%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU614^1 : 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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:37 AM UTC 2026
% Result : Theorem 6.27s 2.39s
% Output : Refutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 3021 ( 851 equ; 0 cnn)
% Maximal formula atoms : 133 ( 58 avg)
% Number of connectives : 1693 ( 113 ~; 83 |; 445 &; 352 @)
% ( 8 <=>; 692 =>; 0 <=; 0 <~>)
% Maximal formula depth : 141 ( 26 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 257 ( 254 usr; 143 con; 0-4 aty)
% Number of variables : 107 ( 0 ^; 81 !; 26 ?; 107 :)
% 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_163,type,
sP0: $i > $i > $o ).
thf(func_def_164,type,
sP1: $i > $o ).
thf(func_def_187,type,
sK24: $i > $o ).
thf(func_def_190,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_195,type,
sK32: $i > $o ).
thf(func_def_198,type,
sK35: $i > $o ).
thf(func_def_209,type,
sK46: $i > $i > $i ).
thf(func_def_214,type,
sK51: $o > $i > $i > $i ).
thf(func_def_224,type,
sK61: $i > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK62: $i > $o ).
thf(func_def_241,type,
sK78: $i > $i > $i ).
thf(func_def_245,type,
sK82: $i > $o ).
thf(func_def_253,type,
sK90: ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK92: $i > $o ).
thf(func_def_264,type,
sK101: $i > $o ).
thf(func_def_266,type,
sK103: $i > $i > $i ).
thf(func_def_289,type,
sK126: $i > $i ).
thf(func_def_292,type,
sK129: $i > $o ).
thf(func_def_294,type,
sK131: $i > ( $i > $o ) > $i ).
thf(func_def_299,type,
sK136: $i > $i ).
thf(func_def_305,type,
sK142: $i > $i ).
thf(func_def_307,type,
sK144: $i > $i ).
thf(func_def_311,type,
sK148: $i > ( $i > $o ) > $i ).
thf(func_def_312,type,
sK149: $i > $o ).
thf(func_def_317,type,
sK154: $i > $i > $i ).
thf(func_def_318,type,
sK155: $i > $i > $i ).
thf(func_def_319,type,
sK156: $i > $i > $i ).
thf(func_def_327,type,
sK164: $i > $o ).
thf(func_def_328,type,
sK165: $i > $i ).
thf(func_def_329,type,
sK166: ( $i > $o ) > $i ).
thf(func_def_332,type,
sK169: $i > $o ).
thf(func_def_338,type,
sK175: $i > $o ).
thf(func_def_341,type,
sK178: ( $i > $i > $o ) > $i > $i ).
thf(func_def_342,type,
sK179: ( $i > $i > $o ) > $i > $i ).
thf(func_def_343,type,
sK180: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_345,type,
sK182: $i > $i > $o ).
thf(func_def_346,type,
sK183: $i > $i ).
thf(func_def_347,type,
sK184: $i > $i ).
thf(func_def_348,type,
sK185: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_349,type,
sK186: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_352,type,
sK189: $i > $o ).
thf(func_def_353,type,
sK190: $i > $o ).
thf(func_def_357,type,
sK194: $i > $o ).
thf(func_def_362,type,
sK199: $i > $i > $i ).
thf(func_def_377,type,
sK214: $i > $o ).
thf(func_def_378,type,
sK215: $i > $o ).
thf(func_def_379,type,
sK216: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_380,type,
sK217: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_387,type,
sK224: $i > $o ).
thf(func_def_390,type,
sK227: $i > ( $i > $o ) > $i ).
thf(func_def_394,type,
sK231: $i > $o ).
thf(func_def_396,type,
sK233: ( $i > $o ) > $i > $i ).
thf(func_def_401,type,
sK238: $i > $i ).
thf(func_def_410,type,
sK247: $i > $o ).
thf(func_def_414,type,
sK251: $i > $o ).
thf(func_def_415,type,
sK252: $i > $o ).
thf(func_def_416,type,
sK253: $i > $i ).
thf(func_def_417,type,
sK254: ( $i > $o ) > $i ).
thf(func_def_418,type,
sK255: $i > $o ).
thf(func_def_419,type,
sK256: $i > $o ).
thf(func_def_421,type,
sK258: ( $i > $o ) > $i ).
thf(func_def_422,type,
sK259: ( $i > $o ) > $i ).
thf(func_def_432,type,
sK269: $i > $i ).
thf(func_def_443,type,
sK280: $i > $o ).
thf(func_def_444,type,
sK281: $i > $o ).
thf(func_def_445,type,
sK282: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_446,type,
sK283: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_447,type,
sK284: $i > $i > $i ).
thf(func_def_450,type,
sK287: ( $i > $o ) > $i ).
thf(func_def_451,type,
sK288: $i > $o ).
thf(func_def_462,type,
sK299: $i > $i ).
thf(func_def_471,type,
sK308: $i > $i > $i ).
thf(func_def_472,type,
sK309: $i > $i ).
thf(func_def_473,type,
sK310: $i > $i ).
thf(func_def_474,type,
sK311: $i > $i ).
thf(func_def_475,type,
sK312: $i > $i ).
thf(func_def_476,type,
sK313: $i > $i > $i ).
thf(func_def_477,type,
sK314: $i > $i > $i > $i ).
thf(func_def_478,type,
sK315: $i > $i > $i > $i ).
thf(func_def_479,type,
sK316: $i > $i > $i > $i ).
thf(func_def_480,type,
sK317: $i > $i > $i ).
thf(func_def_481,type,
sK318: $i > $i > $i ).
thf(func_def_482,type,
sK319: $i > $i > $i ).
thf(func_def_483,type,
sK320: $i > $i > $i ).
thf(func_def_484,type,
sK321: $i > $i ).
thf(func_def_485,type,
sK322: $i > $i > $i > $i ).
thf(func_def_487,type,
sK324: $i > $i ).
thf(func_def_488,type,
sK325: $i > $i ).
thf(func_def_489,type,
sK326: $i > $i ).
thf(func_def_490,type,
sK327: $i > $i ).
thf(func_def_494,type,
sK331: $i > $o ).
thf(func_def_511,type,
sK348: $i > $o ).
thf(func_def_514,type,
sK351: ( $i > $o ) > $i > $i ).
thf(func_def_516,type,
sK353: $i > $o ).
thf(func_def_520,type,
ph357:
!>[X0: $tType] : X0 ).
thf(f2659,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2562,f2641,f2658]) ).
thf(f2658,plain,
~ spl356_1,
inference(avatar_contradiction_clause,[status(thm)],[f2657]) ).
thf(f2657,plain,
( $false
| ~ spl356_1 ),
inference(subsumption_resolution,[status(thm)],[f2476,f2558]) ).
thf(f2558,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl356_1 ),
inference(avatar_component_clause,[status(thm)],[f2557]) ).
thf(f2557,definition,
( spl356_1
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(naming,[spl356_1])],[avatar_definition]) ).
thf(f2476,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1982]) ).
thf(f1982,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f1331,f1583]) ).
thf(f1583,plain,
notinemptyset = $true,
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f926,plain,
( ( powerset__Cong = $true )
& ( foundationAx = $true )
& ( binintersectRsub = $true )
& ( subsetI1 = $true )
& ( powersetI1 = $true )
& ( ( in @ sK207 @ sK208 )
= $true )
& ( $true
= ( in @ sK207 @ ( symdiff @ sK206 @ sK208 ) ) )
& ( $true
= ( in @ sK207 @ sK206 ) )
& ( upairset2IR = $true )
& ( quantDeMorgan4 = $true )
& ( notsubsetI = $true )
& ( symdiffI1 = $true )
& ( binintersectER = $true )
& ( emptyI = $true )
& ( nonemptyImpWitness = $true )
& ( binunionEcases = $true )
& ( emptyinunitempty = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( bs114d = $true )
& ( setminusSubset2 = $true )
& ( symdiffI2 = $true )
& ( binintersectI = $true )
& ( notequalI1 = $true )
& ( subsetE2 = $true )
& ( noeltsimpempty = $true )
& ( in__Cong = $true )
& ( setminusELneg = $true )
& ( setunion__Cong = $true )
& ( binintersectEL = $true )
& ( setadjoinOr = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( dsetconstrER = $true )
& ( setext = $true )
& ( replAx = $true )
& ( dsetconstr__Cong = $true )
& ( exuE3e = $true )
& ( setminusERneg = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setminusLsub = $true )
& ( setadjoinIL = $true )
& ( exu__Cong = $true )
& ( binintersectSubset3 = $true )
& ( powersetsubset = $true )
& ( powersetE = $true )
& ( prop2set2propI = $true )
& ( omegaIndAx = $true )
& ( setminusER = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusIRneg = $true )
& ( wellorderingAx = $true )
& ( setadjoinAx = $true )
& ( setextsub = $true )
& ( eqinunit = $true )
& ( setminusSubset1 = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( setminusEL = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan1 = $true )
& ( exuE1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( notdexE = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyE1 = $true )
& ( prop2setI = $true )
& ( binintersectSubset4 = $true )
& ( vacuousDall = $true )
& ( binintersectSubset2 = $true )
& ( binunionE = $true )
& ( descrp = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( notdallE = $true )
& ( binintersectSubset1 = $true )
& ( notinsingleton = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( emptyinPowerset = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( exuEu = $true )
& ( binunionIR = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub2 = $true )
& ( emptyset__Cong = $true )
& ( setunionI = $true )
& ( setminusI = $true )
& ( sepSubset = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( emptysetimpfalse = $true )
& ( omega0Ax = $true )
& ( emptyInPowerset = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( omegaSAx = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( powersetI = $true )
& ( singletonsswitch = $true )
& ( upairsetE = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( emptyE1 = $true )
& ( setminusILneg = $true )
& ( inPowerset = $true )
& ( notequalI2 = $true )
& ( binintersectSubset5 = $true )
& ( binunionLsub = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( sepInPowerset = $true )
& ( omega__Cong = $true )
& ( descr__Cong = $true )
& ( symdiffE = $true )
& ( dsetconstrEL = $true )
& ( binunionIL = $true )
& ( setextAx = $true )
& ( emptysetsubset = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK206,sK207,sK208])],[f514,f925]) ).
thf(f925,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
=> ( ( ( in @ sK207 @ sK208 )
= $true )
& ( $true
= ( in @ sK207 @ ( symdiff @ sK206 @ sK208 ) ) )
& ( $true
= ( in @ sK207 @ sK206 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f514,plain,
( ( powerset__Cong = $true )
& ( foundationAx = $true )
& ( binintersectRsub = $true )
& ( subsetI1 = $true )
& ( powersetI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( upairset2IR = $true )
& ( quantDeMorgan4 = $true )
& ( notsubsetI = $true )
& ( symdiffI1 = $true )
& ( binintersectER = $true )
& ( emptyI = $true )
& ( nonemptyImpWitness = $true )
& ( binunionEcases = $true )
& ( emptyinunitempty = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( exuI1 = $true )
& ( setbeta = $true )
& ( bs114d = $true )
& ( setminusSubset2 = $true )
& ( symdiffI2 = $true )
& ( binintersectI = $true )
& ( notequalI1 = $true )
& ( subsetE2 = $true )
& ( noeltsimpempty = $true )
& ( in__Cong = $true )
& ( setminusELneg = $true )
& ( setunion__Cong = $true )
& ( binintersectEL = $true )
& ( setadjoinOr = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( dsetconstrER = $true )
& ( setext = $true )
& ( replAx = $true )
& ( dsetconstr__Cong = $true )
& ( exuE3e = $true )
& ( setminusERneg = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setminusLsub = $true )
& ( setadjoinIL = $true )
& ( exu__Cong = $true )
& ( binintersectSubset3 = $true )
& ( powersetsubset = $true )
& ( powersetE = $true )
& ( prop2set2propI = $true )
& ( omegaIndAx = $true )
& ( setminusER = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusIRneg = $true )
& ( wellorderingAx = $true )
& ( setadjoinAx = $true )
& ( setextsub = $true )
& ( eqinunit = $true )
& ( setminusSubset1 = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( setminusEL = $true )
& ( binintersectLsub = $true )
& ( quantDeMorgan1 = $true )
& ( exuE1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( notdexE = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyE1 = $true )
& ( prop2setI = $true )
& ( binintersectSubset4 = $true )
& ( vacuousDall = $true )
& ( binintersectSubset2 = $true )
& ( binunionE = $true )
& ( descrp = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( notdallE = $true )
& ( binintersectSubset1 = $true )
& ( notinsingleton = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( emptyinPowerset = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( exuEu = $true )
& ( binunionIR = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub2 = $true )
& ( emptyset__Cong = $true )
& ( setunionI = $true )
& ( setminusI = $true )
& ( sepSubset = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( emptysetimpfalse = $true )
& ( omega0Ax = $true )
& ( emptyInPowerset = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( omegaSAx = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( powersetI = $true )
& ( singletonsswitch = $true )
& ( upairsetE = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( emptyE1 = $true )
& ( setminusILneg = $true )
& ( inPowerset = $true )
& ( notequalI2 = $true )
& ( binintersectSubset5 = $true )
& ( binunionLsub = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( sepInPowerset = $true )
& ( omega__Cong = $true )
& ( descr__Cong = $true )
& ( symdiffE = $true )
& ( dsetconstrEL = $true )
& ( binunionIL = $true )
& ( setextAx = $true )
& ( emptysetsubset = $true ) ),
inference(flattening,[status(thm)],[f513]) ).
thf(f513,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( 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)],[f424]) ).
thf(f424,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f344]) ).
thf(f344,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f343]) ).
thf(f343,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ~ ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f134]) ).
thf(f134,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
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f133]) ).
thf(f133,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
=> ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',symdiffIneg1) ).
thf(f1331,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ),
inference(cnf_transformation,[status(thm)],[f760]) ).
thf(f760,plain,
( ( ( notinemptyset = $true )
| ( $true
= ( in @ sK110 @ emptyset ) ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110])],[f758,f759]) ).
thf(f759,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) )
=> ( $true
= ( in @ sK110 @ emptyset ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f758,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(rectify,[status(thm)],[f757]) ).
thf(f757,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) ) )
& ( ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) )
| ( notinemptyset != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( notinemptyset = $true )
<=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ),
inference(flattening,[status(thm)],[f336]) ).
thf(f336,plain,
( ( notinemptyset = $true )
<=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ),
inference(fool_elimination,[status(thm)],[f335]) ).
thf(f335,plain,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( notinemptyset
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',notinemptyset) ).
thf(f2641,plain,
~ spl356_2,
inference(avatar_contradiction_clause,[status(thm)],[f2640]) ).
thf(f2640,plain,
( $false
| ~ spl356_2 ),
inference(subsumption_resolution,[status(thm)],[f2639,f1594]) ).
thf(f1594,plain,
( $true
= ( in @ sK207 @ sK206 ) ),
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f2639,plain,
( ( $true
!= ( in @ sK207 @ sK206 ) )
| ~ spl356_2 ),
inference(subsumption_resolution,[status(thm)],[f2638,f1596]) ).
thf(f1596,plain,
( ( in @ sK207 @ sK208 )
= $true ),
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f2638,plain,
( ( ( in @ sK207 @ sK208 )
!= $true )
| ( $true
!= ( in @ sK207 @ sK206 ) )
| ~ spl356_2 ),
inference(trivial_inequality_removal,[status(thm)],[f2636]) ).
thf(f2636,plain,
( ( $true
!= ( in @ sK207 @ sK206 ) )
| ( ( in @ sK207 @ sK208 )
!= $true )
| ( $true != $true )
| ~ spl356_2 ),
inference(superposition,[status(thm)],[f2561,f1595]) ).
thf(f1595,plain,
( $true
= ( in @ sK207 @ ( symdiff @ sK206 @ sK208 ) ) ),
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f2561,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( ( in @ X5 @ X4 )
!= $true ) )
| ~ spl356_2 ),
inference(avatar_component_clause,[status(thm)],[f2560]) ).
thf(f2560,definition,
( spl356_2
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ X6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl356_2])],[avatar_definition]) ).
thf(f2562,plain,
( spl356_1
| spl356_2 ),
inference(avatar_split_clause,[status(thm)],[f2540,f2560,f2557]) ).
thf(f2540,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true = X7 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1837]) ).
thf(f1837,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true = X7 )
| ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( $true != $true )
| ( ( in @ X5 @ X4 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1176,f1473]) ).
thf(f1473,plain,
symdiffE = $true,
inference(cnf_transformation,[status(thm)],[f926]) ).
thf(f1176,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ( $true = X7 )
| ( ( in @ X5 @ X4 )
!= $true )
| ( $true
!= ( in @ X5 @ X6 ) )
| ( symdiffE != $true ) ),
inference(cnf_transformation,[status(thm)],[f582]) ).
thf(f582,plain,
( ( ( symdiffE = $true )
| ( ( ( in @ sK5 @ ( symdiff @ sK4 @ sK6 ) )
= $true )
& ( $true != sK7 )
& ( ( $true = sK7 )
| ( ( in @ sK5 @ sK6 )
!= $true )
| ( $true
= ( in @ sK5 @ sK4 ) ) )
& ( ( $true
!= ( in @ sK5 @ sK4 ) )
| ( ( in @ sK5 @ sK6 )
= $true )
| ( $true = sK7 ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( $true
= ( in @ X5 @ X6 ) )
& ( ( in @ X5 @ X4 )
!= $true ) )
| ( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X6 ) )
& ( $true != X7 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f579,f581,f580]) ).
thf(f580,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
& ( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true = X3 ) ) ) )
=> ( ( ( in @ sK5 @ ( symdiff @ sK4 @ sK6 ) )
= $true )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ sK5 @ sK6 )
!= $true )
| ( $true
= ( in @ sK5 @ sK4 ) ) )
& ( ( $true
!= ( in @ sK5 @ sK4 ) )
| ( ( in @ sK5 @ sK6 )
= $true )
| ( $true = X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f581,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ sK5 @ sK6 )
!= $true )
| ( $true
= ( in @ sK5 @ sK4 ) ) )
& ( ( $true
!= ( in @ sK5 @ sK4 ) )
| ( ( in @ sK5 @ sK6 )
= $true )
| ( $true = X3 ) ) )
=> ( ( $true != sK7 )
& ( ( $true = sK7 )
| ( ( in @ sK5 @ sK6 )
!= $true )
| ( $true
= ( in @ sK5 @ sK4 ) ) )
& ( ( $true
!= ( in @ sK5 @ sK4 ) )
| ( ( in @ sK5 @ sK6 )
= $true )
| ( $true = sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f579,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
& ( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true = X3 ) ) ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ( $true
!= ( in @ X5 @ ( symdiff @ X4 @ X6 ) ) )
| ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( $true
= ( in @ X5 @ X6 ) )
& ( ( in @ X5 @ X4 )
!= $true ) )
| ( ( ( in @ X5 @ X4 )
= $true )
& ( $true
!= ( in @ X5 @ X6 ) )
& ( $true != X7 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(rectify,[status(thm)],[f578]) ).
thf(f578,plain,
( ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
& ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true
= ( in @ X1 @ X0 ) ) )
& ( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true )
| ( $true = X3 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true != X3 ) ) ) )
| ( symdiffE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f536]) ).
thf(f536,plain,
( ( symdiffE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
| ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true != X3 ) ) ) ) ),
inference(flattening,[status(thm)],[f535]) ).
thf(f535,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
= $true )
& ( $true
!= ( in @ X1 @ X0 ) ) )
| ( ( $true != X3 )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true
= ( in @ X1 @ X0 ) ) ) )
| ( $true
!= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(ennf_transformation,[status(thm)],[f411]) ).
thf(f411,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(flattening,[status(thm)],[f243]) ).
thf(f243,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( symdiff @ X0 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(fool_elimination,[status(thm)],[f242]) ).
thf(f242,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> X3 ) )
=> ( ( ~ ( in @ X1 @ X0 )
=> ( ( in @ X1 @ X2 )
=> X3 ) )
=> X3 ) ) )
= symdiffE ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,axiom,
! [X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
=> ! [X0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> X0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> X0 ) )
=> X0 ) ) )
= symdiffE ),
file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',symdiffE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU614^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:29:22 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEU614^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.48 % Domain : Set Theory
% 0.20/0.48 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English : (! A:i.! B:i.! x:i.in x A -> in x B -> ~(in x (symdiff A B)))
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.48 % Source : [Bro08]
% 0.20/0.48 % Names : ZFC116g [Bro08]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.20/0.48 % Syntax : Number of formulae : 283 ( 132 unt; 150 typ; 132 def)
% 0.20/0.48 % Number of atoms : 707 ( 189 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 133 ( 5 avg)
% 0.20/0.48 % Number of connectives : 1137 ( 44 ~; 6 |; 28 &; 727 @)
% 0.20/0.48 % ( 14 <=>; 318 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 140 ( 2 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 153 ( 150 usr; 134 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 383 ( 30 ^; 324 !; 29 ?; 383 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : http://mathgate.info/detsetitem.php?id=492
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(in_type,type,
% 0.20/0.48 in: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(exu_type,type,
% 0.20/0.48 exu: ( $i > $o ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf(exu,definition,
% 0.20/0.48 ( exu
% 0.20/0.48 = ( ^ [Xphi: $i > $o] :
% 0.20/0.48 ? [Xx: $i] :
% 0.20/0.48 ( ( Xphi @ Xx )
% 0.20/0.48 & ! [Xy: $i] :
% 0.20/0.48 ( ( Xphi @ Xy )
% 0.20/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setextAx_type,type,
% 0.20/0.48 setextAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setextAx,definition,
% 0.20/0.48 ( setextAx
% 0.20/0.48 = ( ! [A: $i,B: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 <=> ( in @ Xx @ B ) )
% 0.20/0.48 => ( A = B ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(emptyset_type,type,
% 0.20/0.48 emptyset: $i ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetAx_type,type,
% 0.20/0.48 emptysetAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(emptysetAx,definition,
% 0.20/0.48 ( emptysetAx
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoin_type,type,
% 0.20/0.48 setadjoin: $i > $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinAx_type,type,
% 0.20/0.48 setadjoinAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setadjoinAx,definition,
% 0.20/0.48 ( setadjoinAx
% 0.20/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.48 <=> ( ( Xy = Xx )
% 0.20/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(powerset_type,type,
% 0.20/0.48 powerset: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(powersetAx_type,type,
% 0.20/0.48 powersetAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(powersetAx,definition,
% 0.20/0.48 ( powersetAx
% 0.20/0.48 = ( ! [A: $i,B: $i] :
% 0.20/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.48 <=> ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(setunion_type,type,
% 0.20/0.48 setunion: $i > $i ).
