2.49/1.41
% 2.49/1.41 thf(app,definition,
% 2.49/1.41 ( app
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(infuncsetfunc_type,type,
% 2.49/1.41 infuncsetfunc: $o ).
% 2.49/1.41
% 2.49/1.41 thf(infuncsetfunc,definition,
% 2.49/1.41 ( infuncsetfunc
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ap2p_type,type,
% 2.49/1.41 ap2p: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ap2p,definition,
% 2.49/1.41 ( ap2p
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcinfuncset_type,type,
% 2.49/1.41 funcinfuncset: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcinfuncset,definition,
% 2.49/1.41 ( funcinfuncset
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(lamProp_type,type,
% 2.49/1.41 lamProp: $o ).
% 2.49/1.41
% 2.49/1.41 thf(lamProp,definition,
% 2.49/1.41 ( lamProp
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ( func @ A @ B
% 2.49/1.41 @ ( dpsetconstr @ A @ B
% 2.49/1.41 @ ^ [Xx: $i,Xy: $i] :
% 2.49/1.41 ( ( Xf @ Xx )
% 2.49/1.41 = Xy ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(lam_type,type,
% 2.49/1.41 lam: $i > $i > ( $i > $i ) > $i ).
% 2.49/1.41
% 2.49/1.41 thf(lamp_type,type,
% 2.49/1.41 lamp: $o ).
% 2.49/1.41
% 2.49/1.41 thf(lamp,definition,
% 2.49/1.41 ( lamp
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ( func @ A @ B
% 2.49/1.41 @ ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(lam2p_type,type,
% 2.49/1.41 lam2p: $o ).
% 2.49/1.41
% 2.49/1.41 thf(lam2p,definition,
% 2.49/1.41 ( lam2p
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ( in
% 2.49/1.41 @ ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.49/1.41 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(brelnall1_type,type,
% 2.49/1.41 brelnall1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(brelnall1,definition,
% 2.49/1.41 ( brelnall1
% 2.49/1.41 = ( ! [A: $i,B: $i,R: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ R )
% 2.49/1.41 => ! [Xphi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.49/1.41 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ R )
% 2.49/1.41 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(brelnall2_type,type,
% 2.49/1.41 brelnall2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(brelnall2,definition,
% 2.49/1.41 ( brelnall2
% 2.49/1.41 = ( ! [A: $i,B: $i,R: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ R )
% 2.49/1.41 => ! [Xphi: $i > $o] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.49/1.41 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ R )
% 2.49/1.41 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ex1E2_type,type,
% 2.49/1.41 ex1E2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ex1E2,definition,
% 2.49/1.41 ( ex1E2
% 2.49/1.41 = ( ! [A: $i,Xphi: $i > $o] :
% 2.49/1.41 ( ( ex1 @ A
% 2.49/1.41 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ( Xphi @ Xx )
% 2.49/1.41 => ( ( Xphi @ Xy )
% 2.49/1.41 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp1_type,type,
% 2.49/1.41 funcGraphProp1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp1,definition,
% 2.49/1.41 ( funcGraphProp1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp3_type,type,
% 2.49/1.41 funcGraphProp3: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp3,definition,
% 2.49/1.41 ( funcGraphProp3
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp2_type,type,
% 2.49/1.41 funcGraphProp2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp2,definition,
% 2.49/1.41 ( funcGraphProp2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcextLem_type,type,
% 2.49/1.41 funcextLem: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcextLem,definition,
% 2.49/1.41 ( funcextLem
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xg: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xg )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp4_type,type,
% 2.49/1.41 funcGraphProp4: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcGraphProp4,definition,
% 2.49/1.41 ( funcGraphProp4
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = Xy ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(subbreln_type,type,
% 2.49/1.41 subbreln: $o ).
% 2.49/1.41
% 2.49/1.41 thf(subbreln,definition,
% 2.49/1.41 ( subbreln
% 2.49/1.41 = ( ! [A: $i,B: $i,R: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ R )
% 2.49/1.41 => ! [S: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ S )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.49/1.41 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eqbreln_type,type,
% 2.49/1.41 eqbreln: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eqbreln,definition,
% 2.49/1.41 ( eqbreln
% 2.49/1.41 = ( ! [A: $i,B: $i,R: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ R )
% 2.49/1.41 => ! [S: $i] :
% 2.49/1.41 ( ( breln @ A @ B @ S )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ B )
% 2.49/1.41 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.49/1.41 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.49/1.41 => ( R = S ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcext_type,type,
% 2.49/1.41 funcext: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcext,definition,
% 2.49/1.41 ( funcext
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xg: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xg )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.49/1.41 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(funcext2_type,type,
% 2.49/1.41 funcext2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(funcext2,definition,
% 2.49/1.41 ( funcext2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ! [Xg: $i] :
% 2.49/1.41 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.49/1.41 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ap2apEq1_type,type,
% 2.49/1.41 ap2apEq1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ap2apEq1,definition,
% 2.49/1.41 ( ap2apEq1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ap2apEq2_type,type,
% 2.49/1.41 ap2apEq2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(ap2apEq2,definition,
% 2.49/1.41 ( ap2apEq2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.49/1.41 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(beta1_type,type,
% 2.49/1.41 beta1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(beta1,definition,
% 2.49/1.41 ( beta1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B
% 2.49/1.41 @ ( lam @ A @ B
% 2.49/1.41 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.49/1.41 @ Xx )
% 2.49/1.41 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eta1_type,type,
% 2.49/1.41 eta1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eta1,definition,
% 2.49/1.41 ( eta1
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( func @ A @ B @ Xf )
% 2.49/1.41 => ( ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.49/1.41 = Xf ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(lam2lamEq_type,type,
% 2.49/1.41 lam2lamEq: $o ).
% 2.49/1.41
% 2.49/1.41 thf(lam2lamEq,definition,
% 2.49/1.41 ( lam2lamEq
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ( ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.49/1.41 = ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(beta2_type,type,
% 2.49/1.41 beta2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(beta2,definition,
% 2.49/1.41 ( beta2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.49/1.41 ( ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.49/1.41 => ! [Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ( ( ap @ A @ B
% 2.49/1.41 @ ( lam @ A @ B
% 2.49/1.41 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.49/1.41 @ Xx )
% 2.49/1.41 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(eta2_type,type,
% 2.49/1.41 eta2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(eta2,definition,
% 2.49/1.41 ( eta2
% 2.49/1.41 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.49/1.41 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.49/1.41 => ( ( lam @ A @ B
% 2.49/1.41 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.49/1.41 = Xf ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(iffalseProp1_type,type,
% 2.49/1.41 iffalseProp1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(iffalseProp1,definition,
% 2.49/1.41 ( iffalseProp1
% 2.49/1.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ~ Xphi
% 2.49/1.41 => ( in @ Xy
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xz: $i] :
% 2.49/1.41 ( ( Xphi
% 2.49/1.41 & ( Xz = Xx ) )
% 2.49/1.41 | ( ~ Xphi
% 2.49/1.41 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(iffalseProp2_type,type,
% 2.49/1.41 iffalseProp2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(iffalseProp2,definition,
% 2.49/1.41 ( iffalseProp2
% 2.49/1.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( ~ Xphi
% 2.49/1.41 => ( ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xz: $i] :
% 2.49/1.41 ( ( Xphi
% 2.49/1.41 & ( Xz = Xx ) )
% 2.49/1.41 | ( ~ Xphi
% 2.49/1.41 & ( Xz = Xy ) ) ) )
% 2.49/1.41 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(iftrueProp1_type,type,
% 2.49/1.41 iftrueProp1: $o ).
% 2.49/1.41
% 2.49/1.41 thf(iftrueProp1,definition,
% 2.49/1.41 ( iftrueProp1
% 2.49/1.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( Xphi
% 2.49/1.41 => ( in @ Xx
% 2.49/1.41 @ ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xz: $i] :
% 2.49/1.41 ( ( Xphi
% 2.49/1.41 & ( Xz = Xx ) )
% 2.49/1.41 | ( ~ Xphi
% 2.49/1.41 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(iftrueProp2_type,type,
% 2.49/1.41 iftrueProp2: $o ).
% 2.49/1.41
% 2.49/1.41 thf(iftrueProp2,definition,
% 2.49/1.41 ( iftrueProp2
% 2.49/1.41 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.49/1.41 ( ( in @ Xx @ A )
% 2.49/1.41 => ! [Xy: $i] :
% 2.49/1.41 ( ( in @ Xy @ A )
% 2.49/1.41 => ( Xphi
% 2.49/1.41 => ( ( dsetconstr @ A
% 2.49/1.41 @ ^ [Xz: $i] :
% 2.49/1.41 ( ( Xphi
% 2.49/1.41 & ( Xz = Xx ) )
% 2.49/1.41 | ( ~ Xphi
% 2.49/1.41 & ( Xz = Xy ) ) ) )
% 2.49/1.41 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.49/1.41
% 2.49/1.41 thf(ifSingleton,conjecture,
% 2.49/1.41 ( setextAx
% 2.49/1.41 => ( emptysetAx
% 2.49/1.41 => ( setadjoinAx
% 2.49/1.41 => ( powersetAx
% 2.49/1.41 => ( setunionAx
% 2.49/1.41 => ( omega0Ax
% 2.49/1.41 => ( omegaSAx
% 2.49/1.41 => ( omegaIndAx
% 2.49/1.41 => ( replAx
% 2.49/1.41 => ( foundationAx
% 2.49/1.41 => ( wellorderingAx
% 2.49/1.41 => ( descrp
% 2.49/1.41 => ( dsetconstrI
% 2.49/1.41 => ( dsetconstrEL
% 2.49/1.41 => ( dsetconstrER
% 2.49/1.41 => ( exuE1
% 2.49/1.41 => ( prop2setE
% 2.49/1.41 => ( emptysetE
% 2.49/1.41 => ( emptysetimpfalse
% 2.49/1.41 => ( notinemptyset
% 2.49/1.41 => ( exuE3e
% 2.49/1.41 => ( setext
% 2.49/1.41 => ( emptyI
% 2.49/1.41 => ( noeltsimpempty
% 2.49/1.41 => ( setbeta
% 2.49/1.41 => ( nonemptyE1
% 2.49/1.41 => ( nonemptyI
% 2.49/1.41 => ( nonemptyI1
% 2.49/1.41 => ( setadjoinIL
% 2.49/1.41 => ( emptyinunitempty
% 2.49/1.41 => ( setadjoinIR
% 2.49/1.41 => ( setadjoinE
% 2.49/1.41 => ( setadjoinOr
% 2.49/1.41 => ( setoftrueEq
% 2.49/1.41 => ( powersetI
% 2.49/1.41 => ( emptyinPowerset
% 2.49/1.41 => ( emptyInPowerset
% 2.49/1.41 => ( powersetE
% 2.49/1.41 => ( setunionI
% 2.49/1.41 => ( setunionE
% 2.49/1.41 => ( subPowSU
% 2.49/1.41 => ( exuE2
% 2.49/1.41 => ( nonemptyImpWitness
% 2.49/1.41 => ( uniqinunit
% 2.49/1.41 => ( notinsingleton
% 2.49/1.41 => ( eqinunit
% 2.49/1.41 => ( singletonsswitch
% 2.49/1.41 => ( upairsetE
% 2.49/1.41 => ( upairsetIL
% 2.49/1.41 => ( upairsetIR
% 2.49/1.41 => ( emptyE1
% 2.49/1.41 => ( vacuousDall
% 2.49/1.41 => ( quantDeMorgan1
% 2.49/1.41 => ( quantDeMorgan2
% 2.49/1.41 => ( quantDeMorgan3
% 2.49/1.41 => ( quantDeMorgan4
% 2.49/1.41 => ( prop2setI
% 2.49/1.41 => ( prop2set2propI
% 2.49/1.41 => ( notdexE
% 2.49/1.41 => ( notdallE
% 2.49/1.41 => ( exuI1
% 2.49/1.41 => ( exuI3
% 2.49/1.41 => ( exuI2
% 2.49/1.41 => ( inCongP
% 2.49/1.41 => ( in__Cong
% 2.49/1.41 => ( exuE3u
% 2.49/1.41 => ( exu__Cong
% 2.49/1.41 => ( emptyset__Cong
% 2.49/1.41 => ( setadjoin__Cong
% 2.49/1.41 => ( powerset__Cong
% 2.49/1.41 => ( setunion__Cong
% 2.49/1.41 => ( omega__Cong
% 2.49/1.41 => ( exuEu
% 2.49/1.41 => ( descr__Cong
% 2.49/1.41 => ( dsetconstr__Cong
% 2.49/1.41 => ( subsetI1
% 2.49/1.41 => ( eqimpsubset2
% 2.49/1.41 => ( eqimpsubset1
% 2.49/1.41 => ( subsetI2
% 2.49/1.41 => ( emptysetsubset
% 2.49/1.41 => ( subsetE
% 2.49/1.41 => ( subsetE2
% 2.49/1.41 => ( notsubsetI
% 2.49/1.41 => ( notequalI1
% 2.49/1.41 => ( notequalI2
% 2.49/1.41 => ( subsetRefl
% 2.49/1.41 => ( subsetTrans
% 2.49/1.41 => ( setadjoinSub
% 2.49/1.41 => ( setadjoinSub2
% 2.49/1.41 => ( subset2powerset
% 2.49/1.41 => ( setextsub
% 2.49/1.41 => ( subsetemptysetimpeq
% 2.49/1.41 => ( powersetI1
% 2.49/1.41 => ( powersetE1
% 2.49/1.41 => ( inPowerset
% 2.49/1.41 => ( powersetsubset
% 2.49/1.41 => ( sepInPowerset
% 2.49/1.41 => ( sepSubset
% 2.49/1.41 => ( binunionIL
% 2.49/1.41 => ( upairset2IR
% 2.49/1.41 => ( binunionIR
% 2.49/1.41 => ( binunionEcases
% 2.49/1.41 => ( binunionE
% 2.49/1.41 => ( binunionLsub
% 2.49/1.41 => ( binunionRsub
% 2.49/1.41 => ( binintersectI
% 2.49/1.41 => ( binintersectSubset5
% 2.49/1.41 => ( binintersectEL
% 2.49/1.41 => ( binintersectLsub
% 2.49/1.41 => ( binintersectSubset2
% 2.49/1.41 => ( binintersectSubset3
% 2.49/1.41 => ( binintersectER
% 2.49/1.41 => ( disjointsetsI1
% 2.49/1.41 => ( binintersectRsub
% 2.49/1.42 => ( binintersectSubset4
% 2.49/1.42 => ( binintersectSubset1
% 2.49/1.42 => ( bs114d
% 2.49/1.42 => ( setminusI
% 2.49/1.42 => ( setminusEL
% 2.49/1.42 => ( setminusER
% 2.49/1.42 => ( setminusSubset2
% 2.49/1.42 => ( setminusERneg
% 2.49/1.42 => ( setminusELneg
% 2.49/1.42 => ( setminusILneg
% 2.49/1.42 => ( setminusIRneg
% 2.49/1.42 => ( setminusLsub
% 2.49/1.42 => ( setminusSubset1
% 2.49/1.42 => ( symdiffE
% 2.49/1.42 => ( symdiffI1
% 2.49/1.42 => ( symdiffI2
% 2.49/1.42 => ( symdiffIneg1
% 2.49/1.42 => ( symdiffIneg2
% 2.49/1.42 => ( secondinupair
% 2.49/1.42 => ( setukpairIL
% 2.49/1.42 => ( setukpairIR
% 2.49/1.42 => ( kpairiskpair
% 2.49/1.42 => ( kpairp
% 2.49/1.42 => ( singletonsubset
% 2.49/1.42 => ( singletoninpowerset
% 2.49/1.42 => ( singletoninpowunion
% 2.49/1.42 => ( upairset2E
% 2.49/1.42 => ( upairsubunion
% 2.49/1.42 => ( upairinpowunion
% 2.49/1.42 => ( ubforcartprodlem1
% 2.49/1.42 => ( ubforcartprodlem2
% 2.49/1.42 => ( ubforcartprodlem3
% 2.49/1.42 => ( cartprodpairin
% 2.49/1.42 => ( cartprodmempair1
% 2.49/1.42 => ( cartprodmempair
% 2.49/1.42 => ( setunionE2
% 2.49/1.42 => ( setunionsingleton1
% 2.49/1.42 => ( setunionsingleton2
% 2.49/1.42 => ( setunionsingleton
% 2.49/1.42 => ( singletonprop
% 2.49/1.42 => ( ex1E1
% 2.49/1.42 => ( ex1I
% 2.49/1.42 => ( ex1I2
% 2.49/1.42 => ( singletonsuniq
% 2.49/1.42 => ( setukpairinjL1
% 2.49/1.42 => ( kfstsingleton
% 2.49/1.42 => ( theprop
% 2.49/1.42 => ( kfstpairEq
% 2.49/1.42 => ( cartprodfstin
% 2.49/1.42 => ( setukpairinjL2
% 2.49/1.42 => ( setukpairinjL
% 2.49/1.42 => ( setukpairinjR11
% 2.49/1.42 => ( setukpairinjR12
% 2.49/1.42 => ( setukpairinjR1
% 2.49/1.42 => ( upairequniteq
% 2.49/1.42 => ( setukpairinjR2
% 2.49/1.42 => ( setukpairinjR
% 2.49/1.42 => ( ksndsingleton
% 2.49/1.42 => ( ksndpairEq
% 2.49/1.42 => ( kpairsurjEq
% 2.49/1.42 => ( cartprodsndin
% 2.49/1.42 => ( cartprodpairmemEL
% 2.49/1.42 => ( cartprodpairmemER
% 2.49/1.42 => ( cartprodmempaircEq
% 2.49/1.42 => ( cartprodfstpairEq
% 2.49/1.42 => ( cartprodsndpairEq
% 2.49/1.42 => ( cartprodpairsurjEq
% 2.49/1.42 => ( dpsetconstrI
% 2.49/1.42 => ( dpsetconstrSub
% 2.49/1.42 => ( setOfPairsIsBReln
% 2.49/1.42 => ( dpsetconstrERa
% 2.49/1.42 => ( dpsetconstrEL1
% 2.49/1.42 => ( dpsetconstrEL2
% 2.49/1.42 => ( dpsetconstrER
% 2.49/1.42 => ( funcImageSingleton
% 2.49/1.42 => ( apProp
% 2.49/1.42 => ( app
% 2.49/1.42 => ( infuncsetfunc
% 2.49/1.42 => ( ap2p
% 2.49/1.42 => ( funcinfuncset
% 2.49/1.42 => ( lamProp
% 2.49/1.42 => ( lamp
% 2.49/1.42 => ( lam2p
% 2.49/1.42 => ( brelnall1
% 2.49/1.42 => ( brelnall2
% 2.49/1.42 => ( ex1E2
% 2.49/1.42 => ( funcGraphProp1
% 2.49/1.42 => ( funcGraphProp3
% 2.49/1.42 => ( funcGraphProp2
% 2.49/1.42 => ( funcextLem
% 2.49/1.42 => ( funcGraphProp4
% 2.49/1.42 => ( subbreln
% 2.49/1.42 => ( eqbreln
% 2.49/1.42 => ( funcext
% 2.49/1.42 => ( funcext2
% 2.49/1.42 => ( ap2apEq1
% 2.49/1.42 => ( ap2apEq2
% 2.49/1.42 => ( beta1
% 2.49/1.42 => ( eta1
% 2.49/1.42 => ( lam2lamEq
% 2.49/1.42 => ( beta2
% 2.49/1.42 => ( eta2
% 2.49/1.42 => ( iffalseProp1
% 2.49/1.42 => ( iffalseProp2
% 2.49/1.42 => ( iftrueProp1
% 2.49/1.42 => ( iftrueProp2
% 2.49/1.42 => ! [A: $i,Xphi: $o,Xx: $i] :
% 2.49/1.42 ( ( in @ Xx @ A )
% 2.49/1.42 => ! [Xy: $i] :
% 2.49/1.42 ( ( in @ Xy @ A )
% 2.49/1.42 => ( singleton
% 2.49/1.42 @ ( dsetconstr @ A
% 2.49/1.42 @ ^ [Xz: $i] :
% 2.49/1.42 ( ( Xphi
% 2.49/1.42 & ( Xz = Xx ) )
% 2.49/1.42 | ( ~ Xphi
% 2.49/1.42 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.49/1.42 ------------------------
% 2.49/1.44 % (22916)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/183Mi)
% 2.49/1.44 % (22917)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_22813 for (2999ds/4Mi)
% 2.49/1.44 % (22920)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_22813 for (2999ds/2Mi)
% 2.49/1.44 % (22918)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_22813 for (2999ds/27Mi)
% 2.49/1.44 % (22919)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/2Mi)
% 2.49/1.44 % (22921)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_22813 for (2999ds/275Mi)
% 2.49/1.44 % (22922)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/18Mi)
% 2.49/1.44 % (22919)Instruction limit reached!
