%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU611^1 : 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 : n019.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 09:35:36 AM UTC 2026
% Result : Theorem 2.39s 1.92s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 22 unt; 0 typ; 5 def)
% Number of atoms : 3216 ( 887 equ; 0 cnn)
% Maximal formula atoms : 135 ( 34 avg)
% Number of connectives : 1991 ( 142 ~; 130 |; 429 &; 594 @)
% ( 12 <=>; 684 =>; 0 <=; 0 <~>)
% Maximal formula depth : 140 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 297 ( 294 usr; 145 con; 0-4 aty)
% Number of variables : 208 ( 48 ^; 119 !; 41 ?; 208 :)
% 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_161,type,
sP0: ( $i > $o ) > $o ).
thf(func_def_162,type,
sP1: $i > $i > $i > $o ).
thf(func_def_163,type,
sP2: $i > $i > $o ).
thf(func_def_164,type,
sP3: $i > $i > $o ).
thf(func_def_165,type,
sP4: $i > $i > $o ).
thf(func_def_166,type,
sP5: $i > $o ).
thf(func_def_167,type,
sP6: $i > $i > $o ).
thf(func_def_168,type,
sP7: $i > $i > $o ).
thf(func_def_170,type,
sP9: ( $i > $o ) > $o ).
thf(func_def_171,type,
sP10: $i > ( $i > $o ) > $o ).
thf(func_def_173,type,
sP12: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_174,type,
sP13: $i > ( $i > $i > $o ) > $o ).
thf(func_def_177,type,
sP16: $i > $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_178,type,
sP17: $i > $o ).
thf(func_def_179,type,
sP18: $i > $i > $o ).
thf(func_def_183,type,
sP22: $i > $i > $o > $o ).
thf(func_def_184,type,
sP23: ( $i > $o ) > $o ).
thf(func_def_185,type,
sP24: $i > $i > $o ).
thf(func_def_187,type,
sP26: $i > $i > $i > $o ).
thf(func_def_191,type,
sP30: $o > $i > $i > $o ).
thf(func_def_193,type,
sP32: $i > $o ).
thf(func_def_194,type,
sP33: $i > $o ).
thf(func_def_195,type,
sP34: ( $i > $o ) > $i > $o ).
thf(func_def_197,type,
sP36: $o > $i > $i > $o ).
thf(func_def_198,type,
sP37: $i > $i > $i > $o ).
thf(func_def_199,type,
sP38: ( $i > $o ) > $o ).
thf(func_def_200,type,
sP39: $i > ( $i > $o ) > $o ).
thf(func_def_202,type,
sP41: $i > ( $i > $o ) > $o ).
thf(func_def_204,type,
sP43: ( $i > $o ) > $i > $o ).
thf(func_def_206,type,
sP45: $i > ( $i > $o ) > $o ).
thf(func_def_209,type,
sP48: ( $i > $o ) > $o ).
thf(func_def_224,type,
sK63: $i > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_226,type,
sK65: $i > $o ).
thf(func_def_227,type,
sK66: $i > $i > $i ).
thf(func_def_228,type,
sK67: $i > $i > $i ).
thf(func_def_229,type,
sK68: $i > $i > $i > $i ).
thf(func_def_230,type,
sK69: $i > $i ).
thf(func_def_231,type,
sK70: $i > $i ).
thf(func_def_232,type,
sK71: $i > $i ).
thf(func_def_233,type,
sK72: $i > $i ).
thf(func_def_234,type,
sK73: $i > $i > $i ).
thf(func_def_235,type,
sK74: $i > $i > $i ).
thf(func_def_236,type,
sK75: $i > $i > $i ).
thf(func_def_237,type,
sK76: $i > $i > $i ).
thf(func_def_238,type,
sK77: $i > $i > $i ).
thf(func_def_239,type,
sK78: $i > $i > $i ).
thf(func_def_240,type,
sK79: $i > $i > $i ).
thf(func_def_241,type,
sK80: $i > $i > $i ).
thf(func_def_242,type,
sK81: $i > $i > $i > $i ).
thf(func_def_243,type,
sK82: $i > $i > $i > $i ).
thf(func_def_245,type,
sK84: $i > $i ).
thf(func_def_250,type,
sK89: $i > $i > $i ).
thf(func_def_251,type,
sK90: $i > $i > $i ).
thf(func_def_252,type,
sK91: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK92: ( $i > $o ) > $i ).
thf(func_def_254,type,
sK93: $i > $o ).
thf(func_def_265,type,
sK104: $i > $i ).
thf(func_def_267,type,
sK106: $i > $o ).
thf(func_def_268,type,
sK107: ( $i > $o ) > $i > $i ).
thf(func_def_269,type,
sK108: $i > ( $i > $o ) > $i ).
thf(func_def_272,type,
sK111: $i > $i > $i ).
thf(func_def_275,type,
sK114: $i > $o ).
thf(func_def_283,type,
sK122: $i > $i > $o ).
thf(func_def_285,type,
sK124: $i > ( $i > $i > $o ) > $i ).
thf(func_def_286,type,
sK125: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_287,type,
sK126: $i > ( $i > $i > $o ) > $i ).
thf(func_def_288,type,
sK127: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_291,type,
sK130: $i > $i > $i ).
thf(func_def_302,type,
sK141: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK142: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_306,type,
sK145: $i > $o ).
thf(func_def_307,type,
sK146: $i > $o ).
thf(func_def_323,type,
sK162: $i > $i > $i ).
thf(func_def_324,type,
sK163: $i > $i ).
thf(func_def_329,type,
sK168: $i > $i > $i ).
thf(func_def_331,type,
sK170: $i > $o ).
thf(func_def_332,type,
sK171: $i > $o ).
thf(func_def_333,type,
sK172: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_334,type,
sK173: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_341,type,
sK180: $i > $o ).
thf(func_def_349,type,
sK188: $i > $o ).
thf(func_def_362,type,
sK201: $i > $i > $i ).
thf(func_def_363,type,
sK202: $i > $o ).
thf(func_def_372,type,
sK211: $i > $i > $o > $i ).
thf(func_def_381,type,
sK220: $i > $i ).
thf(func_def_382,type,
sK221: ( $i > $o ) > $i ).
thf(func_def_383,type,
sK222: $i > ( $i > $o ) > $i ).
thf(func_def_384,type,
sK223: $i > $o ).
thf(func_def_387,type,
sK226: $i > $i > $i ).
thf(func_def_403,type,
sK242: $i > $i > $i ).
thf(func_def_405,type,
sK244: $i > $o ).
thf(func_def_410,type,
sK249: $i > $i ).
thf(func_def_414,type,
sK253: $i > $i > $i ).
thf(func_def_418,type,
sK257: ( $i > $o ) > $i ).
thf(func_def_419,type,
sK258: $i > $o ).
thf(func_def_432,type,
sK271: $i > $o ).
thf(func_def_433,type,
sK272: $i > $i ).
thf(func_def_434,type,
sK273: $i > $i ).
thf(func_def_437,type,
sK276: $i > $i ).
thf(func_def_443,type,
sK282: $i > $o ).
thf(func_def_445,type,
sK284: $i > $o ).
thf(func_def_448,type,
sK287: $i > $o ).
thf(func_def_450,type,
sK289: $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK290: ( $i > $o ) > $i > $i ).
thf(func_def_458,type,
sK297: $i > $i > $i > $o ).
thf(func_def_475,type,
sK314: ( $i > $o ) > $i ).
thf(func_def_476,type,
sK315: ( $i > $o ) > $i ).
thf(func_def_477,type,
sK316: $i > $o ).
thf(func_def_481,type,
sK320: $i > $o ).
thf(func_def_483,type,
sK322: $i > ( $i > $o ) > $i ).
thf(func_def_484,type,
sK323: $i > ( $i > $o ) > $i ).
thf(func_def_487,type,
sK326: $i > $o ).
thf(func_def_489,type,
sK328: $i > ( $i > $o ) > $i ).
thf(func_def_490,type,
sK329: $i > ( $i > $o ) > $i ).
thf(func_def_498,type,
sK337: $i > $o ).
thf(func_def_499,type,
sK338: ( $i > $o ) > $i > $i ).
thf(func_def_500,type,
sK339: ( $i > $o ) > $i > $i ).
thf(func_def_502,type,
sK341: $i > $o ).
thf(func_def_503,type,
sK342: ( $i > $o ) > $i > $i ).
thf(func_def_504,type,
sK343: $i > ( $i > $o ) > $i ).
thf(func_def_518,type,
sK357: $i > $o ).
thf(func_def_521,type,
sK360: $i > $o ).
thf(func_def_522,type,
sK361: $i > $o ).
thf(func_def_523,type,
sK362: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_524,type,
sK363: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_525,type,
sK364: ( $i > $o ) > $i ).
thf(func_def_526,type,
sK365: $i > ( $i > $o ) > $i ).
thf(func_def_527,type,
sK366: $i > $o ).
thf(func_def_532,type,
sK371: $i > $o ).
thf(func_def_538,type,
sK377: $i > $o ).
thf(func_def_547,type,
sK386: $i > $o ).
thf(func_def_553,type,
ph392:
!>[X0: $tType] : X0 ).
thf(f5229,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2909,f2999,f3960,f4030,f4036,f4037,f5218]) ).
thf(f5218,plain,
( ~ spl391_80
| ~ spl391_132 ),
inference(avatar_contradiction_clause,[status(thm)],[f5217]) ).
thf(f5217,plain,
( $false
| ~ spl391_80
| ~ spl391_132 ),
inference(trivial_inequality_removal,[status(thm)],[f5207]) ).
thf(f5207,plain,
( ( $false = $true )
| ~ spl391_80
| ~ spl391_132 ),
inference(backward_demodulation,[status(thm)],[f2908,f3959]) ).
thf(f3959,plain,
( ( $false
= ( in @ sK190 @ sK189 ) )
| ~ spl391_132 ),
inference(avatar_component_clause,[status(thm)],[f3958]) ).
thf(f3958,definition,
( spl391_132
<=> ( $false
= ( in @ sK190 @ sK189 ) ) ),
introduced(definition,[new_symbols(naming,[spl391_132])],[avatar_definition]) ).
thf(f2908,plain,
( ( ( in @ sK190 @ sK189 )
= $true )
| ~ spl391_80 ),
inference(avatar_component_clause,[status(thm)],[f2907]) ).
thf(f2907,definition,
( spl391_80
<=> ( ( in @ sK190 @ sK189 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl391_80])],[avatar_definition]) ).
thf(f4037,plain,
( spl391_79
| spl391_80 ),
inference(avatar_split_clause,[status(thm)],[f4022,f2907,f2904]) ).
thf(f2904,definition,
( spl391_79
<=> ( ( in @ sK190 @ sK191 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl391_79])],[avatar_definition]) ).
thf(f4022,plain,
( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4017]) ).
thf(f4017,plain,
( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2423,f3953]) ).
thf(f3953,plain,
( ( in @ sK190 @ ( binunion @ sK189 @ sK191 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3940]) ).
thf(f3940,plain,
( ( $true != $true )
| ( ( in @ sK190 @ ( binunion @ sK189 @ sK191 ) )
= $true ) ),
inference(superposition,[status(thm)],[f2569,f2536]) ).
thf(f2536,plain,
( ( in @ sK190
@ ( dsetconstr @ ( binunion @ sK189 @ sK191 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK191 )
| ~ ( in @ Y0 @ sK189 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2148]) ).
thf(f2148,plain,
( ( in @ sK190
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) )
@ sK189
@ sK191 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1650,f1895]) ).
thf(f1895,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f359]) ).
thf(f359,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f358]) ).
thf(f358,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( binunion @ X3 @ X4 )
@ ^ [X1: $i] :
( ~ ( in @ X1 @ X3 )
| ~ ( in @ X1 @ X4 ) ) ) )
= symdiff ),
file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',symdiff) ).