% 0.20/0.48
% 0.20/0.48 thf(setunionAx_type,type,
% 0.20/0.48 setunionAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(setunionAx,definition,
% 0.20/0.48 ( setunionAx
% 0.20/0.48 = ( ! [A: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.48 <=> ? [B: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omega_type,type,
% 0.20/0.48 omega: $i ).
% 0.20/0.48
% 0.20/0.48 thf(omega0Ax_type,type,
% 0.20/0.48 omega0Ax: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omega0Ax,definition,
% 0.20/0.48 ( omega0Ax
% 0.20/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omegaSAx_type,type,
% 0.20/0.48 omegaSAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omegaSAx,definition,
% 0.20/0.48 ( omegaSAx
% 0.20/0.48 = ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ omega )
% 0.20/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(omegaIndAx_type,type,
% 0.20/0.48 omegaIndAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(omegaIndAx,definition,
% 0.20/0.48 ( omegaIndAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ( ( in @ emptyset @ A )
% 0.20/0.48 & ! [Xx: $i] :
% 0.20/0.48 ( ( ( in @ Xx @ omega )
% 0.20/0.48 & ( in @ Xx @ A ) )
% 0.20/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ omega )
% 0.20/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(replAx_type,type,
% 0.20/0.48 replAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(replAx,definition,
% 0.20/0.48 ( replAx
% 0.20/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.48 ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( exu
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.48 => ? [B: $i] :
% 0.20/0.48 ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 <=> ? [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ A )
% 0.20/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(foundationAx_type,type,
% 0.20/0.48 foundationAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(foundationAx,definition,
% 0.20/0.48 ( foundationAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.48 => ? [B: $i] :
% 0.20/0.48 ( ( in @ B @ A )
% 0.20/0.48 & ~ ? [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ B )
% 0.20/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(wellorderingAx_type,type,
% 0.20/0.48 wellorderingAx: $o ).
% 0.20/0.48
% 0.20/0.48 thf(wellorderingAx,definition,
% 0.20/0.48 ( wellorderingAx
% 0.20/0.48 = ( ! [A: $i] :
% 0.20/0.48 ? [B: $i] :
% 0.20/0.48 ( ! [C: $i] :
% 0.20/0.48 ( ( in @ C @ B )
% 0.20/0.48 => ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ A ) ) )
% 0.20/0.48 & ! [Xx: $i,Xy: $i] :
% 0.20/0.48 ( ( ( in @ Xx @ A )
% 0.20/0.48 & ( in @ Xy @ A ) )
% 0.20/0.48 => ( ! [C: $i] :
% 0.20/0.48 ( ( in @ C @ B )
% 0.20/0.48 => ( ( in @ Xx @ C )
% 0.20/0.48 <=> ( in @ Xy @ C ) ) )
% 0.20/0.48 => ( Xx = Xy ) ) )
% 0.20/0.48 & ! [C: $i,D: $i] :
% 0.20/0.48 ( ( ( in @ C @ B )
% 0.20/0.48 & ( in @ D @ B ) )
% 0.20/0.48 => ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ D ) )
% 0.20/0.48 | ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ D )
% 0.20/0.48 => ( in @ Xx @ C ) ) ) )
% 0.20/0.48 & ! [C: $i] :
% 0.20/0.48 ( ( ! [Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ C )
% 0.20/0.48 => ( in @ Xx @ A ) )
% 0.20/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.48 => ? [D: $i,Xx: $i] :
% 0.20/0.48 ( ( in @ D @ B )
% 0.20/0.48 & ( in @ Xx @ C )
% 0.20/0.48 & ~ ? [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ D )
% 0.20/0.48 & ( in @ Xy @ C ) )
% 0.20/0.48 & ! [E: $i] :
% 0.20/0.48 ( ( in @ E @ B )
% 0.20/0.48 => ( ! [Xy: $i] :
% 0.20/0.48 ( ( in @ Xy @ E )
% 0.20/0.48 => ( in @ Xy @ D ) )
% 0.20/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(descr_type,type,
% 0.20/0.48 descr: ( $i > $o ) > $i ).
% 0.20/0.48
% 0.20/0.48 thf(descrp_type,type,
% 0.20/0.48 descrp: $o ).
% 0.20/0.48
% 0.20/0.48 thf(descrp,definition,
% 0.20/0.48 ( descrp
% 0.20/0.48 = ( ! [Xphi: $i > $o] :
% 0.20/0.48 ( ( exu
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.48 => ( Xphi
% 0.20/0.48 @ ( descr
% 0.20/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstr_type,type,
% 0.20/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrI_type,type,
% 0.20/0.48 dsetconstrI: $o ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrI,definition,
% 0.20/0.48 ( dsetconstrI
% 0.20/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.48 ( ( in @ Xx @ A )
% 0.20/0.48 => ( ( Xphi @ Xx )
% 0.20/0.48 => ( in @ Xx
% 0.20/0.48 @ ( dsetconstr @ A
% 0.20/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrEL_type,type,
% 0.20/0.48 dsetconstrEL: $o ).
% 0.20/0.48
% 0.20/0.48 thf(dsetconstrEL,definition,
% 0.33/0.48 ( dsetconstrEL
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(dsetconstrER_type,type,
% 0.33/0.48 dsetconstrER: $o ).
% 0.33/0.48
% 0.33/0.48 thf(dsetconstrER,definition,
% 0.33/0.48 ( dsetconstrER
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuE1_type,type,
% 0.33/0.48 exuE1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuE1,definition,
% 0.33/0.48 ( exuE1
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ? [Xx: $i] :
% 0.33/0.48 ( ( Xphi @ Xx )
% 0.33/0.48 & ! [Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xy )
% 0.33/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(prop2set_type,type,
% 0.33/0.48 prop2set: $o > $i ).
% 0.33/0.48
% 0.33/0.48 thf(prop2setE_type,type,
% 0.33/0.48 prop2setE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(prop2setE,definition,
% 0.33/0.48 ( prop2setE
% 0.33/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.33/0.48 => Xphi ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetE_type,type,
% 0.33/0.48 emptysetE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetE,definition,
% 0.33/0.48 ( emptysetE
% 0.33/0.48 = ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ emptyset )
% 0.33/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetimpfalse_type,type,
% 0.33/0.48 emptysetimpfalse: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetimpfalse,definition,
% 0.33/0.48 ( emptysetimpfalse
% 0.33/0.48 = ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ emptyset )
% 0.33/0.48 => $false ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notinemptyset_type,type,
% 0.33/0.48 notinemptyset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notinemptyset,definition,
% 0.33/0.48 ( notinemptyset
% 0.33/0.48 = ( ! [Xx: $i] :
% 0.33/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuE3e_type,type,
% 0.33/0.48 exuE3e: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuE3e,definition,
% 0.33/0.48 ( exuE3e
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setext_type,type,
% 0.33/0.48 setext: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setext,definition,
% 0.33/0.48 ( setext
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ B ) )
% 0.33/0.48 => ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ A ) )
% 0.33/0.48 => ( A = B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyI_type,type,
% 0.33/0.48 emptyI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyI,definition,
% 0.33/0.48 ( emptyI
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ~ ( in @ Xx @ A )
% 0.33/0.48 => ( A = emptyset ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(noeltsimpempty_type,type,
% 0.33/0.48 noeltsimpempty: $o ).
% 0.33/0.48
% 0.33/0.48 thf(noeltsimpempty,definition,
% 0.33/0.48 ( noeltsimpempty
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ~ ( in @ Xx @ A )
% 0.33/0.48 => ( A = emptyset ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setbeta_type,type,
% 0.33/0.48 setbeta: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setbeta,definition,
% 0.33/0.48 ( setbeta
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(nonempty_type,type,
% 0.33/0.48 nonempty: $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(nonempty,definition,
% 0.33/0.48 ( nonempty
% 0.33/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyE1_type,type,
% 0.33/0.48 nonemptyE1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyE1,definition,
% 0.33/0.48 ( nonemptyE1
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ( nonempty @ A )
% 0.33/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyI_type,type,
% 0.33/0.48 nonemptyI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyI,definition,
% 0.33/0.48 ( nonemptyI
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ( Xphi @ Xx )
% 0.33/0.48 => ( nonempty
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyI1_type,type,
% 0.33/0.48 nonemptyI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyI1,definition,
% 0.33/0.48 ( nonemptyI1
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.33/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinIL_type,type,
% 0.33/0.48 setadjoinIL: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinIL,definition,
% 0.33/0.48 ( setadjoinIL
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyinunitempty_type,type,
% 0.33/0.48 emptyinunitempty: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyinunitempty,definition,
% 0.33/0.48 ( emptyinunitempty
% 0.33/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinIR_type,type,
% 0.33/0.48 setadjoinIR: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinIR,definition,
% 0.33/0.48 ( setadjoinIR
% 0.33/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/0.48 ( ( in @ Xy @ A )
% 0.33/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinE_type,type,
% 0.33/0.48 setadjoinE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinE,definition,
% 0.33/0.48 ( setadjoinE
% 0.33/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.33/0.48 => ! [Xphi: $o] :
% 0.33/0.48 ( ( ( Xy = Xx )
% 0.33/0.48 => Xphi )
% 0.33/0.48 => ( ( ( in @ Xy @ A )
% 0.33/0.48 => Xphi )
% 0.33/0.48 => Xphi ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinOr_type,type,
% 0.33/0.48 setadjoinOr: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinOr,definition,
% 0.33/0.48 ( setadjoinOr
% 0.33/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.33/0.48 => ( ( Xy = Xx )
% 0.33/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setoftrueEq_type,type,
% 0.33/0.48 setoftrueEq: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setoftrueEq,definition,
% 0.33/0.48 ( setoftrueEq
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xx: $i] : $true )
% 0.33/0.48 = A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powersetI_type,type,
% 0.33/0.48 powersetI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powersetI,definition,
% 0.33/0.48 ( powersetI
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ A ) )
% 0.33/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyinPowerset_type,type,
% 0.33/0.48 emptyinPowerset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyinPowerset,definition,
% 0.33/0.48 ( emptyinPowerset
% 0.33/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyInPowerset_type,type,
% 0.33/0.48 emptyInPowerset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyInPowerset,definition,
% 0.33/0.48 ( emptyInPowerset
% 0.33/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powersetE_type,type,
% 0.33/0.48 powersetE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powersetE,definition,
% 0.33/0.48 ( powersetE
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.33/0.48 => ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setunionI_type,type,
% 0.33/0.48 setunionI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setunionI,definition,
% 0.33/0.48 ( setunionI
% 0.33/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ( ( in @ B @ A )
% 0.33/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setunionE_type,type,
% 0.33/0.48 setunionE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setunionE,definition,
% 0.33/0.48 ( setunionE
% 0.33/0.48 = ( ! [A: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.33/0.48 => ! [Xphi: $o] :
% 0.33/0.48 ( ! [B: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ( ( in @ B @ A )
% 0.33/0.48 => Xphi ) )
% 0.33/0.48 => Xphi ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subPowSU_type,type,
% 0.33/0.48 subPowSU: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subPowSU,definition,
% 0.33/0.48 ( subPowSU
% 0.33/0.48 = ( ! [A: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuE2_type,type,
% 0.33/0.48 exuE2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuE2,definition,
% 0.33/0.48 ( exuE2
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ? [Xx: $i] :
% 0.33/0.48 ! [Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xy )
% 0.33/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyImpWitness_type,type,
% 0.33/0.48 nonemptyImpWitness: $o ).
% 0.33/0.48
% 0.33/0.48 thf(nonemptyImpWitness,definition,
% 0.33/0.48 ( nonemptyImpWitness
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ( nonempty @ A )
% 0.33/0.48 => ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & $true ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(uniqinunit_type,type,
% 0.33/0.48 uniqinunit: $o ).
% 0.33/0.48
% 0.33/0.48 thf(uniqinunit,definition,
% 0.33/0.48 ( uniqinunit
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notinsingleton_type,type,
% 0.33/0.48 notinsingleton: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notinsingleton,definition,
% 0.33/0.48 ( notinsingleton
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx != Xy )
% 0.33/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(eqinunit_type,type,
% 0.33/0.48 eqinunit: $o ).
% 0.33/0.48
% 0.33/0.48 thf(eqinunit,definition,
% 0.33/0.48 ( eqinunit
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(singletonsswitch_type,type,
% 0.33/0.48 singletonsswitch: $o ).
% 0.33/0.48
% 0.33/0.48 thf(singletonsswitch,definition,
% 0.33/0.48 ( singletonsswitch
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetE_type,type,
% 0.33/0.48 upairsetE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetE,definition,
% 0.33/0.48 ( upairsetE
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.33/0.48 => ( ( Xz = Xx )
% 0.33/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetIL_type,type,
% 0.33/0.48 upairsetIL: $o ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetIL,definition,
% 0.33/0.48 ( upairsetIL
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetIR_type,type,
% 0.33/0.48 upairsetIR: $o ).
% 0.33/0.48
% 0.33/0.48 thf(upairsetIR,definition,
% 0.33/0.48 ( upairsetIR
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyE1_type,type,
% 0.33/0.48 emptyE1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyE1,definition,
% 0.33/0.48 ( emptyE1
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ( Xphi @ Xx ) )
% 0.33/0.48 => ( ( ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 = emptyset )
% 0.33/0.48 => $false ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(vacuousDall_type,type,
% 0.33/0.48 vacuousDall: $o ).
% 0.33/0.48
% 0.33/0.48 thf(vacuousDall,definition,
% 0.33/0.48 ( vacuousDall
% 0.33/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ emptyset )
% 0.33/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan1_type,type,
% 0.33/0.48 quantDeMorgan1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan1,definition,
% 0.33/0.48 ( quantDeMorgan1
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ~ ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( Xphi @ Xx ) )
% 0.33/0.48 => ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan2_type,type,
% 0.33/0.48 quantDeMorgan2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan2,definition,
% 0.33/0.48 ( quantDeMorgan2
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ~ ( Xphi @ Xx ) )
% 0.33/0.48 => ~ ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan3_type,type,
% 0.33/0.48 quantDeMorgan3: $o ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan3,definition,
% 0.33/0.48 ( quantDeMorgan3
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ~ ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ( Xphi @ Xx ) )
% 0.33/0.48 => ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan4_type,type,
% 0.33/0.48 quantDeMorgan4: $o ).
% 0.33/0.48
% 0.33/0.48 thf(quantDeMorgan4,definition,
% 0.33/0.48 ( quantDeMorgan4
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ~ ( Xphi @ Xx ) )
% 0.33/0.48 => ~ ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(prop2setI_type,type,
% 0.33/0.48 prop2setI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(prop2setI,definition,
% 0.33/0.48 ( prop2setI
% 0.33/0.48 = ( ! [Xphi: $o] :
% 0.33/0.48 ( Xphi
% 0.33/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(set2prop_type,type,
% 0.33/0.48 set2prop: $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(prop2set2propI_type,type,
% 0.33/0.48 prop2set2propI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(prop2set2propI,definition,
% 0.33/0.48 ( prop2set2propI
% 0.33/0.48 = ( ! [Xphi: $o] :
% 0.33/0.48 ( Xphi
% 0.33/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notdexE_type,type,
% 0.33/0.48 notdexE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notdexE,definition,
% 0.33/0.48 ( notdexE
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ~ ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ( Xphi @ Xx ) )
% 0.33/0.48 => ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notdallE_type,type,
% 0.33/0.48 notdallE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notdallE,definition,
% 0.33/0.48 ( notdallE
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( ~ ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( Xphi @ Xx ) )
% 0.33/0.48 => ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuI1_type,type,
% 0.33/0.48 exuI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuI1,definition,
% 0.33/0.48 ( exuI1
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ? [Xx: $i] :
% 0.33/0.48 ( ( Xphi @ Xx )
% 0.33/0.48 & ! [Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xy )
% 0.33/0.48 => ( Xx = Xy ) ) )
% 0.33/0.48 => ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuI3_type,type,
% 0.33/0.48 exuI3: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuI3,definition,
% 0.33/0.48 ( exuI3
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.33/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xx )
% 0.33/0.48 => ( ( Xphi @ Xy )
% 0.33/0.48 => ( Xx = Xy ) ) )
% 0.33/0.48 => ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuI2_type,type,
% 0.33/0.48 exuI2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuI2,definition,
% 0.33/0.48 ( exuI2
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ? [Xx: $i] :
% 0.33/0.48 ! [Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xy )
% 0.33/0.48 <=> ( Xy = Xx ) )
% 0.33/0.48 => ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(inCongP_type,type,
% 0.33/0.48 inCongP: $o ).
% 0.33/0.48
% 0.33/0.48 thf(inCongP,definition,
% 0.33/0.48 ( inCongP
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(in__Cong_type,type,
% 0.33/0.48 in__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(in__Cong,definition,
% 0.33/0.48 ( in__Cong
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ( ( in @ Xx @ A )
% 0.33/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuE3u_type,type,
% 0.33/0.48 exuE3u: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuE3u,definition,
% 0.33/0.48 ( exuE3u
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xx )
% 0.33/0.48 => ( ( Xphi @ Xy )
% 0.33/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exu__Cong_type,type,
% 0.33/0.48 exu__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exu__Cong,definition,
% 0.33/0.48 ( exu__Cong
% 0.33/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ( ( Xphi @ Xx )
% 0.33/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.33/0.48 => ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 <=> ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptyset__Cong_type,type,
% 0.33/0.48 emptyset__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptyset__Cong,definition,
% 0.33/0.48 ( emptyset__Cong
% 0.33/0.48 = ( emptyset = emptyset ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoin__Cong_type,type,
% 0.33/0.48 setadjoin__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoin__Cong,definition,
% 0.33/0.48 ( setadjoin__Cong
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ! [Xz: $i,Xu: $i] :
% 0.33/0.48 ( ( Xz = Xu )
% 0.33/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.33/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powerset__Cong_type,type,
% 0.33/0.48 powerset__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powerset__Cong,definition,
% 0.33/0.48 ( powerset__Cong
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ( ( powerset @ A )
% 0.33/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setunion__Cong_type,type,
% 0.33/0.48 setunion__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setunion__Cong,definition,
% 0.33/0.48 ( setunion__Cong
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ( ( setunion @ A )
% 0.33/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(omega__Cong_type,type,
% 0.33/0.48 omega__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(omega__Cong,definition,
% 0.33/0.48 ( omega__Cong
% 0.33/0.48 = ( omega = omega ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(exuEu_type,type,
% 0.33/0.48 exuEu: $o ).
% 0.33/0.48
% 0.33/0.48 thf(exuEu,definition,
% 0.33/0.48 ( exuEu
% 0.33/0.48 = ( ! [Xphi: $i > $o] :
% 0.33/0.48 ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xphi @ Xx )
% 0.33/0.48 => ( ( Xphi @ Xy )
% 0.33/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(descr__Cong_type,type,
% 0.33/0.48 descr__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(descr__Cong,definition,
% 0.33/0.48 ( descr__Cong
% 0.33/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.33/0.48 ( ( Xx = Xy )
% 0.33/0.48 => ( ( Xphi @ Xx )
% 0.33/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.33/0.48 => ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 => ( ( exu
% 0.33/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.33/0.48 => ( ( descr
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 = ( descr
% 0.33/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(dsetconstr__Cong_type,type,
% 0.33/0.48 dsetconstr__Cong: $o ).