% 2.49/1.44 % (22919)------------------------------
% 2.49/1.44 % (22919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.44 % (22919)Termination reason: Unknown
% 2.49/1.44 % (22920)Instruction limit reached!
% 2.49/1.44 % (22920)------------------------------
% 2.49/1.44 % (22920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.44 % (22920)Termination reason: Unknown
% 2.49/1.44 % (22920)Termination phase: shuffling
% 2.49/1.44
% 2.49/1.44 % (22920)Memory used [KB]: 1407
% 2.49/1.44 % (22920)Time elapsed: 0.003 s
% 2.49/1.44 % (22920)Instructions burned: 3 (million)
% 2.49/1.44 % (22920)------------------------------
% 2.49/1.44 % (22920)------------------------------
% 2.49/1.44 % (22919)Termination phase: shuffling
% 2.49/1.44
% 2.49/1.44 % (22919)Memory used [KB]: 1407
% 2.49/1.44 % (22919)Time elapsed: 0.003 s
% 2.49/1.44 % (22919)Instructions burned: 3 (million)
% 2.49/1.44 % (22919)------------------------------
% 2.49/1.44 % (22919)------------------------------
% 2.49/1.44 % (22917)Instruction limit reached!
% 2.49/1.44 % (22917)------------------------------
% 2.49/1.44 % (22917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.44 % (22917)Termination reason: Unknown
% 2.49/1.44 % (22917)Termination phase: shuffling
% 2.49/1.44
% 2.49/1.44 % (22917)Memory used [KB]: 1407
% 2.49/1.44 % (22917)Time elapsed: 0.004 s
% 2.49/1.44 % (22917)Instructions burned: 6 (million)
% 2.49/1.44 % (22917)------------------------------
% 2.49/1.44 % (22917)------------------------------
% 2.49/1.45 % (22922)Instruction limit reached!
% 2.49/1.45 % (22922)------------------------------
% 2.49/1.45 % (22922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.45 % (22922)Termination reason: Unknown
% 2.49/1.45 % (22922)Termination phase: shuffling
% 2.49/1.45
% 2.49/1.45 % (22922)Memory used [KB]: 1791
% 2.49/1.45 % (22922)Time elapsed: 0.011 s
% 2.49/1.45 % (22922)Instructions burned: 19 (million)
% 2.49/1.45 % (22922)------------------------------
% 2.49/1.45 % (22922)------------------------------
% 2.49/1.45 % (22918)Instruction limit reached!
% 2.49/1.45 % (22918)------------------------------
% 2.49/1.45 % (22918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.45 % (22918)Termination reason: Unknown
% 2.49/1.45 % (22918)Termination phase: shuffling
% 2.49/1.45
% 2.49/1.45 % (22918)Memory used [KB]: 1918
% 2.49/1.45 % (22918)Time elapsed: 0.014 s
% 2.49/1.45 % (22918)Instructions burned: 27 (million)
% 2.49/1.45 % (22918)------------------------------
% 2.49/1.45 % (22918)------------------------------
% 2.49/1.46 % (22923)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/3Mi)
% 2.49/1.46 % (22924)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_22813 for (2999ds/37Mi)
% 2.49/1.46 % (22923)Instruction limit reached!
% 2.49/1.46 % (22923)------------------------------
% 2.49/1.46 % (22923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.46 % (22923)Termination reason: Unknown
% 2.49/1.46 % (22923)Termination phase: shuffling
% 2.49/1.46
% 2.49/1.46 % (22923)Memory used [KB]: 1407
% 2.49/1.46 % (22923)Time elapsed: 0.003 s
% 2.49/1.46 % (22923)Instructions burned: 3 (million)
% 2.49/1.46 % (22923)------------------------------
% 2.49/1.46 % (22923)------------------------------
% 2.49/1.47 % (22925)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_22813 for (2999ds/15Mi)
% 2.49/1.47 % (22926)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_22813 for (2999ds/3Mi)
% 2.49/1.47 % (22926)Instruction limit reached!
% 2.49/1.47 % (22926)------------------------------
% 2.49/1.47 % (22926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.47 % (22926)Termination reason: Unknown
% 2.49/1.47 % (22926)Termination phase: shuffling
% 2.49/1.47
% 2.49/1.47 % (22926)Memory used [KB]: 1407
% 2.49/1.47 % (22926)Time elapsed: 0.003 s
% 2.49/1.47 % (22926)Instructions burned: 3 (million)
% 2.49/1.47 % (22926)------------------------------
% 2.49/1.47 % (22926)------------------------------
% 2.49/1.47 % (22927)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_22813 for (2999ds/1041Mi)
% 2.49/1.47 % (22925)Instruction limit reached!
% 2.49/1.47 % (22925)------------------------------
% 2.49/1.47 % (22925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.47 % (22925)Termination reason: Unknown
% 2.49/1.47 % (22925)Termination phase: shuffling
% 2.49/1.47
% 2.49/1.47 % (22925)Memory used [KB]: 1663
% 2.49/1.47 % (22925)Time elapsed: 0.009 s
% 2.49/1.47 % (22925)Instructions burned: 16 (million)
% 2.49/1.47 % (22925)------------------------------
% 2.49/1.47 % (22925)------------------------------
% 2.49/1.48 % (22924)Instruction limit reached!
% 2.49/1.48 % (22924)------------------------------
% 2.49/1.48 % (22924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.48 % (22924)Termination reason: Unknown
% 2.49/1.48 % (22924)Termination phase: shuffling
% 2.49/1.48
% 2.49/1.48 % (22924)Memory used [KB]: 2174
% 2.49/1.48 % (22924)Time elapsed: 0.018 s
% 2.49/1.48 % (22924)Instructions burned: 37 (million)
% 2.49/1.48 % (22924)------------------------------
% 2.49/1.48 % (22924)------------------------------
% 2.49/1.48 % (22928)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/7Mi)
% 2.49/1.48 % (22928)Instruction limit reached!
% 2.49/1.48 % (22928)------------------------------
% 2.49/1.48 % (22928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.48 % (22928)Termination reason: Unknown
% 2.49/1.48 % (22928)Termination phase: shuffling
% 2.49/1.48
% 2.49/1.48 % (22928)Memory used [KB]: 1535
% 2.49/1.48 % (22928)Time elapsed: 0.005 s
% 2.49/1.48 % (22928)Instructions burned: 8 (million)
% 2.49/1.48 % (22928)------------------------------
% 2.49/1.48 % (22928)------------------------------
% 2.49/1.48 % (22916)Instruction limit reached!
% 2.49/1.48 % (22916)------------------------------
% 2.49/1.48 % (22916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.48 % (22916)Termination reason: Unknown
% 2.49/1.48 % (22916)Termination phase: Saturation
% 2.49/1.48
% 2.49/1.48 % (22916)Memory used [KB]: 7547
% 2.49/1.48 % (22916)Time elapsed: 0.050 s
% 2.49/1.48 % (22916)Instructions burned: 184 (million)
% 2.49/1.48 % (22916)------------------------------
% 2.49/1.48 % (22916)------------------------------
% 2.49/1.49 % (22929)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/16Mi)
% 2.49/1.49 % (22930)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_22813 for (2999ds/3Mi)
% 2.49/1.49 % (22930)Instruction limit reached!
% 2.49/1.49 % (22930)------------------------------
% 2.49/1.49 % (22930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.49 % (22930)Termination reason: Unknown
% 2.49/1.49 % (22930)Termination phase: shuffling
% 2.49/1.49
% 2.49/1.49 % (22930)Memory used [KB]: 1407
% 2.49/1.49 % (22930)Time elapsed: 0.003 s
% 2.49/1.49 % (22930)Instructions burned: 4 (million)
% 2.49/1.49 % (22930)------------------------------
% 2.49/1.49 % (22930)------------------------------
% 2.49/1.49 % (22929)Instruction limit reached!
% 2.49/1.49 % (22929)------------------------------
% 2.49/1.49 % (22929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.49 % (22929)Termination reason: Unknown
% 2.49/1.49 % (22929)Termination phase: shuffling
% 2.49/1.49
% 2.49/1.49 % (22929)Memory used [KB]: 1663
% 2.49/1.49 % (22929)Time elapsed: 0.009 s
% 2.49/1.49 % (22929)Instructions burned: 17 (million)
% 2.49/1.49 % (22929)------------------------------
% 2.49/1.49 % (22929)------------------------------
% 2.49/1.49 % (22931)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_22813 for (2999ds/3Mi)
% 2.49/1.49 % (22933)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/3Mi)
% 2.49/1.49 % (22931)Instruction limit reached!
% 2.49/1.49 % (22931)------------------------------
% 2.49/1.49 % (22931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.50 % (22931)Termination reason: Unknown
% 2.49/1.50 % (22931)Termination phase: shuffling
% 2.49/1.50
% 2.49/1.50 % (22931)Memory used [KB]: 1407
% 2.49/1.50 % (22931)Time elapsed: 0.003 s
% 2.49/1.50 % (22931)Instructions burned: 4 (million)
% 2.49/1.50 % (22931)------------------------------
% 2.49/1.50 % (22931)------------------------------
% 2.49/1.50 % (22933)Instruction limit reached!
% 2.49/1.50 % (22933)------------------------------
% 2.49/1.50 % (22933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.49/1.50 % (22933)Termination reason: Unknown
% 2.49/1.50 % (22933)Termination phase: shuffling
% 2.49/1.50
% 2.49/1.50 % (22933)Memory used [KB]: 1407
% 2.49/1.50 % (22933)Time elapsed: 0.002 s
% 2.49/1.50 % (22933)Instructions burned: 3 (million)
% 2.49/1.50 % (22933)------------------------------
% 2.49/1.50 % (22933)------------------------------
% 2.52/1.50 % (22932)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/7Mi)
% 2.52/1.50 % (22932)Instruction limit reached!
% 2.52/1.50 % (22932)------------------------------
% 2.52/1.50 % (22932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.50 % (22932)Termination reason: Unknown
% 2.52/1.50 % (22932)Termination phase: shuffling
% 2.52/1.50
% 2.52/1.50 % (22932)Memory used [KB]: 1535
% 2.52/1.50 % (22932)Time elapsed: 0.005 s
% 2.52/1.50 % (22932)Instructions burned: 8 (million)
% 2.52/1.50 % (22932)------------------------------
% 2.52/1.50 % (22932)------------------------------
% 2.52/1.51 % (22937)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/6Mi)
% 2.52/1.51 % (22937)Instruction limit reached!
% 2.52/1.51 % (22937)------------------------------
% 2.52/1.51 % (22937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (22937)Termination reason: Unknown
% 2.52/1.51 % (22937)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (22937)Memory used [KB]: 1535
% 2.52/1.51 % (22937)Time elapsed: 0.003 s
% 2.52/1.51 % (22937)Instructions burned: 7 (million)
% 2.52/1.51 % (22937)------------------------------
% 2.52/1.51 % (22937)------------------------------
% 2.52/1.51 % (22934)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/4Mi)
% 2.52/1.51 % (22935)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/18Mi)
% 2.52/1.51 % (22934)Instruction limit reached!
% 2.52/1.51 % (22934)------------------------------
% 2.52/1.51 % (22934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (22934)Termination reason: Unknown
% 2.52/1.51 % (22934)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (22934)Memory used [KB]: 1407
% 2.52/1.51 % (22934)Time elapsed: 0.004 s
% 2.52/1.51 % (22934)Instructions burned: 5 (million)
% 2.52/1.51 % (22934)------------------------------
% 2.52/1.51 % (22934)------------------------------
% 2.52/1.51 % (22936)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/710Mi)
% 2.52/1.52 % (22939)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_22813 for (2999ds/21Mi)
% 2.52/1.52 % (22935)Instruction limit reached!
% 2.52/1.52 % (22935)------------------------------
% 2.52/1.52 % (22935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (22935)Termination reason: Unknown
% 2.52/1.52 % (22935)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (22935)Memory used [KB]: 1791
% 2.52/1.52 % (22935)Time elapsed: 0.010 s
% 2.52/1.52 % (22935)Instructions burned: 18 (million)
% 2.52/1.52 % (22935)------------------------------
% 2.52/1.52 % (22935)------------------------------
% 2.52/1.52 % (22938)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_22813 for (2999ds/902Mi)
% 2.52/1.52 % (22939)Instruction limit reached!
% 2.52/1.52 % (22939)------------------------------
% 2.52/1.52 % (22939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (22939)Termination reason: Unknown
% 2.52/1.52 % (22939)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (22939)Memory used [KB]: 1791
% 2.52/1.52 % (22939)Time elapsed: 0.008 s
% 2.52/1.52 % (22939)Instructions burned: 24 (million)
% 2.52/1.52 % (22939)------------------------------
% 2.52/1.52 % (22939)------------------------------
% 2.52/1.53 % (22940)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/5Mi)
% 2.52/1.53 % (22940)Instruction limit reached!
% 2.52/1.53 % (22940)------------------------------
% 2.52/1.53 % (22940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (22940)Termination reason: Unknown
% 2.52/1.53 % (22940)Termination phase: shuffling
% 2.52/1.53
% 2.52/1.53 % (22940)Memory used [KB]: 1407
% 2.52/1.53 % (22940)Time elapsed: 0.004 s
% 2.52/1.53 % (22940)Instructions burned: 5 (million)
% 2.52/1.53 % (22940)------------------------------
% 2.52/1.53 % (22940)------------------------------
% 2.52/1.53 % (22941)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_22813 for (2999ds/6Mi)
% 2.52/1.54 % (22941)Instruction limit reached!
% 2.52/1.54 % (22941)------------------------------
% 2.52/1.54 % (22941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.54 % (22941)Termination reason: Unknown
% 2.52/1.54 % (22941)Termination phase: shuffling
% 2.52/1.54
% 2.52/1.54 % (22941)Memory used [KB]: 1535
% 2.52/1.54 % (22941)Time elapsed: 0.005 s
% 2.52/1.54 % (22941)Instructions burned: 7 (million)
% 2.52/1.54 % (22941)------------------------------
% 2.52/1.54 % (22941)------------------------------
% 2.52/1.54 % (22943)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_22813 for (2998ds/779Mi)
% 2.52/1.54 % (22942)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22813 for (2999ds/377Mi)
% 2.52/1.55 % (22944)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_22813 for (2998ds/19Mi)
% 2.52/1.56 % (22944)Instruction limit reached!
% 2.52/1.56 % (22944)------------------------------
% 2.52/1.56 % (22944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.56 % (22944)Termination reason: Unknown
% 2.52/1.56 % (22944)Termination phase: shuffling
% 2.52/1.56
% 2.52/1.56 % (22944)Memory used [KB]: 1791
% 2.52/1.56 % (22944)Time elapsed: 0.010 s
% 2.52/1.56 % (22944)Instructions burned: 19 (million)
% 2.52/1.56 % (22944)------------------------------
% 2.52/1.56 % (22944)------------------------------
% 2.52/1.57 % (22921)Instruction limit reached!
% 2.52/1.57 % (22921)------------------------------
% 2.52/1.57 % (22921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.57 % (22921)Termination reason: Unknown
% 2.52/1.57 % (22921)Termination phase: Saturation
% 2.52/1.57
% 2.52/1.57 % (22921)Memory used [KB]: 9083
% 2.52/1.57 % (22921)Time elapsed: 0.134 s
% 2.52/1.57 % (22921)Instructions burned: 276 (million)
% 2.52/1.57 % (22921)------------------------------
% 2.52/1.57 % (22921)------------------------------
% 2.52/1.58 % (22945)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22813 for (2998ds/879Mi)
% 2.52/1.59 % (22947)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22813 for (2998ds/17Mi)
% 2.52/1.60 % (22947)Instruction limit reached!
% 2.52/1.60 % (22947)------------------------------
% 2.52/1.60 % (22947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.60 % (22947)Termination reason: Unknown
% 2.52/1.60 % (22947)Termination phase: shuffling
% 2.52/1.60
% 2.52/1.60 % (22947)Memory used [KB]: 1791
% 2.52/1.60 % (22947)Time elapsed: 0.010 s
% 2.52/1.60 % (22947)Instructions burned: 18 (million)
% 2.52/1.60 % (22947)------------------------------
% 2.52/1.60 % (22947)------------------------------
% 2.52/1.62 % (22948)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22813 for (2998ds/3Mi)
% 2.52/1.62 % (22948)Instruction limit reached!
% 2.52/1.62 % (22948)------------------------------
% 2.52/1.62 % (22948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (22948)Termination reason: Unknown
% 2.52/1.62 % (22948)Termination phase: shuffling
% 2.52/1.62
% 2.52/1.62 % (22948)Memory used [KB]: 1407
% 2.52/1.62 % (22948)Time elapsed: 0.003 s
% 2.52/1.62 % (22948)Instructions burned: 3 (million)
% 2.52/1.62 % (22948)------------------------------
% 2.52/1.62 % (22948)------------------------------
% 2.52/1.63 % (22949)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22813 for (2998ds/30Mi)
% 2.52/1.65 % (22949)Instruction limit reached!