thf(f1650,plain,
( $true
= ( in @ sK190 @ ( symdiff @ sK189 @ sK191 ) ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f907,plain,
( ( notsubsetI = $true )
& ( sepSubset = $true )
& ( subsetE = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( powersetI = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( exuI3 = $true )
& ( prop2set2propI = $true )
& ( powersetsubset = $true )
& ( inCongP = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( subsetE2 = $true )
& ( setextAx = $true )
& ( sK192 != $true )
& ( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
!= $true )
| ( sK192 = $true ) )
& ( ( sK192 = $true )
| ( ( in @ sK190 @ sK189 )
!= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) )
& ( $true
= ( in @ sK190 @ ( symdiff @ sK189 @ sK191 ) ) )
& ( powerset__Cong = $true )
& ( wellorderingAx = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( exuE3u = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( subsetRefl = $true )
& ( setminusSubset2 = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( subsetTrans = $true )
& ( descr__Cong = $true )
& ( subsetI2 = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( upairset2IR = $true )
& ( setunion__Cong = $true )
& ( setunionAx = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan2 = $true )
& ( descrp = $true )
& ( nonemptyI = $true )
& ( nonemptyI1 = $true )
& ( setminusIRneg = $true )
& ( notdexE = $true )
& ( binintersectSubset4 = $true )
& ( exuI1 = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( setminusI = $true )
& ( subsetI1 = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( setunionE = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( notinsingleton = $true )
& ( inPowerset = $true )
& ( binintersectSubset3 = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( disjointsetsI1 = $true )
& ( powersetE1 = $true )
& ( setadjoin__Cong = $true )
& ( setminusEL = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setminusLsub = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( notinemptyset = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIR = $true )
& ( in__Cong = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( exuI2 = $true )
& ( noeltsimpempty = $true )
& ( binintersectEL = $true )
& ( eqimpsubset2 = $true )
& ( vacuousDall = $true )
& ( emptyinPowerset = $true )
& ( uniqinunit = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( replAx = $true )
& ( binintersectI = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( emptysetE = $true )
& ( sepInPowerset = $true )
& ( setminusILneg = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( binunionLsub = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( emptysetsubset = $true )
& ( dsetconstrEL = $true )
& ( setadjoinSub2 = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( powersetAx = $true )
& ( eqinunit = $true )
& ( foundationAx = $true )
& ( setminusSubset1 = $true )
& ( binintersectLsub = $true )
& ( setminusELneg = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK189,sK190,sK191,sK192])],[f447,f906,f905]) ).
thf(f905,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true = X3 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
= $true ) )
=> ( ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
!= $true )
| ( $true = X3 ) )
& ( ( $true = X3 )
| ( ( in @ sK190 @ sK189 )
!= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) ) )
& ( $true
= ( in @ sK190 @ ( symdiff @ sK189 @ sK191 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f906,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
!= $true )
| ( $true = X3 ) )
& ( ( $true = X3 )
| ( ( in @ sK190 @ sK189 )
!= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) ) )
=> ( ( sK192 != $true )
& ( ( ( in @ sK190 @ sK189 )
= $true )
| ( ( in @ sK190 @ sK191 )
!= $true )
| ( sK192 = $true ) )
& ( ( sK192 = $true )
| ( ( in @ sK190 @ sK189 )
!= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f447,plain,
( ( notsubsetI = $true )
& ( sepSubset = $true )
& ( subsetE = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( powersetI = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( exuI3 = $true )
& ( prop2set2propI = $true )
& ( powersetsubset = $true )
& ( inCongP = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( subsetE2 = $true )
& ( setextAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true
= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
!= $true )
| ( $true = X3 ) )
& ( ( $true = X3 )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X1 @ X2 )
= $true ) ) )
& ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
= $true ) )
& ( powerset__Cong = $true )
& ( wellorderingAx = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( exuE3u = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( subsetRefl = $true )
& ( setminusSubset2 = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( subsetTrans = $true )
& ( descr__Cong = $true )
& ( subsetI2 = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( upairset2IR = $true )
& ( setunion__Cong = $true )
& ( setunionAx = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan2 = $true )
& ( descrp = $true )
& ( nonemptyI = $true )
& ( nonemptyI1 = $true )
& ( setminusIRneg = $true )
& ( notdexE = $true )
& ( binintersectSubset4 = $true )
& ( exuI1 = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( setminusI = $true )
& ( subsetI1 = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( setunionE = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( notinsingleton = $true )
& ( inPowerset = $true )
& ( binintersectSubset3 = $true )
& ( omega0Ax = $true )
& ( omegaIndAx = $true )
& ( disjointsetsI1 = $true )
& ( powersetE1 = $true )
& ( setadjoin__Cong = $true )
& ( setminusEL = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setminusLsub = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( notinemptyset = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIR = $true )
& ( in__Cong = $true )
& ( emptyI = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( exuI2 = $true )
& ( noeltsimpempty = $true )
& ( binintersectEL = $true )
& ( eqimpsubset2 = $true )
& ( vacuousDall = $true )
& ( emptyinPowerset = $true )
& ( uniqinunit = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( replAx = $true )
& ( binintersectI = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( emptysetE = $true )
& ( sepInPowerset = $true )
& ( setminusILneg = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( binunionLsub = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( emptysetsubset = $true )
& ( dsetconstrEL = $true )
& ( setadjoinSub2 = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( powersetAx = $true )
& ( eqinunit = $true )
& ( foundationAx = $true )
& ( setminusSubset1 = $true )
& ( binintersectLsub = $true )
& ( setminusELneg = $true ) ),
inference(flattening,[status(thm)],[f446]) ).
thf(f446,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 ) ) ) )
& ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
= $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)],[f390]) ).
thf(f390,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
= $true )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f180]) ).
thf(f180,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X0 @ X2 ) )
= $true )
=> ! [X3: $o] :
( ( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( $true
!= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f179]) ).
thf(f179,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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f132]) ).
thf(f132,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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f131]) ).
thf(f131,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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',symdiffE) ).
thf(f2569,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ ( dsetconstr @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2568]) ).
thf(f2568,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2208]) ).
thf(f2208,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true != $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1763,f1550]) ).
thf(f1550,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f1763,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( dsetconstrEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ( ( ( in @ sK243
@ ( dsetconstr @ sK245
@ ^ [Y0: $i] : ( sK244 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK243 @ sK245 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f1018,f1019]) ).
thf(f1019,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true )
& ( ( in @ X3 @ X5 )
!= $true ) )
=> ( ( ( in @ sK243
@ ( dsetconstr @ sK245
@ ^ [Y0: $i] : ( sK244 @ Y0 ) ) )
= $true )
& ( $true
!= ( in @ sK243 @ sK245 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1018,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( in @ X3
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true )
& ( ( in @ X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( dsetconstrEL != $true ) )
& ( ( dsetconstrEL = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f462]) ).
thf(f462,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( dsetconstrEL = $true ) ),
inference(ennf_transformation,[status(thm)],[f238]) ).
thf(f238,plain,
( ( dsetconstrEL = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f237]) ).
thf(f237,plain,
( dsetconstrEL
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
( dsetconstrEL
= ( ! [X1: $i,X0: $i > $o,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',dsetconstrEL) ).
thf(f2423,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2107]) ).
thf(f2107,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f1488,f1608]) ).
thf(f1608,plain,
binunionE = $true,
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f1488,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( binunionE != $true ) ),
inference(cnf_transformation,[status(thm)],[f841]) ).
thf(f841,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ( ( ( in @ sK151 @ ( binunion @ sK153 @ sK152 ) )
= $true )
& ( ( in @ sK151 @ sK152 )
!= $true )
& ( ( in @ sK151 @ sK153 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151,sK152,sK153])],[f839,f840]) ).
thf(f840,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
& ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ X5 )
!= $true ) )
=> ( ( ( in @ sK151 @ ( binunion @ sK153 @ sK152 ) )
= $true )
& ( ( in @ sK151 @ sK152 )
!= $true )
& ( ( in @ sK151 @ sK153 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f839,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( binunion @ X5 @ X4 ) ) )
& ( ( in @ X3 @ X4 )
!= $true )
& ( ( in @ X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f838]) ).
thf(f838,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( binunionE != $true ) )
& ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f537]) ).
thf(f537,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
<=> ( binunionE = $true ) ),
inference(flattening,[status(thm)],[f536]) ).
thf(f536,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
!= $true ) )
<=> ( binunionE = $true ) ),
inference(ennf_transformation,[status(thm)],[f375]) ).
thf(f375,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
= $true ) ) )
<=> ( binunionE = $true ) ),
inference(fool_elimination,[status(thm)],[f374]) ).
thf(f374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( binunion @ X2 @ X1 ) )
=> ( ( in @ X0 @ X1 )
| ( in @ X0 @ X2 ) ) )
= binunionE ),
inference(rectify,[status(thm)],[f105]) ).
thf(f105,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
=> ( ( in @ X1 @ X4 )
| ( in @ X1 @ X3 ) ) )
= binunionE ),
file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',binunionE) ).
thf(f4036,plain,
( ~ spl391_79
| ~ spl391_131 ),
inference(avatar_contradiction_clause,[status(thm)],[f4035]) ).
thf(f4035,plain,
( $false
| ~ spl391_79
| ~ spl391_131 ),
inference(trivial_inequality_removal,[status(thm)],[f4034]) ).
thf(f4034,plain,
( ( $false = $true )
| ~ spl391_79
| ~ spl391_131 ),
inference(forward_demodulation,[status(thm)],[f2997,f3956]) ).
thf(f3956,plain,
( ( $false
= ( in @ sK190 @ sK191 ) )
| ~ spl391_131 ),
inference(avatar_component_clause,[status(thm)],[f3955]) ).
thf(f3955,definition,
( spl391_131
<=> ( $false
= ( in @ sK190 @ sK191 ) ) ),
introduced(definition,[new_symbols(naming,[spl391_131])],[avatar_definition]) ).
thf(f2997,plain,
( ( ( in @ sK190 @ sK191 )
= $true )
| ~ spl391_79 ),
inference(avatar_component_clause,[status(thm)],[f2904]) ).
thf(f4030,plain,
~ spl391_78,
inference(avatar_contradiction_clause,[status(thm)],[f4029]) ).
thf(f4029,plain,
( $false
| ~ spl391_78 ),
inference(subsumption_resolution,[status(thm)],[f2902,f1653]) ).
thf(f1653,plain,
sK192 != $true,
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f2902,plain,
( ( sK192 = $true )
| ~ spl391_78 ),
inference(avatar_component_clause,[status(thm)],[f2901]) ).
thf(f2901,definition,
( spl391_78
<=> ( sK192 = $true ) ),
introduced(definition,[new_symbols(naming,[spl391_78])],[avatar_definition]) ).
thf(f3960,plain,
( spl391_131
| spl391_132 ),
inference(avatar_split_clause,[status(thm)],[f3952,f3958,f3955]) ).
thf(f3952,plain,
( ( $false
= ( in @ sK190 @ sK189 ) )
| ( $false
= ( in @ sK190 @ sK191 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f3951]) ).
thf(f3951,plain,
( ( $false
= ( in @ sK190 @ sK191 ) )
| ( ( ~ ( in @ sK190 @ sK189 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f3950]) ).
thf(f3950,plain,
( ( ( ~ ( in @ sK190 @ sK191 ) )
= $true )
| ( ( ~ ( in @ sK190 @ sK189 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3949]) ).
thf(f3949,plain,
( ( ~ ( in @ sK190 @ sK191 )
| ~ ( in @ sK190 @ sK189 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3948]) ).
thf(f3948,plain,
( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK191 )
| ~ ( in @ Y0 @ sK189 ) )
@ sK190 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3941]) ).
thf(f3941,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK191 )
| ~ ( in @ Y0 @ sK189 ) )
@ sK190 )
= $true ) ),
inference(superposition,[status(thm)],[f2452,f2536]) ).
thf(f2452,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) )
!= $true )
| ( ( X1 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2451]) ).
thf(f2451,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2375]) ).
thf(f2375,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( ( X1 @ X2 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2008,f1552]) ).
thf(f1552,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f2008,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f1310]) ).
thf(f1310,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( sK386 @ sK387 )
!= $true )
& ( ( in @ sK387
@ ( dsetconstr @ sK385
@ ^ [Y0: $i] : ( sK386 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK385,sK386,sK387])],[f1308,f1309]) ).