% 0.33/0.48
% 0.33/0.48 thf(dsetconstr__Cong,definition,
% 0.33/0.48 ( dsetconstr__Cong
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ! [Xy: $i] :
% 0.33/0.48 ( ( in @ Xy @ B )
% 0.33/0.48 => ( ( Xx = Xy )
% 0.33/0.48 => ( ( Xphi @ Xx )
% 0.33/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.33/0.48 => ( ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 = ( dsetconstr @ B
% 0.33/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subset_type,type,
% 0.33/0.48 subset: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(disjoint_type,type,
% 0.33/0.48 disjoint: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(setsmeet_type,type,
% 0.33/0.48 setsmeet: $i > $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetI1_type,type,
% 0.33/0.48 subsetI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetI1,definition,
% 0.33/0.48 ( subsetI1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ B ) )
% 0.33/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(eqimpsubset2_type,type,
% 0.33/0.48 eqimpsubset2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(eqimpsubset2,definition,
% 0.33/0.48 ( eqimpsubset2
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(eqimpsubset1_type,type,
% 0.33/0.48 eqimpsubset1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(eqimpsubset1,definition,
% 0.33/0.48 ( eqimpsubset1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( A = B )
% 0.33/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetI2_type,type,
% 0.33/0.48 subsetI2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetI2,definition,
% 0.33/0.48 ( subsetI2
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ! [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ B ) )
% 0.33/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetsubset_type,type,
% 0.33/0.48 emptysetsubset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(emptysetsubset,definition,
% 0.33/0.48 ( emptysetsubset
% 0.33/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetE_type,type,
% 0.33/0.48 subsetE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetE,definition,
% 0.33/0.48 ( subsetE
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetE2_type,type,
% 0.33/0.48 subsetE2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetE2,definition,
% 0.33/0.48 ( subsetE2
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notsubsetI_type,type,
% 0.33/0.48 notsubsetI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notsubsetI,definition,
% 0.33/0.48 ( notsubsetI
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notequalI1_type,type,
% 0.33/0.48 notequalI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notequalI1,definition,
% 0.33/0.48 ( notequalI1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ~ ( subset @ A @ B )
% 0.33/0.48 => ( A != B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(notequalI2_type,type,
% 0.33/0.48 notequalI2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(notequalI2,definition,
% 0.33/0.48 ( notequalI2
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ( A != B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetRefl_type,type,
% 0.33/0.48 subsetRefl: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetRefl,definition,
% 0.33/0.48 ( subsetRefl
% 0.33/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetTrans_type,type,
% 0.33/0.48 subsetTrans: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetTrans,definition,
% 0.33/0.48 ( subsetTrans
% 0.33/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ( subset @ B @ C )
% 0.33/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinSub_type,type,
% 0.33/0.48 setadjoinSub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinSub,definition,
% 0.33/0.48 ( setadjoinSub
% 0.33/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinSub2_type,type,
% 0.33/0.48 setadjoinSub2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setadjoinSub2,definition,
% 0.33/0.48 ( setadjoinSub2
% 0.33/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subset2powerset_type,type,
% 0.33/0.48 subset2powerset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subset2powerset,definition,
% 0.33/0.48 ( subset2powerset
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setextsub_type,type,
% 0.33/0.48 setextsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setextsub,definition,
% 0.33/0.48 ( setextsub
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ( subset @ B @ A )
% 0.33/0.48 => ( A = B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(subsetemptysetimpeq_type,type,
% 0.33/0.48 subsetemptysetimpeq: $o ).
% 0.33/0.48
% 0.33/0.48 thf(subsetemptysetimpeq,definition,
% 0.33/0.48 ( subsetemptysetimpeq
% 0.33/0.48 = ( ! [A: $i] :
% 0.33/0.48 ( ( subset @ A @ emptyset )
% 0.33/0.48 => ( A = emptyset ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powersetI1_type,type,
% 0.33/0.48 powersetI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powersetI1,definition,
% 0.33/0.48 ( powersetI1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ B @ A )
% 0.33/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powersetE1_type,type,
% 0.33/0.48 powersetE1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powersetE1,definition,
% 0.33/0.48 ( powersetE1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.33/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(inPowerset_type,type,
% 0.33/0.48 inPowerset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(inPowerset,definition,
% 0.33/0.48 ( inPowerset
% 0.33/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(powersetsubset_type,type,
% 0.33/0.48 powersetsubset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(powersetsubset,definition,
% 0.33/0.48 ( powersetsubset
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(sepInPowerset_type,type,
% 0.33/0.48 sepInPowerset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(sepInPowerset,definition,
% 0.33/0.48 ( sepInPowerset
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( in
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(sepSubset_type,type,
% 0.33/0.48 sepSubset: $o ).
% 0.33/0.48
% 0.33/0.48 thf(sepSubset,definition,
% 0.33/0.48 ( sepSubset
% 0.33/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.48 ( subset
% 0.33/0.48 @ ( dsetconstr @ A
% 0.33/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.48 @ A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunion_type,type,
% 0.33/0.48 binunion: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(binunionIL_type,type,
% 0.33/0.48 binunionIL: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionIL,definition,
% 0.33/0.48 ( binunionIL
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(upairset2IR_type,type,
% 0.33/0.48 upairset2IR: $o ).
% 0.33/0.48
% 0.33/0.48 thf(upairset2IR,definition,
% 0.33/0.48 ( upairset2IR
% 0.33/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunionIR_type,type,
% 0.33/0.48 binunionIR: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionIR,definition,
% 0.33/0.48 ( binunionIR
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunionEcases_type,type,
% 0.33/0.48 binunionEcases: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionEcases,definition,
% 0.33/0.48 ( binunionEcases
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.33/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/0.48 => ( ( ( in @ Xx @ A )
% 0.33/0.48 => Xphi )
% 0.33/0.48 => ( ( ( in @ Xx @ B )
% 0.33/0.48 => Xphi )
% 0.33/0.48 => Xphi ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunionE_type,type,
% 0.33/0.48 binunionE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionE,definition,
% 0.33/0.48 ( binunionE
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/0.48 => ( ( in @ Xx @ A )
% 0.33/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunionLsub_type,type,
% 0.33/0.48 binunionLsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionLsub,definition,
% 0.33/0.48 ( binunionLsub
% 0.33/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binunionRsub_type,type,
% 0.33/0.48 binunionRsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binunionRsub,definition,
% 0.33/0.48 ( binunionRsub
% 0.33/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersect_type,type,
% 0.33/0.48 binintersect: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectI_type,type,
% 0.33/0.48 binintersectI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectI,definition,
% 0.33/0.48 ( binintersectI
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset5_type,type,
% 0.33/0.48 binintersectSubset5: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset5,definition,
% 0.33/0.48 ( binintersectSubset5
% 0.33/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/0.48 ( ( subset @ C @ A )
% 0.33/0.48 => ( ( subset @ C @ B )
% 0.33/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectEL_type,type,
% 0.33/0.48 binintersectEL: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectEL,definition,
% 0.33/0.48 ( binintersectEL
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectLsub_type,type,
% 0.33/0.48 binintersectLsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectLsub,definition,
% 0.33/0.48 ( binintersectLsub
% 0.33/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset2_type,type,
% 0.33/0.48 binintersectSubset2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset2,definition,
% 0.33/0.48 ( binintersectSubset2
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ( binintersect @ A @ B )
% 0.33/0.48 = A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset3_type,type,
% 0.33/0.48 binintersectSubset3: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset3,definition,
% 0.33/0.48 ( binintersectSubset3
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( ( binintersect @ A @ B )
% 0.33/0.48 = B )
% 0.33/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectER_type,type,
% 0.33/0.48 binintersectER: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectER,definition,
% 0.33/0.48 ( binintersectER
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(disjointsetsI1_type,type,
% 0.33/0.48 disjointsetsI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(disjointsetsI1,definition,
% 0.33/0.48 ( disjointsetsI1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ~ ? [Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 & ( in @ Xx @ B ) )
% 0.33/0.48 => ( ( binintersect @ A @ B )
% 0.33/0.48 = emptyset ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectRsub_type,type,
% 0.33/0.48 binintersectRsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectRsub,definition,
% 0.33/0.48 ( binintersectRsub
% 0.33/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset4_type,type,
% 0.33/0.48 binintersectSubset4: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset4,definition,
% 0.33/0.48 ( binintersectSubset4
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ B @ A )
% 0.33/0.48 => ( ( binintersect @ A @ B )
% 0.33/0.48 = B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset1_type,type,
% 0.33/0.48 binintersectSubset1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(binintersectSubset1,definition,
% 0.33/0.48 ( binintersectSubset1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( ( binintersect @ A @ B )
% 0.33/0.48 = A )
% 0.33/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(bs114d_type,type,
% 0.33/0.48 bs114d: $o ).
% 0.33/0.48
% 0.33/0.48 thf(bs114d,definition,
% 0.33/0.48 ( bs114d
% 0.33/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.33/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(regular_type,type,
% 0.33/0.48 regular: $i > $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminus_type,type,
% 0.33/0.48 setminus: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(setminusI_type,type,
% 0.33/0.48 setminusI: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusI,definition,
% 0.33/0.48 ( setminusI
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusEL_type,type,
% 0.33/0.48 setminusEL: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusEL,definition,
% 0.33/0.48 ( setminusEL
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusER_type,type,
% 0.33/0.48 setminusER: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusER,definition,
% 0.33/0.48 ( setminusER
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusSubset2_type,type,
% 0.33/0.48 setminusSubset2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusSubset2,definition,
% 0.33/0.48 ( setminusSubset2
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( subset @ A @ B )
% 0.33/0.48 => ( ( setminus @ A @ B )
% 0.33/0.48 = emptyset ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusERneg_type,type,
% 0.33/0.48 setminusERneg: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusERneg,definition,
% 0.33/0.48 ( setminusERneg
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.48 => ( ( in @ Xx @ A )
% 0.33/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusELneg_type,type,
% 0.33/0.48 setminusELneg: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusELneg,definition,
% 0.33/0.48 ( setminusELneg
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusILneg_type,type,
% 0.33/0.48 setminusILneg: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusILneg,definition,
% 0.33/0.48 ( setminusILneg
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ~ ( in @ Xx @ A )
% 0.33/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusIRneg_type,type,
% 0.33/0.48 setminusIRneg: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusIRneg,definition,
% 0.33/0.48 ( setminusIRneg
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ B )
% 0.33/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusLsub_type,type,
% 0.33/0.48 setminusLsub: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusLsub,definition,
% 0.33/0.48 ( setminusLsub
% 0.33/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(setminusSubset1_type,type,
% 0.33/0.48 setminusSubset1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(setminusSubset1,definition,
% 0.33/0.48 ( setminusSubset1
% 0.33/0.48 = ( ! [A: $i,B: $i] :
% 0.33/0.48 ( ( ( setminus @ A @ B )
% 0.33/0.48 = emptyset )
% 0.33/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(symdiff_type,type,
% 0.33/0.48 symdiff: $i > $i > $i ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffE_type,type,
% 0.33/0.48 symdiffE: $o ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffE,definition,
% 0.33/0.48 ( symdiffE
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.33/0.48 => ! [Xphi: $o] :
% 0.33/0.48 ( ( ( in @ Xx @ A )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => Xphi ) )
% 0.33/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx @ B )
% 0.33/0.48 => Xphi ) )
% 0.33/0.48 => Xphi ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffI1_type,type,
% 0.33/0.48 symdiffI1: $o ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffI1,definition,
% 0.33/0.48 ( symdiffI1
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ~ ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffI2_type,type,
% 0.33/0.48 symdiffI2: $o ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffI2,definition,
% 0.33/0.48 ( symdiffI2
% 0.33/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ~ ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx @ B )
% 0.33/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 thf(symdiffIneg1,conjecture,
% 0.33/0.48 ( setextAx
% 0.33/0.48 => ( emptysetAx
% 0.33/0.48 => ( setadjoinAx
% 0.33/0.48 => ( powersetAx
% 0.33/0.48 => ( setunionAx
% 0.33/0.48 => ( omega0Ax
% 0.33/0.48 => ( omegaSAx
% 0.33/0.48 => ( omegaIndAx
% 0.33/0.48 => ( replAx
% 0.33/0.48 => ( foundationAx
% 0.33/0.48 => ( wellorderingAx
% 0.33/0.48 => ( descrp
% 0.33/0.48 => ( dsetconstrI
% 0.33/0.48 => ( dsetconstrEL
% 0.33/0.48 => ( dsetconstrER
% 0.33/0.48 => ( exuE1
% 0.33/0.48 => ( prop2setE
% 0.33/0.48 => ( emptysetE
% 0.33/0.48 => ( emptysetimpfalse
% 0.33/0.48 => ( notinemptyset
% 0.33/0.48 => ( exuE3e
% 0.33/0.48 => ( setext
% 0.33/0.48 => ( emptyI
% 0.33/0.48 => ( noeltsimpempty
% 0.33/0.48 => ( setbeta
% 0.33/0.48 => ( nonemptyE1
% 0.33/0.48 => ( nonemptyI
% 0.33/0.48 => ( nonemptyI1
% 0.33/0.48 => ( setadjoinIL
% 0.33/0.48 => ( emptyinunitempty
% 0.33/0.48 => ( setadjoinIR
% 0.33/0.48 => ( setadjoinE
% 0.33/0.48 => ( setadjoinOr
% 0.33/0.48 => ( setoftrueEq
% 0.33/0.48 => ( powersetI
% 0.33/0.48 => ( emptyinPowerset
% 0.33/0.48 => ( emptyInPowerset
% 0.33/0.48 => ( powersetE
% 0.33/0.48 => ( setunionI
% 0.33/0.48 => ( setunionE
% 0.33/0.48 => ( subPowSU
% 0.33/0.48 => ( exuE2
% 0.33/0.48 => ( nonemptyImpWitness
% 0.33/0.48 => ( uniqinunit
% 0.33/0.48 => ( notinsingleton
% 0.33/0.48 => ( eqinunit
% 0.33/0.48 => ( singletonsswitch
% 0.33/0.48 => ( upairsetE
% 0.33/0.48 => ( upairsetIL
% 0.33/0.48 => ( upairsetIR
% 0.33/0.48 => ( emptyE1
% 0.33/0.48 => ( vacuousDall
% 0.33/0.48 => ( quantDeMorgan1
% 0.33/0.48 => ( quantDeMorgan2
% 0.33/0.48 => ( quantDeMorgan3
% 0.33/0.48 => ( quantDeMorgan4
% 0.33/0.48 => ( prop2setI
% 0.33/0.48 => ( prop2set2propI
% 0.33/0.48 => ( notdexE
% 0.33/0.48 => ( notdallE
% 0.33/0.48 => ( exuI1
% 0.33/0.48 => ( exuI3
% 0.33/0.48 => ( exuI2
% 0.33/0.48 => ( inCongP
% 0.33/0.48 => ( in__Cong
% 0.33/0.48 => ( exuE3u
% 0.33/0.48 => ( exu__Cong
% 0.33/0.48 => ( emptyset__Cong
% 0.33/0.48 => ( setadjoin__Cong
% 0.33/0.48 => ( powerset__Cong
% 0.33/0.48 => ( setunion__Cong
% 0.33/0.48 => ( omega__Cong
% 0.33/0.48 => ( exuEu
% 0.33/0.48 => ( descr__Cong
% 0.33/0.48 => ( dsetconstr__Cong
% 0.33/0.48 => ( subsetI1
% 0.33/0.48 => ( eqimpsubset2
% 0.33/0.48 => ( eqimpsubset1
% 0.33/0.48 => ( subsetI2
% 0.33/0.48 => ( emptysetsubset
% 0.33/0.48 => ( subsetE
% 0.33/0.48 => ( subsetE2
% 0.33/0.48 => ( notsubsetI
% 0.33/0.48 => ( notequalI1
% 0.33/0.48 => ( notequalI2
% 0.33/0.48 => ( subsetRefl
% 0.33/0.48 => ( subsetTrans
% 0.33/0.48 => ( setadjoinSub
% 0.33/0.48 => ( setadjoinSub2
% 0.33/0.48 => ( subset2powerset
% 0.33/0.48 => ( setextsub
% 0.33/0.48 => ( subsetemptysetimpeq
% 0.33/0.48 => ( powersetI1
% 0.33/0.48 => ( powersetE1
% 0.33/0.48 => ( inPowerset
% 0.33/0.48 => ( powersetsubset
% 0.33/0.48 => ( sepInPowerset
% 0.33/0.48 => ( sepSubset
% 0.33/0.48 => ( binunionIL
% 0.33/0.48 => ( upairset2IR
% 0.33/0.48 => ( binunionIR
% 0.33/0.48 => ( binunionEcases
% 0.33/0.48 => ( binunionE
% 0.33/0.48 => ( binunionLsub
% 0.33/0.48 => ( binunionRsub
% 0.33/0.48 => ( binintersectI
% 0.33/0.48 => ( binintersectSubset5
% 0.33/0.48 => ( binintersectEL
% 0.33/0.48 => ( binintersectLsub
% 0.33/0.48 => ( binintersectSubset2
% 0.33/0.48 => ( binintersectSubset3
% 0.33/0.48 => ( binintersectER
% 0.33/0.48 => ( disjointsetsI1
% 0.33/0.48 => ( binintersectRsub
% 0.33/0.48 => ( binintersectSubset4
% 0.33/0.48 => ( binintersectSubset1
% 0.33/0.48 => ( bs114d
% 0.33/0.48 => ( setminusI
% 0.33/0.48 => ( setminusEL
% 0.33/0.48 => ( setminusER
% 0.33/0.48 => ( setminusSubset2
% 0.33/0.48 => ( setminusERneg
% 0.33/0.48 => ( setminusELneg
% 0.33/0.48 => ( setminusILneg
% 0.33/0.48 => ( setminusIRneg
% 0.33/0.48 => ( setminusLsub
% 0.33/0.48 => ( setminusSubset1
% 0.33/0.48 => ( symdiffE
% 0.33/0.48 => ( symdiffI1
% 0.33/0.48 => ( symdiffI2
% 0.33/0.48 => ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.48 ( ( in @ Xx @ A )
% 0.33/0.48 => ( ( in @ Xx @ B )
% 0.33/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 %------------------------------------------------------------------------------
% 0.33/0.48 ------------------------
% 2.52/1.65 ---- Embedded in THF ---
% 2.52/1.66 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.52/1.66 %%% Generated on Tue Feb 24 12:29:23 EST 2026
% 2.52/1.66 %%% using '$$dhol' embedding, version 1.3.0.
% 2.52/1.66 %%% Logic specification used:
% 2.52/1.66 %%% thf(spec, logic, $$dhol).
% 2.52/1.66
% 2.52/1.66 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2DTF10053.p
% See solution above
% 2.52/1.66 ------------------------
% 2.52/1.68 ---- Cleaned THF ---
% 2.52/1.68 thf(in_type,type,
% 2.52/1.68 in: $i > $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(exu_type,type,
% 2.52/1.68 exu: ( $i > $o ) > $o ).
% 2.52/1.68
% 2.52/1.68 thf(exu,definition,
% 2.52/1.68 ( exu
% 2.52/1.68 = ( ^ [Xphi: $i > $o] :
% 2.52/1.68 ? [Xx: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 & ! [Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setextAx_type,type,
% 2.52/1.68 setextAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setextAx,definition,
% 2.52/1.68 ( setextAx
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 <=> ( in @ Xx @ B ) )
% 2.52/1.68 => ( A = B ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyset_type,type,
% 2.52/1.68 emptyset: $i ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetAx_type,type,
% 2.52/1.68 emptysetAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetAx,definition,
% 2.52/1.68 ( emptysetAx
% 2.52/1.68 = ( ! [Xx: $i] :
% 2.52/1.68 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoin_type,type,
% 2.52/1.68 setadjoin: $i > $i > $i ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinAx_type,type,
% 2.52/1.68 setadjoinAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinAx,definition,
% 2.52/1.68 ( setadjoinAx
% 2.52/1.68 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.68 <=> ( ( Xy = Xx )
% 2.52/1.68 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(powerset_type,type,
% 2.52/1.68 powerset: $i > $i ).
% 2.52/1.68
% 2.52/1.68 thf(powersetAx_type,type,
% 2.52/1.68 powersetAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(powersetAx,definition,
% 2.52/1.68 ( powersetAx
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( in @ B @ ( powerset @ A ) )
% 2.52/1.68 <=> ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setunion_type,type,
% 2.52/1.68 setunion: $i > $i ).
% 2.52/1.68
% 2.52/1.68 thf(setunionAx_type,type,
% 2.52/1.68 setunionAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setunionAx,definition,
% 2.52/1.68 ( setunionAx
% 2.52/1.68 = ( ! [A: $i,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ ( setunion @ A ) )
% 2.52/1.68 <=> ? [B: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 & ( in @ B @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(omega_type,type,
% 2.52/1.68 omega: $i ).
% 2.52/1.68
% 2.52/1.68 thf(omega0Ax_type,type,
% 2.52/1.68 omega0Ax: $o ).
% 2.52/1.68
% 2.52/1.68 thf(omega0Ax,definition,
% 2.52/1.68 ( omega0Ax
% 2.52/1.68 = ( in @ emptyset @ omega ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(omegaSAx_type,type,
% 2.52/1.68 omegaSAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(omegaSAx,definition,
% 2.52/1.68 ( omegaSAx
% 2.52/1.68 = ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ omega )
% 2.52/1.68 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(omegaIndAx_type,type,
% 2.52/1.68 omegaIndAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(omegaIndAx,definition,
% 2.52/1.68 ( omegaIndAx
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ( ( in @ emptyset @ A )
% 2.52/1.68 & ! [Xx: $i] :
% 2.52/1.68 ( ( ( in @ Xx @ omega )
% 2.52/1.68 & ( in @ Xx @ A ) )
% 2.52/1.68 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.52/1.68 => ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ omega )
% 2.52/1.68 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(replAx_type,type,
% 2.52/1.68 replAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(replAx,definition,
% 2.52/1.68 ( replAx
% 2.52/1.68 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( exu
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.52/1.68 => ? [B: $i] :
% 2.52/1.68 ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 <=> ? [Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ A )
% 2.52/1.68 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(foundationAx_type,type,
% 2.52/1.68 foundationAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(foundationAx,definition,
% 2.52/1.68 ( foundationAx
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.52/1.68 => ? [B: $i] :
% 2.52/1.68 ( ( in @ B @ A )
% 2.52/1.68 & ~ ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(wellorderingAx_type,type,
% 2.52/1.68 wellorderingAx: $o ).