% 2.52/1.65 % (22949)------------------------------
% 2.52/1.65 % (22949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.65 % (22949)Termination reason: Unknown
% 2.52/1.65 % (22949)Termination phase: shuffling
% 2.52/1.65
% 2.52/1.65 % (22949)Memory used [KB]: 1918
% 2.52/1.65 % (22949)Time elapsed: 0.016 s
% 2.52/1.65 % (22949)Instructions burned: 31 (million)
% 2.52/1.65 % (22949)------------------------------
% 2.52/1.65 % (22949)------------------------------
% 2.52/1.67 % (22950)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22813 for (2997ds/127Mi)
% 2.52/1.71 % (22942)Instruction limit reached!
% 2.52/1.71 % (22942)------------------------------
% 2.52/1.71 % (22942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.71 % (22942)Termination reason: Unknown
% 2.52/1.71 % (22942)Termination phase: Saturation
% 2.52/1.71
% 2.52/1.71 % (22942)Memory used [KB]: 8699
% 2.52/1.71 % (22942)Time elapsed: 0.175 s
% 2.52/1.71 % (22942)Instructions burned: 377 (million)
% 2.52/1.71 % (22942)------------------------------
% 2.52/1.71 % (22942)------------------------------
% 2.52/1.72 % (22950)Instruction limit reached!
% 2.52/1.72 % (22950)------------------------------
% 2.52/1.72 % (22950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.72 % (22950)Termination reason: Unknown
% 2.52/1.72 % (22950)Termination phase: Property scanning
% 2.52/1.72
% 2.52/1.72 % (22950)Memory used [KB]: 2430
% 2.52/1.72 % (22950)Time elapsed: 0.057 s
% 2.52/1.72 % (22950)Instructions burned: 128 (million)
% 2.52/1.72 % (22950)------------------------------
% 2.52/1.72 % (22950)------------------------------
% 2.52/1.74 % (22951)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22813 for (2997ds/100Mi)
% 2.52/1.74 % (22952)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_22813 for (2997ds/3Mi)
% 2.52/1.74 % (22952)Instruction limit reached!
% 2.52/1.74 % (22952)------------------------------
% 2.52/1.74 % (22952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.74 % (22952)Termination reason: Unknown
% 2.52/1.74 % (22952)Termination phase: shuffling
% 2.52/1.74
% 2.52/1.74 % (22952)Memory used [KB]: 1407
% 2.52/1.74 % (22952)Time elapsed: 0.003 s
% 2.52/1.74 % (22952)Instructions burned: 3 (million)
% 2.52/1.74 % (22952)------------------------------
% 2.52/1.74 % (22952)------------------------------
% 2.52/1.75 % (22943)Instruction limit reached!
% 2.52/1.75 % (22943)------------------------------
% 2.52/1.75 % (22943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.75 % (22943)Termination reason: Unknown
% 2.52/1.75 % (22943)Termination phase: Saturation
% 2.52/1.75
% 2.52/1.75 % (22943)Memory used [KB]: 7291
% 2.52/1.75 % (22943)Time elapsed: 0.211 s
% 2.52/1.75 % (22943)Instructions burned: 780 (million)
% 2.52/1.75 % (22943)------------------------------
% 2.52/1.75 % (22943)------------------------------
% 2.52/1.75 % (22953)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_22813 for (2996ds/20Mi)
% 2.52/1.76 % (22954)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_22813 for (2996ds/86Mi)
% 2.52/1.76 % (22953)Instruction limit reached!
% 2.52/1.76 % (22953)------------------------------
% 2.52/1.76 % (22953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.77 % (22953)Termination reason: Unknown
% 2.52/1.77 % (22953)Termination phase: shuffling
% 2.52/1.77
% 2.52/1.77 % (22953)Memory used [KB]: 1791
% 2.52/1.77 % (22953)Time elapsed: 0.012 s
% 2.52/1.77 % (22953)Instructions burned: 21 (million)
% 2.52/1.77 % (22953)------------------------------
% 2.52/1.77 % (22953)------------------------------
% 2.52/1.78 % (22951)Instruction limit reached!
% 2.52/1.78 % (22951)------------------------------
% 2.52/1.78 % (22951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.78 % (22951)Termination reason: Unknown
% 2.52/1.78 % (22951)Termination phase: Property scanning
% 2.52/1.78
% 2.52/1.78 % (22951)Memory used [KB]: 2430
% 2.52/1.78 % (22951)Time elapsed: 0.046 s
% 2.52/1.78 % (22951)Instructions burned: 101 (million)
% 2.52/1.78 % (22951)------------------------------
% 2.52/1.78 % (22951)------------------------------
% 2.52/1.78 % (22954)Instruction limit reached!
% 2.52/1.78 % (22954)------------------------------
% 2.52/1.78 % (22954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.78 % (22954)Termination reason: Unknown
% 2.52/1.78 % (22954)Termination phase: Function definition elimination
% 2.52/1.78
% 2.52/1.78 % (22954)Memory used [KB]: 2430
% 2.52/1.78 % (22954)Time elapsed: 0.024 s
% 2.52/1.78 % (22954)Instructions burned: 89 (million)
% 2.52/1.78 % (22954)------------------------------
% 2.52/1.78 % (22954)------------------------------
% 2.52/1.78 % (22955)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_22813 for (2996ds/107Mi)
% 2.52/1.79 % (22956)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_22813 for (2996ds/39Mi)
% 2.52/1.80 % (22957)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_22813 for (2996ds/448Mi)
% 2.52/1.81 % (22956)Instruction limit reached!
% 2.52/1.81 % (22956)------------------------------
% 2.52/1.81 % (22956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.81 % (22956)Termination reason: Unknown
% 2.52/1.81 % (22956)Termination phase: Property scanning
% 2.52/1.81
% 2.52/1.81 % (22956)Memory used [KB]: 2174
% 2.52/1.81 % (22956)Time elapsed: 0.018 s
% 2.52/1.81 % (22956)Instructions burned: 40 (million)
% 2.52/1.81 % (22956)------------------------------
% 2.52/1.81 % (22956)------------------------------
% 2.52/1.83 % (22955)Instruction limit reached!
% 2.52/1.83 % (22955)------------------------------
% 2.52/1.83 % (22955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.83 % (22955)Termination reason: Unknown
% 2.52/1.83 % (22955)Termination phase: Function definition elimination
% 2.52/1.83
% 2.52/1.83 % (22955)Memory used [KB]: 2430
% 2.52/1.83 % (22955)Time elapsed: 0.048 s
% 2.52/1.83 % (22955)Instructions burned: 108 (million)
% 2.52/1.83 % (22955)------------------------------
% 2.52/1.83 % (22955)------------------------------
% 2.52/1.84 % (22958)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_22813 for (2996ds/46Mi)
% 2.52/1.85 % (22959)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_22813 for (2996ds/98Mi)
% 2.52/1.86 % (22958)Instruction limit reached!
% 2.52/1.86 % (22958)------------------------------
% 2.52/1.86 % (22958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.86 % (22958)Termination reason: Unknown
% 2.52/1.86 % (22958)Termination phase: Property scanning
% 2.52/1.86
% 2.52/1.86 % (22958)Memory used [KB]: 2174
% 2.52/1.86 % (22958)Time elapsed: 0.023 s
% 2.52/1.86 % (22958)Instructions burned: 46 (million)
% 2.52/1.86 % (22958)------------------------------
% 2.52/1.86 % (22958)------------------------------
% 2.52/1.86 % (22936)Instruction limit reached!
% 2.52/1.86 % (22936)------------------------------
% 2.52/1.86 % (22936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.86 % (22936)Termination reason: Unknown
% 2.52/1.86 % (22936)Termination phase: Saturation
% 2.52/1.86
% 2.52/1.86 % (22936)Memory used [KB]: 10234
% 2.52/1.86 % (22936)Time elapsed: 0.355 s
% 2.52/1.86 % (22936)Instructions burned: 710 (million)
% 2.52/1.86 % (22936)------------------------------
% 2.52/1.86 % (22936)------------------------------
% 2.52/1.87 % (22927)Instruction limit reached!
% 2.52/1.87 % (22927)------------------------------
% 2.52/1.87 % (22927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.87 % (22927)Termination reason: Unknown
% 2.52/1.87 % (22927)Termination phase: Saturation
% 2.52/1.87
% 2.52/1.87 % (22927)Memory used [KB]: 12920
% 2.52/1.87 % (22927)Time elapsed: 0.402 s
% 2.52/1.87 % (22927)Instructions burned: 1043 (million)
% 2.52/1.87 % (22927)------------------------------
% 2.52/1.87 % (22927)------------------------------
% 2.52/1.88 % (22961)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_22813 for (2995ds/149Mi)
% 2.52/1.88 % (22960)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_22813 for (2995ds/507Mi)
% 2.52/1.89 % (22959)Instruction limit reached!
% 2.52/1.89 % (22959)------------------------------
% 2.52/1.89 % (22959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.89 % (22959)Termination reason: Unknown
% 2.52/1.89 % (22959)Termination phase: Property scanning
% 2.52/1.89
% 2.52/1.89 % (22959)Memory used [KB]: 2430
% 2.52/1.89 % (22959)Time elapsed: 0.045 s
% 2.52/1.89 % (22959)Instructions burned: 100 (million)
% 2.52/1.89 % (22959)------------------------------
% 2.52/1.89 % (22959)------------------------------
% 2.52/1.89 % (22962)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22813 for (2995ds/39Mi)
% 2.52/1.90 % (22963)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_22813 for (2995ds/6Mi)
% 2.52/1.91 % (22962)Instruction limit reached!
% 2.52/1.91 % (22962)------------------------------
% 2.52/1.91 % (22962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (22962)Termination reason: Unknown
% 2.52/1.91 % (22962)Termination phase: Property scanning
% 2.52/1.91
% 2.52/1.91 % (22962)Memory used [KB]: 2174
% 2.52/1.91 % (22962)Time elapsed: 0.020 s
% 2.52/1.91 % (22962)Instructions burned: 40 (million)
% 2.52/1.91 % (22962)------------------------------
% 2.52/1.91 % (22962)------------------------------
% 2.52/1.91 % (22963)Instruction limit reached!
% 2.52/1.91 % (22963)------------------------------
% 2.52/1.91 % (22963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (22963)Termination reason: Unknown
% 2.52/1.91 % (22963)Termination phase: shuffling
% 2.52/1.91
% 2.52/1.91 % (22963)Memory used [KB]: 1535
% 2.52/1.91 % (22963)Time elapsed: 0.005 s
% 2.52/1.91 % (22963)Instructions burned: 8 (million)
% 2.52/1.91 % (22963)------------------------------
% 2.52/1.91 % (22963)------------------------------
% 2.52/1.92 % (22964)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_22813 for (2995ds/1087Mi)
% 2.52/1.92 % (22965)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22813 for (2995ds/47Mi)
% 2.52/1.93 % (22957)Instruction limit reached!
% 2.52/1.93 % (22957)------------------------------
% 2.52/1.93 % (22957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.93 % (22957)Termination reason: Unknown
% 2.52/1.93 % (22957)Termination phase: Saturation
% 2.52/1.93
% 2.52/1.93 % (22957)Memory used [KB]: 7291
% 2.52/1.93 % (22957)Time elapsed: 0.115 s
% 2.52/1.93 % (22957)Instructions burned: 451 (million)
% 2.52/1.93 % (22957)------------------------------
% 2.52/1.93 % (22957)------------------------------
% 2.52/1.94 % (22966)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_22813 for (2995ds/44Mi)
% 2.52/1.95 % (22965)Instruction limit reached!
% 2.52/1.95 % (22965)------------------------------
% 2.52/1.95 % (22965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.95 % (22965)Termination reason: Unknown
% 2.52/1.95 % (22965)Termination phase: Property scanning
% 2.52/1.95
% 2.52/1.95 % (22965)Memory used [KB]: 2302
% 2.52/1.95 % (22965)Time elapsed: 0.023 s
% 2.52/1.95 % (22965)Instructions burned: 48 (million)
% 2.52/1.95 % (22965)------------------------------
% 2.52/1.95 % (22965)------------------------------
% 2.52/1.95 % (22961)Instruction limit reached!
% 2.52/1.95 % (22961)------------------------------
% 2.52/1.95 % (22961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.95 % (22961)Termination reason: Unknown
% 2.52/1.95 % (22961)Termination phase: Saturation
% 2.52/1.95
% 2.52/1.95 % (22961)Memory used [KB]: 7419
% 2.52/1.95 % (22961)Time elapsed: 0.068 s
% 2.52/1.95 % (22961)Instructions burned: 149 (million)
% 2.52/1.95 % (22961)------------------------------
% 2.52/1.95 % (22961)------------------------------
% 2.52/1.95 % (22938)Instruction limit reached!
% 2.52/1.95 % (22938)------------------------------
% 2.52/1.95 % (22938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.95 % (22938)Termination reason: Unknown
% 2.52/1.95 % (22938)Termination phase: Saturation
% 2.52/1.95
% 2.52/1.95 % (22938)Memory used [KB]: 10490
% 2.52/1.95 % (22938)Time elapsed: 0.433 s
% 2.52/1.95 % (22938)Instructions burned: 902 (million)
% 2.52/1.95 % (22938)------------------------------
% 2.52/1.95 % (22938)------------------------------
% 2.52/1.95 % (22966)Instruction limit reached!
% 2.52/1.95 % (22966)------------------------------
% 2.52/1.95 % (22966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.95 % (22966)Termination reason: Unknown
% 2.52/1.95 % (22966)Termination phase: Property scanning
% 2.52/1.95
% 2.52/1.95 % (22966)Memory used [KB]: 2174
% 2.52/1.95 % (22966)Time elapsed: 0.013 s
% 2.52/1.95 % (22966)Instructions burned: 45 (million)
% 2.52/1.95 % (22966)------------------------------
% 2.52/1.95 % (22966)------------------------------
% 2.52/1.96 % (22969)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_22813 for (2994ds/31Mi)
% 2.52/1.96 % (22967)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_22813 for (2994ds/432Mi)
% 2.52/1.96 % (22968)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22813 for (2994ds/62Mi)
% 2.52/1.97 % (22970)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22813 for (2994ds/96Mi)
% 2.52/1.97 % (22969)Instruction limit reached!
% 2.52/1.97 % (22969)------------------------------
% 2.52/1.97 % (22969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.97 % (22969)Termination reason: Unknown
% 2.52/1.97 % (22969)Termination phase: shuffling
% 2.52/1.97
% 2.52/1.97 % (22969)Memory used [KB]: 2046
% 2.52/1.97 % (22969)Time elapsed: 0.010 s
% 2.52/1.97 % (22969)Instructions burned: 33 (million)
% 2.52/1.97 % (22969)------------------------------
% 2.52/1.97 % (22969)------------------------------
% 2.52/1.97 % (22945)Instruction limit reached!
% 2.52/1.97 % (22945)------------------------------
% 2.52/1.97 % (22945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.97 % (22945)Termination reason: Unknown
% 2.52/1.97 % (22945)Termination phase: Saturation
% 2.52/1.97
% 2.52/1.97 % (22945)Memory used [KB]: 9594
% 2.52/1.97 % (22945)Time elapsed: 0.396 s
% 2.52/1.97 % (22945)Instructions burned: 880 (million)
% 2.52/1.97 % (22945)------------------------------
% 2.52/1.97 % (22945)------------------------------
% 2.52/1.98 % (22971)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_22813 for (2994ds/453Mi)
% 2.52/1.99 % (22972)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_22813 for (2994ds/71Mi)
% 2.52/1.99 % (22968)Instruction limit reached!
% 2.52/1.99 % (22968)------------------------------
% 2.52/1.99 % (22968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.99 % (22968)Termination reason: Unknown
% 2.52/1.99 % (22968)Termination phase: Property scanning
% 2.52/1.99
% 2.52/1.99 % (22968)Memory used [KB]: 2302
% 2.52/1.99 % (22968)Time elapsed: 0.029 s
% 2.52/1.99 % (22968)Instructions burned: 62 (million)
% 2.52/1.99 % (22968)------------------------------
% 2.52/1.99 % (22968)------------------------------
% 2.52/2.01 % (22973)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22813 for (2994ds/83Mi)
% 2.52/2.01 % (22970)Instruction limit reached!
% 2.52/2.01 % (22970)------------------------------
% 2.52/2.01 % (22970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/2.01 % (22970)Termination reason: Unknown
% 2.52/2.01 % (22970)Termination phase: Property scanning
% 2.52/2.01
% 2.52/2.01 % (22970)Memory used [KB]: 2430
% 2.52/2.01 % (22970)Time elapsed: 0.044 s
% 2.52/2.01 % (22970)Instructions burned: 97 (million)
% 2.52/2.01 % (22970)------------------------------
% 2.52/2.01 % (22970)------------------------------
% 6.50/2.02 % (22972)Instruction limit reached!
% 6.50/2.02 % (22972)------------------------------
% 6.50/2.02 % (22972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.02 % (22972)Termination reason: Unknown
% 6.50/2.02 % (22972)Termination phase: Property scanning
% 6.50/2.02
% 6.50/2.02 % (22972)Memory used [KB]: 2430
% 6.50/2.02 % (22972)Time elapsed: 0.034 s
% 6.50/2.02 % (22972)Instructions burned: 72 (million)
% 6.50/2.02 % (22972)------------------------------
% 6.50/2.02 % (22972)------------------------------
% 6.50/2.03 % (22975)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22813 for (2994ds/11Mi)
% 6.50/2.03 % (22975)Instruction limit reached!
% 6.50/2.03 % (22975)------------------------------
% 6.50/2.03 % (22975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.03 % (22975)Termination reason: Unknown
% 6.50/2.03 % (22975)Termination phase: shuffling
% 6.50/2.03
% 6.50/2.03 % (22975)Memory used [KB]: 1663
% 6.50/2.03 % (22975)Time elapsed: 0.007 s
% 6.50/2.03 % (22975)Instructions burned: 12 (million)
% 6.50/2.03 % (22975)------------------------------
% 6.50/2.03 % (22975)------------------------------
% 6.50/2.04 % (22976)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_22813 for (2993ds/41Mi)
% 6.50/2.04 % (22973)Instruction limit reached!
% 6.50/2.04 % (22973)------------------------------
% 6.50/2.04 % (22973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.04 % (22973)Termination reason: Unknown
% 6.50/2.04 % (22973)Termination phase: SInE selection
% 6.50/2.04
% 6.50/2.04 % (22973)Memory used [KB]: 2302
% 6.50/2.04 % (22973)Time elapsed: 0.038 s
% 6.50/2.04 % (22973)Instructions burned: 85 (million)
% 6.50/2.04 % (22973)------------------------------
% 6.50/2.04 % (22973)------------------------------
% 6.50/2.05 % (22978)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22813 for (2993ds/6Mi)
% 6.50/2.05 % (22978)Instruction limit reached!
% 6.50/2.05 % (22978)------------------------------
% 6.50/2.05 % (22978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.05 % (22978)Termination reason: Unknown
% 6.50/2.05 % (22978)Termination phase: shuffling
% 6.50/2.05
% 6.50/2.05 % (22978)Memory used [KB]: 1535
% 6.50/2.05 % (22978)Time elapsed: 0.005 s
% 6.50/2.05 % (22978)Instructions burned: 7 (million)
% 6.50/2.05 % (22978)------------------------------
% 6.50/2.05 % (22978)------------------------------
% 6.50/2.05 % (22976)Instruction limit reached!