thf(f1309,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
!= $true )
& ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true ) )
=> ( ( ( sK386 @ sK387 )
!= $true )
& ( ( in @ sK387
@ ( dsetconstr @ sK385
@ ^ [Y0: $i] : ( sK386 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1308,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
!= $true )
& ( ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1307]) ).
thf(f1307,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f425]) ).
thf(f425,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f280]) ).
thf(f280,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f279]) ).
thf(f279,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X3: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',dsetconstrER) ).
thf(f2999,plain,
( spl391_79
| ~ spl391_80
| spl391_78 ),
inference(avatar_split_clause,[status(thm)],[f1651,f2901,f2907,f2904]) ).
thf(f1651,plain,
( ( sK192 = $true )
| ( ( in @ sK190 @ sK189 )
!= $true )
| ( ( in @ sK190 @ sK191 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f2909,plain,
( spl391_78
| ~ spl391_79
| spl391_80 ),
inference(avatar_split_clause,[status(thm)],[f1652,f2907,f2904,f2901]) ).
thf(f1652,plain,
( ( sK192 = $true )
| ( ( in @ sK190 @ sK191 )
!= $true )
| ( ( in @ sK190 @ sK189 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU611^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:28:54 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
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEU611^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English : (! A:i.! B:i.! x:i.in x (symdiff A B) -> (! phi:o.(in x A ->
% 0.19/0.45 % ~(in x B) -> phi) -> (~(in x A) -> in x B -> phi) -> phi))
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.45 % Source : [Bro08]
% 0.19/0.45 % Names : ZFC113g [Bro08]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.73 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.19/0.45 % Syntax : Number of formulae : 278 ( 130 unt; 147 typ; 130 def)
% 0.19/0.45 % Number of atoms : 692 ( 187 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 132 ( 5 avg)
% 0.19/0.45 % Number of connectives : 1112 ( 43 ~; 7 |; 28 &; 711 @)
% 0.19/0.45 % ( 14 <=>; 309 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 139 ( 2 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 150 ( 147 usr; 131 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 377 ( 33 ^; 315 !; 29 ?; 377 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : http://mathgate.info/detsetitem.php?id=489
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(in_type,type,
% 0.19/0.45 in: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(exu_type,type,
% 0.19/0.45 exu: ( $i > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(exu,definition,
% 0.19/0.45 ( exu
% 0.19/0.45 = ( ^ [Xphi: $i > $o] :
% 0.19/0.45 ? [Xx: $i] :
% 0.19/0.45 ( ( Xphi @ Xx )
% 0.19/0.45 & ! [Xy: $i] :
% 0.19/0.45 ( ( Xphi @ Xy )
% 0.19/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setextAx_type,type,
% 0.19/0.45 setextAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setextAx,definition,
% 0.19/0.45 ( setextAx
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 <=> ( in @ Xx @ B ) )
% 0.19/0.45 => ( A = B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptyset_type,type,
% 0.19/0.45 emptyset: $i ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetAx_type,type,
% 0.19/0.45 emptysetAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetAx,definition,
% 0.19/0.45 ( emptysetAx
% 0.19/0.45 = ( ! [Xx: $i] :
% 0.19/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoin_type,type,
% 0.19/0.45 setadjoin: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinAx_type,type,
% 0.19/0.45 setadjoinAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinAx,definition,
% 0.19/0.45 ( setadjoinAx
% 0.19/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.45 <=> ( ( Xy = Xx )
% 0.19/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powerset_type,type,
% 0.19/0.45 powerset: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(powersetAx_type,type,
% 0.19/0.45 powersetAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetAx,definition,
% 0.19/0.45 ( powersetAx
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.45 <=> ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setunion_type,type,
% 0.19/0.45 setunion: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(setunionAx_type,type,
% 0.19/0.45 setunionAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setunionAx,definition,
% 0.19/0.45 ( setunionAx
% 0.19/0.45 = ( ! [A: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.45 <=> ? [B: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(omega_type,type,
% 0.19/0.45 omega: $i ).
% 0.19/0.45
% 0.19/0.45 thf(omega0Ax_type,type,
% 0.19/0.45 omega0Ax: $o ).
% 0.19/0.45
% 0.19/0.45 thf(omega0Ax,definition,
% 0.19/0.45 ( omega0Ax
% 0.19/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(omegaSAx_type,type,
% 0.19/0.45 omegaSAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(omegaSAx,definition,
% 0.19/0.45 ( omegaSAx
% 0.19/0.45 = ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ omega )
% 0.19/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(omegaIndAx_type,type,
% 0.19/0.45 omegaIndAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(omegaIndAx,definition,
% 0.19/0.45 ( omegaIndAx
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ( ( in @ emptyset @ A )
% 0.19/0.45 & ! [Xx: $i] :
% 0.19/0.45 ( ( ( in @ Xx @ omega )
% 0.19/0.45 & ( in @ Xx @ A ) )
% 0.19/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ omega )
% 0.19/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(replAx_type,type,
% 0.19/0.45 replAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(replAx,definition,
% 0.19/0.45 ( replAx
% 0.19/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( exu
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.19/0.45 => ? [B: $i] :
% 0.19/0.45 ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 <=> ? [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(foundationAx_type,type,
% 0.19/0.45 foundationAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(foundationAx,definition,
% 0.19/0.45 ( foundationAx
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.45 => ? [B: $i] :
% 0.19/0.45 ( ( in @ B @ A )
% 0.19/0.45 & ~ ? [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(wellorderingAx_type,type,
% 0.19/0.45 wellorderingAx: $o ).
% 0.19/0.45
% 0.19/0.45 thf(wellorderingAx,definition,
% 0.19/0.45 ( wellorderingAx
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ? [B: $i] :
% 0.19/0.45 ( ! [C: $i] :
% 0.19/0.45 ( ( in @ C @ B )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ C )
% 0.19/0.45 => ( in @ Xx @ A ) ) )
% 0.19/0.45 & ! [Xx: $i,Xy: $i] :
% 0.19/0.45 ( ( ( in @ Xx @ A )
% 0.19/0.45 & ( in @ Xy @ A ) )
% 0.19/0.45 => ( ! [C: $i] :
% 0.19/0.45 ( ( in @ C @ B )
% 0.19/0.45 => ( ( in @ Xx @ C )
% 0.19/0.45 <=> ( in @ Xy @ C ) ) )
% 0.19/0.45 => ( Xx = Xy ) ) )
% 0.19/0.45 & ! [C: $i,D: $i] :
% 0.19/0.45 ( ( ( in @ C @ B )
% 0.19/0.45 & ( in @ D @ B ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ C )
% 0.19/0.45 => ( in @ Xx @ D ) )
% 0.19/0.45 | ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ D )
% 0.19/0.45 => ( in @ Xx @ C ) ) ) )
% 0.19/0.45 & ! [C: $i] :
% 0.19/0.45 ( ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ C )
% 0.19/0.45 => ( in @ Xx @ A ) )
% 0.19/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.19/0.45 => ? [D: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ D @ B )
% 0.19/0.45 & ( in @ Xx @ C )
% 0.19/0.45 & ~ ? [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ D )
% 0.19/0.45 & ( in @ Xy @ C ) )
% 0.19/0.45 & ! [E: $i] :
% 0.19/0.45 ( ( in @ E @ B )
% 0.19/0.45 => ( ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ E )
% 0.19/0.45 => ( in @ Xy @ D ) )
% 0.19/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(descr_type,type,
% 0.19/0.45 descr: ( $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(descrp_type,type,
% 0.19/0.45 descrp: $o ).
% 0.19/0.45
% 0.19/0.45 thf(descrp,definition,
% 0.19/0.45 ( descrp
% 0.19/0.45 = ( ! [Xphi: $i > $o] :
% 0.19/0.45 ( ( exu
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.45 => ( Xphi
% 0.19/0.45 @ ( descr
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstr_type,type,
% 0.19/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrI_type,type,
% 0.19/0.45 dsetconstrI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrI,definition,
% 0.19/0.45 ( dsetconstrI
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( Xphi @ Xx )
% 0.19/0.45 => ( in @ Xx
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrEL_type,type,
% 0.19/0.45 dsetconstrEL: $o ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrEL,definition,
% 0.19/0.45 ( dsetconstrEL
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrER_type,type,
% 0.19/0.45 dsetconstrER: $o ).
% 0.19/0.45
% 0.19/0.45 thf(dsetconstrER,definition,
% 0.19/0.45 ( dsetconstrER
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(exuE1_type,type,
% 0.19/0.45 exuE1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(exuE1,definition,
% 0.19/0.45 ( exuE1
% 0.19/0.45 = ( ! [Xphi: $i > $o] :
% 0.19/0.45 ( ( exu
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.45 => ? [Xx: $i] :
% 0.19/0.45 ( ( Xphi @ Xx )
% 0.19/0.45 & ! [Xy: $i] :
% 0.19/0.45 ( ( Xphi @ Xy )
% 0.19/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(prop2set_type,type,
% 0.19/0.45 prop2set: $o > $i ).
% 0.19/0.45
% 0.19/0.45 thf(prop2setE_type,type,
% 0.19/0.45 prop2setE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(prop2setE,definition,
% 0.19/0.45 ( prop2setE
% 0.19/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.19/0.45 => Xphi ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetE_type,type,
% 0.19/0.45 emptysetE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetE,definition,
% 0.19/0.45 ( emptysetE
% 0.19/0.45 = ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ emptyset )
% 0.19/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetimpfalse_type,type,
% 0.19/0.45 emptysetimpfalse: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptysetimpfalse,definition,
% 0.19/0.45 ( emptysetimpfalse
% 0.19/0.45 = ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ emptyset )
% 0.19/0.45 => $false ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(notinemptyset_type,type,
% 0.19/0.45 notinemptyset: $o ).
% 0.19/0.45
% 0.19/0.45 thf(notinemptyset,definition,
% 0.19/0.45 ( notinemptyset
% 0.19/0.45 = ( ! [Xx: $i] :
% 0.19/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(exuE3e_type,type,
% 0.19/0.45 exuE3e: $o ).
% 0.19/0.45
% 0.19/0.45 thf(exuE3e,definition,
% 0.19/0.45 ( exuE3e
% 0.19/0.45 = ( ! [Xphi: $i > $o] :
% 0.19/0.45 ( ( exu
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setext_type,type,
% 0.19/0.45 setext: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setext,definition,
% 0.19/0.45 ( setext
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ Xx @ B ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 => ( in @ Xx @ A ) )
% 0.19/0.45 => ( A = B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptyI_type,type,
% 0.19/0.45 emptyI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptyI,definition,
% 0.19/0.45 ( emptyI
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ~ ( in @ Xx @ A )
% 0.19/0.45 => ( A = emptyset ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(noeltsimpempty_type,type,
% 0.19/0.45 noeltsimpempty: $o ).