% 2.52/1.68
% 2.52/1.68 thf(wellorderingAx,definition,
% 2.52/1.68 ( wellorderingAx
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ? [B: $i] :
% 2.52/1.68 ( ! [C: $i] :
% 2.52/1.68 ( ( in @ C @ B )
% 2.52/1.68 => ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ C )
% 2.52/1.68 => ( in @ Xx @ A ) ) )
% 2.52/1.68 & ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( ( in @ Xx @ A )
% 2.52/1.68 & ( in @ Xy @ A ) )
% 2.52/1.68 => ( ! [C: $i] :
% 2.52/1.68 ( ( in @ C @ B )
% 2.52/1.68 => ( ( in @ Xx @ C )
% 2.52/1.68 <=> ( in @ Xy @ C ) ) )
% 2.52/1.68 => ( Xx = Xy ) ) )
% 2.52/1.68 & ! [C: $i,D: $i] :
% 2.52/1.68 ( ( ( in @ C @ B )
% 2.52/1.68 & ( in @ D @ B ) )
% 2.52/1.68 => ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ C )
% 2.52/1.68 => ( in @ Xx @ D ) )
% 2.52/1.68 | ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ D )
% 2.52/1.68 => ( in @ Xx @ C ) ) ) )
% 2.52/1.68 & ! [C: $i] :
% 2.52/1.68 ( ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ C )
% 2.52/1.68 => ( in @ Xx @ A ) )
% 2.52/1.68 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.52/1.68 => ? [D: $i,Xx: $i] :
% 2.52/1.68 ( ( in @ D @ B )
% 2.52/1.68 & ( in @ Xx @ C )
% 2.52/1.68 & ~ ? [Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ D )
% 2.52/1.68 & ( in @ Xy @ C ) )
% 2.52/1.68 & ! [E: $i] :
% 2.52/1.68 ( ( in @ E @ B )
% 2.52/1.68 => ( ! [Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ E )
% 2.52/1.68 => ( in @ Xy @ D ) )
% 2.52/1.68 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(descr_type,type,
% 2.52/1.68 descr: ( $i > $o ) > $i ).
% 2.52/1.68
% 2.52/1.68 thf(descrp_type,type,
% 2.52/1.68 descrp: $o ).
% 2.52/1.68
% 2.52/1.68 thf(descrp,definition,
% 2.52/1.68 ( descrp
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ( Xphi
% 2.52/1.68 @ ( descr
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstr_type,type,
% 2.52/1.68 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrI_type,type,
% 2.52/1.68 dsetconstrI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrI,definition,
% 2.52/1.68 ( dsetconstrI
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( ( Xphi @ Xx )
% 2.52/1.68 => ( in @ Xx
% 2.52/1.68 @ ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrEL_type,type,
% 2.52/1.68 dsetconstrEL: $o ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrEL,definition,
% 2.52/1.68 ( dsetconstrEL
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx
% 2.52/1.68 @ ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.68 => ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrER_type,type,
% 2.52/1.68 dsetconstrER: $o ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstrER,definition,
% 2.52/1.68 ( dsetconstrER
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx
% 2.52/1.68 @ ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.68 => ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuE1_type,type,
% 2.52/1.68 exuE1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuE1,definition,
% 2.52/1.68 ( exuE1
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ? [Xx: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 & ! [Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(prop2set_type,type,
% 2.52/1.68 prop2set: $o > $i ).
% 2.52/1.68
% 2.52/1.68 thf(prop2setE_type,type,
% 2.52/1.68 prop2setE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(prop2setE,definition,
% 2.52/1.68 ( prop2setE
% 2.52/1.68 = ( ! [Xphi: $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.52/1.68 => Xphi ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetE_type,type,
% 2.52/1.68 emptysetE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetE,definition,
% 2.52/1.68 ( emptysetE
% 2.52/1.68 = ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ emptyset )
% 2.52/1.68 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetimpfalse_type,type,
% 2.52/1.68 emptysetimpfalse: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptysetimpfalse,definition,
% 2.52/1.68 ( emptysetimpfalse
% 2.52/1.68 = ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ emptyset )
% 2.52/1.68 => $false ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(notinemptyset_type,type,
% 2.52/1.68 notinemptyset: $o ).
% 2.52/1.68
% 2.52/1.68 thf(notinemptyset,definition,
% 2.52/1.68 ( notinemptyset
% 2.52/1.68 = ( ! [Xx: $i] :
% 2.52/1.68 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuE3e_type,type,
% 2.52/1.68 exuE3e: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuE3e,definition,
% 2.52/1.68 ( exuE3e
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setext_type,type,
% 2.52/1.68 setext: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setext,definition,
% 2.52/1.68 ( setext
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( in @ Xx @ B ) )
% 2.52/1.68 => ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 => ( in @ Xx @ A ) )
% 2.52/1.68 => ( A = B ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyI_type,type,
% 2.52/1.68 emptyI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyI,definition,
% 2.52/1.68 ( emptyI
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ~ ( in @ Xx @ A )
% 2.52/1.68 => ( A = emptyset ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(noeltsimpempty_type,type,
% 2.52/1.68 noeltsimpempty: $o ).
% 2.52/1.68
% 2.52/1.68 thf(noeltsimpempty,definition,
% 2.52/1.68 ( noeltsimpempty
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ~ ( in @ Xx @ A )
% 2.52/1.68 => ( A = emptyset ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setbeta_type,type,
% 2.52/1.68 setbeta: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setbeta,definition,
% 2.52/1.68 ( setbeta
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( ( in @ Xx
% 2.52/1.68 @ ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.52/1.68 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(nonempty_type,type,
% 2.52/1.68 nonempty: $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(nonempty,definition,
% 2.52/1.68 ( nonempty
% 2.52/1.68 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyE1_type,type,
% 2.52/1.68 nonemptyE1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyE1,definition,
% 2.52/1.68 ( nonemptyE1
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ( nonempty @ A )
% 2.52/1.68 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyI_type,type,
% 2.52/1.68 nonemptyI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyI,definition,
% 2.52/1.68 ( nonemptyI
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( ( Xphi @ Xx )
% 2.52/1.68 => ( nonempty
% 2.52/1.68 @ ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyI1_type,type,
% 2.52/1.68 nonemptyI1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyI1,definition,
% 2.52/1.68 ( nonemptyI1
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.52/1.68 => ( nonempty @ A ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinIL_type,type,
% 2.52/1.68 setadjoinIL: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinIL,definition,
% 2.52/1.68 ( setadjoinIL
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyinunitempty_type,type,
% 2.52/1.68 emptyinunitempty: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyinunitempty,definition,
% 2.52/1.68 ( emptyinunitempty
% 2.52/1.68 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinIR_type,type,
% 2.52/1.68 setadjoinIR: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinIR,definition,
% 2.52/1.68 ( setadjoinIR
% 2.52/1.68 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ A )
% 2.52/1.68 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinE_type,type,
% 2.52/1.68 setadjoinE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinE,definition,
% 2.52/1.68 ( setadjoinE
% 2.52/1.68 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.68 => ! [Xphi: $o] :
% 2.52/1.68 ( ( ( Xy = Xx )
% 2.52/1.68 => Xphi )
% 2.52/1.68 => ( ( ( in @ Xy @ A )
% 2.52/1.68 => Xphi )
% 2.52/1.68 => Xphi ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinOr_type,type,
% 2.52/1.68 setadjoinOr: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoinOr,definition,
% 2.52/1.68 ( setadjoinOr
% 2.52/1.68 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.52/1.68 => ( ( Xy = Xx )
% 2.52/1.68 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setoftrueEq_type,type,
% 2.52/1.68 setoftrueEq: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setoftrueEq,definition,
% 2.52/1.68 ( setoftrueEq
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xx: $i] : $true )
% 2.52/1.68 = A ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(powersetI_type,type,
% 2.52/1.68 powersetI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(powersetI,definition,
% 2.52/1.68 ( powersetI
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 => ( in @ Xx @ A ) )
% 2.52/1.68 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyinPowerset_type,type,
% 2.52/1.68 emptyinPowerset: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyinPowerset,definition,
% 2.52/1.68 ( emptyinPowerset
% 2.52/1.68 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyInPowerset_type,type,
% 2.52/1.68 emptyInPowerset: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyInPowerset,definition,
% 2.52/1.68 ( emptyInPowerset
% 2.52/1.68 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(powersetE_type,type,
% 2.52/1.68 powersetE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(powersetE,definition,
% 2.52/1.68 ( powersetE
% 2.52/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.68 ( ( in @ B @ ( powerset @ A ) )
% 2.52/1.68 => ( ( in @ Xx @ B )
% 2.52/1.68 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setunionI_type,type,
% 2.52/1.68 setunionI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setunionI,definition,
% 2.52/1.68 ( setunionI
% 2.52/1.68 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 => ( ( in @ B @ A )
% 2.52/1.68 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setunionE_type,type,
% 2.52/1.68 setunionE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setunionE,definition,
% 2.52/1.68 ( setunionE
% 2.52/1.68 = ( ! [A: $i,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ ( setunion @ A ) )
% 2.52/1.68 => ! [Xphi: $o] :
% 2.52/1.68 ( ! [B: $i] :
% 2.52/1.68 ( ( in @ Xx @ B )
% 2.52/1.68 => ( ( in @ B @ A )
% 2.52/1.68 => Xphi ) )
% 2.52/1.68 => Xphi ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(subPowSU_type,type,
% 2.52/1.68 subPowSU: $o ).
% 2.52/1.68
% 2.52/1.68 thf(subPowSU,definition,
% 2.52/1.68 ( subPowSU
% 2.52/1.68 = ( ! [A: $i,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuE2_type,type,
% 2.52/1.68 exuE2: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuE2,definition,
% 2.52/1.68 ( exuE2
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ? [Xx: $i] :
% 2.52/1.68 ! [Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xy )
% 2.52/1.68 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyImpWitness_type,type,
% 2.52/1.68 nonemptyImpWitness: $o ).
% 2.52/1.68
% 2.52/1.68 thf(nonemptyImpWitness,definition,
% 2.52/1.68 ( nonemptyImpWitness
% 2.52/1.68 = ( ! [A: $i] :
% 2.52/1.68 ( ( nonempty @ A )
% 2.52/1.68 => ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & $true ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(uniqinunit_type,type,
% 2.52/1.68 uniqinunit: $o ).
% 2.52/1.68
% 2.52/1.68 thf(uniqinunit,definition,
% 2.52/1.68 ( uniqinunit
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.52/1.68 => ( Xx = Xy ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(notinsingleton_type,type,
% 2.52/1.68 notinsingleton: $o ).
% 2.52/1.68
% 2.52/1.68 thf(notinsingleton,definition,
% 2.52/1.68 ( notinsingleton
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx != Xy )
% 2.52/1.68 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(eqinunit_type,type,
% 2.52/1.68 eqinunit: $o ).
% 2.52/1.68
% 2.52/1.68 thf(eqinunit,definition,
% 2.52/1.68 ( eqinunit
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(singletonsswitch_type,type,
% 2.52/1.68 singletonsswitch: $o ).
% 2.52/1.68
% 2.52/1.68 thf(singletonsswitch,definition,
% 2.52/1.68 ( singletonsswitch
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.52/1.68 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetE_type,type,
% 2.52/1.68 upairsetE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetE,definition,
% 2.52/1.68 ( upairsetE
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.52/1.68 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.52/1.68 => ( ( Xz = Xx )
% 2.52/1.68 | ( Xz = Xy ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetIL_type,type,
% 2.52/1.68 upairsetIL: $o ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetIL,definition,
% 2.52/1.68 ( upairsetIL
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetIR_type,type,
% 2.52/1.68 upairsetIR: $o ).
% 2.52/1.68
% 2.52/1.68 thf(upairsetIR,definition,
% 2.52/1.68 ( upairsetIR
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyE1_type,type,
% 2.52/1.68 emptyE1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyE1,definition,
% 2.52/1.68 ( emptyE1
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ( Xphi @ Xx ) )
% 2.52/1.68 => ( ( ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 = emptyset )
% 2.52/1.68 => $false ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(vacuousDall_type,type,
% 2.52/1.68 vacuousDall: $o ).
% 2.52/1.68
% 2.52/1.68 thf(vacuousDall,definition,
% 2.52/1.68 ( vacuousDall
% 2.52/1.68 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ emptyset )
% 2.52/1.68 => ( Xphi @ Xx ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan1_type,type,
% 2.52/1.68 quantDeMorgan1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan1,definition,
% 2.52/1.68 ( quantDeMorgan1
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ~ ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( Xphi @ Xx ) )
% 2.52/1.68 => ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan2_type,type,
% 2.52/1.68 quantDeMorgan2: $o ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan2,definition,
% 2.52/1.68 ( quantDeMorgan2
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ~ ( Xphi @ Xx ) )
% 2.52/1.68 => ~ ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan3_type,type,
% 2.52/1.68 quantDeMorgan3: $o ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan3,definition,
% 2.52/1.68 ( quantDeMorgan3
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ~ ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ( Xphi @ Xx ) )
% 2.52/1.68 => ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan4_type,type,
% 2.52/1.68 quantDeMorgan4: $o ).
% 2.52/1.68
% 2.52/1.68 thf(quantDeMorgan4,definition,
% 2.52/1.68 ( quantDeMorgan4
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ~ ( Xphi @ Xx ) )
% 2.52/1.68 => ~ ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(prop2setI_type,type,
% 2.52/1.68 prop2setI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(prop2setI,definition,
% 2.52/1.68 ( prop2setI
% 2.52/1.68 = ( ! [Xphi: $o] :
% 2.52/1.68 ( Xphi
% 2.52/1.68 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(set2prop_type,type,
% 2.52/1.68 set2prop: $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(prop2set2propI_type,type,
% 2.52/1.68 prop2set2propI: $o ).
% 2.52/1.68
% 2.52/1.68 thf(prop2set2propI,definition,
% 2.52/1.68 ( prop2set2propI
% 2.52/1.68 = ( ! [Xphi: $o] :
% 2.52/1.68 ( Xphi
% 2.52/1.68 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(notdexE_type,type,
% 2.52/1.68 notdexE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(notdexE,definition,
% 2.52/1.68 ( notdexE
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ~ ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ( Xphi @ Xx ) )
% 2.52/1.68 => ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(notdallE_type,type,
% 2.52/1.68 notdallE: $o ).
% 2.52/1.68
% 2.52/1.68 thf(notdallE,definition,
% 2.52/1.68 ( notdallE
% 2.52/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.68 ( ~ ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( Xphi @ Xx ) )
% 2.52/1.68 => ? [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuI1_type,type,
% 2.52/1.68 exuI1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuI1,definition,
% 2.52/1.68 ( exuI1
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ? [Xx: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 & ! [Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) )
% 2.52/1.68 => ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuI3_type,type,
% 2.52/1.68 exuI3: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuI3,definition,
% 2.52/1.68 ( exuI3
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.52/1.68 => ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 => ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) )
% 2.52/1.68 => ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuI2_type,type,
% 2.52/1.68 exuI2: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuI2,definition,
% 2.52/1.68 ( exuI2
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ? [Xx: $i] :
% 2.52/1.68 ! [Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xy )
% 2.52/1.68 <=> ( Xy = Xx ) )
% 2.52/1.68 => ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(inCongP_type,type,
% 2.52/1.68 inCongP: $o ).
% 2.52/1.68
% 2.52/1.68 thf(inCongP,definition,
% 2.52/1.68 ( inCongP
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( A = B )
% 2.52/1.68 => ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ( ( in @ Xx @ A )
% 2.52/1.68 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(in__Cong_type,type,
% 2.52/1.68 in__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(in__Cong,definition,
% 2.52/1.68 ( in__Cong
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( A = B )
% 2.52/1.68 => ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ( ( in @ Xx @ A )
% 2.52/1.68 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuE3u_type,type,
% 2.52/1.68 exuE3u: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuE3u,definition,
% 2.52/1.68 ( exuE3u
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 => ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exu__Cong_type,type,
% 2.52/1.68 exu__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exu__Cong,definition,
% 2.52/1.68 ( exu__Cong
% 2.52/1.68 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.68 ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ( ( Xphi @ Xx )
% 2.52/1.68 <=> ( Xpsi @ Xy ) ) )
% 2.52/1.68 => ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 <=> ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(emptyset__Cong_type,type,
% 2.52/1.68 emptyset__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(emptyset__Cong,definition,
% 2.52/1.68 ( emptyset__Cong
% 2.52/1.68 = ( emptyset = emptyset ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoin__Cong_type,type,
% 2.52/1.68 setadjoin__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setadjoin__Cong,definition,
% 2.52/1.68 ( setadjoin__Cong
% 2.52/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ! [Xz: $i,Xu: $i] :
% 2.52/1.68 ( ( Xz = Xu )
% 2.52/1.68 => ( ( setadjoin @ Xx @ Xz )
% 2.52/1.68 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(powerset__Cong_type,type,
% 2.52/1.68 powerset__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(powerset__Cong,definition,
% 2.52/1.68 ( powerset__Cong
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( A = B )
% 2.52/1.68 => ( ( powerset @ A )
% 2.52/1.68 = ( powerset @ B ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(setunion__Cong_type,type,
% 2.52/1.68 setunion__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(setunion__Cong,definition,
% 2.52/1.68 ( setunion__Cong
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( A = B )
% 2.52/1.68 => ( ( setunion @ A )
% 2.52/1.68 = ( setunion @ B ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(omega__Cong_type,type,
% 2.52/1.68 omega__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(omega__Cong,definition,
% 2.52/1.68 ( omega__Cong
% 2.52/1.68 = ( omega = omega ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(exuEu_type,type,
% 2.52/1.68 exuEu: $o ).
% 2.52/1.68
% 2.52/1.68 thf(exuEu,definition,
% 2.52/1.68 ( exuEu
% 2.52/1.68 = ( ! [Xphi: $i > $o] :
% 2.52/1.68 ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xphi @ Xx )
% 2.52/1.68 => ( ( Xphi @ Xy )
% 2.52/1.68 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(descr__Cong_type,type,
% 2.52/1.68 descr__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(descr__Cong,definition,
% 2.52/1.68 ( descr__Cong
% 2.52/1.68 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.68 ( ! [Xx: $i,Xy: $i] :
% 2.52/1.68 ( ( Xx = Xy )
% 2.52/1.68 => ( ( Xphi @ Xx )
% 2.52/1.68 <=> ( Xpsi @ Xy ) ) )
% 2.52/1.68 => ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 => ( ( exu
% 2.52/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.52/1.68 => ( ( descr
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 = ( descr
% 2.52/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstr__Cong_type,type,
% 2.52/1.68 dsetconstr__Cong: $o ).
% 2.52/1.68
% 2.52/1.68 thf(dsetconstr__Cong,definition,
% 2.52/1.68 ( dsetconstr__Cong
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ( A = B )
% 2.52/1.68 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ! [Xy: $i] :
% 2.52/1.68 ( ( in @ Xy @ B )
% 2.52/1.68 => ( ( Xx = Xy )
% 2.52/1.68 => ( ( Xphi @ Xx )
% 2.52/1.68 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.52/1.68 => ( ( dsetconstr @ A
% 2.52/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.68 = ( dsetconstr @ B
% 2.52/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.52/1.68
% 2.52/1.68 thf(subset_type,type,
% 2.52/1.68 subset: $i > $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(disjoint_type,type,
% 2.52/1.68 disjoint: $i > $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(setsmeet_type,type,
% 2.52/1.68 setsmeet: $i > $i > $o ).
% 2.52/1.68
% 2.52/1.68 thf(subsetI1_type,type,
% 2.52/1.68 subsetI1: $o ).
% 2.52/1.68
% 2.52/1.68 thf(subsetI1,definition,
% 2.52/1.68 ( subsetI1
% 2.52/1.68 = ( ! [A: $i,B: $i] :
% 2.52/1.68 ( ! [Xx: $i] :
% 2.52/1.68 ( ( in @ Xx @ A )
% 2.52/1.68 => ( in @ Xx @ B ) )
% 2.52/1.69 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(eqimpsubset2_type,type,
% 2.52/1.69 eqimpsubset2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(eqimpsubset2,definition,
% 2.52/1.69 ( eqimpsubset2
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( A = B )
% 2.52/1.69 => ( subset @ B @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(eqimpsubset1_type,type,
% 2.52/1.69 eqimpsubset1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(eqimpsubset1,definition,
% 2.52/1.69 ( eqimpsubset1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( A = B )
% 2.52/1.69 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetI2_type,type,
% 2.52/1.69 subsetI2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetI2,definition,
% 2.52/1.69 ( subsetI2
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ! [Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( in @ Xx @ B ) )
% 2.52/1.69 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(emptysetsubset_type,type,
% 2.52/1.69 emptysetsubset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(emptysetsubset,definition,
% 2.52/1.69 ( emptysetsubset
% 2.52/1.69 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetE_type,type,
% 2.52/1.69 subsetE: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetE,definition,
% 2.52/1.69 ( subsetE
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ( in @ Xx @ A )
% 2.52/1.69 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetE2_type,type,
% 2.52/1.69 subsetE2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetE2,definition,
% 2.52/1.69 ( subsetE2
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(notsubsetI_type,type,
% 2.52/1.69 notsubsetI: $o ).
% 2.52/1.69
% 2.52/1.69 thf(notsubsetI,definition,
% 2.52/1.69 ( notsubsetI
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(notequalI1_type,type,
% 2.52/1.69 notequalI1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(notequalI1,definition,
% 2.52/1.69 ( notequalI1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ~ ( subset @ A @ B )
% 2.52/1.69 => ( A != B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(notequalI2_type,type,
% 2.52/1.69 notequalI2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(notequalI2,definition,
% 2.52/1.69 ( notequalI2
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ( A != B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetRefl_type,type,
% 2.52/1.69 subsetRefl: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetRefl,definition,
% 2.52/1.69 ( subsetRefl
% 2.52/1.69 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetTrans_type,type,
% 2.52/1.69 subsetTrans: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetTrans,definition,
% 2.52/1.69 ( subsetTrans
% 2.52/1.69 = ( ! [A: $i,B: $i,C: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ( subset @ B @ C )
% 2.52/1.69 => ( subset @ A @ C ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setadjoinSub_type,type,
% 2.52/1.69 setadjoinSub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setadjoinSub,definition,
% 2.52/1.69 ( setadjoinSub
% 2.52/1.69 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setadjoinSub2_type,type,
% 2.52/1.69 setadjoinSub2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setadjoinSub2,definition,
% 2.52/1.69 ( setadjoinSub2
% 2.52/1.69 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subset2powerset_type,type,
% 2.52/1.69 subset2powerset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subset2powerset,definition,
% 2.52/1.69 ( subset2powerset
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setextsub_type,type,
% 2.52/1.69 setextsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setextsub,definition,
% 2.52/1.69 ( setextsub
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ( subset @ B @ A )
% 2.52/1.69 => ( A = B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(subsetemptysetimpeq_type,type,
% 2.52/1.69 subsetemptysetimpeq: $o ).