% 6.50/2.05 % (22976)------------------------------
% 6.50/2.05 % (22976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.05 % (22976)Termination reason: Unknown
% 6.50/2.05 % (22976)Termination phase: Property scanning
% 6.50/2.05
% 6.50/2.05 % (22976)Memory used [KB]: 2302
% 6.50/2.05 % (22976)Time elapsed: 0.020 s
% 6.50/2.05 % (22976)Instructions burned: 41 (million)
% 6.50/2.05 % (22976)------------------------------
% 6.50/2.05 % (22976)------------------------------
% 6.50/2.06 % (22979)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22813 for (2993ds/150Mi)
% 6.50/2.07 % (22980)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22813 for (2993ds/343Mi)
% 6.50/2.07 % (22981)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_22813 for (2993ds/109Mi)
% 6.50/2.12 % (22981)Instruction limit reached!
% 6.50/2.12 % (22981)------------------------------
% 6.50/2.12 % (22981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.12 % (22981)Termination reason: Unknown
% 6.50/2.12 % (22981)Termination phase: Function definition elimination
% 6.50/2.12
% 6.50/2.12 % (22981)Memory used [KB]: 2430
% 6.50/2.12 % (22981)Time elapsed: 0.048 s
% 6.50/2.12 % (22981)Instructions burned: 109 (million)
% 6.50/2.12 % (22981)------------------------------
% 6.50/2.12 % (22981)------------------------------
% 7.02/2.12 % (22967)Instruction limit reached!
% 7.02/2.12 % (22967)------------------------------
% 7.02/2.12 % (22967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.12 % (22967)Termination reason: Unknown
% 7.02/2.12 % (22967)Termination phase: Saturation
% 7.02/2.12
% 7.02/2.12 % (22967)Memory used [KB]: 2814
% 7.02/2.12 % (22967)Time elapsed: 0.157 s
% 7.02/2.12 % (22967)Instructions burned: 434 (million)
% 7.02/2.12 % (22967)------------------------------
% 7.02/2.12 % (22967)------------------------------
% 7.02/2.12 % (22971)Instruction limit reached!
% 7.02/2.12 % (22971)------------------------------
% 7.02/2.12 % (22971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.12 % (22971)Termination reason: Unknown
% 7.02/2.12 % (22971)Termination phase: Saturation
% 7.02/2.12
% 7.02/2.12 % (22971)Memory used [KB]: 7291
% 7.02/2.12 % (22971)Time elapsed: 0.126 s
% 7.02/2.12 % (22971)Instructions burned: 453 (million)
% 7.02/2.12 % (22971)------------------------------
% 7.02/2.12 % (22971)------------------------------
% 7.02/2.12 % (22960)Instruction limit reached!
% 7.02/2.12 % (22960)------------------------------
% 7.02/2.12 % (22960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.12 % (22960)Termination reason: Unknown
% 7.02/2.12 % (22960)Termination phase: Saturation
% 7.02/2.12
% 7.02/2.12 % (22960)Memory used [KB]: 7931
% 7.02/2.12 % (22960)Time elapsed: 0.269 s
% 7.02/2.12 % (22960)Instructions burned: 507 (million)
% 7.02/2.12 % (22960)------------------------------
% 7.02/2.12 % (22960)------------------------------
% 7.02/2.13 % (22979)Instruction limit reached!
% 7.02/2.13 % (22979)------------------------------
% 7.02/2.13 % (22979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.13 % (22979)Termination reason: Unknown
% 7.02/2.13 % (22979)Termination phase: Property scanning
% 7.02/2.13
% 7.02/2.13 % (22979)Memory used [KB]: 3965
% 7.02/2.13 % (22979)Time elapsed: 0.071 s
% 7.02/2.13 % (22979)Instructions burned: 151 (million)
% 7.02/2.13 % (22979)------------------------------
% 7.02/2.13 % (22979)------------------------------
% 7.02/2.13 % (22982)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_22813 for (2993ds/253Mi)
% 7.02/2.13 % (22983)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22813 for (2993ds/140Mi)
% 7.02/2.13 % (22984)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_22813 for (2993ds/614Mi)
% 7.02/2.14 % (22985)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_22813 for (2993ds/202Mi)
% 7.02/2.15 % (22986)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_22813 for (2992ds/339Mi)
% 7.02/2.19 % (22983)Instruction limit reached!
% 7.02/2.19 % (22983)------------------------------
% 7.02/2.19 % (22983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.19 % (22983)Termination reason: Unknown
% 7.02/2.19 % (22983)Termination phase: Saturation
% 7.02/2.19
% 7.02/2.20 % (22983)Memory used [KB]: 7036
% 7.02/2.20 % (22983)Time elapsed: 0.063 s
% 7.02/2.20 % (22983)Instructions burned: 141 (million)
% 7.02/2.20 % (22983)------------------------------
% 7.02/2.20 % (22983)------------------------------
% 7.36/2.21 % (22987)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_22813 for (2992ds/283Mi)
% 7.36/2.22 % (22980)Instruction limit reached!
% 7.36/2.22 % (22980)------------------------------
% 7.36/2.22 % (22980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.36/2.22 % (22980)Termination reason: Unknown
% 7.36/2.22 % (22980)Termination phase: Saturation
% 7.36/2.22
% 7.36/2.22 % (22980)Memory used [KB]: 8443
% 7.36/2.22 % (22980)Time elapsed: 0.156 s
% 7.36/2.22 % (22980)Instructions burned: 343 (million)
% 7.36/2.22 % (22980)------------------------------
% 7.36/2.22 % (22980)------------------------------
% 7.36/2.23 % (22988)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22813 for (2992ds/134Mi)
% 7.36/2.23 % (22985)Instruction limit reached!
% 7.36/2.23 % (22985)------------------------------
% 7.36/2.23 % (22985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.36/2.23 % (22985)Termination reason: Unknown
% 7.36/2.23 % (22985)Termination phase: Saturation
% 7.36/2.23
% 7.36/2.23 % (22985)Memory used [KB]: 4733
% 7.36/2.23 % (22985)Time elapsed: 0.096 s
% 7.36/2.23 % (22985)Instructions burned: 203 (million)
% 7.36/2.23 % (22985)------------------------------
% 7.36/2.23 % (22985)------------------------------
% 7.36/2.25 % (22982)Instruction limit reached!
% 7.36/2.25 % (22982)------------------------------
% 7.36/2.25 % (22982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.36/2.25 % (22982)Termination reason: Unknown
% 7.36/2.25 % (22982)Termination phase: Saturation
% 7.36/2.25
% 7.36/2.25 % (22982)Memory used [KB]: 9338
% 7.36/2.25 % (22982)Time elapsed: 0.122 s
% 7.36/2.25 % (22982)Instructions burned: 253 (million)
% 7.36/2.25 % (22982)------------------------------
% 7.36/2.25 % (22982)------------------------------
% 7.36/2.26 % (22989)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22813 for (2991ds/298Mi)
% 7.36/2.27 % (22988)Instruction limit reached!
% 7.36/2.27 % (22988)------------------------------
% 7.36/2.27 % (22988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.36/2.27 % (22988)Termination reason: Unknown
% 7.36/2.27 % (22988)Termination phase: Saturation
% 7.36/2.27
% 7.36/2.27 % (22988)Memory used [KB]: 7036
% 7.36/2.27 % (22988)Time elapsed: 0.037 s
% 7.36/2.27 % (22988)Instructions burned: 137 (million)
% 7.36/2.27 % (22988)------------------------------
% 7.36/2.27 % (22988)------------------------------
% 7.36/2.27 % (22990)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22813 for (2991ds/192Mi)
% 7.36/2.28 % (22991)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_22813 for (2991ds/258Mi)
% 7.92/2.30 % (22986)Instruction limit reached!
% 7.92/2.30 % (22986)------------------------------
% 7.92/2.30 % (22986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.30 % (22986)Termination reason: Unknown
% 7.92/2.30 % (22986)Termination phase: Saturation
% 7.92/2.30
% 7.92/2.30 % (22986)Memory used [KB]: 7675
% 7.92/2.30 % (22986)Time elapsed: 0.155 s
% 7.92/2.30 % (22986)Instructions burned: 339 (million)
% 7.92/2.30 % (22986)------------------------------
% 7.92/2.30 % (22986)------------------------------
% 7.92/2.32 % (22992)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_22813 for (2991ds/90Mi)
% 7.92/2.33 % (22987)Instruction limit reached!
% 7.92/2.33 % (22987)------------------------------
% 7.92/2.33 % (22987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.33 % (22987)Termination reason: Unknown
% 7.92/2.33 % (22987)Termination phase: Saturation
% 7.92/2.33
% 7.92/2.33 % (22987)Memory used [KB]: 7291
% 7.92/2.33 % (22987)Time elapsed: 0.119 s
% 7.92/2.33 % (22987)Instructions burned: 283 (million)
% 7.92/2.33 % (22987)------------------------------
% 7.92/2.33 % (22987)------------------------------
% 7.92/2.34 % (22992)Instruction limit reached!
% 7.92/2.34 % (22992)------------------------------
% 7.92/2.34 % (22992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.34 % (22992)Termination reason: Unknown
% 7.92/2.34 % (22992)Termination phase: Function definition elimination
% 7.92/2.34
% 7.92/2.34 % (22992)Memory used [KB]: 2430
% 7.92/2.34 % (22992)Time elapsed: 0.028 s
% 7.92/2.34 % (22992)Instructions burned: 90 (million)
% 7.92/2.34 % (22992)------------------------------
% 7.92/2.34 % (22992)------------------------------
% 7.92/2.35 % (22993)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_22813 for (2990ds/231Mi)
% 7.92/2.35 % (22994)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_22813 for (2990ds/458Mi)
% 7.92/2.36 % (22990)Instruction limit reached!
% 7.92/2.36 % (22990)------------------------------
% 7.92/2.36 % (22990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.36 % (22990)Termination reason: Unknown
% 7.92/2.36 % (22990)Termination phase: Saturation
% 7.92/2.36
% 7.92/2.36 % (22990)Memory used [KB]: 7547
% 7.92/2.36 % (22990)Time elapsed: 0.087 s
% 7.92/2.36 % (22990)Instructions burned: 192 (million)
% 7.92/2.36 % (22990)------------------------------
% 7.92/2.36 % (22990)------------------------------
% 7.92/2.36 % (22991)Instruction limit reached!
% 7.92/2.36 % (22991)------------------------------
% 7.92/2.36 % (22991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.36 % (22991)Termination reason: Unknown
% 7.92/2.36 % (22991)Termination phase: Saturation
% 7.92/2.36
% 7.92/2.36 % (22991)Memory used [KB]: 7931
% 7.92/2.36 % (22991)Time elapsed: 0.084 s
% 7.92/2.36 % (22991)Instructions burned: 258 (million)
% 7.92/2.36 % (22991)------------------------------
% 7.92/2.36 % (22991)------------------------------
% 7.92/2.37 % (22995)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_22813 for (2990ds/31Mi)
% 7.92/2.38 % (22996)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_22813 for (2990ds/297Mi)
% 7.92/2.38 % (22989)Instruction limit reached!
% 7.92/2.38 % (22989)------------------------------
% 7.92/2.38 % (22989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.38 % (22989)Termination reason: Unknown
% 7.92/2.38 % (22989)Termination phase: Saturation
% 7.92/2.38
% 7.92/2.38 % (22989)Memory used [KB]: 7291
% 7.92/2.38 % (22989)Time elapsed: 0.125 s
% 7.92/2.38 % (22989)Instructions burned: 299 (million)
% 7.92/2.38 % (22989)------------------------------
% 7.92/2.38 % (22989)------------------------------
% 7.92/2.38 % (22984)Instruction limit reached!
% 7.92/2.38 % (22984)------------------------------
% 7.92/2.38 % (22984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.38 % (22984)Termination reason: Unknown
% 7.92/2.38 % (22984)Termination phase: Saturation
% 7.92/2.38
% 7.92/2.38 % (22984)Memory used [KB]: 9338
% 7.92/2.38 % (22984)Time elapsed: 0.246 s
% 7.92/2.38 % (22984)Instructions burned: 615 (million)
% 7.92/2.38 % (22984)------------------------------
% 7.92/2.38 % (22984)------------------------------
% 7.92/2.39 % (22995)Instruction limit reached!
% 7.92/2.39 % (22995)------------------------------
% 7.92/2.39 % (22995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.39 % (22995)Termination reason: Unknown
% 7.92/2.39 % (22995)Termination phase: shuffling
% 7.92/2.39
% 7.92/2.39 % (22995)Memory used [KB]: 1918
% 7.92/2.39 % (22995)Time elapsed: 0.016 s
% 7.92/2.39 % (22995)Instructions burned: 32 (million)
% 7.92/2.39 % (22995)------------------------------
% 7.92/2.39 % (22995)------------------------------
% 7.92/2.40 % (22998)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_22813 for (2990ds/182Mi)
% 8.99/2.40 % (22997)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_22813 for (2990ds/987Mi)
% 8.99/2.40 % (22999)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_22813 for (2990ds/182Mi)
% 8.99/2.45 % (22993)Instruction limit reached!
% 8.99/2.45 % (22993)------------------------------
% 8.99/2.45 % (22993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.45 % (22993)Termination reason: Unknown
% 8.99/2.45 % (22993)Termination phase: Saturation
% 8.99/2.45
% 8.99/2.45 % (22993)Memory used [KB]: 11257
% 8.99/2.45 % (22993)Time elapsed: 0.108 s
% 8.99/2.45 % (22993)Instructions burned: 231 (million)
% 8.99/2.45 % (22993)------------------------------
% 8.99/2.45 % (22993)------------------------------
% 8.99/2.47 % (22964)Instruction limit reached!
% 8.99/2.47 % (22964)------------------------------
% 8.99/2.47 % (22964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.47 % (22964)Termination reason: Unknown
% 8.99/2.47 % (22964)Termination phase: Saturation
% 8.99/2.47
% 8.99/2.47 % (22964)Memory used [KB]: 11001
% 8.99/2.47 % (22964)Time elapsed: 0.568 s
% 8.99/2.47 % (22964)Instructions burned: 1088 (million)
% 8.99/2.47 % (22964)------------------------------
% 8.99/2.47 % (22964)------------------------------
% 8.99/2.48 % (22998)Instruction limit reached!
% 8.99/2.48 % (22998)------------------------------
% 8.99/2.48 % (22998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.48 % (22998)Termination reason: Unknown
% 8.99/2.48 % (22998)Termination phase: Saturation
% 8.99/2.48
% 8.99/2.48 % (22998)Memory used [KB]: 7547
% 8.99/2.48 % (22998)Time elapsed: 0.082 s
% 8.99/2.48 % (22998)Instructions burned: 182 (million)
% 8.99/2.48 % (22998)------------------------------
% 8.99/2.48 % (22998)------------------------------
% 8.99/2.48 % (23000)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_22813 for (2989ds/154Mi)
% 8.99/2.48 % (23001)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_22813 for (2989ds/79Mi)
% 8.99/2.49 % (22999)Instruction limit reached!
% 8.99/2.49 % (22999)------------------------------
% 8.99/2.49 % (22999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.49 % (22999)Termination reason: Unknown
% 8.99/2.49 % (22999)Termination phase: Saturation
% 8.99/2.49
% 8.99/2.49 % (22999)Memory used [KB]: 8699
% 8.99/2.49 % (22999)Time elapsed: 0.086 s
% 8.99/2.49 % (22999)Instructions burned: 182 (million)
% 8.99/2.49 % (22999)------------------------------
% 8.99/2.49 % (22999)------------------------------
% 8.99/2.49 % (22994)Instruction limit reached!
% 8.99/2.49 % (22994)------------------------------
% 8.99/2.49 % (22994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.49 % (22994)Termination reason: Unknown
% 8.99/2.49 % (22994)Termination phase: Saturation
% 8.99/2.49
% 8.99/2.49 % (22994)Memory used [KB]: 9338
% 8.99/2.49 % (22994)Time elapsed: 0.136 s
% 8.99/2.49 % (22994)Instructions burned: 458 (million)
% 8.99/2.49 % (22994)------------------------------
% 8.99/2.49 % (22994)------------------------------
% 8.99/2.49 % (23002)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_22813 for (2989ds/216Mi)
% 9.53/2.50 % (22996)Instruction limit reached!
% 9.53/2.50 % (22996)------------------------------
% 9.53/2.50 % (22996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.50 % (22996)Termination reason: Unknown
% 9.53/2.50 % (22996)Termination phase: Saturation
% 9.53/2.50
% 9.53/2.50 % (22996)Memory used [KB]: 7291
% 9.53/2.50 % (22996)Time elapsed: 0.124 s
% 9.53/2.50 % (22996)Instructions burned: 299 (million)
% 9.53/2.50 % (22996)------------------------------
% 9.53/2.50 % (22996)------------------------------
% 9.53/2.50 % (23004)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_22813 for (2989ds/922Mi)
% 9.53/2.51 % (23003)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22813 for (2989ds/114Mi)
% 9.53/2.51 % (23005)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_22813 for (2989ds/182Mi)
% 9.53/2.51 % (23000)Instruction limit reached!
% 9.53/2.51 % (23000)------------------------------
% 9.53/2.51 % (23000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.51 % (23000)Termination reason: Unknown
% 9.53/2.51 % (23000)Termination phase: Saturation
% 9.53/2.52
% 9.53/2.52 % (23000)Memory used [KB]: 7036
% 9.53/2.52 % (23000)Time elapsed: 0.040 s
% 9.53/2.52 % (23000)Instructions burned: 155 (million)
% 9.53/2.52 % (23000)------------------------------
% 9.53/2.52 % (23000)------------------------------
% 9.53/2.52 % (23001)Instruction limit reached!
% 9.53/2.52 % (23001)------------------------------
% 9.53/2.52 % (23001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.52 % (23001)Termination reason: Unknown
% 9.53/2.52 % (23001)Termination phase: Property scanning
% 9.53/2.52
% 9.53/2.52 % (23001)Memory used [KB]: 2430
% 9.53/2.52 % (23001)Time elapsed: 0.037 s
% 9.53/2.52 % (23001)Instructions burned: 79 (million)
% 9.53/2.52 % (23001)------------------------------
% 9.53/2.52 % (23001)------------------------------
% 9.53/2.52 % (23006)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_22813 for (2989ds/164Mi)
% 9.53/2.54 % (23007)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_22813 for (2989ds/50Mi)
% 9.53/2.56 % (23007)Instruction limit reached!
% 9.53/2.56 % (23007)------------------------------
% 9.53/2.56 % (23007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.56 % (23007)Termination reason: Unknown
% 9.53/2.56 % (23007)Termination phase: Property scanning
% 9.53/2.56
% 9.53/2.56 % (23007)Memory used [KB]: 2302
% 9.53/2.56 % (23007)Time elapsed: 0.024 s
% 9.53/2.56 % (23007)Instructions burned: 51 (million)
% 9.53/2.56 % (23007)------------------------------
% 9.53/2.56 % (23007)------------------------------
% 9.53/2.56 % (23003)Instruction limit reached!