% 0.19/0.45
% 0.19/0.45 thf(noeltsimpempty,definition,
% 0.19/0.45 ( noeltsimpempty
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ~ ( in @ Xx @ A )
% 0.19/0.45 => ( A = emptyset ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setbeta_type,type,
% 0.19/0.45 setbeta: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setbeta,definition,
% 0.19/0.45 ( setbeta
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(nonempty_type,type,
% 0.19/0.45 nonempty: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(nonempty,definition,
% 0.19/0.45 ( nonempty
% 0.19/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyE1_type,type,
% 0.19/0.45 nonemptyE1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyE1,definition,
% 0.19/0.45 ( nonemptyE1
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ( nonempty @ A )
% 0.19/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyI_type,type,
% 0.19/0.45 nonemptyI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyI,definition,
% 0.19/0.45 ( nonemptyI
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( Xphi @ Xx )
% 0.19/0.45 => ( nonempty
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyI1_type,type,
% 0.19/0.45 nonemptyI1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyI1,definition,
% 0.19/0.45 ( nonemptyI1
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIL_type,type,
% 0.19/0.45 setadjoinIL: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIL,definition,
% 0.19/0.45 ( setadjoinIL
% 0.19/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptyinunitempty_type,type,
% 0.19/0.45 emptyinunitempty: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptyinunitempty,definition,
% 0.19/0.45 ( emptyinunitempty
% 0.19/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIR_type,type,
% 0.19/0.45 setadjoinIR: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinIR,definition,
% 0.19/0.45 ( setadjoinIR
% 0.19/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinE_type,type,
% 0.19/0.45 setadjoinE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinE,definition,
% 0.19/0.45 ( setadjoinE
% 0.19/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.45 => ! [Xphi: $o] :
% 0.19/0.45 ( ( ( Xy = Xx )
% 0.19/0.45 => Xphi )
% 0.19/0.45 => ( ( ( in @ Xy @ A )
% 0.19/0.45 => Xphi )
% 0.19/0.45 => Xphi ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinOr_type,type,
% 0.19/0.45 setadjoinOr: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setadjoinOr,definition,
% 0.19/0.45 ( setadjoinOr
% 0.19/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.45 => ( ( Xy = Xx )
% 0.19/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setoftrueEq_type,type,
% 0.19/0.45 setoftrueEq: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setoftrueEq,definition,
% 0.19/0.45 ( setoftrueEq
% 0.19/0.45 = ( ! [A: $i] :
% 0.19/0.45 ( ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xx: $i] : $true )
% 0.19/0.45 = A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powersetI_type,type,
% 0.19/0.45 powersetI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetI,definition,
% 0.19/0.45 ( powersetI
% 0.19/0.45 = ( ! [A: $i,B: $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 => ( in @ Xx @ A ) )
% 0.19/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptyinPowerset_type,type,
% 0.19/0.45 emptyinPowerset: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptyinPowerset,definition,
% 0.19/0.45 ( emptyinPowerset
% 0.19/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(emptyInPowerset_type,type,
% 0.19/0.45 emptyInPowerset: $o ).
% 0.19/0.45
% 0.19/0.45 thf(emptyInPowerset,definition,
% 0.19/0.45 ( emptyInPowerset
% 0.19/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powersetE_type,type,
% 0.19/0.45 powersetE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetE,definition,
% 0.19/0.45 ( powersetE
% 0.19/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.45 => ( ( in @ Xx @ B )
% 0.19/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setunionI_type,type,
% 0.19/0.45 setunionI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setunionI,definition,
% 0.19/0.45 ( setunionI
% 0.19/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 => ( ( in @ B @ A )
% 0.19/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setunionE_type,type,
% 0.19/0.45 setunionE: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setunionE,definition,
% 0.19/0.45 ( setunionE
% 0.19/0.45 = ( ! [A: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.45 => ! [Xphi: $o] :
% 0.19/0.45 ( ! [B: $i] :
% 0.19/0.45 ( ( in @ Xx @ B )
% 0.19/0.45 => ( ( in @ B @ A )
% 0.19/0.45 => Xphi ) )
% 0.19/0.45 => Xphi ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(subPowSU_type,type,
% 0.19/0.45 subPowSU: $o ).
% 0.19/0.45
% 0.19/0.45 thf(subPowSU,definition,
% 0.19/0.45 ( subPowSU
% 0.19/0.45 = ( ! [A: $i,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(exuE2_type,type,
% 0.19/0.45 exuE2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(exuE2,definition,
% 0.19/0.45 ( exuE2
% 0.19/0.45 = ( ! [Xphi: $i > $o] :
% 0.19/0.45 ( ( exu
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.45 => ? [Xx: $i] :
% 0.19/0.45 ! [Xy: $i] :
% 0.19/0.45 ( ( Xphi @ Xy )
% 0.19/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyImpWitness_type,type,
% 0.19/0.45 nonemptyImpWitness: $o ).
% 0.19/0.45
% 0.19/0.45 thf(nonemptyImpWitness,definition,
% 0.19/0.46 ( nonemptyImpWitness
% 0.19/0.46 = ( ! [A: $i] :
% 0.19/0.46 ( ( nonempty @ A )
% 0.19/0.46 => ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & $true ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(uniqinunit_type,type,
% 0.19/0.46 uniqinunit: $o ).
% 0.19/0.46
% 0.19/0.46 thf(uniqinunit,definition,
% 0.19/0.46 ( uniqinunit
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notinsingleton_type,type,
% 0.19/0.46 notinsingleton: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notinsingleton,definition,
% 0.19/0.46 ( notinsingleton
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx != Xy )
% 0.19/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(eqinunit_type,type,
% 0.19/0.46 eqinunit: $o ).
% 0.19/0.46
% 0.19/0.46 thf(eqinunit,definition,
% 0.19/0.46 ( eqinunit
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(singletonsswitch_type,type,
% 0.19/0.46 singletonsswitch: $o ).
% 0.19/0.46
% 0.19/0.46 thf(singletonsswitch,definition,
% 0.19/0.46 ( singletonsswitch
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetE_type,type,
% 0.19/0.46 upairsetE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetE,definition,
% 0.19/0.46 ( upairsetE
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.46 => ( ( Xz = Xx )
% 0.19/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetIL_type,type,
% 0.19/0.46 upairsetIL: $o ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetIL,definition,
% 0.19/0.46 ( upairsetIL
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetIR_type,type,
% 0.19/0.46 upairsetIR: $o ).
% 0.19/0.46
% 0.19/0.46 thf(upairsetIR,definition,
% 0.19/0.46 ( upairsetIR
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(emptyE1_type,type,
% 0.19/0.46 emptyE1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(emptyE1,definition,
% 0.19/0.46 ( emptyE1
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( Xphi @ Xx ) )
% 0.19/0.46 => ( ( ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 = emptyset )
% 0.19/0.46 => $false ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(vacuousDall_type,type,
% 0.19/0.46 vacuousDall: $o ).
% 0.19/0.46
% 0.19/0.46 thf(vacuousDall,definition,
% 0.19/0.46 ( vacuousDall
% 0.19/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ emptyset )
% 0.19/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan1_type,type,
% 0.19/0.46 quantDeMorgan1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan1,definition,
% 0.19/0.46 ( quantDeMorgan1
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ~ ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( Xphi @ Xx ) )
% 0.19/0.46 => ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan2_type,type,
% 0.19/0.46 quantDeMorgan2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan2,definition,
% 0.19/0.46 ( quantDeMorgan2
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ~ ( Xphi @ Xx ) )
% 0.19/0.46 => ~ ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan3_type,type,
% 0.19/0.46 quantDeMorgan3: $o ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan3,definition,
% 0.19/0.46 ( quantDeMorgan3
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ~ ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( Xphi @ Xx ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan4_type,type,
% 0.19/0.46 quantDeMorgan4: $o ).
% 0.19/0.46
% 0.19/0.46 thf(quantDeMorgan4,definition,
% 0.19/0.46 ( quantDeMorgan4
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ~ ( Xphi @ Xx ) )
% 0.19/0.46 => ~ ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(prop2setI_type,type,
% 0.19/0.46 prop2setI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(prop2setI,definition,
% 0.19/0.46 ( prop2setI
% 0.19/0.46 = ( ! [Xphi: $o] :
% 0.19/0.46 ( Xphi
% 0.19/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(set2prop_type,type,
% 0.19/0.46 set2prop: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(prop2set2propI_type,type,
% 0.19/0.46 prop2set2propI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(prop2set2propI,definition,
% 0.19/0.46 ( prop2set2propI
% 0.19/0.46 = ( ! [Xphi: $o] :
% 0.19/0.46 ( Xphi
% 0.19/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notdexE_type,type,
% 0.19/0.46 notdexE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notdexE,definition,
% 0.19/0.46 ( notdexE
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ~ ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( Xphi @ Xx ) )
% 0.19/0.46 => ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notdallE_type,type,
% 0.19/0.46 notdallE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notdallE,definition,
% 0.19/0.46 ( notdallE
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ~ ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( Xphi @ Xx ) )
% 0.19/0.46 => ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exuI1_type,type,
% 0.19/0.46 exuI1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exuI1,definition,
% 0.19/0.46 ( exuI1
% 0.19/0.46 = ( ! [Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ( ( Xphi @ Xx )
% 0.19/0.46 & ! [Xy: $i] :
% 0.19/0.46 ( ( Xphi @ Xy )
% 0.19/0.46 => ( Xx = Xy ) ) )
% 0.19/0.46 => ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exuI3_type,type,
% 0.19/0.46 exuI3: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exuI3,definition,
% 0.19/0.46 ( exuI3
% 0.19/0.46 = ( ! [Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.19/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xphi @ Xx )
% 0.19/0.46 => ( ( Xphi @ Xy )
% 0.19/0.46 => ( Xx = Xy ) ) )
% 0.19/0.46 => ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exuI2_type,type,
% 0.19/0.46 exuI2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exuI2,definition,
% 0.19/0.46 ( exuI2
% 0.19/0.46 = ( ! [Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ! [Xy: $i] :
% 0.19/0.46 ( ( Xphi @ Xy )
% 0.19/0.46 <=> ( Xy = Xx ) )
% 0.19/0.46 => ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(inCongP_type,type,
% 0.19/0.46 inCongP: $o ).
% 0.19/0.46
% 0.19/0.46 thf(inCongP,definition,
% 0.19/0.46 ( inCongP
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(in__Cong_type,type,
% 0.19/0.46 in__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(in__Cong,definition,
% 0.19/0.46 ( in__Cong
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( in @ Xx @ A )
% 0.19/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exuE3u_type,type,
% 0.19/0.46 exuE3u: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exuE3u,definition,
% 0.19/0.46 ( exuE3u
% 0.19/0.46 = ( ! [Xphi: $i > $o] :
% 0.19/0.46 ( ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xphi @ Xx )
% 0.19/0.46 => ( ( Xphi @ Xy )
% 0.19/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exu__Cong_type,type,
% 0.19/0.46 exu__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exu__Cong,definition,
% 0.19/0.46 ( exu__Cong
% 0.19/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( Xphi @ Xx )
% 0.19/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.46 => ( ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 <=> ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(emptyset__Cong_type,type,
% 0.19/0.46 emptyset__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(emptyset__Cong,definition,
% 0.19/0.46 ( emptyset__Cong
% 0.19/0.46 = ( emptyset = emptyset ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoin__Cong_type,type,
% 0.19/0.46 setadjoin__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoin__Cong,definition,
% 0.19/0.46 ( setadjoin__Cong
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ! [Xz: $i,Xu: $i] :
% 0.19/0.46 ( ( Xz = Xu )
% 0.19/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.19/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(powerset__Cong_type,type,
% 0.19/0.46 powerset__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(powerset__Cong,definition,
% 0.19/0.46 ( powerset__Cong
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ( ( powerset @ A )
% 0.19/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setunion__Cong_type,type,
% 0.19/0.46 setunion__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setunion__Cong,definition,
% 0.19/0.46 ( setunion__Cong
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ( ( setunion @ A )
% 0.19/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(omega__Cong_type,type,
% 0.19/0.46 omega__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(omega__Cong,definition,
% 0.19/0.46 ( omega__Cong
% 0.19/0.46 = ( omega = omega ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(exuEu_type,type,
% 0.19/0.46 exuEu: $o ).
% 0.19/0.46
% 0.19/0.46 thf(exuEu,definition,
% 0.19/0.46 ( exuEu
% 0.19/0.46 = ( ! [Xphi: $i > $o] :
% 0.19/0.46 ( ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 => ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xphi @ Xx )
% 0.19/0.46 => ( ( Xphi @ Xy )
% 0.19/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(descr__Cong_type,type,
% 0.19/0.46 descr__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(descr__Cong,definition,
% 0.19/0.46 ( descr__Cong
% 0.19/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( Xx = Xy )
% 0.19/0.46 => ( ( Xphi @ Xx )
% 0.19/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.46 => ( ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 => ( ( exu
% 0.19/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.46 => ( ( descr
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 = ( descr
% 0.19/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(dsetconstr__Cong_type,type,
% 0.19/0.46 dsetconstr__Cong: $o ).