% 2.52/1.69
% 2.52/1.69 thf(subsetemptysetimpeq,definition,
% 2.52/1.69 ( subsetemptysetimpeq
% 2.52/1.69 = ( ! [A: $i] :
% 2.52/1.69 ( ( subset @ A @ emptyset )
% 2.52/1.69 => ( A = emptyset ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(powersetI1_type,type,
% 2.52/1.69 powersetI1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(powersetI1,definition,
% 2.52/1.69 ( powersetI1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ B @ A )
% 2.52/1.69 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(powersetE1_type,type,
% 2.52/1.69 powersetE1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(powersetE1,definition,
% 2.52/1.69 ( powersetE1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( in @ B @ ( powerset @ A ) )
% 2.52/1.69 => ( subset @ B @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(inPowerset_type,type,
% 2.52/1.69 inPowerset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(inPowerset,definition,
% 2.52/1.69 ( inPowerset
% 2.52/1.69 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(powersetsubset_type,type,
% 2.52/1.69 powersetsubset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(powersetsubset,definition,
% 2.52/1.69 ( powersetsubset
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(sepInPowerset_type,type,
% 2.52/1.69 sepInPowerset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(sepInPowerset,definition,
% 2.52/1.69 ( sepInPowerset
% 2.52/1.69 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.69 ( in
% 2.52/1.69 @ ( dsetconstr @ A
% 2.52/1.69 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.69 @ ( powerset @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(sepSubset_type,type,
% 2.52/1.69 sepSubset: $o ).
% 2.52/1.69
% 2.52/1.69 thf(sepSubset,definition,
% 2.52/1.69 ( sepSubset
% 2.52/1.69 = ( ! [A: $i,Xphi: $i > $o] :
% 2.52/1.69 ( subset
% 2.52/1.69 @ ( dsetconstr @ A
% 2.52/1.69 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.52/1.69 @ A ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunion_type,type,
% 2.52/1.69 binunion: $i > $i > $i ).
% 2.52/1.69
% 2.52/1.69 thf(binunionIL_type,type,
% 2.52/1.69 binunionIL: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionIL,definition,
% 2.52/1.69 ( binunionIL
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(upairset2IR_type,type,
% 2.52/1.69 upairset2IR: $o ).
% 2.52/1.69
% 2.52/1.69 thf(upairset2IR,definition,
% 2.52/1.69 ( upairset2IR
% 2.52/1.69 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunionIR_type,type,
% 2.52/1.69 binunionIR: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionIR,definition,
% 2.52/1.69 ( binunionIR
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ B )
% 2.52/1.69 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunionEcases_type,type,
% 2.52/1.69 binunionEcases: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionEcases,definition,
% 2.52/1.69 ( binunionEcases
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.52/1.69 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.52/1.69 => ( ( ( in @ Xx @ A )
% 2.52/1.69 => Xphi )
% 2.52/1.69 => ( ( ( in @ Xx @ B )
% 2.52/1.69 => Xphi )
% 2.52/1.69 => Xphi ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunionE_type,type,
% 2.52/1.69 binunionE: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionE,definition,
% 2.52/1.69 ( binunionE
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.52/1.69 => ( ( in @ Xx @ A )
% 2.52/1.69 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunionLsub_type,type,
% 2.52/1.69 binunionLsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionLsub,definition,
% 2.52/1.69 ( binunionLsub
% 2.52/1.69 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binunionRsub_type,type,
% 2.52/1.69 binunionRsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binunionRsub,definition,
% 2.52/1.69 ( binunionRsub
% 2.52/1.69 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersect_type,type,
% 2.52/1.69 binintersect: $i > $i > $i ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectI_type,type,
% 2.52/1.69 binintersectI: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectI,definition,
% 2.52/1.69 ( binintersectI
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ( in @ Xx @ B )
% 2.52/1.69 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset5_type,type,
% 2.52/1.69 binintersectSubset5: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset5,definition,
% 2.52/1.69 ( binintersectSubset5
% 2.52/1.69 = ( ! [A: $i,B: $i,C: $i] :
% 2.52/1.69 ( ( subset @ C @ A )
% 2.52/1.69 => ( ( subset @ C @ B )
% 2.52/1.69 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectEL_type,type,
% 2.52/1.69 binintersectEL: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectEL,definition,
% 2.52/1.69 ( binintersectEL
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.52/1.69 => ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectLsub_type,type,
% 2.52/1.69 binintersectLsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectLsub,definition,
% 2.52/1.69 ( binintersectLsub
% 2.52/1.69 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset2_type,type,
% 2.52/1.69 binintersectSubset2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset2,definition,
% 2.52/1.69 ( binintersectSubset2
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ( binintersect @ A @ B )
% 2.52/1.69 = A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset3_type,type,
% 2.52/1.69 binintersectSubset3: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset3,definition,
% 2.52/1.69 ( binintersectSubset3
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( ( binintersect @ A @ B )
% 2.52/1.69 = B )
% 2.52/1.69 => ( subset @ B @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectER_type,type,
% 2.52/1.69 binintersectER: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectER,definition,
% 2.52/1.69 ( binintersectER
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.52/1.69 => ( in @ Xx @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(disjointsetsI1_type,type,
% 2.52/1.69 disjointsetsI1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(disjointsetsI1,definition,
% 2.52/1.69 ( disjointsetsI1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ~ ? [Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 & ( in @ Xx @ B ) )
% 2.52/1.69 => ( ( binintersect @ A @ B )
% 2.52/1.69 = emptyset ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectRsub_type,type,
% 2.52/1.69 binintersectRsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectRsub,definition,
% 2.52/1.69 ( binintersectRsub
% 2.52/1.69 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset4_type,type,
% 2.52/1.69 binintersectSubset4: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset4,definition,
% 2.52/1.69 ( binintersectSubset4
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ B @ A )
% 2.52/1.69 => ( ( binintersect @ A @ B )
% 2.52/1.69 = B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset1_type,type,
% 2.52/1.69 binintersectSubset1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(binintersectSubset1,definition,
% 2.52/1.69 ( binintersectSubset1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( ( binintersect @ A @ B )
% 2.52/1.69 = A )
% 2.52/1.69 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(bs114d_type,type,
% 2.52/1.69 bs114d: $o ).
% 2.52/1.69
% 2.52/1.69 thf(bs114d,definition,
% 2.52/1.69 ( bs114d
% 2.52/1.69 = ( ! [A: $i,B: $i,C: $i] :
% 2.52/1.69 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.52/1.69 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(regular_type,type,
% 2.52/1.69 regular: $i > $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminus_type,type,
% 2.52/1.69 setminus: $i > $i > $i ).
% 2.52/1.69
% 2.52/1.69 thf(setminusI_type,type,
% 2.52/1.69 setminusI: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusI,definition,
% 2.52/1.69 ( setminusI
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusEL_type,type,
% 2.52/1.69 setminusEL: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusEL,definition,
% 2.52/1.69 ( setminusEL
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.52/1.69 => ( in @ Xx @ A ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusER_type,type,
% 2.52/1.69 setminusER: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusER,definition,
% 2.52/1.69 ( setminusER
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.52/1.69 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusSubset2_type,type,
% 2.52/1.69 setminusSubset2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusSubset2,definition,
% 2.52/1.69 ( setminusSubset2
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( subset @ A @ B )
% 2.52/1.69 => ( ( setminus @ A @ B )
% 2.52/1.69 = emptyset ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusERneg_type,type,
% 2.52/1.69 setminusERneg: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusERneg,definition,
% 2.52/1.69 ( setminusERneg
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.52/1.69 => ( ( in @ Xx @ A )
% 2.52/1.69 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusELneg_type,type,
% 2.52/1.69 setminusELneg: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusELneg,definition,
% 2.52/1.69 ( setminusELneg
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusILneg_type,type,
% 2.52/1.69 setminusILneg: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusILneg,definition,
% 2.52/1.69 ( setminusILneg
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ~ ( in @ Xx @ A )
% 2.52/1.69 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusIRneg_type,type,
% 2.52/1.69 setminusIRneg: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusIRneg,definition,
% 2.52/1.69 ( setminusIRneg
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ B )
% 2.52/1.69 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusLsub_type,type,
% 2.52/1.69 setminusLsub: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusLsub,definition,
% 2.52/1.69 ( setminusLsub
% 2.52/1.69 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(setminusSubset1_type,type,
% 2.52/1.69 setminusSubset1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(setminusSubset1,definition,
% 2.52/1.69 ( setminusSubset1
% 2.52/1.69 = ( ! [A: $i,B: $i] :
% 2.52/1.69 ( ( ( setminus @ A @ B )
% 2.52/1.69 = emptyset )
% 2.52/1.69 => ( subset @ A @ B ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(symdiff_type,type,
% 2.52/1.69 symdiff: $i > $i > $i ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffE_type,type,
% 2.52/1.69 symdiffE: $o ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffE,definition,
% 2.52/1.69 ( symdiffE
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.52/1.69 => ! [Xphi: $o] :
% 2.52/1.69 ( ( ( in @ Xx @ A )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => Xphi ) )
% 2.52/1.69 => ( ( ~ ( in @ Xx @ A )
% 2.52/1.69 => ( ( in @ Xx @ B )
% 2.52/1.69 => Xphi ) )
% 2.52/1.69 => Xphi ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffI1_type,type,
% 2.52/1.69 symdiffI1: $o ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffI1,definition,
% 2.52/1.69 ( symdiffI1
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ~ ( in @ Xx @ B )
% 2.52/1.69 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffI2_type,type,
% 2.52/1.69 symdiffI2: $o ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffI2,definition,
% 2.52/1.69 ( symdiffI2
% 2.52/1.69 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ~ ( in @ Xx @ A )
% 2.52/1.69 => ( ( in @ Xx @ B )
% 2.52/1.69 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.52/1.69
% 2.52/1.69 thf(symdiffIneg1,conjecture,
% 2.52/1.69 ( setextAx
% 2.52/1.69 => ( emptysetAx
% 2.52/1.69 => ( setadjoinAx
% 2.52/1.69 => ( powersetAx
% 2.52/1.69 => ( setunionAx
% 2.52/1.69 => ( omega0Ax
% 2.52/1.69 => ( omegaSAx
% 2.52/1.69 => ( omegaIndAx
% 2.52/1.69 => ( replAx
% 2.52/1.69 => ( foundationAx
% 2.52/1.69 => ( wellorderingAx
% 2.52/1.69 => ( descrp
% 2.52/1.69 => ( dsetconstrI
% 2.52/1.69 => ( dsetconstrEL
% 2.52/1.69 => ( dsetconstrER
% 2.52/1.69 => ( exuE1
% 2.52/1.69 => ( prop2setE
% 2.52/1.69 => ( emptysetE
% 2.52/1.69 => ( emptysetimpfalse
% 2.52/1.69 => ( notinemptyset
% 2.52/1.69 => ( exuE3e
% 2.52/1.69 => ( setext
% 2.52/1.69 => ( emptyI
% 2.52/1.69 => ( noeltsimpempty
% 2.52/1.69 => ( setbeta
% 2.52/1.69 => ( nonemptyE1
% 2.52/1.69 => ( nonemptyI
% 2.52/1.69 => ( nonemptyI1
% 2.52/1.69 => ( setadjoinIL
% 2.52/1.69 => ( emptyinunitempty
% 2.52/1.69 => ( setadjoinIR
% 2.52/1.69 => ( setadjoinE
% 2.52/1.69 => ( setadjoinOr
% 2.52/1.69 => ( setoftrueEq
% 2.52/1.69 => ( powersetI
% 2.52/1.69 => ( emptyinPowerset
% 2.52/1.69 => ( emptyInPowerset
% 2.52/1.69 => ( powersetE
% 2.52/1.69 => ( setunionI
% 2.52/1.69 => ( setunionE
% 2.52/1.69 => ( subPowSU
% 2.52/1.69 => ( exuE2
% 2.52/1.69 => ( nonemptyImpWitness
% 2.52/1.69 => ( uniqinunit
% 2.52/1.69 => ( notinsingleton
% 2.52/1.69 => ( eqinunit
% 2.52/1.69 => ( singletonsswitch
% 2.52/1.69 => ( upairsetE
% 2.52/1.69 => ( upairsetIL
% 2.52/1.69 => ( upairsetIR
% 2.52/1.69 => ( emptyE1
% 2.52/1.69 => ( vacuousDall
% 2.52/1.69 => ( quantDeMorgan1
% 2.52/1.69 => ( quantDeMorgan2
% 2.52/1.69 => ( quantDeMorgan3
% 2.52/1.69 => ( quantDeMorgan4
% 2.52/1.69 => ( prop2setI
% 2.52/1.69 => ( prop2set2propI
% 2.52/1.69 => ( notdexE
% 2.52/1.69 => ( notdallE
% 2.52/1.69 => ( exuI1
% 2.52/1.69 => ( exuI3
% 2.52/1.69 => ( exuI2
% 2.52/1.69 => ( inCongP
% 2.52/1.69 => ( in__Cong
% 2.52/1.69 => ( exuE3u
% 2.52/1.69 => ( exu__Cong
% 2.52/1.69 => ( emptyset__Cong
% 2.52/1.69 => ( setadjoin__Cong
% 2.52/1.69 => ( powerset__Cong
% 2.52/1.69 => ( setunion__Cong
% 2.52/1.69 => ( omega__Cong
% 2.52/1.69 => ( exuEu
% 2.52/1.69 => ( descr__Cong
% 2.52/1.69 => ( dsetconstr__Cong
% 2.52/1.69 => ( subsetI1
% 2.52/1.69 => ( eqimpsubset2
% 2.52/1.69 => ( eqimpsubset1
% 2.52/1.69 => ( subsetI2
% 2.52/1.69 => ( emptysetsubset
% 2.52/1.69 => ( subsetE
% 2.52/1.69 => ( subsetE2
% 2.52/1.69 => ( notsubsetI
% 2.52/1.69 => ( notequalI1
% 2.52/1.69 => ( notequalI2
% 2.52/1.69 => ( subsetRefl
% 2.52/1.69 => ( subsetTrans
% 2.52/1.69 => ( setadjoinSub
% 2.52/1.69 => ( setadjoinSub2
% 2.52/1.69 => ( subset2powerset
% 2.52/1.69 => ( setextsub
% 2.52/1.69 => ( subsetemptysetimpeq
% 2.52/1.69 => ( powersetI1
% 2.52/1.69 => ( powersetE1
% 2.52/1.69 => ( inPowerset
% 2.52/1.69 => ( powersetsubset
% 2.52/1.69 => ( sepInPowerset
% 2.52/1.69 => ( sepSubset
% 2.52/1.69 => ( binunionIL
% 2.52/1.69 => ( upairset2IR
% 2.52/1.69 => ( binunionIR
% 2.52/1.69 => ( binunionEcases
% 2.52/1.69 => ( binunionE
% 2.52/1.69 => ( binunionLsub
% 2.52/1.69 => ( binunionRsub
% 2.52/1.69 => ( binintersectI
% 2.52/1.69 => ( binintersectSubset5
% 2.52/1.69 => ( binintersectEL
% 2.52/1.69 => ( binintersectLsub
% 2.52/1.69 => ( binintersectSubset2
% 2.52/1.69 => ( binintersectSubset3
% 2.52/1.69 => ( binintersectER
% 2.52/1.69 => ( disjointsetsI1
% 2.52/1.69 => ( binintersectRsub
% 2.52/1.69 => ( binintersectSubset4
% 2.52/1.69 => ( binintersectSubset1
% 2.52/1.69 => ( bs114d
% 2.52/1.69 => ( setminusI
% 2.52/1.69 => ( setminusEL
% 2.52/1.69 => ( setminusER
% 2.52/1.69 => ( setminusSubset2
% 2.52/1.69 => ( setminusERneg
% 2.52/1.69 => ( setminusELneg
% 2.52/1.69 => ( setminusILneg
% 2.52/1.69 => ( setminusIRneg
% 2.52/1.69 => ( setminusLsub
% 2.52/1.69 => ( setminusSubset1
% 2.52/1.69 => ( symdiffE
% 2.52/1.69 => ( symdiffI1
% 2.52/1.69 => ( symdiffI2
% 2.52/1.69 => ! [A: $i,B: $i,Xx: $i] :
% 2.52/1.69 ( ( in @ Xx @ A )
% 2.52/1.69 => ( ( in @ Xx @ B )
% 2.52/1.69 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.52/1.69 ------------------------
% 2.70/1.71 % (10208)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/183Mi)
% 2.70/1.71 % (10209)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_10053 for (2999ds/4Mi)
% 2.70/1.71 % (10212)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_10053 for (2999ds/2Mi)
% 2.70/1.71 % (10210)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_10053 for (2999ds/27Mi)
% 2.70/1.71 % (10213)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_10053 for (2999ds/275Mi)
% 2.70/1.71 % (10214)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/18Mi)
% 2.70/1.71 % (10211)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/2Mi)
% 2.70/1.71 % (10211)Instruction limit reached!
% 2.70/1.71 % (10211)------------------------------
% 2.70/1.71 % (10211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.71 % (10211)Termination reason: Unknown
% 2.70/1.71 % (10211)Termination phase: shuffling
% 2.70/1.71
% 2.70/1.71 % (10211)Memory used [KB]: 1151
% 2.70/1.71 % (10211)Time elapsed: 0.003 s
% 2.70/1.71 % (10211)Instructions burned: 2 (million)
% 2.70/1.71 % (10211)------------------------------
% 2.70/1.71 % (10211)------------------------------
% 2.70/1.71 % (10212)Instruction limit reached!
% 2.70/1.71 % (10212)------------------------------
% 2.70/1.71 % (10212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.71 % (10212)Termination reason: Unknown
% 2.70/1.71 % (10212)Termination phase: shuffling
% 2.70/1.71
% 2.70/1.71 % (10212)Memory used [KB]: 1151
% 2.70/1.71 % (10212)Time elapsed: 0.003 s
% 2.70/1.71 % (10212)Instructions burned: 3 (million)
% 2.70/1.71 % (10212)------------------------------
% 2.70/1.71 % (10212)------------------------------
% 2.70/1.71 % (10209)Instruction limit reached!
% 2.70/1.71 % (10209)------------------------------
% 2.70/1.71 % (10209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.71 % (10209)Termination reason: Unknown
% 2.70/1.71 % (10209)Termination phase: shuffling
% 2.70/1.71
% 2.70/1.71 % (10209)Memory used [KB]: 1279
% 2.70/1.71 % (10209)Time elapsed: 0.004 s
% 2.70/1.71 % (10209)Instructions burned: 4 (million)
% 2.70/1.71 % (10209)------------------------------
% 2.70/1.71 % (10209)------------------------------
% 2.70/1.72 % (10214)Instruction limit reached!
% 2.70/1.72 % (10214)------------------------------
% 2.70/1.72 % (10214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.72 % (10214)Termination reason: Unknown
% 2.70/1.72 % (10214)Termination phase: Preprocessing 3
% 2.70/1.72
% 2.70/1.72 % (10214)Memory used [KB]: 1535
% 2.70/1.72 % (10214)Time elapsed: 0.011 s
% 2.70/1.72 % (10214)Instructions burned: 19 (million)
% 2.70/1.72 % (10214)------------------------------
% 2.70/1.72 % (10214)------------------------------
% 2.70/1.72 % (10210)Instruction limit reached!
% 2.70/1.72 % (10210)------------------------------
% 2.70/1.72 % (10210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.72 % (10210)Termination reason: Unknown
% 2.70/1.72 % (10210)Termination phase: Property scanning
% 2.70/1.72
% 2.70/1.72 % (10210)Memory used [KB]: 1663
% 2.70/1.72 % (10210)Time elapsed: 0.015 s
% 2.70/1.72 % (10210)Instructions burned: 28 (million)
% 2.70/1.72 % (10210)------------------------------
% 2.70/1.72 % (10210)------------------------------
% 2.70/1.73 % (10215)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/3Mi)
% 2.70/1.73 % (10216)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_10053 for (2999ds/37Mi)
% 2.70/1.73 % (10217)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_10053 for (2999ds/15Mi)
% 2.70/1.73 % (10215)Instruction limit reached!
% 2.70/1.73 % (10215)------------------------------
% 2.70/1.73 % (10215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.73 % (10215)Termination reason: Unknown
% 2.70/1.73 % (10215)Termination phase: shuffling
% 2.70/1.73
% 2.70/1.73 % (10215)Memory used [KB]: 1151
% 2.70/1.73 % (10215)Time elapsed: 0.003 s
% 2.70/1.73 % (10215)Instructions burned: 3 (million)
% 2.70/1.73 % (10215)------------------------------
% 2.70/1.73 % (10215)------------------------------
% 2.70/1.74 % (10217)Instruction limit reached!
% 2.70/1.74 % (10217)------------------------------
% 2.70/1.74 % (10217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.74 % (10218)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_10053 for (2999ds/3Mi)
% 2.70/1.74 % (10217)Termination reason: Unknown
% 2.70/1.74 % (10217)Termination phase: Property scanning
% 2.70/1.74
% 2.70/1.74 % (10217)Memory used [KB]: 1407
% 2.70/1.74 % (10217)Time elapsed: 0.009 s
% 2.70/1.74 % (10217)Instructions burned: 16 (million)
% 2.70/1.74 % (10217)------------------------------
% 2.70/1.74 % (10217)------------------------------
% 2.70/1.74 % (10218)Instruction limit reached!