% 9.53/2.56 % (23003)------------------------------
% 9.53/2.56 % (23003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.56 % (23003)Termination reason: Unknown
% 9.53/2.56 % (23003)Termination phase: Property scanning
% 9.53/2.56
% 9.53/2.56 % (23003)Memory used [KB]: 2430
% 9.53/2.56 % (23003)Time elapsed: 0.052 s
% 9.53/2.56 % (23003)Instructions burned: 115 (million)
% 9.53/2.56 % (23003)------------------------------
% 9.53/2.56 % (23003)------------------------------
% 9.53/2.57 % (23006)Instruction limit reached!
% 9.53/2.57 % (23006)------------------------------
% 9.53/2.57 % (23006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.57 % (23006)Termination reason: Unknown
% 9.53/2.57 % (23006)Termination phase: Saturation
% 9.53/2.57
% 9.53/2.57 % (23006)Memory used [KB]: 2558
% 9.53/2.57 % (23006)Time elapsed: 0.042 s
% 9.53/2.57 % (23006)Instructions burned: 165 (million)
% 9.53/2.57 % (23006)------------------------------
% 9.53/2.57 % (23006)------------------------------
% 9.53/2.58 % (23010)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_22813 for (2988ds/267Mi)
% 9.53/2.58 % (23008)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22813 for (2988ds/368Mi)
% 9.53/2.58 % (23009)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_22813 for (2988ds/1021Mi)
% 9.53/2.58 % (23002)Instruction limit reached!
% 9.53/2.58 % (23002)------------------------------
% 9.53/2.58 % (23002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.58 % (23002)Termination reason: Unknown
% 9.53/2.58 % (23002)Termination phase: Saturation
% 9.53/2.58
% 9.53/2.58 % (23002)Memory used [KB]: 7291
% 9.53/2.58 % (23002)Time elapsed: 0.091 s
% 9.53/2.58 % (23002)Instructions burned: 217 (million)
% 9.53/2.58 % (23002)------------------------------
% 9.53/2.58 % (23002)------------------------------
% 9.53/2.59 % (23005)Instruction limit reached!
% 9.53/2.59 % (23005)------------------------------
% 9.53/2.59 % (23005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.59 % (23005)Termination reason: Unknown
% 9.53/2.59 % (23005)Termination phase: Saturation
% 9.53/2.59
% 9.53/2.59 % (23005)Memory used [KB]: 7291
% 9.53/2.59 % (23005)Time elapsed: 0.078 s
% 9.53/2.59 % (23005)Instructions burned: 182 (million)
% 9.53/2.59 % (23005)------------------------------
% 9.53/2.59 % (23005)------------------------------
% 10.13/2.60 % (23011)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_22813 for (2988ds/204Mi)
% 10.13/2.61 % (23012)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_22813 for (2988ds/26Mi)
% 10.13/2.62 % (23012)Instruction limit reached!
% 10.13/2.62 % (23012)------------------------------
% 10.13/2.62 % (23012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.62 % (23012)Termination reason: Unknown
% 10.13/2.62 % (23012)Termination phase: shuffling
% 10.13/2.62
% 10.13/2.62 % (23012)Memory used [KB]: 1918
% 10.13/2.62 % (23012)Time elapsed: 0.014 s
% 10.13/2.62 % (23012)Instructions burned: 27 (million)
% 10.13/2.62 % (23012)------------------------------
% 10.13/2.62 % (23012)------------------------------
% 10.13/2.64 % (23014)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_22813 for (2987ds/53Mi)
% 10.13/2.66 % (23014)Instruction limit reached!
% 10.13/2.66 % (23014)------------------------------
% 10.13/2.66 % (23014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.66 % (23014)Termination reason: Unknown
% 10.13/2.66 % (23014)Termination phase: Property scanning
% 10.13/2.66
% 10.13/2.66 % (23014)Memory used [KB]: 2302
% 10.13/2.66 % (23014)Time elapsed: 0.026 s
% 10.13/2.66 % (23014)Instructions burned: 55 (million)
% 10.13/2.66 % (23014)------------------------------
% 10.13/2.66 % (23014)------------------------------
% 10.13/2.66 % (23010)Instruction limit reached!
% 10.13/2.66 % (23010)------------------------------
% 10.13/2.66 % (23010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.66 % (23010)Termination reason: Unknown
% 10.13/2.66 % (23010)Termination phase: Saturation
% 10.13/2.66
% 10.13/2.66 % (23010)Memory used [KB]: 7291
% 10.13/2.66 % (23010)Time elapsed: 0.090 s
% 10.13/2.66 % (23010)Instructions burned: 269 (million)
% 10.13/2.66 % (23010)------------------------------
% 10.13/2.66 % (23010)------------------------------
% 10.13/2.68 % (23015)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_22813 for (2987ds/4436Mi)
% 10.13/2.68 % (23016)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_22813 for (2987ds/1539Mi)
% 10.13/2.69 % (23011)Instruction limit reached!
% 10.13/2.69 % (23011)------------------------------
% 10.13/2.69 % (23011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.13/2.69 % (23011)Termination reason: Unknown
% 10.13/2.69 % (23011)Termination phase: Saturation
% 10.13/2.69
% 10.13/2.69 % (23011)Memory used [KB]: 7547
% 10.13/2.69 % (23011)Time elapsed: 0.091 s
% 10.13/2.69 % (23011)Instructions burned: 205 (million)
% 10.13/2.69 % (23011)------------------------------
% 10.13/2.69 % (23011)------------------------------
% 10.41/2.70 % (23008)Instruction limit reached!
% 10.41/2.70 % (23008)------------------------------
% 10.41/2.70 % (23008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.41/2.70 % (23008)Termination reason: Unknown
% 10.41/2.70 % (23008)Termination phase: Saturation
% 10.41/2.70
% 10.41/2.70 % (23008)Memory used [KB]: 8571
% 10.41/2.70 % (23008)Time elapsed: 0.123 s
% 10.41/2.70 % (23008)Instructions burned: 370 (million)
% 10.41/2.70 % (23008)------------------------------
% 10.41/2.70 % (23008)------------------------------
% 10.41/2.70 % (23017)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_22813 for (2987ds/408Mi)
% 10.41/2.71 % (23018)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_22813 for (2987ds/5205Mi)
% 10.41/2.78 % (22997)Instruction limit reached!
% 10.41/2.78 % (22997)------------------------------
% 10.41/2.78 % (22997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.41/2.78 % (22997)Termination reason: Unknown
% 10.41/2.78 % (22997)Termination phase: Saturation
% 10.41/2.78
% 10.41/2.78 % (22997)Memory used [KB]: 13048
% 10.41/2.78 % (22997)Time elapsed: 0.381 s
% 10.41/2.78 % (22997)Instructions burned: 987 (million)
% 10.41/2.78 % (22997)------------------------------
% 10.41/2.78 % (22997)------------------------------
% 10.41/2.79 % (23019)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_22813 for (2986ds/1913Mi)
% 10.94/2.88 % (23017)Instruction limit reached!
% 10.94/2.88 % (23017)------------------------------
% 10.94/2.88 % (23017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.88 % (23017)Termination reason: Unknown
% 10.94/2.88 % (23017)Termination phase: Saturation
% 10.94/2.88
% 10.94/2.88 % (23017)Memory used [KB]: 10106
% 10.94/2.88 % (23017)Time elapsed: 0.174 s
% 10.94/2.88 % (23017)Instructions burned: 410 (million)
% 10.94/2.88 % (23017)------------------------------
% 10.94/2.88 % (23017)------------------------------
% 10.94/2.89 % (23021)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_22813 for (2985ds/4350Mi)
% 11.13/2.95 % (23004)Instruction limit reached!
% 11.13/2.95 % (23004)------------------------------
% 11.13/2.95 % (23004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.13/2.95 % (23004)Termination reason: Unknown
% 11.13/2.95 % (23004)Termination phase: Saturation
% 11.13/2.95
% 11.13/2.95 % (23004)Memory used [KB]: 10490
% 11.13/2.95 % (23004)Time elapsed: 0.452 s
% 11.13/2.95 % (23004)Instructions burned: 922 (million)
% 11.13/2.95 % (23004)------------------------------
% 11.13/2.95 % (23004)------------------------------
% 11.13/2.97 % (23022)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_22813 for (2984ds/68Mi)
% 11.13/3.00 % (23022)Instruction limit reached!
% 11.13/3.00 % (23022)------------------------------
% 11.13/3.00 % (23022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.13/3.00 % (23022)Termination reason: Unknown
% 11.13/3.00 % (23022)Termination phase: SInE selection
% 11.13/3.00
% 11.13/3.00 % (23022)Memory used [KB]: 2302
% 11.13/3.00 % (23022)Time elapsed: 0.034 s
% 11.13/3.00 % (23022)Instructions burned: 70 (million)
% 11.13/3.00 % (23022)------------------------------
% 11.13/3.00 % (23022)------------------------------
% 11.13/3.03 % (23023)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_22813 for (2984ds/358Mi)
% 13.49/3.08 % (23009)Instruction limit reached!
% 13.49/3.08 % (23009)------------------------------
% 13.49/3.08 % (23009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.49/3.08 % (23009)Termination reason: Unknown
% 13.49/3.08 % (23009)Termination phase: Saturation
% 13.49/3.08
% 13.49/3.08 % (23009)Memory used [KB]: 11769
% 13.49/3.08 % (23009)Time elapsed: 0.500 s
% 13.49/3.08 % (23009)Instructions burned: 1024 (million)
% 13.49/3.08 % (23009)------------------------------
% 13.49/3.08 % (23009)------------------------------
% 13.49/3.09 % (23024)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_22813 for (2983ds/31Mi)
% 13.49/3.10 % (23024)Instruction limit reached!
% 13.49/3.10 % (23024)------------------------------
% 13.49/3.10 % (23024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.49/3.10 % (23024)Termination reason: Unknown
% 13.49/3.10 % (23024)Termination phase: shuffling
% 13.49/3.10
% 13.49/3.10 % (23024)Memory used [KB]: 2046
% 13.49/3.10 % (23024)Time elapsed: 0.010 s
% 13.49/3.10 % (23024)Instructions burned: 31 (million)
% 13.49/3.10 % (23024)------------------------------
% 13.49/3.10 % (23024)------------------------------
% 13.49/3.11 % (23025)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22813 for (2983ds/279Mi)
% 14.07/3.19 % (23023)Instruction limit reached!
% 14.07/3.19 % (23023)------------------------------
% 14.07/3.19 % (23023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.19 % (23023)Termination reason: Unknown
% 14.07/3.19 % (23023)Termination phase: Saturation
% 14.07/3.19
% 14.07/3.19 % (23023)Memory used [KB]: 8315
% 14.07/3.19 % (23023)Time elapsed: 0.162 s
% 14.07/3.19 % (23023)Instructions burned: 359 (million)
% 14.07/3.19 % (23023)------------------------------
% 14.07/3.19 % (23023)------------------------------
% 14.07/3.19 % (23025)Instruction limit reached!
% 14.07/3.19 % (23025)------------------------------
% 14.07/3.19 % (23025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.19 % (23025)Termination reason: Unknown
% 14.07/3.19 % (23025)Termination phase: Saturation
% 14.07/3.19
% 14.07/3.19 % (23025)Memory used [KB]: 7291
% 14.07/3.19 % (23025)Time elapsed: 0.082 s
% 14.07/3.19 % (23025)Instructions burned: 279 (million)
% 14.07/3.19 % (23025)------------------------------
% 14.07/3.19 % (23025)------------------------------
% 14.68/3.20 % (23026)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22813 for (2982ds/258Mi)
% 14.68/3.21 % (23027)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_22813 for (2982ds/26Mi)
% 14.68/3.22 % (23027)Instruction limit reached!
% 14.68/3.22 % (23027)------------------------------
% 14.68/3.22 % (23027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.68/3.22 % (23027)Termination reason: Unknown
% 14.68/3.22 % (23027)Termination phase: shuffling
% 14.68/3.22
% 14.68/3.22 % (23027)Memory used [KB]: 1918
% 14.68/3.22 % (23027)Time elapsed: 0.014 s
% 14.68/3.22 % (23027)Instructions burned: 28 (million)
% 14.68/3.22 % (23027)------------------------------
% 14.68/3.22 % (23027)------------------------------
% 14.68/3.23 % (23028)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_22813 for (2982ds/995Mi)
% 15.22/3.30 % (23026)Instruction limit reached!
% 15.22/3.30 % (23026)------------------------------
% 15.22/3.30 % (23026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.22/3.30 % (23026)Termination reason: Unknown
% 15.22/3.30 % (23026)Termination phase: Saturation
% 15.22/3.30
% 15.22/3.30 % (23026)Memory used [KB]: 8315
% 15.22/3.30 % (23026)Time elapsed: 0.106 s
% 15.22/3.30 % (23026)Instructions burned: 258 (million)
% 15.22/3.30 % (23026)------------------------------
% 15.22/3.30 % (23026)------------------------------
% 15.22/3.32 % (23029)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_22813 for (2981ds/373Mi)
% 15.84/3.44 % (23016)Instruction limit reached!
% 15.84/3.44 % (23016)------------------------------
% 15.84/3.44 % (23016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.44 % (23016)Termination reason: Unknown
% 15.84/3.44 % (23016)Termination phase: Saturation
% 15.84/3.44
% 15.84/3.44 % (23016)Memory used [KB]: 10106
% 15.84/3.44 % (23016)Time elapsed: 0.764 s
% 15.84/3.44 % (23016)Instructions burned: 1540 (million)
% 15.84/3.44 % (23016)------------------------------
% 15.84/3.44 % (23016)------------------------------
% 15.84/3.45 % (23030)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_22813 for (2979ds/253Mi)
% 15.84/3.46 % (23029)Instruction limit reached!
% 15.84/3.46 % (23029)------------------------------
% 15.84/3.46 % (23029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.46 % (23029)Termination reason: Unknown
% 15.84/3.46 % (23029)Termination phase: Saturation
% 15.84/3.46
% 15.84/3.46 % (23029)Memory used [KB]: 8443
% 15.84/3.46 % (23029)Time elapsed: 0.142 s
% 15.84/3.46 % (23029)Instructions burned: 373 (million)
% 15.84/3.46 % (23029)------------------------------
% 15.84/3.46 % (23029)------------------------------
% 15.84/3.47 % (23031)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_22813 for (2979ds/832Mi)
% 16.44/3.54 % (23030)Instruction limit reached!
% 16.44/3.54 % (23030)------------------------------
% 16.44/3.54 % (23030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.44/3.54 % (23030)Termination reason: Unknown
% 16.44/3.54 % (23030)Termination phase: Saturation
% 16.44/3.54
% 16.44/3.54 % (23030)Memory used [KB]: 7291
% 16.44/3.54 % (23030)Time elapsed: 0.085 s
% 16.44/3.54 % (23030)Instructions burned: 255 (million)
% 16.44/3.54 % (23030)------------------------------
% 16.44/3.54 % (23030)------------------------------
% 16.44/3.55 % (23032)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_22813 for (2978ds/668Mi)
% 16.94/3.62 % (23028)Instruction limit reached!
% 16.94/3.62 % (23028)------------------------------
% 16.94/3.62 % (23028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.94/3.62 % (23028)Termination reason: Unknown
% 16.94/3.62 % (23028)Termination phase: Saturation
% 16.94/3.62
% 16.94/3.62 % (23028)Memory used [KB]: 12281
% 16.94/3.62 % (23028)Time elapsed: 0.387 s
% 16.94/3.62 % (23028)Instructions burned: 996 (million)
% 16.94/3.62 % (23028)------------------------------
% 16.94/3.62 % (23028)------------------------------
% 16.94/3.64 % (23033)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_22813 for (2978ds/40Mi)
% 16.94/3.65 % (23033)Instruction limit reached!
% 16.94/3.65 % (23033)------------------------------
% 16.94/3.65 % (23033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.94/3.65 % (23033)Termination reason: Unknown
% 16.94/3.65 % (23033)Termination phase: Property scanning
% 16.94/3.65
% 16.94/3.65 % (23033)Memory used [KB]: 2174
% 16.94/3.65 % (23033)Time elapsed: 0.012 s
% 16.94/3.65 % (23033)Instructions burned: 40 (million)
% 16.94/3.65 % (23033)------------------------------
% 16.94/3.65 % (23033)------------------------------
% 16.94/3.67 % (23034)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_22813 for (2977ds/294Mi)
% 17.76/3.73 % (23019)Instruction limit reached!
% 17.76/3.73 % (23019)------------------------------
% 17.76/3.73 % (23019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/3.73 % (23019)Termination reason: Unknown
% 17.76/3.73 % (23019)Termination phase: Saturation
% 17.76/3.73
% 17.76/3.73 % (23019)Memory used [KB]: 4989
% 17.76/3.73 % (23019)Time elapsed: 0.942 s
% 17.76/3.73 % (23019)Instructions burned: 1914 (million)
% 17.76/3.73 % (23019)------------------------------
% 17.76/3.73 % (23019)------------------------------
% 17.76/3.74 % (23031)First to succeed.
% 17.76/3.74 % (23032)Instruction limit reached!
% 17.76/3.74 % (23032)------------------------------
% 17.76/3.74 % (23032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/3.74 % (23032)Termination reason: Unknown
% 17.76/3.74 % (23032)Termination phase: Saturation
% 17.76/3.74
% 17.76/3.74 % (23032)Memory used [KB]: 17142
% 17.76/3.74 % (23032)Time elapsed: 0.195 s
% 17.76/3.74 % (23032)Instructions burned: 670 (million)
% 17.76/3.74 % (23032)------------------------------
% 17.76/3.74 % (23032)------------------------------
% 17.76/3.74 % (23035)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_22813 for (2976ds/187Mi)
% 17.76/3.75 % (23031)Refutation found. Thanks to Tanya!
% 17.76/3.75 % SZS status Theorem for DTF2THF_22813
% 17.76/3.75 % SZS output start Proof for DTF2THF_22813
% 17.76/3.75 thf(func_def_0, type, in: $i > $i > $o).
% 17.76/3.75 thf(func_def_1, type, exu: ($i > $o) > $o).
% 17.76/3.75 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 17.76/3.75 thf(func_def_8, type, powerset: $i > $i).
% 17.76/3.75 thf(func_def_10, type, setunion: $i > $i).
% 17.76/3.75 thf(func_def_19, type, descr: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_26, type, prop2set: $o > $i).
% 17.76/3.75 thf(func_def_36, type, nonempty: $i > $o).
% 17.76/3.75 thf(func_def_69, type, set2prop: $i > $o).
% 17.76/3.75 thf(func_def_88, type, subset: $i > $i > $o).
% 17.76/3.75 thf(func_def_89, type, disjoint: $i > $i > $o).