% 0.19/0.46
% 0.19/0.46 thf(dsetconstr__Cong,definition,
% 0.19/0.46 ( dsetconstr__Cong
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.46 ( ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ! [Xy: $i] :
% 0.19/0.46 ( ( in @ Xy @ B )
% 0.19/0.46 => ( ( Xx = Xy )
% 0.19/0.46 => ( ( Xphi @ Xx )
% 0.19/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.19/0.46 => ( ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 = ( dsetconstr @ B
% 0.19/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subset_type,type,
% 0.19/0.46 subset: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(disjoint_type,type,
% 0.19/0.46 disjoint: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(setsmeet_type,type,
% 0.19/0.46 setsmeet: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetI1_type,type,
% 0.19/0.46 subsetI1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetI1,definition,
% 0.19/0.46 ( subsetI1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xx @ B ) )
% 0.19/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(eqimpsubset2_type,type,
% 0.19/0.46 eqimpsubset2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(eqimpsubset2,definition,
% 0.19/0.46 ( eqimpsubset2
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(eqimpsubset1_type,type,
% 0.19/0.46 eqimpsubset1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(eqimpsubset1,definition,
% 0.19/0.46 ( eqimpsubset1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( A = B )
% 0.19/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetI2_type,type,
% 0.19/0.46 subsetI2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetI2,definition,
% 0.19/0.46 ( subsetI2
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xx @ B ) )
% 0.19/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(emptysetsubset_type,type,
% 0.19/0.46 emptysetsubset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(emptysetsubset,definition,
% 0.19/0.46 ( emptysetsubset
% 0.19/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetE_type,type,
% 0.19/0.46 subsetE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetE,definition,
% 0.19/0.46 ( subsetE
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetE2_type,type,
% 0.19/0.46 subsetE2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetE2,definition,
% 0.19/0.46 ( subsetE2
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notsubsetI_type,type,
% 0.19/0.46 notsubsetI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notsubsetI,definition,
% 0.19/0.46 ( notsubsetI
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notequalI1_type,type,
% 0.19/0.46 notequalI1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notequalI1,definition,
% 0.19/0.46 ( notequalI1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ~ ( subset @ A @ B )
% 0.19/0.46 => ( A != B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(notequalI2_type,type,
% 0.19/0.46 notequalI2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(notequalI2,definition,
% 0.19/0.46 ( notequalI2
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ( A != B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetRefl_type,type,
% 0.19/0.46 subsetRefl: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetRefl,definition,
% 0.19/0.46 ( subsetRefl
% 0.19/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetTrans_type,type,
% 0.19/0.46 subsetTrans: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetTrans,definition,
% 0.19/0.46 ( subsetTrans
% 0.19/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ( subset @ B @ C )
% 0.19/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoinSub_type,type,
% 0.19/0.46 setadjoinSub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoinSub,definition,
% 0.19/0.46 ( setadjoinSub
% 0.19/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoinSub2_type,type,
% 0.19/0.46 setadjoinSub2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setadjoinSub2,definition,
% 0.19/0.46 ( setadjoinSub2
% 0.19/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subset2powerset_type,type,
% 0.19/0.46 subset2powerset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subset2powerset,definition,
% 0.19/0.46 ( subset2powerset
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setextsub_type,type,
% 0.19/0.46 setextsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setextsub,definition,
% 0.19/0.46 ( setextsub
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ( subset @ B @ A )
% 0.19/0.46 => ( A = B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(subsetemptysetimpeq_type,type,
% 0.19/0.46 subsetemptysetimpeq: $o ).
% 0.19/0.46
% 0.19/0.46 thf(subsetemptysetimpeq,definition,
% 0.19/0.46 ( subsetemptysetimpeq
% 0.19/0.46 = ( ! [A: $i] :
% 0.19/0.46 ( ( subset @ A @ emptyset )
% 0.19/0.46 => ( A = emptyset ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(powersetI1_type,type,
% 0.19/0.46 powersetI1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(powersetI1,definition,
% 0.19/0.46 ( powersetI1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ B @ A )
% 0.19/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(powersetE1_type,type,
% 0.19/0.46 powersetE1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(powersetE1,definition,
% 0.19/0.46 ( powersetE1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(inPowerset_type,type,
% 0.19/0.46 inPowerset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(inPowerset,definition,
% 0.19/0.46 ( inPowerset
% 0.19/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(powersetsubset_type,type,
% 0.19/0.46 powersetsubset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(powersetsubset,definition,
% 0.19/0.46 ( powersetsubset
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sepInPowerset_type,type,
% 0.19/0.46 sepInPowerset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(sepInPowerset,definition,
% 0.19/0.46 ( sepInPowerset
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( in
% 0.19/0.46 @ ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(sepSubset_type,type,
% 0.19/0.46 sepSubset: $o ).
% 0.19/0.46
% 0.19/0.46 thf(sepSubset,definition,
% 0.19/0.46 ( sepSubset
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( subset
% 0.19/0.46 @ ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunion_type,type,
% 0.19/0.46 binunion: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(binunionIL_type,type,
% 0.19/0.46 binunionIL: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionIL,definition,
% 0.19/0.46 ( binunionIL
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(upairset2IR_type,type,
% 0.19/0.46 upairset2IR: $o ).
% 0.19/0.46
% 0.19/0.46 thf(upairset2IR,definition,
% 0.19/0.46 ( upairset2IR
% 0.19/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunionIR_type,type,
% 0.19/0.46 binunionIR: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionIR,definition,
% 0.19/0.46 ( binunionIR
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ B )
% 0.19/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunionEcases_type,type,
% 0.19/0.46 binunionEcases: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionEcases,definition,
% 0.19/0.46 ( binunionEcases
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.46 => ( ( ( in @ Xx @ A )
% 0.19/0.46 => Xphi )
% 0.19/0.46 => ( ( ( in @ Xx @ B )
% 0.19/0.46 => Xphi )
% 0.19/0.46 => Xphi ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunionE_type,type,
% 0.19/0.46 binunionE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionE,definition,
% 0.19/0.46 ( binunionE
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.46 => ( ( in @ Xx @ A )
% 0.19/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunionLsub_type,type,
% 0.19/0.46 binunionLsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionLsub,definition,
% 0.19/0.46 ( binunionLsub
% 0.19/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binunionRsub_type,type,
% 0.19/0.46 binunionRsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binunionRsub,definition,
% 0.19/0.46 ( binunionRsub
% 0.19/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersect_type,type,
% 0.19/0.46 binintersect: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectI_type,type,
% 0.19/0.46 binintersectI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectI,definition,
% 0.19/0.46 ( binintersectI
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ( in @ Xx @ B )
% 0.19/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset5_type,type,
% 0.19/0.46 binintersectSubset5: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset5,definition,
% 0.19/0.46 ( binintersectSubset5
% 0.19/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.46 ( ( subset @ C @ A )
% 0.19/0.46 => ( ( subset @ C @ B )
% 0.19/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectEL_type,type,
% 0.19/0.46 binintersectEL: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectEL,definition,
% 0.19/0.46 ( binintersectEL
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectLsub_type,type,
% 0.19/0.46 binintersectLsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectLsub,definition,
% 0.19/0.46 ( binintersectLsub
% 0.19/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset2_type,type,
% 0.19/0.46 binintersectSubset2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset2,definition,
% 0.19/0.46 ( binintersectSubset2
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ( binintersect @ A @ B )
% 0.19/0.46 = A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset3_type,type,
% 0.19/0.46 binintersectSubset3: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset3,definition,
% 0.19/0.46 ( binintersectSubset3
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( ( binintersect @ A @ B )
% 0.19/0.46 = B )
% 0.19/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectER_type,type,
% 0.19/0.46 binintersectER: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectER,definition,
% 0.19/0.46 ( binintersectER
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(disjointsetsI1_type,type,
% 0.19/0.46 disjointsetsI1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(disjointsetsI1,definition,
% 0.19/0.46 ( disjointsetsI1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ~ ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( in @ Xx @ B ) )
% 0.19/0.46 => ( ( binintersect @ A @ B )
% 0.19/0.46 = emptyset ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectRsub_type,type,
% 0.19/0.46 binintersectRsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectRsub,definition,
% 0.19/0.46 ( binintersectRsub
% 0.19/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset4_type,type,
% 0.19/0.46 binintersectSubset4: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset4,definition,
% 0.19/0.46 ( binintersectSubset4
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ B @ A )
% 0.19/0.46 => ( ( binintersect @ A @ B )
% 0.19/0.46 = B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset1_type,type,
% 0.19/0.46 binintersectSubset1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(binintersectSubset1,definition,
% 0.19/0.46 ( binintersectSubset1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( ( binintersect @ A @ B )
% 0.19/0.46 = A )
% 0.19/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(bs114d_type,type,
% 0.19/0.46 bs114d: $o ).
% 0.19/0.46
% 0.19/0.46 thf(bs114d,definition,
% 0.19/0.46 ( bs114d
% 0.19/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.19/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(regular_type,type,
% 0.19/0.46 regular: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminus_type,type,
% 0.19/0.46 setminus: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(setminusI_type,type,
% 0.19/0.46 setminusI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusI,definition,
% 0.19/0.46 ( setminusI
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusEL_type,type,
% 0.19/0.46 setminusEL: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusEL,definition,
% 0.19/0.46 ( setminusEL
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusER_type,type,
% 0.19/0.46 setminusER: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusER,definition,
% 0.19/0.46 ( setminusER
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusSubset2_type,type,
% 0.19/0.46 setminusSubset2: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusSubset2,definition,
% 0.19/0.46 ( setminusSubset2
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( subset @ A @ B )
% 0.19/0.46 => ( ( setminus @ A @ B )
% 0.19/0.46 = emptyset ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusERneg_type,type,
% 0.19/0.46 setminusERneg: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusERneg,definition,
% 0.19/0.46 ( setminusERneg
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.46 => ( ( in @ Xx @ A )
% 0.19/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusELneg_type,type,
% 0.19/0.46 setminusELneg: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusELneg,definition,
% 0.19/0.46 ( setminusELneg
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusILneg_type,type,
% 0.19/0.46 setminusILneg: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusILneg,definition,
% 0.19/0.46 ( setminusILneg
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ~ ( in @ Xx @ A )
% 0.19/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusIRneg_type,type,
% 0.19/0.46 setminusIRneg: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusIRneg,definition,
% 0.19/0.46 ( setminusIRneg
% 0.19/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ B )
% 0.19/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusLsub_type,type,
% 0.19/0.46 setminusLsub: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusLsub,definition,
% 0.19/0.46 ( setminusLsub
% 0.19/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(setminusSubset1_type,type,
% 0.19/0.46 setminusSubset1: $o ).