% 2.70/1.74 % (10218)------------------------------
% 2.70/1.74 % (10218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.74 % (10218)Termination reason: Unknown
% 2.70/1.74 % (10218)Termination phase: shuffling
% 2.70/1.74
% 2.70/1.74 % (10218)Memory used [KB]: 1279
% 2.70/1.74 % (10218)Time elapsed: 0.003 s
% 2.70/1.74 % (10218)Instructions burned: 3 (million)
% 2.70/1.74 % (10218)------------------------------
% 2.70/1.74 % (10218)------------------------------
% 2.70/1.74 % (10219)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_10053 for (2999ds/1041Mi)
% 2.70/1.74 % (10216)Instruction limit reached!
% 2.70/1.74 % (10216)------------------------------
% 2.70/1.74 % (10216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.74 % (10216)Termination reason: Unknown
% 2.70/1.74 % (10216)Termination phase: Property scanning
% 2.70/1.74
% 2.70/1.74 % (10216)Memory used [KB]: 1663
% 2.70/1.74 % (10216)Time elapsed: 0.018 s
% 2.70/1.74 % (10216)Instructions burned: 37 (million)
% 2.70/1.74 % (10216)------------------------------
% 2.70/1.74 % (10216)------------------------------
% 2.70/1.75 % (10220)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/7Mi)
% 2.70/1.75 % (10220)Instruction limit reached!
% 2.70/1.75 % (10220)------------------------------
% 2.70/1.75 % (10220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.75 % (10220)Termination reason: Unknown
% 2.70/1.75 % (10220)Termination phase: shuffling
% 2.70/1.75
% 2.70/1.75 % (10220)Memory used [KB]: 1279
% 2.70/1.75 % (10220)Time elapsed: 0.005 s
% 2.70/1.75 % (10220)Instructions burned: 8 (million)
% 2.70/1.75 % (10220)------------------------------
% 2.70/1.75 % (10220)------------------------------
% 2.70/1.75 % (10221)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/16Mi)
% 2.70/1.75 % (10222)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_10053 for (2999ds/3Mi)
% 2.70/1.75 % (10222)Instruction limit reached!
% 2.70/1.75 % (10222)------------------------------
% 2.70/1.75 % (10222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.75 % (10222)Termination reason: Unknown
% 2.70/1.75 % (10222)Termination phase: shuffling
% 2.70/1.75
% 2.70/1.75 % (10222)Memory used [KB]: 1279
% 2.70/1.75 % (10222)Time elapsed: 0.003 s
% 2.70/1.75 % (10222)Instructions burned: 3 (million)
% 2.70/1.75 % (10222)------------------------------
% 2.70/1.75 % (10222)------------------------------
% 2.70/1.76 % (10221)Instruction limit reached!
% 2.70/1.76 % (10221)------------------------------
% 2.70/1.76 % (10221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.76 % (10221)Termination reason: Unknown
% 2.70/1.76 % (10221)Termination phase: shuffling
% 2.70/1.76
% 2.70/1.76 % (10221)Memory used [KB]: 1535
% 2.70/1.76 % (10221)Time elapsed: 0.009 s
% 2.70/1.76 % (10221)Instructions burned: 17 (million)
% 2.70/1.76 % (10221)------------------------------
% 2.70/1.76 % (10221)------------------------------
% 2.70/1.76 % (10223)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_10053 for (2999ds/3Mi)
% 2.70/1.76 % (10223)Instruction limit reached!
% 2.70/1.76 % (10223)------------------------------
% 2.70/1.76 % (10223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.76 % (10223)Termination reason: Unknown
% 2.70/1.76 % (10223)Termination phase: shuffling
% 2.70/1.76
% 2.70/1.76 % (10223)Memory used [KB]: 1279
% 2.70/1.76 % (10223)Time elapsed: 0.003 s
% 2.70/1.76 % (10223)Instructions burned: 3 (million)
% 2.70/1.76 % (10223)------------------------------
% 2.70/1.76 % (10223)------------------------------
% 2.70/1.76 % (10224)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/7Mi)
% 2.70/1.77 % (10224)Instruction limit reached!
% 2.70/1.77 % (10224)------------------------------
% 2.70/1.77 % (10224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.77 % (10224)Termination reason: Unknown
% 2.70/1.77 % (10224)Termination phase: shuffling
% 2.70/1.77
% 2.70/1.77 % (10224)Memory used [KB]: 1279
% 2.70/1.77 % (10224)Time elapsed: 0.005 s
% 2.70/1.77 % (10224)Instructions burned: 8 (million)
% 2.70/1.77 % (10224)------------------------------
% 2.70/1.77 % (10224)------------------------------
% 2.70/1.77 % (10225)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/3Mi)
% 2.70/1.77 % (10225)Instruction limit reached!
% 2.70/1.77 % (10225)------------------------------
% 2.70/1.77 % (10225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.77 % (10225)Termination reason: Unknown
% 2.70/1.77 % (10225)Termination phase: shuffling
% 2.70/1.77
% 2.70/1.77 % (10225)Memory used [KB]: 1279
% 2.70/1.77 % (10225)Time elapsed: 0.003 s
% 2.70/1.77 % (10225)Instructions burned: 4 (million)
% 2.70/1.77 % (10225)------------------------------
% 2.70/1.77 % (10225)------------------------------
% 2.70/1.78 % (10226)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/4Mi)
% 2.70/1.78 % (10226)Instruction limit reached!
% 2.70/1.78 % (10226)------------------------------
% 2.70/1.78 % (10226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.78 % (10226)Termination reason: Unknown
% 2.70/1.78 % (10226)Termination phase: shuffling
% 2.70/1.78
% 2.70/1.78 % (10226)Memory used [KB]: 1279
% 2.70/1.78 % (10226)Time elapsed: 0.003 s
% 2.70/1.78 % (10226)Instructions burned: 4 (million)
% 2.70/1.78 % (10226)------------------------------
% 2.70/1.78 % (10226)------------------------------
% 2.70/1.78 % (10227)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/18Mi)
% 2.70/1.78 % (10228)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/710Mi)
% 2.70/1.79 % (10227)Instruction limit reached!
% 2.70/1.79 % (10227)------------------------------
% 2.70/1.79 % (10227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.79 % (10227)Termination reason: Unknown
% 2.70/1.79 % (10227)Termination phase: shuffling
% 2.70/1.79
% 2.70/1.79 % (10227)Memory used [KB]: 1535
% 2.70/1.79 % (10227)Time elapsed: 0.010 s
% 2.70/1.79 % (10227)Instructions burned: 19 (million)
% 2.70/1.79 % (10227)------------------------------
% 2.70/1.79 % (10227)------------------------------
% 2.70/1.79 % (10229)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/6Mi)
% 2.70/1.79 % (10229)Instruction limit reached!
% 2.70/1.79 % (10229)------------------------------
% 2.70/1.79 % (10229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.79 % (10229)Termination reason: Unknown
% 2.70/1.79 % (10229)Termination phase: shuffling
% 2.70/1.79
% 2.70/1.79 % (10229)Memory used [KB]: 1279
% 2.70/1.79 % (10229)Time elapsed: 0.004 s
% 2.70/1.79 % (10229)Instructions burned: 6 (million)
% 2.70/1.79 % (10229)------------------------------
% 2.70/1.79 % (10229)------------------------------
% 2.70/1.79 % (10230)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_10053 for (2999ds/902Mi)
% 2.70/1.80 % (10208)Instruction limit reached!
% 2.70/1.80 % (10208)------------------------------
% 2.70/1.80 % (10208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.80 % (10208)Termination reason: Unknown
% 2.70/1.80 % (10208)Termination phase: Saturation
% 2.70/1.80
% 2.70/1.80 % (10208)Memory used [KB]: 7036
% 2.70/1.80 % (10208)Time elapsed: 0.087 s
% 2.70/1.80 % (10208)Instructions burned: 183 (million)
% 2.70/1.80 % (10208)------------------------------
% 2.70/1.80 % (10208)------------------------------
% 2.70/1.80 % (10231)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_10053 for (2999ds/21Mi)
% 2.70/1.81 % (10232)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10053 for (2999ds/5Mi)
% 2.70/1.81 % (10232)Instruction limit reached!
% 2.70/1.81 % (10232)------------------------------
% 2.70/1.81 % (10232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.81 % (10232)Termination reason: Unknown
% 2.70/1.81 % (10232)Termination phase: shuffling
% 2.70/1.81
% 2.70/1.81 % (10232)Memory used [KB]: 1279
% 2.70/1.81 % (10232)Time elapsed: 0.004 s
% 2.70/1.81 % (10232)Instructions burned: 6 (million)
% 2.70/1.81 % (10232)------------------------------
% 2.70/1.81 % (10232)------------------------------
% 2.70/1.81 % (10231)Instruction limit reached!
% 2.70/1.81 % (10231)------------------------------
% 2.70/1.81 % (10231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.81 % (10231)Termination reason: Unknown
% 2.70/1.81 % (10231)Termination phase: Property scanning
% 2.70/1.81
% 2.70/1.81 % (10231)Memory used [KB]: 1663
% 2.70/1.81 % (10231)Time elapsed: 0.011 s
% 2.70/1.81 % (10231)Instructions burned: 21 (million)
% 2.70/1.81 % (10231)------------------------------
% 2.70/1.81 % (10231)------------------------------
% 2.70/1.81 % (10233)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_10053 for (2999ds/6Mi)
% 2.70/1.82 % (10233)Instruction limit reached!
% 2.70/1.82 % (10233)------------------------------
% 2.70/1.82 % (10233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.82 % (10233)Termination reason: Unknown
% 2.70/1.82 % (10233)Termination phase: shuffling
% 2.70/1.82
% 2.70/1.82 % (10233)Memory used [KB]: 1279
% 2.70/1.82 % (10233)Time elapsed: 0.005 s
% 2.70/1.82 % (10233)Instructions burned: 8 (million)
% 2.70/1.82 % (10233)------------------------------
% 2.70/1.82 % (10233)------------------------------
% 2.70/1.83 % (10234)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/377Mi)
% 2.70/1.83 % (10235)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_10053 for (2998ds/779Mi)
% 2.70/1.83 % (10236)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_10053 for (2998ds/19Mi)
% 2.70/1.84 % (10236)Instruction limit reached!
% 2.70/1.84 % (10236)------------------------------
% 2.70/1.84 % (10236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.84 % (10236)Termination reason: Unknown
% 2.70/1.84 % (10236)Termination phase: shuffling
% 2.70/1.84
% 2.70/1.84 % (10236)Memory used [KB]: 1663
% 2.70/1.84 % (10236)Time elapsed: 0.010 s
% 2.70/1.84 % (10236)Instructions burned: 19 (million)
% 2.70/1.84 % (10236)------------------------------
% 2.70/1.84 % (10236)------------------------------
% 2.70/1.85 % (10213)Instruction limit reached!
% 2.70/1.85 % (10213)------------------------------
% 2.70/1.85 % (10213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.85 % (10213)Termination reason: Unknown
% 2.70/1.85 % (10213)Termination phase: Saturation
% 2.70/1.85
% 2.70/1.85 % (10213)Memory used [KB]: 7931
% 2.70/1.85 % (10213)Time elapsed: 0.138 s
% 2.70/1.85 % (10213)Instructions burned: 276 (million)
% 2.70/1.85 % (10213)------------------------------
% 2.70/1.85 % (10213)------------------------------
% 2.70/1.86 % (10237)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/879Mi)
% 2.70/1.86 % (10230)Refutation not found, incomplete strategy
% 2.70/1.86 % (10230)------------------------------
% 2.70/1.86 % (10230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.86 % (10230)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.86
% 2.70/1.86
% 2.70/1.86 % (10230)Memory used [KB]: 7291
% 2.70/1.86 % (10230)Time elapsed: 0.066 s
% 2.70/1.86 % (10230)Instructions burned: 134 (million)
% 2.70/1.86 % (10230)------------------------------
% 2.70/1.86 % (10230)------------------------------
% 2.70/1.86 % (10238)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/17Mi)
% 2.70/1.87 % (10238)Instruction limit reached!
% 2.70/1.87 % (10238)------------------------------
% 2.70/1.87 % (10238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.87 % (10238)Termination reason: Unknown
% 2.70/1.87 % (10238)Termination phase: shuffling
% 2.70/1.87
% 2.70/1.87 % (10238)Memory used [KB]: 1407
% 2.70/1.87 % (10238)Time elapsed: 0.009 s
% 2.70/1.87 % (10238)Instructions burned: 17 (million)
% 2.70/1.87 % (10238)------------------------------
% 2.70/1.87 % (10238)------------------------------
% 2.70/1.87 % (10239)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/3Mi)
% 2.70/1.88 % (10239)Instruction limit reached!
% 2.70/1.88 % (10239)------------------------------
% 2.70/1.88 % (10239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.88 % (10239)Termination reason: Unknown
% 2.70/1.88 % (10239)Termination phase: shuffling
% 2.70/1.88
% 2.70/1.88 % (10239)Memory used [KB]: 1151
% 2.70/1.88 % (10239)Time elapsed: 0.003 s
% 2.70/1.88 % (10239)Instructions burned: 3 (million)
% 2.70/1.88 % (10239)------------------------------
% 2.70/1.88 % (10239)------------------------------
% 2.70/1.89 % (10240)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/30Mi)
% 2.70/1.89 % (10241)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/127Mi)
% 2.70/1.90 % (10240)Instruction limit reached!
% 2.70/1.90 % (10240)------------------------------
% 2.70/1.90 % (10240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.90 % (10240)Termination reason: Unknown
% 2.70/1.90 % (10240)Termination phase: Property scanning
% 2.70/1.90
% 2.70/1.90 % (10240)Memory used [KB]: 1663
% 2.70/1.90 % (10240)Time elapsed: 0.015 s
% 2.70/1.90 % (10240)Instructions burned: 30 (million)
% 2.70/1.90 % (10240)------------------------------
% 2.70/1.90 % (10240)------------------------------
% 2.70/1.92 % (10242)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10053 for (2998ds/100Mi)
% 2.70/1.95 % (10241)Instruction limit reached!
% 2.70/1.95 % (10241)------------------------------
% 2.70/1.95 % (10241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.95 % (10241)Termination reason: Unknown
% 2.70/1.95 % (10241)Termination phase: Saturation
% 2.70/1.95
% 2.70/1.95 % (10241)Memory used [KB]: 6780
% 2.70/1.95 % (10241)Time elapsed: 0.058 s
% 2.70/1.95 % (10241)Instructions burned: 127 (million)
% 2.70/1.95 % (10241)------------------------------
% 2.70/1.95 % (10241)------------------------------
% 2.70/1.96 % (10242)Instruction limit reached!
% 2.70/1.96 % (10242)------------------------------
% 2.70/1.96 % (10242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.96 % (10242)Termination reason: Unknown
% 2.70/1.96 % (10242)Termination phase: Saturation
% 2.70/1.96
% 2.70/1.96 % (10242)Memory used [KB]: 6396
% 2.70/1.96 % (10242)Time elapsed: 0.047 s
% 2.70/1.96 % (10242)Instructions burned: 100 (million)
% 2.70/1.96 % (10242)------------------------------
% 2.70/1.96 % (10242)------------------------------
% 2.70/1.97 % (10243)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_10053 for (2997ds/3Mi)
% 2.70/1.97 % (10243)Instruction limit reached!
% 2.70/1.97 % (10243)------------------------------
% 2.70/1.97 % (10243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.97 % (10243)Termination reason: Unknown
% 2.70/1.97 % (10243)Termination phase: shuffling
% 2.70/1.97
% 2.70/1.97 % (10243)Memory used [KB]: 1151
% 2.70/1.97 % (10243)Time elapsed: 0.003 s
% 2.70/1.97 % (10243)Instructions burned: 3 (million)
% 2.70/1.97 % (10243)------------------------------
% 2.70/1.97 % (10243)------------------------------
% 2.70/1.98 % (10244)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_10053 for (2997ds/20Mi)
% 2.70/1.98 % (10245)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_10053 for (2997ds/86Mi)
% 2.70/1.99 % (10244)Instruction limit reached!
% 2.70/1.99 % (10244)------------------------------
% 2.70/1.99 % (10244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.99 % (10244)Termination reason: Unknown
% 2.70/1.99 % (10244)Termination phase: SInE selection
% 2.70/1.99
% 2.70/1.99 % (10244)Memory used [KB]: 1407
% 2.70/1.99 % (10244)Time elapsed: 0.011 s
% 2.70/1.99 % (10244)Instructions burned: 21 (million)
% 2.70/1.99 % (10244)------------------------------
% 2.70/1.99 % (10244)------------------------------
% 2.70/2.00 % (10234)Refutation not found, non-redundant clauses discarded% (10234)------------------------------
% 2.70/2.00 % (10234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.00 % (10234)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.70/2.00
% 2.70/2.00 % (10234)Memory used [KB]: 7419
% 2.70/2.00 % (10234)Time elapsed: 0.178 s
% 2.70/2.00 % (10234)Instructions burned: 366 (million)
% 2.70/2.00 % (10234)------------------------------
% 2.70/2.00 % (10234)------------------------------
% 2.70/2.00 % (10246)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_10053 for (2997ds/107Mi)
% 2.70/2.02 % (10247)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_10053 for (2997ds/39Mi)
% 2.70/2.02 % (10245)Instruction limit reached!
% 2.70/2.02 % (10245)------------------------------
% 2.70/2.02 % (10245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/2.02 % (10245)Termination reason: Unknown
% 2.70/2.02 % (10245)Termination phase: Saturation
% 2.70/2.02
% 2.70/2.02 % (10245)Memory used [KB]: 6396
% 2.70/2.02 % (10245)Time elapsed: 0.040 s
% 2.70/2.02 % (10245)Instructions burned: 87 (million)
% 2.70/2.02 % (10245)------------------------------
% 2.70/2.02 % (10245)------------------------------
% 4.92/2.04 % (10247)Instruction limit reached!
% 4.92/2.04 % (10247)------------------------------
% 4.92/2.04 % (10247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.04 % (10247)Termination reason: Unknown
% 4.92/2.04 % (10247)Termination phase: Property scanning
% 4.92/2.04
% 4.92/2.04 % (10247)Memory used [KB]: 1663
% 4.92/2.04 % (10247)Time elapsed: 0.019 s
% 4.92/2.04 % (10247)Instructions burned: 39 (million)
% 4.92/2.04 % (10247)------------------------------
% 4.92/2.04 % (10247)------------------------------
% 4.92/2.04 % (10248)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_10053 for (2996ds/448Mi)
% 4.92/2.05 % (10246)Instruction limit reached!
% 4.92/2.05 % (10246)------------------------------
% 4.92/2.05 % (10246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.05 % (10246)Termination reason: Unknown
% 4.92/2.05 % (10246)Termination phase: Saturation
% 4.92/2.05
% 4.92/2.05 % (10246)Memory used [KB]: 6652
% 4.92/2.05 % (10246)Time elapsed: 0.049 s
% 4.92/2.05 % (10246)Instructions burned: 108 (million)
% 4.92/2.05 % (10246)------------------------------
% 4.92/2.05 % (10246)------------------------------
% 4.92/2.05 % (10249)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_10053 for (2996ds/46Mi)
% 4.92/2.07 % (10250)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_10053 for (2996ds/98Mi)
% 4.92/2.07 % (10249)Instruction limit reached!
% 4.92/2.07 % (10249)------------------------------
% 4.92/2.07 % (10249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.07 % (10249)Termination reason: Unknown
% 4.92/2.07 % (10249)Termination phase: Property scanning
% 4.92/2.07
% 4.92/2.07 % (10249)Memory used [KB]: 1663
% 4.92/2.07 % (10249)Time elapsed: 0.022 s
% 4.92/2.07 % (10249)Instructions burned: 47 (million)
% 4.92/2.07 % (10249)------------------------------
% 4.92/2.07 % (10249)------------------------------
% 4.92/2.09 % (10251)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_10053 for (2996ds/507Mi)
% 4.92/2.11 % (10235)Instruction limit reached!
% 4.92/2.11 % (10235)------------------------------
% 4.92/2.11 % (10235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.11 % (10235)Termination reason: Unknown
% 4.92/2.11 % (10235)Termination phase: Saturation
% 4.92/2.11
% 4.92/2.11 % (10235)Memory used [KB]: 6524
% 4.92/2.11 % (10235)Time elapsed: 0.280 s
% 4.92/2.11 % (10235)Instructions burned: 779 (million)
% 4.92/2.11 % (10235)------------------------------
% 4.92/2.11 % (10235)------------------------------
% 4.92/2.11 % (10250)Instruction limit reached!
% 4.92/2.11 % (10250)------------------------------
% 4.92/2.11 % (10250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.11 % (10250)Termination reason: Unknown
% 4.92/2.11 % (10250)Termination phase: Saturation
% 4.92/2.11
% 4.92/2.11 % (10250)Memory used [KB]: 1791
% 4.92/2.11 % (10250)Time elapsed: 0.043 s
% 4.92/2.11 % (10250)Instructions burned: 99 (million)
% 4.92/2.11 % (10250)------------------------------
% 4.92/2.11 % (10250)------------------------------
% 4.92/2.11 % (10228)Refutation not found, non-redundant clauses discarded% (10228)------------------------------
% 4.92/2.11 % (10228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.11 % (10228)Termination reason: Refutation not found, non-redundant clauses discarded
% 4.92/2.11
% 4.92/2.11 % (10228)Memory used [KB]: 8699
% 4.92/2.11 % (10228)Time elapsed: 0.331 s
% 4.92/2.11 % (10228)Instructions burned: 659 (million)
% 4.92/2.11 % (10228)------------------------------
% 4.92/2.11 % (10228)------------------------------
% 4.92/2.12 % (10252)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_10053 for (2995ds/149Mi)
% 4.92/2.12 % (10219)Instruction limit reached!