% 17.76/3.75 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 17.76/3.75 thf(func_def_114, type, binunion: $i > $i > $i).
% 17.76/3.75 thf(func_def_122, type, binintersect: $i > $i > $i).
% 17.76/3.75 thf(func_def_135, type, regular: $i > $o).
% 17.76/3.75 thf(func_def_136, type, setminus: $i > $i > $i).
% 17.76/3.75 thf(func_def_147, type, symdiff: $i > $i > $i).
% 17.76/3.75 thf(func_def_153, type, iskpair: $i > $o).
% 17.76/3.75 thf(func_def_158, type, kpair: $i > $i > $i).
% 17.76/3.75 thf(func_def_160, type, cartprod: $i > $i > $i).
% 17.76/3.75 thf(func_def_177, type, singleton: $i > $o).
% 17.76/3.75 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 17.76/3.75 thf(func_def_184, type, atmost1p: $i > $o).
% 17.76/3.75 thf(func_def_185, type, atleast2p: $i > $o).
% 17.76/3.75 thf(func_def_186, type, atmost2p: $i > $o).
% 17.76/3.75 thf(func_def_187, type, upairsetp: $i > $o).
% 17.76/3.75 thf(func_def_191, type, kfst: $i > $i).
% 17.76/3.75 thf(func_def_203, type, ksnd: $i > $i).
% 17.76/3.75 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 17.76/3.75 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 17.76/3.75 thf(func_def_222, type, func: $i > $i > $i > $o).
% 17.76/3.75 thf(func_def_223, type, funcSet: $i > $i > $i).
% 17.76/3.75 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 17.76/3.75 thf(func_def_274, type, sP3: $i > $i > $o).
% 17.76/3.75 thf(func_def_275, type, sP4: $i > $o).
% 17.76/3.75 thf(func_def_276, type, sP5: $i > $i > $o).
% 17.76/3.75 thf(func_def_277, type, sP6: $i > $i > $o).
% 17.76/3.75 thf(func_def_279, type, sP8: $i > $i > $i > $o > $o).
% 17.76/3.75 thf(func_def_280, type, sP9: $i > $i > $i > $i > $o).
% 17.76/3.75 thf(func_def_284, type, sK13: $i > $i > $i).
% 17.76/3.75 thf(func_def_313, type, sK42: $i > $o).
% 17.76/3.75 thf(func_def_315, type, sK44: ($i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_316, type, sK45: ($i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_331, type, sK60: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_332, type, sK61: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_333, type, sK62: $i > $o).
% 17.76/3.75 thf(func_def_336, type, sK65: $i > ($i > $i) > $i > $i).
% 17.76/3.75 thf(func_def_338, type, sK67: $i > $i).
% 17.76/3.75 thf(func_def_344, type, sK73: $i > $i).
% 17.76/3.75 thf(func_def_346, type, sK75: $i > $i > $i).
% 17.76/3.75 thf(func_def_349, type, sK78: ($i > $o) > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_350, type, sK79: ($i > $o) > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_351, type, sK80: $i > $o).
% 17.76/3.75 thf(func_def_352, type, sK81: $i > $o).
% 17.76/3.75 thf(func_def_359, type, sK88: $o > $i > $i > $i).
% 17.76/3.75 thf(func_def_372, type, sK101: $i > $i).
% 17.76/3.75 thf(func_def_375, type, sK104: $i > $i > ($i > $i) > $i).
% 17.76/3.75 thf(func_def_381, type, sK110: $i > $i > $o).
% 17.76/3.75 thf(func_def_382, type, sK111: $i > $i).
% 17.76/3.75 thf(func_def_383, type, sK112: $i > $i).
% 17.76/3.75 thf(func_def_384, type, sK113: ($i > $i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_385, type, sK114: ($i > $i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_386, type, sK115: $i > ($i > $i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_390, type, sK119: $i > $i > $o).
% 17.76/3.75 thf(func_def_392, type, sK121: ($i > $o) > ($i > $o) > $i > $i > $i).
% 17.76/3.75 thf(func_def_393, type, sK122: ($i > $o) > ($i > $o) > $i > $i > $i).
% 17.76/3.75 thf(func_def_396, type, sK125: $i > $o).
% 17.76/3.75 thf(func_def_397, type, sK126: $i > $o).
% 17.76/3.75 thf(func_def_402, type, sK131: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_420, type, sK149: $i > $i).
% 17.76/3.75 thf(func_def_423, type, sK152: $i > $o).
% 17.76/3.75 thf(func_def_439, type, sK168: $i > $i > $o).
% 17.76/3.75 thf(func_def_448, type, sK177: $i > $i).
% 17.76/3.75 thf(func_def_451, type, sK180: $i > ($i > $i) > $i > $i).
% 17.76/3.75 thf(func_def_468, type, sK197: ($i > $i) > $i > $i > $i).
% 17.76/3.75 thf(func_def_471, type, sK200: $i > $i).
% 17.76/3.75 thf(func_def_474, type, sK203: $i > $i).
% 17.76/3.75 thf(func_def_475, type, sK204: $i > $i).
% 17.76/3.75 thf(func_def_476, type, sK205: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_477, type, sK206: $i > $o).
% 17.76/3.75 thf(func_def_486, type, sK215: $i > $i > $o).
% 17.76/3.75 thf(func_def_491, type, sK220: $i > $i > $i).
% 17.76/3.75 thf(func_def_492, type, sK221: $i > $i > $i).
% 17.76/3.75 thf(func_def_493, type, sK222: $i > $i > $i).
% 17.76/3.75 thf(func_def_494, type, sK223: $i > $i > $i).
% 17.76/3.75 thf(func_def_495, type, sK224: $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_496, type, sK225: $i > $i).
% 17.76/3.75 thf(func_def_497, type, sK226: $i > $i).
% 17.76/3.75 thf(func_def_498, type, sK227: $i > $i).
% 17.76/3.75 thf(func_def_499, type, sK228: $i > $i).
% 17.76/3.75 thf(func_def_500, type, sK229: $i > $i > $i).
% 17.76/3.75 thf(func_def_501, type, sK230: $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_502, type, sK231: $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_503, type, sK232: $i > $i > $i).
% 17.76/3.75 thf(func_def_504, type, sK233: $i > $i > $i).
% 17.76/3.75 thf(func_def_505, type, sK234: $i > $i).
% 17.76/3.75 thf(func_def_506, type, sK235: $i > $i > $i).
% 17.76/3.75 thf(func_def_508, type, sK237: $i > $i).
% 17.76/3.75 thf(func_def_509, type, sK238: $i > $i).
% 17.76/3.75 thf(func_def_516, type, sK245: $i > $o).
% 17.76/3.75 thf(func_def_517, type, sK246: $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_518, type, sK247: $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_527, type, sK256: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_528, type, sK257: $i > $o).
% 17.76/3.75 thf(func_def_529, type, sK258: $i > $i).
% 17.76/3.75 thf(func_def_544, type, sK273: $i > $i).
% 17.76/3.75 thf(func_def_551, type, sK280: $i > $i > $o).
% 17.76/3.75 thf(func_def_570, type, sK299: $i > $o).
% 17.76/3.75 thf(func_def_583, type, sK312: $i > $i > $o).
% 17.76/3.75 thf(func_def_586, type, sK315: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_587, type, sK316: $i > $o).
% 17.76/3.75 thf(func_def_593, type, sK322: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_609, type, sK338: $i > $o).
% 17.76/3.75 thf(func_def_612, type, sK341: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_613, type, sK342: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_616, type, sK345: $i > $o).
% 17.76/3.75 thf(func_def_622, type, sK351: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_623, type, sK352: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_630, type, sK359: $i > $i).
% 17.76/3.75 thf(func_def_643, type, sK372: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_644, type, sK373: $i > $o).
% 17.76/3.75 thf(func_def_665, type, sK394: $i > $i > $i).
% 17.76/3.75 thf(func_def_673, type, sK402: $i > $i > $i).
% 17.76/3.75 thf(func_def_686, type, sK415: $i > $o).
% 17.76/3.75 thf(func_def_694, type, sK423: $i > $o).
% 17.76/3.75 thf(func_def_699, type, sK428: $i > $o).
% 17.76/3.75 thf(func_def_701, type, sK430: ($i > $o) > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_702, type, sK431: ($i > $o) > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_707, type, sK436: $i > $o).
% 17.76/3.75 thf(func_def_709, type, sK438: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_710, type, sK439: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_715, type, sK444: $i > $o).
% 17.76/3.75 thf(func_def_718, type, sK447: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_725, type, sK454: $i > $i > $i).
% 17.76/3.75 thf(func_def_726, type, sK455: ($i > $o) > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_727, type, sK456: ($i > $o) > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_731, type, sK460: $i > $o).
% 17.76/3.75 thf(func_def_738, type, sK467: $i > $o).
% 17.76/3.75 thf(func_def_742, type, sK471: $i > $i > $i).
% 17.76/3.75 thf(func_def_771, type, sK500: $i > $o).
% 17.76/3.75 thf(func_def_774, type, sK503: $i > $o).
% 17.76/3.75 thf(func_def_804, type, sK533: ($i > $i) > $i > $i > $i).
% 17.76/3.75 thf(func_def_807, type, sK536: $i > $i).
% 17.76/3.75 thf(func_def_818, type, sK547: $i > $o).
% 17.76/3.75 thf(func_def_823, type, sK552: $i > $o).
% 17.76/3.75 thf(func_def_824, type, sK553: $i > $i).
% 17.76/3.75 thf(func_def_825, type, sK554: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_826, type, sK555: $i > $o).
% 17.76/3.75 thf(func_def_829, type, sK558: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_833, type, sK562: $i > $o).
% 17.76/3.75 thf(func_def_841, type, sK570: $i > $o).
% 17.76/3.75 thf(func_def_843, type, sK572: $i > $o).
% 17.76/3.75 thf(func_def_845, type, sK574: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_846, type, sK575: ($i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_848, type, sK577: $i > $o).
% 17.76/3.75 thf(func_def_859, type, sK588: $i > $i > $i).
% 17.76/3.75 thf(func_def_863, type, sK592: $i > $o).
% 17.76/3.75 thf(func_def_864, type, sK593: ($i > $o) > $i).
% 17.76/3.75 thf(func_def_865, type, sK594: $i > $o).
% 17.76/3.75 thf(func_def_868, type, sK597: $i > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_883, type, sK612: $i > $i > $o).
% 17.76/3.75 thf(func_def_897, type, sK626: $i > $i).
% 17.76/3.75 thf(func_def_901, type, sK630: $i > $i > $i).
% 17.76/3.75 thf(func_def_902, type, sK631: $i > $i > $i).
% 17.76/3.75 thf(func_def_909, type, sK638: $i > $i > $o).
% 17.76/3.75 thf(func_def_915, type, sK644: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_916, type, sK645: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_917, type, sK646: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_918, type, sK647: $i > $i > $i > $i > $i).
% 17.76/3.75 thf(func_def_928, type, sK657: ($i > $o) > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_929, type, sK658: ($i > $o) > ($i > $o) > $i).
% 17.76/3.75 thf(func_def_930, type, sK659: $i > $o).
% 17.76/3.75 thf(func_def_931, type, sK660: $i > $o).
% 17.76/3.75 thf(func_def_932, type, sK661: $i > $o).
% 17.76/3.75 thf(func_def_935, type, sK664: $i > $i).
% 17.76/3.75 thf(func_def_939, type, sK668: $i > $i > ($i > $i) > $i).
% 17.76/3.75 thf(func_def_951, type, sK680: $i > $i > $i).
% 17.76/3.75 thf(func_def_953, type, sK682: $i > $o).
% 17.76/3.75 thf(func_def_955, type, sK684: $i > ($i > $o) > $i > $i).
% 17.76/3.75 thf(func_def_964, type, ph693: !>[X0: $tType]:(X0)).
% 17.76/3.75 thf(f4138,plain,(
% 17.76/3.75 $false),
% 17.76/3.75 inference(avatar_sat_refutation,[status(thm)],[f3472,f3608,f3704,f3709,f3712,f3768,f3775,f3784,f3997,f4137])).
% 17.76/3.75 thf(f4137,plain,(
% 17.76/3.75 spl692_5 | spl692_1 | ~spl692_4 | ~spl692_7 | ~spl692_10),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f4136,f3770,f3706,f3465,f3454,f3697])).
% 17.76/3.75 thf(f3697,definition,(
% 17.76/3.75 spl692_5 <=> ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | (sK321 != X0))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_5])],[avatar_definition])).
% 17.76/3.75 thf(f3454,definition,(
% 17.76/3.75 spl692_1 <=> ($true = sK320)),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_1])],[avatar_definition])).
% 17.76/3.75 thf(f3465,definition,(
% 17.76/3.75 spl692_4 <=> ($true = sP0)),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_4])],[avatar_definition])).
% 17.76/3.75 thf(f3706,definition,(
% 17.76/3.75 spl692_7 <=> (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_7])],[avatar_definition])).
% 17.76/3.75 thf(f3770,definition,(
% 17.76/3.75 spl692_10 <=> (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_10])],[avatar_definition])).
% 17.76/3.75 thf(f4136,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | (sK321 != X0)) ) | (spl692_1 | ~spl692_4 | ~spl692_7 | ~spl692_10)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f4135,f3455])).
% 17.76/3.75 thf(f3455,plain,(
% 17.76/3.75 ($true != sK320) | spl692_1),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3454])).
% 17.76/3.75 thf(f4135,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true = sK320) | (sK321 != X0) | ((in @ X0 @ sK318) != $true)) ) | (~spl692_4 | ~spl692_7 | ~spl692_10)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f4134,f2627])).
% 17.76/3.75 thf(f2627,plain,(
% 17.76/3.75 ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) != $true)),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1432])).
% 17.76/3.75 thf(f1432,plain,(
% 17.76/3.75 (binunionE = $true) & (notsubsetI = $true) & (subsetTrans = $true) & ((((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) != $true) & ((in @ sK321 @ sK318) = $true)) & ((in @ sK319 @ sK318) = $true)) & (singletoninpowunion = $true) & (binintersectSubset5 = $true) & (ubforcartprodlem3 = $true) & (emptysetimpfalse = $true) & (omega__Cong = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (kpairp = $true) & (setminusERneg = $true) & (lam2p = $true) & (emptyinunitempty = $true) & (binunionIL = $true) & (binunionRsub = $true) & (setunionE2 = $true) & (replAx = $true) & (powersetI1 = $true) & (setukpairIR = $true) & (subsetE2 = $true) & (emptyInPowerset = $true) & (setadjoin__Cong = $true) & (setminusLsub = $true) & (emptyE1 = $true) & (upairsetIL = $true) & (emptysetsubset = $true) & (setukpairinjR = $true) & (cartprodfstpairEq = $true) & (setminusELneg = $true) & (theprop = $true) & (cartprodmempair1 = $true) & (ubforcartprodlem1 = $true) & (exuE2 = $true) & (subPowSU = $true) & (setext = $true) & (exuE1 = $true) & (binintersectI = $true) & (binintersectEL = $true) & (eqimpsubset1 = $true) & (binintersectSubset1 = $true) & (singletoninpowerset = $true) & (symdiffIneg1 = $true) & (setminusI = $true) & (dpsetconstrEL1 = $true) & (binintersectRsub = $true) & (funcext = $true) & (inCongP = $true) & (setadjoinAx = $true) & (cartprodsndin = $true) & (infuncsetfunc = $true) & (emptysetE = $true) & (powersetAx = $true) & (subbreln = $true) & (iftrueProp1 = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & (setunion__Cong = $true) & (setminusER = $true) & (quantDeMorgan4 = $true) & (bs114d = $true) & (cartprodpairmemER = $true) & (setunionAx = $true) & (setunionsingleton = $true) & (funcext2 = $true) & (ubforcartprodlem2 = $true) & (powersetE = $true) & (funcGraphProp1 = $true) & (sepSubset = $true) & (cartprodfstin = $true) & (setunionsingleton2 = $true) & (kfstpairEq = $true) & (symdiffI2 = $true) & (quantDeMorgan3 = $true) & (exuI1 = $true) & (subsetE = $true) & (symdiffE = $true) & (beta1 = $true) & (binunionEcases = $true) & (foundationAx = $true) & (secondinupair = $true) & (dpsetconstrERa = $true) & (exuE3e = $true) & (singletonsuniq = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (binintersectSubset3 = $true) & (binintersectLsub = $true) & (cartprodmempair = $true) & (sepInPowerset = $true) & (subsetI1 = $true) & (binintersectSubset4 = $true) & (in__Cong = $true) & (uniqinunit = $true) & (lamp = $true) & (apProp = $true) & (brelnall1 = $true) & (setbeta = $true) & (disjointsetsI1 = $true) & (eta2 = $true) & (brelnall2 = $true) & (setunionI = $true) & (notdallE = $true) & (binintersectER = $true) & (funcGraphProp2 = $true) & (prop2setI = $true) & (emptyset__Cong = $true) & (cartprodpairmemEL = $true) & (iftrueProp2 = $true) & (eqimpsubset2 = $true) & (iffalseProp1 = $true) & (powersetE1 = $true) & (cartprodpairin = $true) & (exuI3 = $true) & (setunionE = $true) & (binunionLsub = $true) & (symdiffIneg2 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (funcinfuncset = $true) & (noeltsimpempty = $true) & (ksndpairEq = $true) & (upairsubunion = $true) & (nonemptyI1 = $true) & (lam2lamEq = $true) & (descr__Cong = $true) & (symdiffI1 = $true) & (eqinunit = $true) & (eta1 = $true) & (setminusSubset2 = $true) & (inPowerset = $true) & (upairequniteq = $true) & (setukpairinjR12 = $true) & (exuEu = $true) & (funcGraphProp3 = $true) & (ex1I = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (kpairsurjEq = $true) & (dsetconstrI = $true) & (funcextLem = $true) & (ap2apEq1 = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (iffalseProp2 = $true) & (setminusSubset1 = $true) & (ap2p = $true) & (dpsetconstrSub = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (subsetemptysetimpeq = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (notdexE = $true) & (binunionIR = $true) & (exuE3u = $true) & (cartprodmempaircEq = $true) & (emptyinPowerset = $true) & (upairinpowunion = $true) & (dpsetconstrI = $true) & (setunionsingleton1 = $true) & (setukpairinjL = $true) & (setadjoinSub2 = $true) & (nonemptyImpWitness = $true) & (setminusILneg = $true) & (ap2apEq2 = $true) & (setminusEL = $true) & (singletonprop = $true) & (setadjoinSub = $true) & (notinemptyset = $true) & (setoftrueEq = $true) & (ksndsingleton = $true) & (app = $true) & (kfstsingleton = $true) & (setukpairinjR2 = $true) & (beta2 = $true) & (setukpairinjL2 = $true) & (setukpairIL = $true) & (setadjoinE = $true) & (setOfPairsIsBReln = $true) & (subsetRefl = $true) & (setextAx = $true) & (dsetconstr__Cong = $true) & (prop2set2propI = $true) & (emptyI = $true) & (nonemptyI = $true) & (dsetconstrER = $true) & (subset2powerset = $true) & (vacuousDall = $true) & (notequalI1 = $true) & (upairsetE = $true) & (notequalI2 = $true) & (singletonsswitch = $true) & (ex1E2 = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & (funcImageSingleton = $true) & (funcGraphProp4 = $true) & (upairset2E = $true) & (prop2setE = $true) & (dpsetconstrEL2 = $true) & (descrp = $true) & (ex1I2 = $true) & (dpsetconstrER = $true) & (emptysetAx = $true) & (ex1E1 = $true) & (nonemptyE1 = $true) & (omega0Ax = $true) & (setminusIRneg = $true) & (setextsub = $true) & (lamProp = $true) & (setukpairinjR1 = $true) & (singletonsubset = $true) & (powersetI = $true) & (setadjoinOr = $true) & (eqbreln = $true) & (upairset2IR = $true) & (notinsingleton = $true) & (cartprodpairsurjEq = $true) & (binintersectSubset2 = $true)),
% 17.76/3.75 inference(skolemisation,[status(esa),new_symbols(skolem,[sK318,sK319,sK320,sK321])],[f900,f1431,f1430])).