% 0.19/0.46
% 0.19/0.46 thf(setminusSubset1,definition,
% 0.19/0.46 ( setminusSubset1
% 0.19/0.46 = ( ! [A: $i,B: $i] :
% 0.19/0.46 ( ( ( setminus @ A @ B )
% 0.19/0.46 = emptyset )
% 0.19/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(symdiff_type,type,
% 0.19/0.46 symdiff: $i > $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(symdiff,definition,
% 0.19/0.46 ( symdiff
% 0.19/0.46 = ( ^ [A: $i,B: $i] :
% 0.19/0.46 ( dsetconstr @ ( binunion @ A @ B )
% 0.19/0.46 @ ^ [Xx: $i] :
% 0.19/0.46 ( ~ ( in @ Xx @ A )
% 0.19/0.46 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(symdiffE,conjecture,
% 0.19/0.46 ( setextAx
% 0.19/0.46 => ( emptysetAx
% 0.19/0.46 => ( setadjoinAx
% 0.19/0.46 => ( powersetAx
% 0.19/0.46 => ( setunionAx
% 0.19/0.46 => ( omega0Ax
% 0.19/0.46 => ( omegaSAx
% 0.19/0.46 => ( omegaIndAx
% 0.19/0.46 => ( replAx
% 0.19/0.46 => ( foundationAx
% 0.19/0.46 => ( wellorderingAx
% 0.19/0.46 => ( descrp
% 0.19/0.46 => ( dsetconstrI
% 0.19/0.46 => ( dsetconstrEL
% 0.19/0.46 => ( dsetconstrER
% 0.19/0.46 => ( exuE1
% 0.19/0.46 => ( prop2setE
% 0.19/0.46 => ( emptysetE
% 0.19/0.46 => ( emptysetimpfalse
% 0.19/0.46 => ( notinemptyset
% 0.19/0.46 => ( exuE3e
% 0.19/0.46 => ( setext
% 0.19/0.46 => ( emptyI
% 0.19/0.46 => ( noeltsimpempty
% 0.19/0.46 => ( setbeta
% 0.19/0.46 => ( nonemptyE1
% 0.19/0.46 => ( nonemptyI
% 0.19/0.46 => ( nonemptyI1
% 0.19/0.46 => ( setadjoinIL
% 0.19/0.46 => ( emptyinunitempty
% 0.19/0.46 => ( setadjoinIR
% 0.19/0.46 => ( setadjoinE
% 0.19/0.46 => ( setadjoinOr
% 0.19/0.46 => ( setoftrueEq
% 0.19/0.46 => ( powersetI
% 0.19/0.46 => ( emptyinPowerset
% 0.19/0.46 => ( emptyInPowerset
% 0.19/0.46 => ( powersetE
% 0.19/0.46 => ( setunionI
% 0.19/0.46 => ( setunionE
% 0.19/0.46 => ( subPowSU
% 0.19/0.46 => ( exuE2
% 0.19/0.46 => ( nonemptyImpWitness
% 0.19/0.46 => ( uniqinunit
% 0.19/0.46 => ( notinsingleton
% 0.19/0.46 => ( eqinunit
% 0.19/0.46 => ( singletonsswitch
% 0.19/0.46 => ( upairsetE
% 0.19/0.46 => ( upairsetIL
% 0.19/0.46 => ( upairsetIR
% 0.19/0.46 => ( emptyE1
% 0.19/0.46 => ( vacuousDall
% 0.19/0.46 => ( quantDeMorgan1
% 0.19/0.46 => ( quantDeMorgan2
% 0.19/0.46 => ( quantDeMorgan3
% 0.19/0.46 => ( quantDeMorgan4
% 0.19/0.46 => ( prop2setI
% 0.19/0.46 => ( prop2set2propI
% 0.19/0.46 => ( notdexE
% 0.19/0.46 => ( notdallE
% 0.19/0.46 => ( exuI1
% 0.19/0.46 => ( exuI3
% 0.19/0.46 => ( exuI2
% 0.19/0.46 => ( inCongP
% 0.19/0.46 => ( in__Cong
% 0.19/0.46 => ( exuE3u
% 0.19/0.46 => ( exu__Cong
% 0.19/0.46 => ( emptyset__Cong
% 0.19/0.46 => ( setadjoin__Cong
% 0.19/0.46 => ( powerset__Cong
% 0.19/0.46 => ( setunion__Cong
% 0.19/0.46 => ( omega__Cong
% 0.19/0.46 => ( exuEu
% 0.19/0.46 => ( descr__Cong
% 0.19/0.46 => ( dsetconstr__Cong
% 0.19/0.46 => ( subsetI1
% 0.19/0.46 => ( eqimpsubset2
% 0.19/0.46 => ( eqimpsubset1
% 0.19/0.46 => ( subsetI2
% 0.19/0.46 => ( emptysetsubset
% 0.19/0.46 => ( subsetE
% 0.19/0.46 => ( subsetE2
% 0.19/0.46 => ( notsubsetI
% 0.19/0.46 => ( notequalI1
% 0.19/0.46 => ( notequalI2
% 0.19/0.46 => ( subsetRefl
% 0.19/0.46 => ( subsetTrans
% 0.19/0.46 => ( setadjoinSub
% 0.19/0.46 => ( setadjoinSub2
% 0.19/0.46 => ( subset2powerset
% 0.19/0.46 => ( setextsub
% 0.19/0.46 => ( subsetemptysetimpeq
% 0.19/0.46 => ( powersetI1
% 0.19/0.46 => ( powersetE1
% 0.19/0.46 => ( inPowerset
% 0.19/0.46 => ( powersetsubset
% 0.19/0.46 => ( sepInPowerset
% 0.19/0.46 => ( sepSubset
% 0.19/0.46 => ( binunionIL
% 0.19/0.46 => ( upairset2IR
% 0.19/0.46 => ( binunionIR
% 0.19/0.46 => ( binunionEcases
% 0.19/0.46 => ( binunionE
% 0.19/0.46 => ( binunionLsub
% 0.19/0.46 => ( binunionRsub
% 0.19/0.46 => ( binintersectI
% 0.19/0.46 => ( binintersectSubset5
% 0.19/0.46 => ( binintersectEL
% 0.19/0.46 => ( binintersectLsub
% 0.19/0.46 => ( binintersectSubset2
% 0.19/0.46 => ( binintersectSubset3
% 0.19/0.46 => ( binintersectER
% 0.19/0.46 => ( disjointsetsI1
% 0.19/0.46 => ( binintersectRsub
% 0.19/0.46 => ( binintersectSubset4
% 0.19/0.46 => ( binintersectSubset1
% 0.19/0.46 => ( bs114d
% 0.19/0.46 => ( setminusI
% 0.19/0.46 => ( setminusEL
% 0.19/0.46 => ( setminusER
% 0.19/0.46 => ( setminusSubset2
% 0.19/0.46 => ( setminusERneg
% 0.19/0.46 => ( setminusELneg
% 0.19/0.46 => ( setminusILneg
% 0.19/0.46 => ( setminusIRneg
% 0.19/0.46 => ( setminusLsub
% 0.19/0.46 => ( setminusSubset1
% 0.19/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.19/0.46 => ! [Xphi: $o] :
% 0.19/0.46 ( ( ( in @ Xx @ A )
% 0.19/0.46 => ( ~ ( in @ Xx @ B )
% 0.19/0.46 => Xphi ) )
% 0.19/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.19/0.46 => ( ( in @ Xx @ B )
% 0.19/0.46 => Xphi ) )
% 0.19/0.46 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 2.21/1.35 ---- Embedded in THF ---
% 2.21/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.21/1.35 %%% Generated on Tue Feb 24 12:28:55 EST 2026
% 2.21/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 2.21/1.35 %%% Logic specification used:
% 2.21/1.35 %%% thf(spec, logic, $$dhol).
% 2.21/1.35
% 2.21/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2DTF10434.p
% See solution above
% 2.21/1.35 ------------------------
% 2.21/1.37 ---- Cleaned THF ---
% 2.21/1.37 thf(in_type,type,
% 2.21/1.37 in: $i > $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(exu_type,type,
% 2.21/1.37 exu: ( $i > $o ) > $o ).
% 2.21/1.37
% 2.21/1.37 thf(exu,definition,
% 2.21/1.37 ( exu
% 2.21/1.37 = ( ^ [Xphi: $i > $o] :
% 2.21/1.37 ? [Xx: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 & ! [Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setextAx_type,type,
% 2.21/1.37 setextAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setextAx,definition,
% 2.21/1.37 ( setextAx
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 <=> ( in @ Xx @ B ) )
% 2.21/1.37 => ( A = B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyset_type,type,
% 2.21/1.37 emptyset: $i ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetAx_type,type,
% 2.21/1.37 emptysetAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetAx,definition,
% 2.21/1.37 ( emptysetAx
% 2.21/1.37 = ( ! [Xx: $i] :
% 2.21/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoin_type,type,
% 2.21/1.37 setadjoin: $i > $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinAx_type,type,
% 2.21/1.37 setadjoinAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinAx,definition,
% 2.21/1.37 ( setadjoinAx
% 2.21/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.21/1.37 <=> ( ( Xy = Xx )
% 2.21/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powerset_type,type,
% 2.21/1.37 powerset: $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(powersetAx_type,type,
% 2.21/1.37 powersetAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetAx,definition,
% 2.21/1.37 ( powersetAx
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.21/1.37 <=> ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setunion_type,type,
% 2.21/1.37 setunion: $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(setunionAx_type,type,
% 2.21/1.37 setunionAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setunionAx,definition,
% 2.21/1.37 ( setunionAx
% 2.21/1.37 = ( ! [A: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 2.21/1.37 <=> ? [B: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 & ( in @ B @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(omega_type,type,
% 2.21/1.37 omega: $i ).
% 2.21/1.37
% 2.21/1.37 thf(omega0Ax_type,type,
% 2.21/1.37 omega0Ax: $o ).
% 2.21/1.37
% 2.21/1.37 thf(omega0Ax,definition,
% 2.21/1.37 ( omega0Ax
% 2.21/1.37 = ( in @ emptyset @ omega ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(omegaSAx_type,type,
% 2.21/1.37 omegaSAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(omegaSAx,definition,
% 2.21/1.37 ( omegaSAx
% 2.21/1.37 = ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ omega )
% 2.21/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(omegaIndAx_type,type,
% 2.21/1.37 omegaIndAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(omegaIndAx,definition,
% 2.21/1.37 ( omegaIndAx
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ( ( in @ emptyset @ A )
% 2.21/1.37 & ! [Xx: $i] :
% 2.21/1.37 ( ( ( in @ Xx @ omega )
% 2.21/1.37 & ( in @ Xx @ A ) )
% 2.21/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.21/1.37 => ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ omega )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(replAx_type,type,
% 2.21/1.37 replAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(replAx,definition,
% 2.21/1.37 ( replAx
% 2.21/1.37 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( exu
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.21/1.37 => ? [B: $i] :
% 2.21/1.37 ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 <=> ? [Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ A )
% 2.21/1.37 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(foundationAx_type,type,
% 2.21/1.37 foundationAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(foundationAx,definition,
% 2.21/1.37 ( foundationAx
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.21/1.37 => ? [B: $i] :
% 2.21/1.37 ( ( in @ B @ A )
% 2.21/1.37 & ~ ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(wellorderingAx_type,type,
% 2.21/1.37 wellorderingAx: $o ).
% 2.21/1.37
% 2.21/1.37 thf(wellorderingAx,definition,
% 2.21/1.37 ( wellorderingAx
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ? [B: $i] :
% 2.21/1.37 ( ! [C: $i] :
% 2.21/1.37 ( ( in @ C @ B )
% 2.21/1.37 => ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ C )
% 2.21/1.37 => ( in @ Xx @ A ) ) )
% 2.21/1.37 & ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( ( in @ Xx @ A )
% 2.21/1.37 & ( in @ Xy @ A ) )
% 2.21/1.37 => ( ! [C: $i] :
% 2.21/1.37 ( ( in @ C @ B )
% 2.21/1.37 => ( ( in @ Xx @ C )
% 2.21/1.37 <=> ( in @ Xy @ C ) ) )
% 2.21/1.37 => ( Xx = Xy ) ) )
% 2.21/1.37 & ! [C: $i,D: $i] :
% 2.21/1.37 ( ( ( in @ C @ B )
% 2.21/1.37 & ( in @ D @ B ) )
% 2.21/1.37 => ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ C )
% 2.21/1.37 => ( in @ Xx @ D ) )
% 2.21/1.37 | ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ D )
% 2.21/1.37 => ( in @ Xx @ C ) ) ) )
% 2.21/1.37 & ! [C: $i] :
% 2.21/1.37 ( ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ C )
% 2.21/1.37 => ( in @ Xx @ A ) )
% 2.21/1.37 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.21/1.37 => ? [D: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ D @ B )
% 2.21/1.37 & ( in @ Xx @ C )
% 2.21/1.37 & ~ ? [Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ D )
% 2.21/1.37 & ( in @ Xy @ C ) )
% 2.21/1.37 & ! [E: $i] :
% 2.21/1.37 ( ( in @ E @ B )
% 2.21/1.37 => ( ! [Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ E )
% 2.21/1.37 => ( in @ Xy @ D ) )
% 2.21/1.37 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(descr_type,type,
% 2.21/1.37 descr: ( $i > $o ) > $i ).
% 2.21/1.37
% 2.21/1.37 thf(descrp_type,type,
% 2.21/1.37 descrp: $o ).
% 2.21/1.37
% 2.21/1.37 thf(descrp,definition,
% 2.21/1.37 ( descrp
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ( Xphi
% 2.21/1.37 @ ( descr
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstr_type,type,
% 2.21/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrI_type,type,
% 2.21/1.37 dsetconstrI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrI,definition,
% 2.21/1.37 ( dsetconstrI
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ( Xphi @ Xx )
% 2.21/1.37 => ( in @ Xx
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrEL_type,type,
% 2.21/1.37 dsetconstrEL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrEL,definition,
% 2.21/1.37 ( dsetconstrEL
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrER_type,type,
% 2.21/1.37 dsetconstrER: $o ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstrER,definition,
% 2.21/1.37 ( dsetconstrER
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.21/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuE1_type,type,
% 2.21/1.37 exuE1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuE1,definition,
% 2.21/1.37 ( exuE1
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ? [Xx: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 & ! [Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(prop2set_type,type,
% 2.21/1.37 prop2set: $o > $i ).