% 4.92/2.12 % (10219)------------------------------
% 4.92/2.12 % (10219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.92/2.12 % (10219)Termination reason: Unknown
% 4.92/2.12 % (10219)Termination phase: Saturation
% 4.92/2.12
% 4.92/2.12 % (10219)Memory used [KB]: 8699
% 4.92/2.12 % (10219)Time elapsed: 0.385 s
% 4.92/2.12 % (10219)Instructions burned: 1041 (million)
% 4.92/2.12 % (10219)------------------------------
% 4.92/2.12 % (10219)------------------------------
% 4.92/2.12 % (10253)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10053 for (2995ds/39Mi)
% 5.50/2.13 % (10254)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_10053 for (2995ds/6Mi)
% 5.50/2.13 % (10254)Instruction limit reached!
% 5.50/2.13 % (10254)------------------------------
% 5.50/2.13 % (10254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.13 % (10254)Termination reason: Unknown
% 5.50/2.13 % (10254)Termination phase: shuffling
% 5.50/2.13
% 5.50/2.13 % (10254)Memory used [KB]: 1279
% 5.50/2.13 % (10254)Time elapsed: 0.004 s
% 5.50/2.13 % (10254)Instructions burned: 6 (million)
% 5.50/2.13 % (10254)------------------------------
% 5.50/2.13 % (10254)------------------------------
% 5.50/2.14 % (10255)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_10053 for (2995ds/1087Mi)
% 5.50/2.14 % (10253)Instruction limit reached!
% 5.50/2.14 % (10253)------------------------------
% 5.50/2.14 % (10253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.14 % (10253)Termination reason: Unknown
% 5.50/2.14 % (10253)Termination phase: Property scanning
% 5.50/2.14
% 5.50/2.14 % (10253)Memory used [KB]: 1663
% 5.50/2.14 % (10253)Time elapsed: 0.019 s
% 5.50/2.14 % (10253)Instructions burned: 40 (million)
% 5.50/2.14 % (10253)------------------------------
% 5.50/2.14 % (10253)------------------------------
% 5.50/2.15 % (10256)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10053 for (2995ds/47Mi)
% 5.50/2.16 % (10257)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_10053 for (2995ds/44Mi)
% 5.50/2.17 % (10256)Instruction limit reached!
% 5.50/2.17 % (10256)------------------------------
% 5.50/2.17 % (10256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.17 % (10256)Termination reason: Unknown
% 5.50/2.17 % (10256)Termination phase: Property scanning
% 5.50/2.17
% 5.50/2.17 % (10256)Memory used [KB]: 1791
% 5.50/2.17 % (10256)Time elapsed: 0.022 s
% 5.50/2.17 % (10256)Instructions burned: 47 (million)
% 5.50/2.17 % (10256)------------------------------
% 5.50/2.17 % (10256)------------------------------
% 5.50/2.18 % (10257)Instruction limit reached!
% 5.50/2.18 % (10257)------------------------------
% 5.50/2.18 % (10257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.18 % (10257)Termination reason: Unknown
% 5.50/2.18 % (10257)Termination phase: Property scanning
% 5.50/2.18
% 5.50/2.18 % (10257)Memory used [KB]: 1663
% 5.50/2.18 % (10257)Time elapsed: 0.021 s
% 5.50/2.18 % (10257)Instructions burned: 45 (million)
% 5.50/2.18 % (10257)------------------------------
% 5.50/2.18 % (10257)------------------------------
% 5.50/2.19 % (10258)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_10053 for (2995ds/432Mi)
% 5.50/2.19 % (10259)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10053 for (2995ds/62Mi)
% 5.50/2.19 % (10252)Instruction limit reached!
% 5.50/2.19 % (10252)------------------------------
% 5.50/2.19 % (10252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.19 % (10252)Termination reason: Unknown
% 5.50/2.19 % (10252)Termination phase: Saturation
% 5.50/2.19
% 5.50/2.19 % (10252)Memory used [KB]: 6908
% 5.50/2.19 % (10252)Time elapsed: 0.074 s
% 5.50/2.19 % (10252)Instructions burned: 150 (million)
% 5.50/2.19 % (10252)------------------------------
% 5.50/2.19 % (10252)------------------------------
% 5.78/2.20 % (10248)Instruction limit reached!
% 5.78/2.20 % (10248)------------------------------
% 5.78/2.20 % (10248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.20 % (10248)Termination reason: Unknown
% 5.78/2.20 % (10248)Termination phase: Saturation
% 5.78/2.20
% 5.78/2.20 % (10248)Memory used [KB]: 6524
% 5.78/2.20 % (10248)Time elapsed: 0.167 s
% 5.78/2.20 % (10248)Instructions burned: 449 (million)
% 5.78/2.20 % (10248)------------------------------
% 5.78/2.20 % (10248)------------------------------
% 5.78/2.21 % (10260)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_10053 for (2995ds/31Mi)
% 5.78/2.22 % (10261)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10053 for (2994ds/96Mi)
% 5.78/2.22 % (10259)Instruction limit reached!
% 5.78/2.22 % (10259)------------------------------
% 5.78/2.22 % (10259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.22 % (10259)Termination reason: Unknown
% 5.78/2.22 % (10259)Termination phase: Saturation
% 5.78/2.22
% 5.78/2.22 % (10259)Memory used [KB]: 1663
% 5.78/2.22 % (10259)Time elapsed: 0.028 s
% 5.78/2.22 % (10259)Instructions burned: 62 (million)
% 5.78/2.22 % (10259)------------------------------
% 5.78/2.22 % (10259)------------------------------
% 5.78/2.23 % (10260)Instruction limit reached!
% 5.78/2.23 % (10260)------------------------------
% 5.78/2.23 % (10260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.23 % (10260)Termination reason: Unknown
% 5.78/2.23 % (10260)Termination phase: Preprocessing 2
% 5.78/2.23
% 5.78/2.23 % (10260)Memory used [KB]: 1663
% 5.78/2.23 % (10260)Time elapsed: 0.016 s
% 5.78/2.23 % (10260)Instructions burned: 31 (million)
% 5.78/2.23 % (10260)------------------------------
% 5.78/2.23 % (10260)------------------------------
% 5.78/2.24 % (10262)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_10053 for (2994ds/453Mi)
% 5.78/2.24 % (10263)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_10053 for (2994ds/71Mi)
% 5.78/2.26 % (10261)Instruction limit reached!
% 5.78/2.26 % (10261)------------------------------
% 5.78/2.26 % (10261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.26 % (10261)Termination reason: Unknown
% 5.78/2.26 % (10261)Termination phase: Saturation
% 5.78/2.26
% 5.78/2.26 % (10261)Memory used [KB]: 6652
% 5.78/2.26 % (10261)Time elapsed: 0.045 s
% 5.78/2.26 % (10261)Instructions burned: 98 (million)
% 5.78/2.26 % (10261)------------------------------
% 5.78/2.26 % (10261)------------------------------
% 5.78/2.27 % (10263)Instruction limit reached!
% 5.78/2.27 % (10263)------------------------------
% 5.78/2.27 % (10263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.27 % (10263)Termination reason: Unknown
% 5.78/2.27 % (10263)Termination phase: Saturation
% 5.78/2.27
% 5.78/2.27 % (10263)Memory used [KB]: 6268
% 5.78/2.27 % (10263)Time elapsed: 0.033 s
% 5.78/2.27 % (10263)Instructions burned: 72 (million)
% 5.78/2.27 % (10263)------------------------------
% 5.78/2.27 % (10263)------------------------------
% 5.78/2.28 % (10264)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10053 for (2994ds/83Mi)
% 5.78/2.29 % (10265)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10053 for (2994ds/11Mi)
% 5.78/2.29 % (10265)Instruction limit reached!
% 5.78/2.29 % (10265)------------------------------
% 5.78/2.29 % (10265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.29 % (10265)Termination reason: Unknown
% 5.78/2.29 % (10265)Termination phase: shuffling
% 5.78/2.29
% 5.78/2.29 % (10265)Memory used [KB]: 1407
% 5.78/2.29 % (10265)Time elapsed: 0.006 s
% 5.78/2.29 % (10265)Instructions burned: 11 (million)
% 5.78/2.29 % (10265)------------------------------
% 5.78/2.29 % (10265)------------------------------
% 5.78/2.29 % (10237)Instruction limit reached!
% 5.78/2.29 % (10237)------------------------------
% 5.78/2.29 % (10237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.29 % (10237)Termination reason: Unknown
% 5.78/2.29 % (10237)Termination phase: Saturation
% 5.78/2.29
% 5.78/2.29 % (10237)Memory used [KB]: 7931
% 5.78/2.29 % (10237)Time elapsed: 0.440 s
% 5.78/2.29 % (10237)Instructions burned: 879 (million)
% 5.78/2.29 % (10237)------------------------------
% 5.78/2.29 % (10237)------------------------------
% 6.27/2.31 % (10266)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_10053 for (2994ds/41Mi)
% 6.27/2.31 % (10267)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10053 for (2994ds/6Mi)
% 6.27/2.31 % (10267)Instruction limit reached!
% 6.27/2.31 % (10267)------------------------------
% 6.27/2.31 % (10267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.31 % (10267)Termination reason: Unknown
% 6.27/2.31 % (10267)Termination phase: shuffling
% 6.27/2.31
% 6.27/2.31 % (10267)Memory used [KB]: 1279
% 6.27/2.31 % (10267)Time elapsed: 0.005 s
% 6.27/2.31 % (10267)Instructions burned: 7 (million)
% 6.27/2.31 % (10267)------------------------------
% 6.27/2.31 % (10267)------------------------------
% 6.27/2.31 % (10264)Instruction limit reached!
% 6.27/2.31 % (10264)------------------------------
% 6.27/2.31 % (10264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.31 % (10264)Termination reason: Unknown
% 6.27/2.31 % (10264)Termination phase: Saturation
% 6.27/2.31
% 6.27/2.31 % (10264)Memory used [KB]: 6268
% 6.27/2.31 % (10264)Time elapsed: 0.038 s
% 6.27/2.31 % (10264)Instructions burned: 84 (million)
% 6.27/2.31 % (10264)------------------------------
% 6.27/2.31 % (10264)------------------------------
% 6.27/2.33 % (10266)Instruction limit reached!
% 6.27/2.33 % (10266)------------------------------
% 6.27/2.33 % (10266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.33 % (10266)Termination reason: Unknown
% 6.27/2.33 % (10266)Termination phase: Property scanning
% 6.27/2.33
% 6.27/2.33 % (10266)Memory used [KB]: 1663
% 6.27/2.33 % (10266)Time elapsed: 0.020 s
% 6.27/2.33 % (10266)Instructions burned: 41 (million)
% 6.27/2.33 % (10266)------------------------------
% 6.27/2.33 % (10266)------------------------------
% 6.27/2.33 % (10268)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10053 for (2993ds/150Mi)
% 6.27/2.33 % (10269)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10053 for (2993ds/343Mi)
% 6.27/2.33 % (10251)Instruction limit reached!
% 6.27/2.33 % (10251)------------------------------
% 6.27/2.33 % (10251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.33 % (10251)Termination reason: Unknown
% 6.27/2.33 % (10251)Termination phase: Saturation
% 6.27/2.33
% 6.27/2.33 % (10251)Memory used [KB]: 7164
% 6.27/2.33 % (10251)Time elapsed: 0.244 s
% 6.27/2.33 % (10251)Instructions burned: 508 (million)
% 6.27/2.33 % (10251)------------------------------
% 6.27/2.33 % (10251)------------------------------
% 6.27/2.34 % (10270)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_10053 for (2993ds/109Mi)
% 6.27/2.35 % (10271)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_10053 for (2993ds/253Mi)
% 6.27/2.36 % (10258)Instruction limit reached!
% 6.27/2.36 % (10258)------------------------------
% 6.27/2.36 % (10258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.36 % (10258)Termination reason: Unknown
% 6.27/2.36 % (10258)Termination phase: Saturation
% 6.27/2.36
% 6.27/2.36 % (10258)Memory used [KB]: 2942
% 6.27/2.36 % (10258)Time elapsed: 0.171 s
% 6.27/2.36 % (10258)Instructions burned: 433 (million)
% 6.27/2.36 % (10258)------------------------------
% 6.27/2.36 % (10258)------------------------------
% 6.27/2.37 % (10272)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10053 for (2993ds/140Mi)
% 6.27/2.38 % (10268)First to succeed.
% 6.27/2.39 % (10268)Refutation found. Thanks to Tanya!
% 6.27/2.39 % SZS status Theorem for DTF2THF_10053
% 6.27/2.39 % SZS output start Proof for DTF2THF_10053
% 6.27/2.39 thf(func_def_0, type, in: $i > $i > $o).
% 6.27/2.39 thf(func_def_1, type, exu: ($i > $o) > $o).
% 6.27/2.39 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 6.27/2.39 thf(func_def_8, type, powerset: $i > $i).
% 6.27/2.39 thf(func_def_10, type, setunion: $i > $i).
% 6.27/2.39 thf(func_def_19, type, descr: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_26, type, prop2set: $o > $i).
% 6.27/2.39 thf(func_def_36, type, nonempty: $i > $o).
% 6.27/2.39 thf(func_def_69, type, set2prop: $i > $o).
% 6.27/2.39 thf(func_def_88, type, subset: $i > $i > $o).
% 6.27/2.39 thf(func_def_89, type, disjoint: $i > $i > $o).
% 6.27/2.39 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 6.27/2.39 thf(func_def_114, type, binunion: $i > $i > $i).
% 6.27/2.39 thf(func_def_122, type, binintersect: $i > $i > $i).
% 6.27/2.39 thf(func_def_135, type, regular: $i > $o).
% 6.27/2.39 thf(func_def_136, type, setminus: $i > $i > $i).
% 6.27/2.39 thf(func_def_147, type, symdiff: $i > $i > $i).
% 6.27/2.39 thf(func_def_163, type, sP0: $i > $i > $o).
% 6.27/2.39 thf(func_def_164, type, sP1: $i > $o).
% 6.27/2.39 thf(func_def_187, type, sK24: $i > $o).
% 6.27/2.39 thf(func_def_190, type, sK27: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_195, type, sK32: $i > $o).
% 6.27/2.39 thf(func_def_198, type, sK35: $i > $o).
% 6.27/2.39 thf(func_def_209, type, sK46: $i > $i > $i).
% 6.27/2.39 thf(func_def_214, type, sK51: $o > $i > $i > $i).
% 6.27/2.39 thf(func_def_224, type, sK61: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_225, type, sK62: $i > $o).
% 6.27/2.39 thf(func_def_241, type, sK78: $i > $i > $i).
% 6.27/2.39 thf(func_def_245, type, sK82: $i > $o).
% 6.27/2.39 thf(func_def_253, type, sK90: ($i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_255, type, sK92: $i > $o).
% 6.27/2.39 thf(func_def_264, type, sK101: $i > $o).
% 6.27/2.39 thf(func_def_266, type, sK103: $i > $i > $i).
% 6.27/2.39 thf(func_def_289, type, sK126: $i > $i).
% 6.27/2.39 thf(func_def_292, type, sK129: $i > $o).
% 6.27/2.39 thf(func_def_294, type, sK131: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_299, type, sK136: $i > $i).
% 6.27/2.39 thf(func_def_305, type, sK142: $i > $i).
% 6.27/2.39 thf(func_def_307, type, sK144: $i > $i).
% 6.27/2.39 thf(func_def_311, type, sK148: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_312, type, sK149: $i > $o).
% 6.27/2.39 thf(func_def_317, type, sK154: $i > $i > $i).
% 6.27/2.39 thf(func_def_318, type, sK155: $i > $i > $i).
% 6.27/2.39 thf(func_def_319, type, sK156: $i > $i > $i).
% 6.27/2.39 thf(func_def_327, type, sK164: $i > $o).
% 6.27/2.39 thf(func_def_328, type, sK165: $i > $i).
% 6.27/2.39 thf(func_def_329, type, sK166: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_332, type, sK169: $i > $o).
% 6.27/2.39 thf(func_def_338, type, sK175: $i > $o).
% 6.27/2.39 thf(func_def_341, type, sK178: ($i > $i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_342, type, sK179: ($i > $i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_343, type, sK180: $i > ($i > $i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_345, type, sK182: $i > $i > $o).
% 6.27/2.39 thf(func_def_346, type, sK183: $i > $i).
% 6.27/2.39 thf(func_def_347, type, sK184: $i > $i).
% 6.27/2.39 thf(func_def_348, type, sK185: ($i > $o) > ($i > $o) > $i > $i > $i).
% 6.27/2.39 thf(func_def_349, type, sK186: ($i > $o) > ($i > $o) > $i > $i > $i).
% 6.27/2.39 thf(func_def_352, type, sK189: $i > $o).
% 6.27/2.39 thf(func_def_353, type, sK190: $i > $o).
% 6.27/2.39 thf(func_def_357, type, sK194: $i > $o).
% 6.27/2.39 thf(func_def_362, type, sK199: $i > $i > $i).
% 6.27/2.39 thf(func_def_377, type, sK214: $i > $o).
% 6.27/2.39 thf(func_def_378, type, sK215: $i > $o).
% 6.27/2.39 thf(func_def_379, type, sK216: ($i > $o) > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_380, type, sK217: ($i > $o) > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_387, type, sK224: $i > $o).
% 6.27/2.39 thf(func_def_390, type, sK227: $i > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_394, type, sK231: $i > $o).
% 6.27/2.39 thf(func_def_396, type, sK233: ($i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_401, type, sK238: $i > $i).
% 6.27/2.39 thf(func_def_410, type, sK247: $i > $o).
% 6.27/2.39 thf(func_def_414, type, sK251: $i > $o).
% 6.27/2.39 thf(func_def_415, type, sK252: $i > $o).
% 6.27/2.39 thf(func_def_416, type, sK253: $i > $i).
% 6.27/2.39 thf(func_def_417, type, sK254: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_418, type, sK255: $i > $o).
% 6.27/2.39 thf(func_def_419, type, sK256: $i > $o).
% 6.27/2.39 thf(func_def_421, type, sK258: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_422, type, sK259: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_432, type, sK269: $i > $i).
% 6.27/2.39 thf(func_def_443, type, sK280: $i > $o).
% 6.27/2.39 thf(func_def_444, type, sK281: $i > $o).
% 6.27/2.39 thf(func_def_445, type, sK282: ($i > $o) > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_446, type, sK283: ($i > $o) > ($i > $o) > $i).
% 6.27/2.39 thf(func_def_447, type, sK284: $i > $i > $i).
% 6.27/2.39 thf(func_def_450, type, sK287: ($i > $o) > $i).
% 6.27/2.39 thf(func_def_451, type, sK288: $i > $o).
% 6.27/2.39 thf(func_def_462, type, sK299: $i > $i).
% 6.27/2.39 thf(func_def_471, type, sK308: $i > $i > $i).
% 6.27/2.39 thf(func_def_472, type, sK309: $i > $i).
% 6.27/2.39 thf(func_def_473, type, sK310: $i > $i).
% 6.27/2.39 thf(func_def_474, type, sK311: $i > $i).
% 6.27/2.39 thf(func_def_475, type, sK312: $i > $i).
% 6.27/2.39 thf(func_def_476, type, sK313: $i > $i > $i).
% 6.27/2.39 thf(func_def_477, type, sK314: $i > $i > $i > $i).
% 6.27/2.39 thf(func_def_478, type, sK315: $i > $i > $i > $i).
% 6.27/2.39 thf(func_def_479, type, sK316: $i > $i > $i > $i).
% 6.27/2.39 thf(func_def_480, type, sK317: $i > $i > $i).
% 6.27/2.39 thf(func_def_481, type, sK318: $i > $i > $i).
% 6.27/2.39 thf(func_def_482, type, sK319: $i > $i > $i).
% 6.27/2.39 thf(func_def_483, type, sK320: $i > $i > $i).
% 6.27/2.39 thf(func_def_484, type, sK321: $i > $i).
% 6.27/2.39 thf(func_def_485, type, sK322: $i > $i > $i > $i).
% 6.27/2.39 thf(func_def_487, type, sK324: $i > $i).
% 6.27/2.39 thf(func_def_488, type, sK325: $i > $i).
% 6.27/2.39 thf(func_def_489, type, sK326: $i > $i).
% 6.27/2.39 thf(func_def_490, type, sK327: $i > $i).
% 6.27/2.39 thf(func_def_494, type, sK331: $i > $o).
% 6.27/2.39 thf(func_def_511, type, sK348: $i > $o).
% 6.27/2.39 thf(func_def_514, type, sK351: ($i > $o) > $i > $i).
% 6.27/2.39 thf(func_def_516, type, sK353: $i > $o).
% 6.27/2.39 thf(func_def_520, type, ph357: !>[X0: $tType]:(X0)).
% 6.27/2.39 thf(f2659,plain,(
% 6.27/2.39 $false),
% 6.27/2.39 inference(avatar_sat_refutation,[status(thm)],[f2562,f2641,f2658])).
% 6.27/2.39 thf(f2658,plain,(
% 6.27/2.39 ~spl356_1),
% 6.27/2.39 inference(avatar_contradiction_clause,[status(thm)],[f2657])).
% 6.27/2.39 thf(f2657,plain,(
% 6.27/2.39 $false | ~spl356_1),
% 6.27/2.39 inference(subsumption_resolution,[status(thm)],[f2476,f2558])).