% 17.76/3.75 thf(f1430,plain,(
% 17.76/3.75 ? [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X1 @ X0) = $true)) => (? [X3 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (X3 = Y0)))))) != $true) & ($true = (in @ X3 @ sK318))) & ((in @ sK319 @ sK318) = $true))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f1431,plain,(
% 17.76/3.75 ? [X3 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (X3 = Y0)))))) != $true) & ($true = (in @ X3 @ sK318))) => (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) != $true) & ((in @ sK321 @ sK318) = $true))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f900,plain,(
% 17.76/3.75 (binunionE = $true) & (notsubsetI = $true) & (subsetTrans = $true) & ? [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X1 @ X0) = $true)) & (singletoninpowunion = $true) & (binintersectSubset5 = $true) & (ubforcartprodlem3 = $true) & (emptysetimpfalse = $true) & (omega__Cong = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (kpairp = $true) & (setminusERneg = $true) & (lam2p = $true) & (emptyinunitempty = $true) & (binunionIL = $true) & (binunionRsub = $true) & (setunionE2 = $true) & (replAx = $true) & (powersetI1 = $true) & (setukpairIR = $true) & (subsetE2 = $true) & (emptyInPowerset = $true) & (setadjoin__Cong = $true) & (setminusLsub = $true) & (emptyE1 = $true) & (upairsetIL = $true) & (emptysetsubset = $true) & (setukpairinjR = $true) & (cartprodfstpairEq = $true) & (setminusELneg = $true) & (theprop = $true) & (cartprodmempair1 = $true) & (ubforcartprodlem1 = $true) & (exuE2 = $true) & (subPowSU = $true) & (setext = $true) & (exuE1 = $true) & (binintersectI = $true) & (binintersectEL = $true) & (eqimpsubset1 = $true) & (binintersectSubset1 = $true) & (singletoninpowerset = $true) & (symdiffIneg1 = $true) & (setminusI = $true) & (dpsetconstrEL1 = $true) & (binintersectRsub = $true) & (funcext = $true) & (inCongP = $true) & (setadjoinAx = $true) & (cartprodsndin = $true) & (infuncsetfunc = $true) & (emptysetE = $true) & (powersetAx = $true) & (subbreln = $true) & (iftrueProp1 = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & (setunion__Cong = $true) & (setminusER = $true) & (quantDeMorgan4 = $true) & (bs114d = $true) & (cartprodpairmemER = $true) & (setunionAx = $true) & (setunionsingleton = $true) & (funcext2 = $true) & (ubforcartprodlem2 = $true) & (powersetE = $true) & (funcGraphProp1 = $true) & (sepSubset = $true) & (cartprodfstin = $true) & (setunionsingleton2 = $true) & (kfstpairEq = $true) & (symdiffI2 = $true) & (quantDeMorgan3 = $true) & (exuI1 = $true) & (subsetE = $true) & (symdiffE = $true) & (beta1 = $true) & (binunionEcases = $true) & (foundationAx = $true) & (secondinupair = $true) & (dpsetconstrERa = $true) & (exuE3e = $true) & (singletonsuniq = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (binintersectSubset3 = $true) & (binintersectLsub = $true) & (cartprodmempair = $true) & (sepInPowerset = $true) & (subsetI1 = $true) & (binintersectSubset4 = $true) & (in__Cong = $true) & (uniqinunit = $true) & (lamp = $true) & (apProp = $true) & (brelnall1 = $true) & (setbeta = $true) & (disjointsetsI1 = $true) & (eta2 = $true) & (brelnall2 = $true) & (setunionI = $true) & (notdallE = $true) & (binintersectER = $true) & (funcGraphProp2 = $true) & (prop2setI = $true) & (emptyset__Cong = $true) & (cartprodpairmemEL = $true) & (iftrueProp2 = $true) & (eqimpsubset2 = $true) & (iffalseProp1 = $true) & (powersetE1 = $true) & (cartprodpairin = $true) & (exuI3 = $true) & (setunionE = $true) & (binunionLsub = $true) & (symdiffIneg2 = $true) & (quantDeMorgan1 = $true) & (setukpairinjL1 = $true) & (funcinfuncset = $true) & (noeltsimpempty = $true) & (ksndpairEq = $true) & (upairsubunion = $true) & (nonemptyI1 = $true) & (lam2lamEq = $true) & (descr__Cong = $true) & (symdiffI1 = $true) & (eqinunit = $true) & (eta1 = $true) & (setminusSubset2 = $true) & (inPowerset = $true) & (upairequniteq = $true) & (setukpairinjR12 = $true) & (exuEu = $true) & (funcGraphProp3 = $true) & (ex1I = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (kpairsurjEq = $true) & (dsetconstrI = $true) & (funcextLem = $true) & (ap2apEq1 = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (iffalseProp2 = $true) & (setminusSubset1 = $true) & (ap2p = $true) & (dpsetconstrSub = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (subsetemptysetimpeq = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (notdexE = $true) & (binunionIR = $true) & (exuE3u = $true) & (cartprodmempaircEq = $true) & (emptyinPowerset = $true) & (upairinpowunion = $true) & (dpsetconstrI = $true) & (setunionsingleton1 = $true) & (setukpairinjL = $true) & (setadjoinSub2 = $true) & (nonemptyImpWitness = $true) & (setminusILneg = $true) & (ap2apEq2 = $true) & (setminusEL = $true) & (singletonprop = $true) & (setadjoinSub = $true) & (notinemptyset = $true) & (setoftrueEq = $true) & (ksndsingleton = $true) & (app = $true) & (kfstsingleton = $true) & (setukpairinjR2 = $true) & (beta2 = $true) & (setukpairinjL2 = $true) & (setukpairIL = $true) & (setadjoinE = $true) & (setOfPairsIsBReln = $true) & (subsetRefl = $true) & (setextAx = $true) & (dsetconstr__Cong = $true) & (prop2set2propI = $true) & (emptyI = $true) & (nonemptyI = $true) & (dsetconstrER = $true) & (subset2powerset = $true) & (vacuousDall = $true) & (notequalI1 = $true) & (upairsetE = $true) & (notequalI2 = $true) & (singletonsswitch = $true) & (ex1E2 = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & (funcImageSingleton = $true) & (funcGraphProp4 = $true) & (upairset2E = $true) & (prop2setE = $true) & (dpsetconstrEL2 = $true) & (descrp = $true) & (ex1I2 = $true) & (dpsetconstrER = $true) & (emptysetAx = $true) & (ex1E1 = $true) & (nonemptyE1 = $true) & (omega0Ax = $true) & (setminusIRneg = $true) & (setextsub = $true) & (lamProp = $true) & (setukpairinjR1 = $true) & (singletonsubset = $true) & (powersetI = $true) & (setadjoinOr = $true) & (eqbreln = $true) & (upairset2IR = $true) & (notinsingleton = $true) & (cartprodpairsurjEq = $true) & (binintersectSubset2 = $true)),
% 17.76/3.75 inference(flattening,[status(thm)],[f899])).
% 17.76/3.75 thf(f899,plain,(
% 17.76/3.75 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $o] : (? [X3 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0)))))) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X1 @ X0) = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 17.76/3.75 inference(ennf_transformation,[status(thm)],[f456])).
% 17.76/3.75 thf(f456,plain,(
% 17.76/3.75 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ! [X0 : $i,X1 : $i,X2 : $o] : (((in @ X1 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X3 = Y0)))))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.76/3.75 inference(fool_elimination,[status(thm)],[f455])).
% 17.76/3.75 thf(f455,plain,(
% 17.76/3.75 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X0 : $i,X1 : $i,X2 : $o] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X3 = X4) & ~X2) | ((X1 = X4) & X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.76/3.75 inference(rectify,[status(thm)],[f227])).
% 17.76/3.75 thf(f227,negated_conjecture,(
% 17.76/3.75 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X3 : $i,X1 : $i,X0 : $o] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[X8 : $i] : (((X2 = X8) & ~X0) | ((X1 = X8) & X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.76/3.75 inference(negated_conjecture,[status(cth)],[f226])).
% 17.76/3.75 thf(f226,conjecture,(
% 17.76/3.75 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => ! [X3 : $i,X1 : $i,X0 : $o] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[X8 : $i] : (((X2 = X8) & ~X0) | ((X1 = X8) & X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.76/3.75 file('/export/starexec/sandbox/tmp/tmp.WuDOtMIMiy/DTF2THF_22813.p',ifSingleton)).
% 17.76/3.75 thf(f4134,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | (sK321 != X0) | ($true = sK320)) ) | (~spl692_4 | ~spl692_7 | ~spl692_10)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f4133,f3771])).
% 17.76/3.75 thf(f3771,plain,(
% 17.76/3.75 (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ~spl692_10),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3770])).
% 17.76/3.75 thf(f4133,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | (sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($true = sK320) | (sK321 != X0)) ) | (~spl692_4 | ~spl692_7)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f4124,f3466])).
% 17.76/3.75 thf(f3466,plain,(
% 17.76/3.75 ($true = sP0) | ~spl692_4),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3465])).
% 17.76/3.75 thf(f4124,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (sK321 != X0) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($true = sK320) | (sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ((in @ X0 @ sK318) != $true)) ) | ~spl692_7),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f4123])).
% 17.76/3.75 thf(f4123,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true = sK320) | ($true != sP0) | ((in @ X0 @ sK318) != $true) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($false = (sK321 = X0))) ) | ~spl692_7),
% 17.76/3.75 inference(not_proxy_clausification,[status(thm)],[f4122])).
% 17.76/3.75 thf(f4122,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((in @ X0 @ sK318) != $true) | ($true != sP0) | ($false = (~ sK320)) | (sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($false = (sK321 = X0))) ) | ~spl692_7),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f4118])).
% 17.76/3.75 thf(f4118,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (((~ sK320) & (sK321 = X0)) = $false) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((in @ X0 @ sK318) != $true) | (sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) ) | ~spl692_7),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f4117])).
% 17.76/3.75 thf(f4117,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0) | (((sK320 & (sK319 = X0)) | ((~ sK320) & (sK321 = X0))) != $true) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((in @ X0 @ sK318) != $true)) ) | ~spl692_7),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f4114])).
% 17.76/3.75 thf(f4114,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($true != sP0) | (sK321 != (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ((in @ X0 @ sK318) != $true) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true)) ) | ~spl692_7),
% 17.76/3.75 inference(superposition,[status(thm)],[f3280,f3708])).
% 17.76/3.75 thf(f3708,plain,(
% 17.76/3.75 (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ~spl692_7),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3706])).
% 17.76/3.75 thf(f3280,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((sK44 @ X6 @ X5) != (sK45 @ X6 @ X5)) | ((in @ X9 @ X5) != $true) | ($true != sP0) | ((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ((X6 @ X9) != $true)) )),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f2055])).
% 17.76/3.75 thf(f2055,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ((in @ X9 @ X5) != $true) | ($true != sP0) | ((sK44 @ X6 @ X5) != (sK45 @ X6 @ X5)) | ((X6 @ X9) != $true)) )),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1027])).
% 17.76/3.75 thf(f1027,plain,(
% 17.76/3.75 (($true = sP0) | (! [X2 : $i] : (((in @ X2 @ sK41) != $true) | ! [X3 : $i] : (($true != (sK42 @ X2)) | (X2 = X3) | ((sK42 @ X3) != $true) | ((in @ X3 @ sK41) != $true))) & (((sK42 @ sK43) = $true) & ((in @ sK43 @ sK41) = $true)) & ($true != (singleton @ (dsetconstr @ sK41 @ (^[Y0 : $i]: (sK42 @ Y0))))))) & (! [X5 : $i,X6 : $i > $o] : ((($true = (in @ (sK44 @ X6 @ X5) @ X5)) & (($true = (X6 @ (sK44 @ X6 @ X5))) & ((sK44 @ X6 @ X5) != (sK45 @ X6 @ X5)) & ($true = (X6 @ (sK45 @ X6 @ X5))) & ($true = (in @ (sK45 @ X6 @ X5) @ X5)))) | ! [X9 : $i] : (((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true)) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true)) | ($true != sP0))),
% 17.76/3.75 inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44,sK45])],[f1022,f1026,f1025,f1024,f1023])).
% 17.76/3.75 thf(f1023,plain,(
% 17.76/3.75 ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ! [X3 : $i] : (((X1 @ X2) != $true) | (X2 = X3) | ((X1 @ X3) != $true) | ((in @ X3 @ X0) != $true))) & ? [X4 : $i] : (((X1 @ X4) = $true) & ((in @ X4 @ X0) = $true)) & ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) => (! [X2 : $i] : (((in @ X2 @ sK41) != $true) | ! [X3 : $i] : (($true != (sK42 @ X2)) | (X2 = X3) | ((sK42 @ X3) != $true) | ((in @ X3 @ sK41) != $true))) & ? [X4 : $i] : (((sK42 @ X4) = $true) & ($true = (in @ X4 @ sK41))) & ($true != (singleton @ (dsetconstr @ sK41 @ (^[Y0 : $i]: (sK42 @ Y0))))))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f1024,plain,(
% 17.76/3.75 ? [X4 : $i] : (((sK42 @ X4) = $true) & ($true = (in @ X4 @ sK41))) => (((sK42 @ sK43) = $true) & ((in @ sK43 @ sK41) = $true))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f1025,plain,(
% 17.76/3.75 ! [X5 : $i,X6 : $i > $o] : (? [X7 : $i] : (((in @ X7 @ X5) = $true) & ? [X8 : $i] : (((X6 @ X7) = $true) & (X7 != X8) & ((X6 @ X8) = $true) & ((in @ X8 @ X5) = $true))) => (($true = (in @ (sK44 @ X6 @ X5) @ X5)) & ? [X8 : $i] : (($true = (X6 @ (sK44 @ X6 @ X5))) & ((sK44 @ X6 @ X5) != X8) & ((X6 @ X8) = $true) & ((in @ X8 @ X5) = $true))))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f1026,plain,(
% 17.76/3.75 ! [X5 : $i,X6 : $i > $o] : (? [X8 : $i] : (($true = (X6 @ (sK44 @ X6 @ X5))) & ((sK44 @ X6 @ X5) != X8) & ((X6 @ X8) = $true) & ((in @ X8 @ X5) = $true)) => (($true = (X6 @ (sK44 @ X6 @ X5))) & ((sK44 @ X6 @ X5) != (sK45 @ X6 @ X5)) & ($true = (X6 @ (sK45 @ X6 @ X5))) & ($true = (in @ (sK45 @ X6 @ X5) @ X5))))),
% 17.76/3.75 introduced(definition,[],[choice_axiom])).
% 17.76/3.75 thf(f1022,plain,(
% 17.76/3.75 (($true = sP0) | ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ! [X3 : $i] : (((X1 @ X2) != $true) | (X2 = X3) | ((X1 @ X3) != $true) | ((in @ X3 @ X0) != $true))) & ? [X4 : $i] : (((X1 @ X4) = $true) & ((in @ X4 @ X0) = $true)) & ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true))) & (! [X5 : $i,X6 : $i > $o] : (? [X7 : $i] : (((in @ X7 @ X5) = $true) & ? [X8 : $i] : (((X6 @ X7) = $true) & (X7 != X8) & ((X6 @ X8) = $true) & ((in @ X8 @ X5) = $true))) | ! [X9 : $i] : (((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true)) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true)) | ($true != sP0))),
% 17.76/3.75 inference(rectify,[status(thm)],[f1021])).
% 17.76/3.75 thf(f1021,plain,(
% 17.76/3.75 (($true = sP0) | ? [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) != $true) | ! [X3 : $i] : (((X1 @ X2) != $true) | (X2 = X3) | ((X1 @ X3) != $true) | ((in @ X3 @ X0) != $true))) & ? [X4 : $i] : (((X1 @ X4) = $true) & ((in @ X4 @ X0) = $true)) & ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true))) & (! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((X1 @ X2) = $true) & (X2 != X3) & ((X1 @ X3) = $true) & ((in @ X3 @ X0) = $true))) | ! [X4 : $i] : (((X1 @ X4) != $true) | ((in @ X4 @ X0) != $true)) | ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)) | ($true != sP0))),
% 17.76/3.75 inference(nnf_transformation,[status(thm)],[f954])).
% 17.76/3.75 thf(f954,plain,(
% 17.76/3.75 ($true = sP0) <=> ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((X1 @ X2) = $true) & (X2 != X3) & ((X1 @ X3) = $true) & ((in @ X3 @ X0) = $true))) | ! [X4 : $i] : (((X1 @ X4) != $true) | ((in @ X4 @ X0) != $true)) | ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 17.76/3.75 thf(f3997,plain,(
% 17.76/3.75 ~spl692_5),
% 17.76/3.75 inference(avatar_contradiction_clause,[status(thm)],[f3996])).
% 17.76/3.75 thf(f3996,plain,(
% 17.76/3.75 $false | ~spl692_5),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3973])).
% 17.76/3.75 thf(f3973,plain,(
% 17.76/3.75 (sK321 != sK321) | ($true != $true) | ~spl692_5),
% 17.76/3.75 inference(superposition,[status(thm)],[f3698,f2626])).
% 17.76/3.75 thf(f2626,plain,(
% 17.76/3.75 ((in @ sK321 @ sK318) = $true)),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1432])).
% 17.76/3.75 thf(f3698,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | (sK321 != X0)) ) | ~spl692_5),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3697])).
% 17.76/3.75 thf(f3784,plain,(
% 17.76/3.75 spl692_10 | ~spl692_4 | spl692_1 | spl692_5),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f3416,f3697,f3454,f3465,f3770])).
% 17.76/3.75 thf(f3416,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true = sK320) | ((in @ X0 @ sK318) != $true) | (sK321 != X0) | (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0)) )),
% 17.76/3.75 inference(duplicate_literal_removal,[status(thm)],[f3415])).
% 17.76/3.75 thf(f3415,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ((in @ X0 @ sK318) != $true) | (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true = sK320) | ($true = sK320) | (sK321 != X0)) )),
% 17.76/3.75 inference(not_proxy_clausification,[status(thm)],[f3414])).