% 2.21/1.37
% 2.21/1.37 thf(prop2setE_type,type,
% 2.21/1.37 prop2setE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(prop2setE,definition,
% 2.21/1.37 ( prop2setE
% 2.21/1.37 = ( ! [Xphi: $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.21/1.37 => Xphi ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetE_type,type,
% 2.21/1.37 emptysetE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetE,definition,
% 2.21/1.37 ( emptysetE
% 2.21/1.37 = ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ emptyset )
% 2.21/1.37 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetimpfalse_type,type,
% 2.21/1.37 emptysetimpfalse: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetimpfalse,definition,
% 2.21/1.37 ( emptysetimpfalse
% 2.21/1.37 = ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ emptyset )
% 2.21/1.37 => $false ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notinemptyset_type,type,
% 2.21/1.37 notinemptyset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notinemptyset,definition,
% 2.21/1.37 ( notinemptyset
% 2.21/1.37 = ( ! [Xx: $i] :
% 2.21/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuE3e_type,type,
% 2.21/1.37 exuE3e: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuE3e,definition,
% 2.21/1.37 ( exuE3e
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setext_type,type,
% 2.21/1.37 setext: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setext,definition,
% 2.21/1.37 ( setext
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ B ) )
% 2.21/1.37 => ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ A ) )
% 2.21/1.37 => ( A = B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyI_type,type,
% 2.21/1.37 emptyI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyI,definition,
% 2.21/1.37 ( emptyI
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ~ ( in @ Xx @ A )
% 2.21/1.37 => ( A = emptyset ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(noeltsimpempty_type,type,
% 2.21/1.37 noeltsimpempty: $o ).
% 2.21/1.37
% 2.21/1.37 thf(noeltsimpempty,definition,
% 2.21/1.37 ( noeltsimpempty
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ~ ( in @ Xx @ A )
% 2.21/1.37 => ( A = emptyset ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setbeta_type,type,
% 2.21/1.37 setbeta: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setbeta,definition,
% 2.21/1.37 ( setbeta
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ( in @ Xx
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.21/1.37 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(nonempty_type,type,
% 2.21/1.37 nonempty: $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(nonempty,definition,
% 2.21/1.37 ( nonempty
% 2.21/1.37 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyE1_type,type,
% 2.21/1.37 nonemptyE1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyE1,definition,
% 2.21/1.37 ( nonemptyE1
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ( nonempty @ A )
% 2.21/1.37 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyI_type,type,
% 2.21/1.37 nonemptyI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyI,definition,
% 2.21/1.37 ( nonemptyI
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ( Xphi @ Xx )
% 2.21/1.37 => ( nonempty
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyI1_type,type,
% 2.21/1.37 nonemptyI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyI1,definition,
% 2.21/1.37 ( nonemptyI1
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.21/1.37 => ( nonempty @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinIL_type,type,
% 2.21/1.37 setadjoinIL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinIL,definition,
% 2.21/1.37 ( setadjoinIL
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyinunitempty_type,type,
% 2.21/1.37 emptyinunitempty: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyinunitempty,definition,
% 2.21/1.37 ( emptyinunitempty
% 2.21/1.37 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinIR_type,type,
% 2.21/1.37 setadjoinIR: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinIR,definition,
% 2.21/1.37 ( setadjoinIR
% 2.21/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ A )
% 2.21/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinE_type,type,
% 2.21/1.37 setadjoinE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinE,definition,
% 2.21/1.37 ( setadjoinE
% 2.21/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.21/1.37 => ! [Xphi: $o] :
% 2.21/1.37 ( ( ( Xy = Xx )
% 2.21/1.37 => Xphi )
% 2.21/1.37 => ( ( ( in @ Xy @ A )
% 2.21/1.37 => Xphi )
% 2.21/1.37 => Xphi ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinOr_type,type,
% 2.21/1.37 setadjoinOr: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinOr,definition,
% 2.21/1.37 ( setadjoinOr
% 2.21/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.21/1.37 => ( ( Xy = Xx )
% 2.21/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setoftrueEq_type,type,
% 2.21/1.37 setoftrueEq: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setoftrueEq,definition,
% 2.21/1.37 ( setoftrueEq
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xx: $i] : $true )
% 2.21/1.37 = A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powersetI_type,type,
% 2.21/1.37 powersetI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetI,definition,
% 2.21/1.37 ( powersetI
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ A ) )
% 2.21/1.37 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyinPowerset_type,type,
% 2.21/1.37 emptyinPowerset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyinPowerset,definition,
% 2.21/1.37 ( emptyinPowerset
% 2.21/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyInPowerset_type,type,
% 2.21/1.37 emptyInPowerset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyInPowerset,definition,
% 2.21/1.37 ( emptyInPowerset
% 2.21/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powersetE_type,type,
% 2.21/1.37 powersetE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetE,definition,
% 2.21/1.37 ( powersetE
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.21/1.37 => ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setunionI_type,type,
% 2.21/1.37 setunionI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setunionI,definition,
% 2.21/1.37 ( setunionI
% 2.21/1.37 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( ( in @ B @ A )
% 2.21/1.37 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setunionE_type,type,
% 2.21/1.37 setunionE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setunionE,definition,
% 2.21/1.37 ( setunionE
% 2.21/1.37 = ( ! [A: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 2.21/1.37 => ! [Xphi: $o] :
% 2.21/1.37 ( ! [B: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( ( in @ B @ A )
% 2.21/1.37 => Xphi ) )
% 2.21/1.37 => Xphi ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subPowSU_type,type,
% 2.21/1.37 subPowSU: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subPowSU,definition,
% 2.21/1.37 ( subPowSU
% 2.21/1.37 = ( ! [A: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuE2_type,type,
% 2.21/1.37 exuE2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuE2,definition,
% 2.21/1.37 ( exuE2
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ? [Xx: $i] :
% 2.21/1.37 ! [Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xy )
% 2.21/1.37 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyImpWitness_type,type,
% 2.21/1.37 nonemptyImpWitness: $o ).
% 2.21/1.37
% 2.21/1.37 thf(nonemptyImpWitness,definition,
% 2.21/1.37 ( nonemptyImpWitness
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ( nonempty @ A )
% 2.21/1.37 => ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & $true ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(uniqinunit_type,type,
% 2.21/1.37 uniqinunit: $o ).
% 2.21/1.37
% 2.21/1.37 thf(uniqinunit,definition,
% 2.21/1.37 ( uniqinunit
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.21/1.37 => ( Xx = Xy ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notinsingleton_type,type,
% 2.21/1.37 notinsingleton: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notinsingleton,definition,
% 2.21/1.37 ( notinsingleton
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx != Xy )
% 2.21/1.37 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(eqinunit_type,type,
% 2.21/1.37 eqinunit: $o ).
% 2.21/1.37
% 2.21/1.37 thf(eqinunit,definition,
% 2.21/1.37 ( eqinunit
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(singletonsswitch_type,type,
% 2.21/1.37 singletonsswitch: $o ).
% 2.21/1.37
% 2.21/1.37 thf(singletonsswitch,definition,
% 2.21/1.37 ( singletonsswitch
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.21/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetE_type,type,
% 2.21/1.37 upairsetE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetE,definition,
% 2.21/1.37 ( upairsetE
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.21/1.37 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.21/1.37 => ( ( Xz = Xx )
% 2.21/1.37 | ( Xz = Xy ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetIL_type,type,
% 2.21/1.37 upairsetIL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetIL,definition,
% 2.21/1.37 ( upairsetIL
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetIR_type,type,
% 2.21/1.37 upairsetIR: $o ).
% 2.21/1.37
% 2.21/1.37 thf(upairsetIR,definition,
% 2.21/1.37 ( upairsetIR
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyE1_type,type,
% 2.21/1.37 emptyE1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyE1,definition,
% 2.21/1.37 ( emptyE1
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ( Xphi @ Xx ) )
% 2.21/1.37 => ( ( ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 = emptyset )
% 2.21/1.37 => $false ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(vacuousDall_type,type,
% 2.21/1.37 vacuousDall: $o ).
% 2.21/1.37
% 2.21/1.37 thf(vacuousDall,definition,
% 2.21/1.37 ( vacuousDall
% 2.21/1.37 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ emptyset )
% 2.21/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan1_type,type,
% 2.21/1.37 quantDeMorgan1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan1,definition,
% 2.21/1.37 ( quantDeMorgan1
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ~ ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( Xphi @ Xx ) )
% 2.21/1.37 => ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan2_type,type,
% 2.21/1.37 quantDeMorgan2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan2,definition,
% 2.21/1.37 ( quantDeMorgan2
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ~ ( Xphi @ Xx ) )
% 2.21/1.37 => ~ ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan3_type,type,
% 2.21/1.37 quantDeMorgan3: $o ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan3,definition,
% 2.21/1.37 ( quantDeMorgan3
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ~ ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ( Xphi @ Xx ) )
% 2.21/1.37 => ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan4_type,type,
% 2.21/1.37 quantDeMorgan4: $o ).
% 2.21/1.37
% 2.21/1.37 thf(quantDeMorgan4,definition,
% 2.21/1.37 ( quantDeMorgan4
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ~ ( Xphi @ Xx ) )
% 2.21/1.37 => ~ ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(prop2setI_type,type,
% 2.21/1.37 prop2setI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(prop2setI,definition,
% 2.21/1.37 ( prop2setI
% 2.21/1.37 = ( ! [Xphi: $o] :
% 2.21/1.37 ( Xphi
% 2.21/1.37 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(set2prop_type,type,
% 2.21/1.37 set2prop: $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(prop2set2propI_type,type,
% 2.21/1.37 prop2set2propI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(prop2set2propI,definition,
% 2.21/1.37 ( prop2set2propI
% 2.21/1.37 = ( ! [Xphi: $o] :
% 2.21/1.37 ( Xphi
% 2.21/1.37 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notdexE_type,type,
% 2.21/1.37 notdexE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notdexE,definition,
% 2.21/1.37 ( notdexE
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ~ ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ( Xphi @ Xx ) )
% 2.21/1.37 => ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notdallE_type,type,
% 2.21/1.37 notdallE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notdallE,definition,
% 2.21/1.37 ( notdallE
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( ~ ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( Xphi @ Xx ) )
% 2.21/1.37 => ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuI1_type,type,
% 2.21/1.37 exuI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuI1,definition,
% 2.21/1.37 ( exuI1
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ? [Xx: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 & ! [Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) )
% 2.21/1.37 => ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuI3_type,type,
% 2.21/1.37 exuI3: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuI3,definition,
% 2.21/1.37 ( exuI3
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.21/1.37 => ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 => ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) )
% 2.21/1.37 => ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuI2_type,type,
% 2.21/1.37 exuI2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuI2,definition,
% 2.21/1.37 ( exuI2
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ? [Xx: $i] :
% 2.21/1.37 ! [Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xy )
% 2.21/1.37 <=> ( Xy = Xx ) )
% 2.21/1.37 => ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(inCongP_type,type,
% 2.21/1.37 inCongP: $o ).