% 6.27/2.39 thf(f2558,plain,(
% 6.27/2.39 ( ! [X7 : $o] : (($true = X7)) ) | ~spl356_1),
% 6.27/2.39 inference(avatar_component_clause,[status(thm)],[f2557])).
% 6.27/2.39 thf(f2557,definition,(
% 6.27/2.39 spl356_1 <=> ! [X7 : $o] : ($true = X7)),
% 6.27/2.39 introduced(definition,[new_symbols(naming,[spl356_1])],[avatar_definition])).
% 6.27/2.39 thf(f2476,plain,(
% 6.27/2.39 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true)) )),
% 6.27/2.39 inference(trivial_inequality_removal,[status(thm)],[f1982])).
% 6.27/2.39 thf(f1982,plain,(
% 6.27/2.39 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | ($true != $true)) )),
% 6.27/2.39 inference(definition_unfolding,[status(thm)],[f1331,f1583])).
% 6.27/2.39 thf(f1583,plain,(
% 6.27/2.39 (notinemptyset = $true)),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f926])).
% 6.27/2.39 thf(f926,plain,(
% 6.27/2.39 (powerset__Cong = $true) & (foundationAx = $true) & (binintersectRsub = $true) & (subsetI1 = $true) & (powersetI1 = $true) & (((in @ sK207 @ sK208) = $true) & ($true = (in @ sK207 @ (symdiff @ sK206 @ sK208))) & ($true = (in @ sK207 @ sK206))) & (upairset2IR = $true) & (quantDeMorgan4 = $true) & (notsubsetI = $true) & (symdiffI1 = $true) & (binintersectER = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (binunionEcases = $true) & (emptyinunitempty = $true) & (exuE3u = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (exuI1 = $true) & (setbeta = $true) & (bs114d = $true) & (setminusSubset2 = $true) & (symdiffI2 = $true) & (binintersectI = $true) & (notequalI1 = $true) & (subsetE2 = $true) & (noeltsimpempty = $true) & (in__Cong = $true) & (setminusELneg = $true) & (setunion__Cong = $true) & (binintersectEL = $true) & (setadjoinOr = $true) & (emptysetE = $true) & (upairsetIL = $true) & (dsetconstrER = $true) & (setext = $true) & (replAx = $true) & (dsetconstr__Cong = $true) & (exuE3e = $true) & (setminusERneg = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setminusLsub = $true) & (setadjoinIL = $true) & (exu__Cong = $true) & (binintersectSubset3 = $true) & (powersetsubset = $true) & (powersetE = $true) & (prop2set2propI = $true) & (omegaIndAx = $true) & (setminusER = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (setminusIRneg = $true) & (wellorderingAx = $true) & (setadjoinAx = $true) & (setextsub = $true) & (eqinunit = $true) & (setminusSubset1 = $true) & (inCongP = $true) & (prop2setE = $true) & (setminusEL = $true) & (binintersectLsub = $true) & (quantDeMorgan1 = $true) & (exuE1 = $true) & (eqimpsubset2 = $true) & (subsetE = $true) & (notdexE = $true) & (quantDeMorgan3 = $true) & (nonemptyE1 = $true) & (prop2setI = $true) & (binintersectSubset4 = $true) & (vacuousDall = $true) & (binintersectSubset2 = $true) & (binunionE = $true) & (descrp = $true) & (eqimpsubset1 = $true) & (exuI2 = $true) & (notdallE = $true) & (binintersectSubset1 = $true) & (notinsingleton = $true) & (setoftrueEq = $true) & (quantDeMorgan2 = $true) & (disjointsetsI1 = $true) & (nonemptyI = $true) & (setunionAx = $true) & (powersetAx = $true) & (emptyinPowerset = $true) & (emptysetAx = $true) & (upairsetIR = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (exuEu = $true) & (binunionIR = $true) & (setadjoinIR = $true) & (setadjoinSub2 = $true) & (emptyset__Cong = $true) & (setunionI = $true) & (setminusI = $true) & (sepSubset = $true) & (subset2powerset = $true) & (subsetTrans = $true) & (emptysetimpfalse = $true) & (omega0Ax = $true) & (emptyInPowerset = $true) & (subsetI2 = $true) & (nonemptyI1 = $true) & (omegaSAx = $true) & (setadjoinSub = $true) & (dsetconstrI = $true) & (powersetI = $true) & (singletonsswitch = $true) & (upairsetE = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (emptyE1 = $true) & (setminusILneg = $true) & (inPowerset = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (binunionLsub = $true) & (uniqinunit = $true) & (setunionE = $true) & (sepInPowerset = $true) & (omega__Cong = $true) & (descr__Cong = $true) & (symdiffE = $true) & (dsetconstrEL = $true) & (binunionIL = $true) & (setextAx = $true) & (emptysetsubset = $true)),
% 6.27/2.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK206,sK207,sK208])],[f514,f925])).
% 6.27/2.39 thf(f925,plain,(
% 6.27/2.39 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ($true = (in @ X1 @ X0))) => (((in @ sK207 @ sK208) = $true) & ($true = (in @ sK207 @ (symdiff @ sK206 @ sK208))) & ($true = (in @ sK207 @ sK206)))),
% 6.27/2.39 introduced(definition,[],[choice_axiom])).
% 6.27/2.39 thf(f514,plain,(
% 6.27/2.39 (powerset__Cong = $true) & (foundationAx = $true) & (binintersectRsub = $true) & (subsetI1 = $true) & (powersetI1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) & ($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ($true = (in @ X1 @ X0))) & (upairset2IR = $true) & (quantDeMorgan4 = $true) & (notsubsetI = $true) & (symdiffI1 = $true) & (binintersectER = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (binunionEcases = $true) & (emptyinunitempty = $true) & (exuE3u = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (exuI1 = $true) & (setbeta = $true) & (bs114d = $true) & (setminusSubset2 = $true) & (symdiffI2 = $true) & (binintersectI = $true) & (notequalI1 = $true) & (subsetE2 = $true) & (noeltsimpempty = $true) & (in__Cong = $true) & (setminusELneg = $true) & (setunion__Cong = $true) & (binintersectEL = $true) & (setadjoinOr = $true) & (emptysetE = $true) & (upairsetIL = $true) & (dsetconstrER = $true) & (setext = $true) & (replAx = $true) & (dsetconstr__Cong = $true) & (exuE3e = $true) & (setminusERneg = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setminusLsub = $true) & (setadjoinIL = $true) & (exu__Cong = $true) & (binintersectSubset3 = $true) & (powersetsubset = $true) & (powersetE = $true) & (prop2set2propI = $true) & (omegaIndAx = $true) & (setminusER = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (setminusIRneg = $true) & (wellorderingAx = $true) & (setadjoinAx = $true) & (setextsub = $true) & (eqinunit = $true) & (setminusSubset1 = $true) & (inCongP = $true) & (prop2setE = $true) & (setminusEL = $true) & (binintersectLsub = $true) & (quantDeMorgan1 = $true) & (exuE1 = $true) & (eqimpsubset2 = $true) & (subsetE = $true) & (notdexE = $true) & (quantDeMorgan3 = $true) & (nonemptyE1 = $true) & (prop2setI = $true) & (binintersectSubset4 = $true) & (vacuousDall = $true) & (binintersectSubset2 = $true) & (binunionE = $true) & (descrp = $true) & (eqimpsubset1 = $true) & (exuI2 = $true) & (notdallE = $true) & (binintersectSubset1 = $true) & (notinsingleton = $true) & (setoftrueEq = $true) & (quantDeMorgan2 = $true) & (disjointsetsI1 = $true) & (nonemptyI = $true) & (setunionAx = $true) & (powersetAx = $true) & (emptyinPowerset = $true) & (emptysetAx = $true) & (upairsetIR = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (exuEu = $true) & (binunionIR = $true) & (setadjoinIR = $true) & (setadjoinSub2 = $true) & (emptyset__Cong = $true) & (setunionI = $true) & (setminusI = $true) & (sepSubset = $true) & (subset2powerset = $true) & (subsetTrans = $true) & (emptysetimpfalse = $true) & (omega0Ax = $true) & (emptyInPowerset = $true) & (subsetI2 = $true) & (nonemptyI1 = $true) & (omegaSAx = $true) & (setadjoinSub = $true) & (dsetconstrI = $true) & (powersetI = $true) & (singletonsswitch = $true) & (upairsetE = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (emptyE1 = $true) & (setminusILneg = $true) & (inPowerset = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (binunionLsub = $true) & (uniqinunit = $true) & (setunionE = $true) & (sepInPowerset = $true) & (omega__Cong = $true) & (descr__Cong = $true) & (symdiffE = $true) & (dsetconstrEL = $true) & (binunionIL = $true) & (setextAx = $true) & (emptysetsubset = $true)),
% 6.27/2.39 inference(flattening,[status(thm)],[f513])).
% 6.27/2.39 thf(f513,plain,(
% 6.27/2.39 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ((in @ X1 @ X2) = $true)) & ($true = (in @ X1 @ X0))) & (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)),
% 6.27/2.39 inference(ennf_transformation,[status(thm)],[f424])).
% 6.27/2.39 thf(f424,plain,(
% 6.27/2.39 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ($true != (in @ X1 @ (symdiff @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.27/2.39 inference(flattening,[status(thm)],[f344])).
% 6.27/2.39 thf(f344,plain,(
% 6.27/2.39 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ~($true = (in @ X1 @ (symdiff @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.27/2.39 inference(fool_elimination,[status(thm)],[f343])).
% 6.27/2.39 thf(f343,plain,(
% 6.27/2.39 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => ~(in @ X1 @ (symdiff @ X0 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.27/2.39 inference(rectify,[status(thm)],[f134])).
% 6.27/2.39 thf(f134,negated_conjecture,(
% 6.27/2.39 ~(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 => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.27/2.39 inference(negated_conjecture,[status(cth)],[f133])).
% 6.27/2.39 thf(f133,conjecture,(
% 6.27/2.39 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 => ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 6.27/2.39 file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',symdiffIneg1)).
% 6.27/2.39 thf(f1331,plain,(
% 6.27/2.39 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (notinemptyset != $true)) )),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f760])).
% 6.27/2.39 thf(f760,plain,(
% 6.27/2.39 ((notinemptyset = $true) | ($true = (in @ sK110 @ emptyset))) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (notinemptyset != $true))),
% 6.27/2.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK110])],[f758,f759])).
% 6.27/2.39 thf(f759,plain,(
% 6.27/2.39 ? [X0 : $i] : ($true = (in @ X0 @ emptyset)) => ($true = (in @ sK110 @ emptyset))),
% 6.27/2.39 introduced(definition,[],[choice_axiom])).
% 6.27/2.39 thf(f758,plain,(
% 6.27/2.39 ((notinemptyset = $true) | ? [X0 : $i] : ($true = (in @ X0 @ emptyset))) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (notinemptyset != $true))),
% 6.27/2.39 inference(rectify,[status(thm)],[f757])).
% 6.27/2.39 thf(f757,plain,(
% 6.27/2.39 ((notinemptyset = $true) | ? [X0 : $i] : ($true = (in @ X0 @ emptyset))) & (! [X0 : $i] : ($true != (in @ X0 @ emptyset)) | (notinemptyset != $true))),
% 6.27/2.39 inference(nnf_transformation,[status(thm)],[f423])).
% 6.27/2.39 thf(f423,plain,(
% 6.27/2.39 (notinemptyset = $true) <=> ! [X0 : $i] : ($true != (in @ X0 @ emptyset))),
% 6.27/2.39 inference(flattening,[status(thm)],[f336])).
% 6.27/2.39 thf(f336,plain,(
% 6.27/2.39 (notinemptyset = $true) <=> ! [X0 : $i] : ~($true = (in @ X0 @ emptyset))),
% 6.27/2.39 inference(fool_elimination,[status(thm)],[f335])).
% 6.27/2.39 thf(f335,plain,(
% 6.27/2.39 (notinemptyset = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 6.27/2.39 inference(rectify,[status(thm)],[f21])).
% 6.27/2.39 thf(f21,axiom,(
% 6.27/2.39 (notinemptyset = ! [X1 : $i] : ~(in @ X1 @ emptyset))),
% 6.27/2.39 file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',notinemptyset)).
% 6.27/2.39 thf(f2641,plain,(
% 6.27/2.39 ~spl356_2),
% 6.27/2.39 inference(avatar_contradiction_clause,[status(thm)],[f2640])).
% 6.27/2.39 thf(f2640,plain,(
% 6.27/2.39 $false | ~spl356_2),
% 6.27/2.39 inference(subsumption_resolution,[status(thm)],[f2639,f1594])).
% 6.27/2.39 thf(f1594,plain,(
% 6.27/2.39 ($true = (in @ sK207 @ sK206))),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f926])).
% 6.27/2.39 thf(f2639,plain,(
% 6.27/2.39 ($true != (in @ sK207 @ sK206)) | ~spl356_2),
% 6.27/2.39 inference(subsumption_resolution,[status(thm)],[f2638,f1596])).
% 6.27/2.39 thf(f1596,plain,(
% 6.27/2.39 ((in @ sK207 @ sK208) = $true)),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f926])).
% 6.27/2.39 thf(f2638,plain,(
% 6.27/2.39 ((in @ sK207 @ sK208) != $true) | ($true != (in @ sK207 @ sK206)) | ~spl356_2),
% 6.27/2.39 inference(trivial_inequality_removal,[status(thm)],[f2636])).
% 6.27/2.39 thf(f2636,plain,(
% 6.27/2.39 ($true != (in @ sK207 @ sK206)) | ((in @ sK207 @ sK208) != $true) | ($true != $true) | ~spl356_2),
% 6.27/2.39 inference(superposition,[status(thm)],[f2561,f1595])).
% 6.27/2.39 thf(f1595,plain,(
% 6.27/2.39 ($true = (in @ sK207 @ (symdiff @ sK206 @ sK208)))),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f926])).
% 6.27/2.39 thf(f2561,plain,(
% 6.27/2.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ($true != (in @ X5 @ X6)) | ((in @ X5 @ X4) != $true)) ) | ~spl356_2),
% 6.27/2.39 inference(avatar_component_clause,[status(thm)],[f2560])).
% 6.27/2.39 thf(f2560,definition,(
% 6.27/2.39 spl356_2 <=> ! [X6 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ((in @ X5 @ X4) != $true) | ($true != (in @ X5 @ X6)))),
% 6.27/2.39 introduced(definition,[new_symbols(naming,[spl356_2])],[avatar_definition])).
% 6.27/2.39 thf(f2562,plain,(
% 6.27/2.39 spl356_1 | spl356_2),
% 6.27/2.39 inference(avatar_split_clause,[status(thm)],[f2540,f2560,f2557])).
% 6.27/2.39 thf(f2540,plain,(
% 6.27/2.39 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ($true != (in @ X5 @ X6)) | ((in @ X5 @ X4) != $true) | ($true = X7)) )),
% 6.27/2.39 inference(trivial_inequality_removal,[status(thm)],[f1837])).
% 6.27/2.39 thf(f1837,plain,(
% 6.27/2.39 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true = X7) | ($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ($true != (in @ X5 @ X6)) | ($true != $true) | ((in @ X5 @ X4) != $true)) )),
% 6.27/2.39 inference(definition_unfolding,[status(thm)],[f1176,f1473])).
% 6.27/2.39 thf(f1473,plain,(
% 6.27/2.39 (symdiffE = $true)),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f926])).
% 6.27/2.39 thf(f1176,plain,(
% 6.27/2.39 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ($true = X7) | ((in @ X5 @ X4) != $true) | ($true != (in @ X5 @ X6)) | (symdiffE != $true)) )),
% 6.27/2.39 inference(cnf_transformation,[status(thm)],[f582])).
% 6.27/2.39 thf(f582,plain,(
% 6.27/2.39 ((symdiffE = $true) | (((in @ sK5 @ (symdiff @ sK4 @ sK6)) = $true) & (($true != sK7) & (($true = sK7) | ((in @ sK5 @ sK6) != $true) | ($true = (in @ sK5 @ sK4))) & (($true != (in @ sK5 @ sK4)) | ((in @ sK5 @ sK6) = $true) | ($true = sK7))))) & (! [X4 : $i,X5 : $i,X6 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ! [X7 : $o] : (($true = X7) | (($true != X7) & ($true = (in @ X5 @ X6)) & ((in @ X5 @ X4) != $true)) | (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X6)) & ($true != X7)))) | (symdiffE != $true))),
% 6.27/2.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f579,f581,f580])).
% 6.27/2.39 thf(f580,plain,(
% 6.27/2.39 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X1 @ X2) != $true) | ($true = (in @ X1 @ X0))) & (($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true) | ($true = X3)))) => (((in @ sK5 @ (symdiff @ sK4 @ sK6)) = $true) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ sK5 @ sK6) != $true) | ($true = (in @ sK5 @ sK4))) & (($true != (in @ sK5 @ sK4)) | ((in @ sK5 @ sK6) = $true) | ($true = X3))))),
% 6.27/2.39 introduced(definition,[],[choice_axiom])).
% 6.27/2.39 thf(f581,plain,(
% 6.27/2.39 ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ sK5 @ sK6) != $true) | ($true = (in @ sK5 @ sK4))) & (($true != (in @ sK5 @ sK4)) | ((in @ sK5 @ sK6) = $true) | ($true = X3))) => (($true != sK7) & (($true = sK7) | ((in @ sK5 @ sK6) != $true) | ($true = (in @ sK5 @ sK4))) & (($true != (in @ sK5 @ sK4)) | ((in @ sK5 @ sK6) = $true) | ($true = sK7)))),
% 6.27/2.39 introduced(definition,[],[choice_axiom])).
% 6.27/2.39 thf(f579,plain,(
% 6.27/2.39 ((symdiffE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X1 @ X2) != $true) | ($true = (in @ X1 @ X0))) & (($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true) | ($true = X3))))) & (! [X4 : $i,X5 : $i,X6 : $i] : (($true != (in @ X5 @ (symdiff @ X4 @ X6))) | ! [X7 : $o] : (($true = X7) | (($true != X7) & ($true = (in @ X5 @ X6)) & ((in @ X5 @ X4) != $true)) | (((in @ X5 @ X4) = $true) & ($true != (in @ X5 @ X6)) & ($true != X7)))) | (symdiffE != $true))),
% 6.27/2.39 inference(rectify,[status(thm)],[f578])).
% 6.27/2.39 thf(f578,plain,(
% 6.27/2.39 ((symdiffE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X0 @ X2))) & ? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X1 @ X2) != $true) | ($true = (in @ X1 @ X0))) & (($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true) | ($true = X3))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (symdiff @ X0 @ X2))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ X0))) | (($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true) & ($true != X3)))) | (symdiffE != $true))),
% 6.27/2.39 inference(nnf_transformation,[status(thm)],[f536])).
% 6.27/2.39 thf(f536,plain,(
% 6.27/2.39 (symdiffE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (symdiff @ X0 @ X2))) | ! [X3 : $o] : (($true = X3) | (($true != X3) & ((in @ X1 @ X2) = $true) & ($true != (in @ X1 @ X0))) | (($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true) & ($true != X3))))),
% 6.27/2.39 inference(flattening,[status(thm)],[f535])).
% 6.27/2.39 thf(f535,plain,(
% 6.27/2.39 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((($true = X3) | ((($true != X3) & ((in @ X1 @ X2) = $true)) & ($true != (in @ X1 @ X0)))) | ((($true != X3) & ((in @ X1 @ X2) != $true)) & ($true = (in @ X1 @ X0)))) | ($true != (in @ X1 @ (symdiff @ X0 @ X2)))) <=> (symdiffE = $true)),
% 6.27/2.39 inference(ennf_transformation,[status(thm)],[f411])).
% 6.27/2.39 thf(f411,plain,(
% 6.27/2.39 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X0 @ X2))) => ! [X3 : $o] : ((($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) != $true) => ($true = X3))) => ((($true != (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ($true = X3))) => ($true = X3)))) <=> (symdiffE = $true)),
% 6.27/2.39 inference(flattening,[status(thm)],[f243])).
% 6.27/2.39 thf(f243,plain,(
% 6.27/2.39 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (symdiff @ X0 @ X2))) => ! [X3 : $o] : ((($true = (in @ X1 @ X0)) => (~((in @ X1 @ X2) = $true) => ($true = X3))) => ((~($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ($true = X3))) => ($true = X3)))) <=> (symdiffE = $true)),
% 6.27/2.39 inference(fool_elimination,[status(thm)],[f242])).
% 6.27/2.39 thf(f242,plain,(
% 6.27/2.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (symdiff @ X0 @ X2)) => ! [X3 : $o] : (((in @ X1 @ X0) => (~(in @ X1 @ X2) => X3)) => ((~(in @ X1 @ X0) => ((in @ X1 @ X2) => X3)) => X3))) = symdiffE)),
% 6.27/2.39 inference(rectify,[status(thm)],[f130])).
% 6.27/2.39 thf(f130,axiom,(
% 6.27/2.39 (! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))) = symdiffE)),
% 6.27/2.39 file('/export/starexec/sandbox/tmp/tmp.PO2KFwXtBb/DTF2THF_10053.p',symdiffE)).
% 6.27/2.39 % SZS output end Proof for DTF2THF_10053
% 6.27/2.39 % (10268)------------------------------
% 6.27/2.39 % (10268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.27/2.39 % (10268)Termination reason: Refutation
% 6.27/2.39
% 6.27/2.39 % (10268)Memory used [KB]: 7547
% 6.27/2.39 % (10268)Time elapsed: 0.060 s
% 6.27/2.39 % (10268)Instructions burned: 113 (million)
% 6.27/2.39 % (10268)------------------------------
% 6.27/2.39 % (10268)------------------------------
% 6.27/2.39 % (10207)Success in time 0.703 s
%------------------------------------------------------------------------------