% 17.76/3.75 thf(f3414,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($false = (~ sK320)) | (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0) | (sK321 != X0) | ((in @ X0 @ sK318) != $true) | ($true = sK320)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3412])).
% 17.76/3.75 thf(f3412,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ((in @ X0 @ sK318) != $true) | (sK321 != X0) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ($false = (~ sK320)) | (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3411])).
% 17.76/3.75 thf(f3411,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($false = (sK321 = X0)) | ((in @ X0 @ sK318) != $true) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ($false = (~ sK320)) | ($true != sP0)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3410])).
% 17.76/3.75 thf(f3410,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ($true != sP0) | ($false = (sK321 = X0)) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true) | ($false = (~ sK320))) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3396])).
% 17.76/3.75 thf(f3396,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (((~ sK320) & (sK321 = X0)) = $false) | ((sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3395])).
% 17.76/3.75 thf(f3395,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((~ sK320) & (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | (((~ sK320) & (sK321 = X0)) = $false) | ($true != sP0) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3371])).
% 17.76/3.75 thf(f3371,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | ((~ sK320) & (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) = $true) | ((in @ X0 @ sK318) != $true) | ($true != sP0) | (((~ sK320) & (sK321 = X0)) = $false)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3370])).
% 17.76/3.75 thf(f3370,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((sK320 & (sK319 = X0)) | ((~ sK320) & (sK321 = X0))) != $true) | ((in @ X0 @ sK318) != $true) | (((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | ((~ sK320) & (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) = $true) | ($true != sP0)) )),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f3369])).
% 17.76/3.75 thf(f3369,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true = ((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true) | ((in @ X0 @ sK318) != $true) | ($true != sP0)) )),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3304])).
% 17.76/3.75 thf(f3304,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != $true) | ($true = ((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | ($true != sP0) | ((in @ X0 @ sK318) != $true) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true)) )),
% 17.76/3.75 inference(superposition,[status(thm)],[f2627,f3243])).
% 17.76/3.75 thf(f3243,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ($true = (X6 @ (sK44 @ X6 @ X5))) | ($true != sP0) | ((in @ X9 @ X5) != $true) | ((X6 @ X9) != $true)) )),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f2056])).
% 17.76/3.75 thf(f2056,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((X6 @ X9) != $true) | ($true = (X6 @ (sK44 @ X6 @ X5))) | ($true != sP0) | ((in @ X9 @ X5) != $true) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true)) )),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1027])).
% 17.76/3.75 thf(f3775,plain,(
% 17.76/3.75 spl692_3 | spl692_2 | spl692_9 | ~spl692_4),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f3386,f3465,f3765,f3458,f3461])).
% 17.76/3.75 thf(f3461,definition,(
% 17.76/3.75 spl692_3 <=> ($false = sK320)),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_3])],[avatar_definition])).
% 17.76/3.75 thf(f3458,definition,(
% 17.76/3.75 spl692_2 <=> ! [X0 : $i] : ((sK319 != X0) | ((in @ X0 @ sK318) != $true))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_2])],[avatar_definition])).
% 17.76/3.75 thf(f3765,definition,(
% 17.76/3.75 spl692_9 <=> ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) = sK319)),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_9])],[avatar_definition])).
% 17.76/3.75 thf(f3386,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) = sK319) | (sK319 != X0) | ($false = sK320) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3385])).
% 17.76/3.75 thf(f3385,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ((in @ X0 @ sK318) != $true) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) = sK319) | ((sK319 = X0) = $false) | ($false = sK320)) )),
% 17.76/3.75 inference(duplicate_literal_removal,[status(thm)],[f3384])).
% 17.76/3.75 thf(f3384,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ($false = sK320) | ($true != sP0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) = sK319) | ((sK319 = X0) = $false) | ($false = sK320)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3383])).
% 17.76/3.75 thf(f3383,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ($false = sK320) | ((sK320 & (sK319 = X0)) = $false) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) = sK319) | ($true != sP0)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3382])).
% 17.76/3.75 thf(f3382,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ((in @ X0 @ sK318) != $true) | ((sK320 & (sK319 = X0)) = $false) | ($true != sP0) | ($false = sK320)) )),
% 17.76/3.75 inference(not_proxy_clausification,[status(thm)],[f3376])).
% 17.76/3.75 thf(f3376,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ((~ sK320) = $true) | ((sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ((sK320 & (sK319 = X0)) = $false) | ($true != sP0)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3375])).
% 17.76/3.75 thf(f3375,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true) | ((sK320 & (sK319 = X0)) = $false) | ($true != sP0) | ((~ sK320) = $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3373])).
% 17.76/3.75 thf(f3373,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (((~ sK320) & (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true) | ((sK320 & (sK319 = X0)) = $false)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3372])).
% 17.76/3.75 thf(f3372,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((sK320 & (sK319 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | ((~ sK320) & (sK321 = (sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) = $true) | ($true != sP0) | ((sK320 & (sK319 = X0)) = $false) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3370])).
% 17.76/3.75 thf(f3768,plain,(
% 17.76/3.75 ~spl692_9 | spl692_2 | spl692_3 | ~spl692_4 | ~spl692_6),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f3739,f3701,f3465,f3461,f3458,f3765])).
% 17.76/3.75 thf(f3701,definition,(
% 17.76/3.75 spl692_6 <=> (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))),
% 17.76/3.75 introduced(definition,[new_symbols(naming,[spl692_6])],[avatar_definition])).
% 17.76/3.75 thf(f3739,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 != X0) | ((in @ X0 @ sK318) != $true) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319)) ) | (spl692_3 | ~spl692_4 | ~spl692_6)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f3738,f3466])).
% 17.76/3.75 thf(f3738,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ((in @ X0 @ sK318) != $true) | (sK319 != X0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319)) ) | (spl692_3 | ~spl692_6)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f3737,f2627])).
% 17.76/3.75 thf(f3737,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($true != sP0) | (sK319 != X0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319) | ((in @ X0 @ sK318) != $true)) ) | (spl692_3 | ~spl692_6)),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f3733,f3462])).
% 17.76/3.75 thf(f3462,plain,(
% 17.76/3.75 ($false != sK320) | spl692_3),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3461])).
% 17.76/3.75 thf(f3733,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ($true != sP0) | (sK319 != X0) | ($false = sK320) | ((in @ X0 @ sK318) != $true)) ) | ~spl692_6),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3732])).
% 17.76/3.75 thf(f3732,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((sK319 = X0) = $false) | ($false = sK320) | ($true != sP0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319) | ((in @ X0 @ sK318) != $true)) ) | ~spl692_6),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3731])).
% 17.76/3.75 thf(f3731,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK320 & (sK319 = X0)) = $false) | ($true != sP0) | ((in @ X0 @ sK318) != $true) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true)) ) | ~spl692_6),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3729])).
% 17.76/3.75 thf(f3729,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (((sK320 & (sK319 = X0)) | ((~ sK320) & (sK321 = X0))) != $true) | ((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((in @ X0 @ sK318) != $true) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319)) ) | ~spl692_6),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f3719])).
% 17.76/3.75 thf(f3719,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((singleton @ (dsetconstr @ sK318 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))))) = $true) | ((in @ X0 @ sK318) != $true) | ($true != sP0) | ((sK44 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318) != sK319) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true)) ) | ~spl692_6),
% 17.76/3.75 inference(superposition,[status(thm)],[f3280,f3703])).
% 17.76/3.75 thf(f3703,plain,(
% 17.76/3.75 (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ~spl692_6),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3701])).
% 17.76/3.75 thf(f3712,plain,(
% 17.76/3.75 ~spl692_1 | ~spl692_3),
% 17.76/3.75 inference(avatar_contradiction_clause,[status(thm)],[f3711])).
% 17.76/3.75 thf(f3711,plain,(
% 17.76/3.75 $false | (~spl692_1 | ~spl692_3)),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3710])).
% 17.76/3.75 thf(f3710,plain,(
% 17.76/3.75 ($false = $true) | (~spl692_1 | ~spl692_3)),
% 17.76/3.75 inference(forward_demodulation,[status(thm)],[f3456,f3463])).
% 17.76/3.75 thf(f3463,plain,(
% 17.76/3.75 ($false = sK320) | ~spl692_3),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3461])).
% 17.76/3.75 thf(f3456,plain,(
% 17.76/3.75 ($true = sK320) | ~spl692_1),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3454])).
% 17.76/3.75 thf(f3709,plain,(
% 17.76/3.75 spl692_7 | ~spl692_4 | spl692_1 | spl692_5),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f3344,f3697,f3454,f3465,f3706])).
% 17.76/3.75 thf(f3344,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true = sK320) | ((in @ X0 @ sK318) != $true) | (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0) | (sK321 != X0)) )),
% 17.76/3.75 inference(duplicate_literal_removal,[status(thm)],[f3343])).
% 17.76/3.75 thf(f3343,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true = sK320) | ((in @ X0 @ sK318) != $true) | (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true = sK320) | (sK321 != X0) | ($true != sP0)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3341])).
% 17.76/3.75 thf(f3341,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 != X0) | ($true != sP0) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true = sK320) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3340])).
% 17.76/3.75 thf(f3340,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 != X0) | ($true = sK320) | ($true != sP0) | ((in @ X0 @ sK318) != $true) | ((sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))))) )),
% 17.76/3.75 inference(not_proxy_clausification,[status(thm)],[f3339])).
% 17.76/3.75 thf(f3339,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK321 != X0) | ((in @ X0 @ sK318) != $true) | ($false = (~ sK320)) | ($true != sP0) | ((sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))))) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3338])).
% 17.76/3.75 thf(f3338,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ($false = (sK321 = X0)) | ((sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | ($false = (~ sK320)) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3327])).
% 17.76/3.75 thf(f3327,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((~ sK320) & (sK321 = X0)) = $false) | ((in @ X0 @ sK318) != $true) | ($true != sP0) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | ((sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3309])).
% 17.76/3.75 thf(f3309,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | (((~ sK320) & (sK321 = X0)) = $false) | ((in @ X0 @ sK318) != $true) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | ($true != sP0)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3308])).
% 17.76/3.75 thf(f3308,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ($true != sP0) | (((sK320 & (sK319 = X0)) | ((~ sK320) & (sK321 = X0))) != $true) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))))) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3307])).
% 17.76/3.75 thf(f3307,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ($true = ((sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) | ((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))))) | (((sK320 & (sK319 = X0)) | ((~ sK320) & (sK321 = X0))) != $true) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f3306])).
% 17.76/3.75 thf(f3306,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3305])).
% 17.76/3.75 thf(f3305,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($true != sP0) | ($true != $true) | ((in @ X0 @ sK318) != $true) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | (((^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ X0) != $true)) )),
% 17.76/3.75 inference(superposition,[status(thm)],[f2627,f3227])).
% 17.76/3.75 thf(f3227,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ($true != sP0) | ((X6 @ X9) != $true) | ($true = (X6 @ (sK45 @ X6 @ X5))) | ((in @ X9 @ X5) != $true)) )),
% 17.76/3.75 inference(beta_eta_normalization,[status(thm)],[f2054])).
% 17.76/3.75 thf(f2054,plain,(
% 17.76/3.75 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((X6 @ X9) != $true) | ($true != sP0) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ($true = (X6 @ (sK45 @ X6 @ X5))) | ((in @ X9 @ X5) != $true)) )),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1027])).
% 17.76/3.75 thf(f3704,plain,(
% 17.76/3.75 spl692_6 | spl692_3 | spl692_2 | ~spl692_4),
% 17.76/3.75 inference(avatar_split_clause,[status(thm)],[f3325,f3465,f3458,f3461,f3701])).
% 17.76/3.75 thf(f3325,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0) | ($false = sK320) | ((in @ X0 @ sK318) != $true) | (sK319 != X0)) )),
% 17.76/3.75 inference(duplicate_literal_removal,[status(thm)],[f3324])).
% 17.76/3.75 thf(f3324,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 != X0) | (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0) | ($false = sK320) | ($false = sK320) | ((in @ X0 @ sK318) != $true)) )),
% 17.76/3.75 inference(not_proxy_clausification,[status(thm)],[f3323])).
% 17.76/3.75 thf(f3323,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 != X0) | ($false = sK320) | ((~ sK320) = $true) | ((in @ X0 @ sK318) != $true) | (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($true != sP0)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3321])).
% 17.76/3.75 thf(f3321,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 != X0) | (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ($false = sK320) | ((in @ X0 @ sK318) != $true) | ($true != sP0) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3320])).
% 17.76/3.75 thf(f3320,plain,(
% 17.76/3.75 ( ! [X0 : $i] : ((sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) | ((in @ X0 @ sK318) != $true) | ($false = sK320) | ((sK319 = X0) = $false) | ($true != sP0) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true)) )),
% 17.76/3.75 inference(equality_proxy_clausification,[status(thm)],[f3312])).
% 17.76/3.75 thf(f3312,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | ($false = sK320) | ((sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)) = $true) | ($true != sP0) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((sK319 = X0) = $false)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3311])).
% 17.76/3.75 thf(f3311,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (($false = sK320) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | ($true != sP0) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ((in @ X0 @ sK318) != $true) | ((sK319 = X0) = $false)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3310])).
% 17.76/3.75 thf(f3310,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((sK320 & (sK319 = X0)) = $false) | ($true = (sK320 & (sK319 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318)))) | ((in @ X0 @ sK318) != $true) | (((~ sK320) & (sK321 = (sK45 @ (^[Y0 : $i]: ((sK320 & (sK319 = Y0)) | ((~ sK320) & (sK321 = Y0)))) @ sK318))) = $true) | ($true != sP0)) )),
% 17.76/3.75 inference(binary_proxy_clausification,[status(thm)],[f3308])).
% 17.76/3.75 thf(f3608,plain,(
% 17.76/3.75 ~spl692_2),
% 17.76/3.75 inference(avatar_contradiction_clause,[status(thm)],[f3607])).
% 17.76/3.75 thf(f3607,plain,(
% 17.76/3.75 $false | ~spl692_2),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3554])).
% 17.76/3.75 thf(f3554,plain,(
% 17.76/3.75 (sK319 != sK319) | ($true != $true) | ~spl692_2),
% 17.76/3.75 inference(superposition,[status(thm)],[f3459,f2625])).
% 17.76/3.75 thf(f2625,plain,(
% 17.76/3.75 ((in @ sK319 @ sK318) = $true)),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1432])).
% 17.76/3.75 thf(f3459,plain,(
% 17.76/3.75 ( ! [X0 : $i] : (((in @ X0 @ sK318) != $true) | (sK319 != X0)) ) | ~spl692_2),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3458])).
% 17.76/3.75 thf(f3472,plain,(
% 17.76/3.75 spl692_4),
% 17.76/3.75 inference(avatar_contradiction_clause,[status(thm)],[f3471])).
% 17.76/3.75 thf(f3471,plain,(
% 17.76/3.75 $false | spl692_4),
% 17.76/3.75 inference(subsumption_resolution,[status(thm)],[f3470,f2460])).
% 17.76/3.75 thf(f2460,plain,(
% 17.76/3.75 (singletonprop = $true)),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1432])).
% 17.76/3.75 thf(f3470,plain,(
% 17.76/3.75 (singletonprop != $true) | spl692_4),
% 17.76/3.75 inference(trivial_inequality_removal,[status(thm)],[f3469])).
% 17.76/3.75 thf(f3469,plain,(
% 17.76/3.75 ($true != $true) | (singletonprop != $true) | spl692_4),
% 17.76/3.75 inference(superposition,[status(thm)],[f3467,f2062])).
% 17.76/3.75 thf(f2062,plain,(
% 17.76/3.75 ($true = sP0) | (singletonprop != $true)),
% 17.76/3.75 inference(cnf_transformation,[status(thm)],[f1028])).
% 17.76/3.75 thf(f1028,plain,(
% 17.76/3.75 ((singletonprop = $true) | ($true != sP0)) & (($true = sP0) | (singletonprop != $true))),
% 17.76/3.75 inference(nnf_transformation,[status(thm)],[f955])).
% 17.76/3.75 thf(f955,plain,(
% 17.76/3.75 (singletonprop = $true) <=> ($true = sP0)),
% 17.76/3.75 inference(definition_folding,[status(thm)],[f850,f954])).
% 17.76/3.75 thf(f850,plain,(
% 17.76/3.75 (singletonprop = $true) <=> ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ? [X3 : $i] : (((X1 @ X2) = $true) & (X2 != X3) & ((X1 @ X3) = $true) & ((in @ X3 @ X0) = $true))) | ! [X4 : $i] : (((X1 @ X4) != $true) | ((in @ X4 @ X0) != $true)) | ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))),
% 17.76/3.75 inference(flattening,[status(thm)],[f849])).
% 17.76/3.75 thf(f849,plain,(
% 17.76/3.75 ! [X0 : $i,X1 : $i > $o] : ((((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ! [X4 : $i] : (((X1 @ X4) != $true) | ((in @ X4 @ X0) != $true))) | ? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ((X1 @ X3) = $true)) & ((X1 @ X2) = $true)) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true))) <=> (singletonprop = $true)),
% 17.76/3.75 inference(ennf_transformation,[status(thm)],[f626])).
% 17.76/3.75 thf(f626,plain,(
% 17.76/3.75 ! [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((X1 @ X2) = $true) => (((X1 @ X3) = $true) => (X2 = X3))))) => (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X1 @ X4) = $true)) => ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true))) <=> (singletonprop = $true)),
% 17.76/3.75 inference(fool_elimination,[status(thm)],[f625])).
% 17.76/3.75 thf(f625,plain,(
% 17.76/3.75 (singletonprop = ! [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((in @ X4 @ X0) & (X1 @ X4)) => (singleton @ (dsetconstr @ X0 @ (^[X5 : $i] : (X1 @ X5)))))))),
% 17.76/3.75 inference(rectify,[status(thm)],[f157])).
% 17.76/3.75 thf(f157,axiom,(
% 17.76/3.75 (singletonprop = ! [X3 : $i,X0 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1 : $i] : ((in @ X1 @ X3) & (X0 @ X1)) => (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))))),
% 17.76/3.75 file('/export/starexec/sandbox/tmp/tmp.WuDOtMIMiy/DTF2THF_22813.p',singletonprop)).
% 17.76/3.75 thf(f3467,plain,(
% 17.76/3.75 ($true != sP0) | spl692_4),
% 17.76/3.75 inference(avatar_component_clause,[status(thm)],[f3465])).
% 17.76/3.75 % SZS output end Proof for DTF2THF_22813
% 17.76/3.75 % (23031)------------------------------
% 17.76/3.75 % (23031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/3.75 % (23031)Termination reason: Refutation
% 17.76/3.75
% 17.76/3.75 % (23031)Memory used [KB]: 10234
% 17.76/3.75 % (23031)Time elapsed: 0.279 s
% 17.76/3.75 % (23031)Instructions burned: 557 (million)
% 17.76/3.75 % (23031)------------------------------
% 17.76/3.75 % (23031)------------------------------
% 17.76/3.75 % (22915)Success in time 2.321 s
%------------------------------------------------------------------------------