% 2.21/1.37
% 2.21/1.37 thf(inCongP,definition,
% 2.21/1.37 ( inCongP
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(in__Cong_type,type,
% 2.21/1.37 in__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(in__Cong,definition,
% 2.21/1.37 ( in__Cong
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ( ( in @ Xx @ A )
% 2.21/1.37 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuE3u_type,type,
% 2.21/1.37 exuE3u: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuE3u,definition,
% 2.21/1.37 ( exuE3u
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 => ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exu__Cong_type,type,
% 2.21/1.37 exu__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exu__Cong,definition,
% 2.21/1.37 ( exu__Cong
% 2.21/1.37 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.21/1.37 ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ( ( Xphi @ Xx )
% 2.21/1.37 <=> ( Xpsi @ Xy ) ) )
% 2.21/1.37 => ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 <=> ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptyset__Cong_type,type,
% 2.21/1.37 emptyset__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptyset__Cong,definition,
% 2.21/1.37 ( emptyset__Cong
% 2.21/1.37 = ( emptyset = emptyset ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoin__Cong_type,type,
% 2.21/1.37 setadjoin__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoin__Cong,definition,
% 2.21/1.37 ( setadjoin__Cong
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ! [Xz: $i,Xu: $i] :
% 2.21/1.37 ( ( Xz = Xu )
% 2.21/1.37 => ( ( setadjoin @ Xx @ Xz )
% 2.21/1.37 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powerset__Cong_type,type,
% 2.21/1.37 powerset__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powerset__Cong,definition,
% 2.21/1.37 ( powerset__Cong
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ( ( powerset @ A )
% 2.21/1.37 = ( powerset @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setunion__Cong_type,type,
% 2.21/1.37 setunion__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setunion__Cong,definition,
% 2.21/1.37 ( setunion__Cong
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ( ( setunion @ A )
% 2.21/1.37 = ( setunion @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(omega__Cong_type,type,
% 2.21/1.37 omega__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(omega__Cong,definition,
% 2.21/1.37 ( omega__Cong
% 2.21/1.37 = ( omega = omega ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(exuEu_type,type,
% 2.21/1.37 exuEu: $o ).
% 2.21/1.37
% 2.21/1.37 thf(exuEu,definition,
% 2.21/1.37 ( exuEu
% 2.21/1.37 = ( ! [Xphi: $i > $o] :
% 2.21/1.37 ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xphi @ Xx )
% 2.21/1.37 => ( ( Xphi @ Xy )
% 2.21/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(descr__Cong_type,type,
% 2.21/1.37 descr__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(descr__Cong,definition,
% 2.21/1.37 ( descr__Cong
% 2.21/1.37 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.21/1.37 ( ! [Xx: $i,Xy: $i] :
% 2.21/1.37 ( ( Xx = Xy )
% 2.21/1.37 => ( ( Xphi @ Xx )
% 2.21/1.37 <=> ( Xpsi @ Xy ) ) )
% 2.21/1.37 => ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 => ( ( exu
% 2.21/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.21/1.37 => ( ( descr
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 = ( descr
% 2.21/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstr__Cong_type,type,
% 2.21/1.37 dsetconstr__Cong: $o ).
% 2.21/1.37
% 2.21/1.37 thf(dsetconstr__Cong,definition,
% 2.21/1.37 ( dsetconstr__Cong
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ! [Xy: $i] :
% 2.21/1.37 ( ( in @ Xy @ B )
% 2.21/1.37 => ( ( Xx = Xy )
% 2.21/1.37 => ( ( Xphi @ Xx )
% 2.21/1.37 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.21/1.37 => ( ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 = ( dsetconstr @ B
% 2.21/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subset_type,type,
% 2.21/1.37 subset: $i > $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(disjoint_type,type,
% 2.21/1.37 disjoint: $i > $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(setsmeet_type,type,
% 2.21/1.37 setsmeet: $i > $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetI1_type,type,
% 2.21/1.37 subsetI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetI1,definition,
% 2.21/1.37 ( subsetI1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ B ) )
% 2.21/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(eqimpsubset2_type,type,
% 2.21/1.37 eqimpsubset2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(eqimpsubset2,definition,
% 2.21/1.37 ( eqimpsubset2
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(eqimpsubset1_type,type,
% 2.21/1.37 eqimpsubset1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(eqimpsubset1,definition,
% 2.21/1.37 ( eqimpsubset1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( A = B )
% 2.21/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetI2_type,type,
% 2.21/1.37 subsetI2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetI2,definition,
% 2.21/1.37 ( subsetI2
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ! [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ B ) )
% 2.21/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetsubset_type,type,
% 2.21/1.37 emptysetsubset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(emptysetsubset,definition,
% 2.21/1.37 ( emptysetsubset
% 2.21/1.37 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetE_type,type,
% 2.21/1.37 subsetE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetE,definition,
% 2.21/1.37 ( subsetE
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetE2_type,type,
% 2.21/1.37 subsetE2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetE2,definition,
% 2.21/1.37 ( subsetE2
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notsubsetI_type,type,
% 2.21/1.37 notsubsetI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notsubsetI,definition,
% 2.21/1.37 ( notsubsetI
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notequalI1_type,type,
% 2.21/1.37 notequalI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notequalI1,definition,
% 2.21/1.37 ( notequalI1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ~ ( subset @ A @ B )
% 2.21/1.37 => ( A != B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(notequalI2_type,type,
% 2.21/1.37 notequalI2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(notequalI2,definition,
% 2.21/1.37 ( notequalI2
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => ( A != B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetRefl_type,type,
% 2.21/1.37 subsetRefl: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetRefl,definition,
% 2.21/1.37 ( subsetRefl
% 2.21/1.37 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetTrans_type,type,
% 2.21/1.37 subsetTrans: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetTrans,definition,
% 2.21/1.37 ( subsetTrans
% 2.21/1.37 = ( ! [A: $i,B: $i,C: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ( subset @ B @ C )
% 2.21/1.37 => ( subset @ A @ C ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinSub_type,type,
% 2.21/1.37 setadjoinSub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinSub,definition,
% 2.21/1.37 ( setadjoinSub
% 2.21/1.37 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinSub2_type,type,
% 2.21/1.37 setadjoinSub2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setadjoinSub2,definition,
% 2.21/1.37 ( setadjoinSub2
% 2.21/1.37 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subset2powerset_type,type,
% 2.21/1.37 subset2powerset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subset2powerset,definition,
% 2.21/1.37 ( subset2powerset
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setextsub_type,type,
% 2.21/1.37 setextsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setextsub,definition,
% 2.21/1.37 ( setextsub
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ( subset @ B @ A )
% 2.21/1.37 => ( A = B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(subsetemptysetimpeq_type,type,
% 2.21/1.37 subsetemptysetimpeq: $o ).
% 2.21/1.37
% 2.21/1.37 thf(subsetemptysetimpeq,definition,
% 2.21/1.37 ( subsetemptysetimpeq
% 2.21/1.37 = ( ! [A: $i] :
% 2.21/1.37 ( ( subset @ A @ emptyset )
% 2.21/1.37 => ( A = emptyset ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powersetI1_type,type,
% 2.21/1.37 powersetI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetI1,definition,
% 2.21/1.37 ( powersetI1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ B @ A )
% 2.21/1.37 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powersetE1_type,type,
% 2.21/1.37 powersetE1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetE1,definition,
% 2.21/1.37 ( powersetE1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.21/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(inPowerset_type,type,
% 2.21/1.37 inPowerset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(inPowerset,definition,
% 2.21/1.37 ( inPowerset
% 2.21/1.37 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(powersetsubset_type,type,
% 2.21/1.37 powersetsubset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(powersetsubset,definition,
% 2.21/1.37 ( powersetsubset
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(sepInPowerset_type,type,
% 2.21/1.37 sepInPowerset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(sepInPowerset,definition,
% 2.21/1.37 ( sepInPowerset
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( in
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 @ ( powerset @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(sepSubset_type,type,
% 2.21/1.37 sepSubset: $o ).
% 2.21/1.37
% 2.21/1.37 thf(sepSubset,definition,
% 2.21/1.37 ( sepSubset
% 2.21/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.21/1.37 ( subset
% 2.21/1.37 @ ( dsetconstr @ A
% 2.21/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.21/1.37 @ A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunion_type,type,
% 2.21/1.37 binunion: $i > $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(binunionIL_type,type,
% 2.21/1.37 binunionIL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionIL,definition,
% 2.21/1.37 ( binunionIL
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(upairset2IR_type,type,
% 2.21/1.37 upairset2IR: $o ).
% 2.21/1.37
% 2.21/1.37 thf(upairset2IR,definition,
% 2.21/1.37 ( upairset2IR
% 2.21/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunionIR_type,type,
% 2.21/1.37 binunionIR: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionIR,definition,
% 2.21/1.37 ( binunionIR
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunionEcases_type,type,
% 2.21/1.37 binunionEcases: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionEcases,definition,
% 2.21/1.37 ( binunionEcases
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.21/1.37 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.21/1.37 => ( ( ( in @ Xx @ A )
% 2.21/1.37 => Xphi )
% 2.21/1.37 => ( ( ( in @ Xx @ B )
% 2.21/1.37 => Xphi )
% 2.21/1.37 => Xphi ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunionE_type,type,
% 2.21/1.37 binunionE: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionE,definition,
% 2.21/1.37 ( binunionE
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.21/1.37 => ( ( in @ Xx @ A )
% 2.21/1.37 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunionLsub_type,type,
% 2.21/1.37 binunionLsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionLsub,definition,
% 2.21/1.37 ( binunionLsub
% 2.21/1.37 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binunionRsub_type,type,
% 2.21/1.37 binunionRsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binunionRsub,definition,
% 2.21/1.37 ( binunionRsub
% 2.21/1.37 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersect_type,type,
% 2.21/1.37 binintersect: $i > $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectI_type,type,
% 2.21/1.37 binintersectI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectI,definition,
% 2.21/1.37 ( binintersectI
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset5_type,type,
% 2.21/1.37 binintersectSubset5: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset5,definition,
% 2.21/1.37 ( binintersectSubset5
% 2.21/1.37 = ( ! [A: $i,B: $i,C: $i] :
% 2.21/1.37 ( ( subset @ C @ A )
% 2.21/1.37 => ( ( subset @ C @ B )
% 2.21/1.37 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectEL_type,type,
% 2.21/1.37 binintersectEL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectEL,definition,
% 2.21/1.37 ( binintersectEL
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectLsub_type,type,
% 2.21/1.37 binintersectLsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectLsub,definition,
% 2.21/1.37 ( binintersectLsub
% 2.21/1.37 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset2_type,type,
% 2.21/1.37 binintersectSubset2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset2,definition,
% 2.21/1.37 ( binintersectSubset2
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ( binintersect @ A @ B )
% 2.21/1.37 = A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset3_type,type,
% 2.21/1.37 binintersectSubset3: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset3,definition,
% 2.21/1.37 ( binintersectSubset3
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( ( binintersect @ A @ B )
% 2.21/1.37 = B )
% 2.21/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectER_type,type,
% 2.21/1.37 binintersectER: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectER,definition,
% 2.21/1.37 ( binintersectER
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.21/1.37 => ( in @ Xx @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(disjointsetsI1_type,type,
% 2.21/1.37 disjointsetsI1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(disjointsetsI1,definition,
% 2.21/1.37 ( disjointsetsI1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ~ ? [Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 & ( in @ Xx @ B ) )
% 2.21/1.37 => ( ( binintersect @ A @ B )
% 2.21/1.37 = emptyset ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectRsub_type,type,
% 2.21/1.37 binintersectRsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectRsub,definition,
% 2.21/1.37 ( binintersectRsub
% 2.21/1.37 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset4_type,type,
% 2.21/1.37 binintersectSubset4: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset4,definition,
% 2.21/1.37 ( binintersectSubset4
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ B @ A )
% 2.21/1.37 => ( ( binintersect @ A @ B )
% 2.21/1.37 = B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset1_type,type,
% 2.21/1.37 binintersectSubset1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(binintersectSubset1,definition,
% 2.21/1.37 ( binintersectSubset1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( ( binintersect @ A @ B )
% 2.21/1.37 = A )
% 2.21/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(bs114d_type,type,
% 2.21/1.37 bs114d: $o ).
% 2.21/1.37
% 2.21/1.37 thf(bs114d,definition,
% 2.21/1.37 ( bs114d
% 2.21/1.37 = ( ! [A: $i,B: $i,C: $i] :
% 2.21/1.37 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.21/1.37 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(regular_type,type,
% 2.21/1.37 regular: $i > $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminus_type,type,
% 2.21/1.37 setminus: $i > $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(setminusI_type,type,
% 2.21/1.37 setminusI: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusI,definition,
% 2.21/1.37 ( setminusI
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ A )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusEL_type,type,
% 2.21/1.37 setminusEL: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusEL,definition,
% 2.21/1.37 ( setminusEL
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.21/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusER_type,type,
% 2.21/1.37 setminusER: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusER,definition,
% 2.21/1.37 ( setminusER
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.21/1.37 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusSubset2_type,type,
% 2.21/1.37 setminusSubset2: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusSubset2,definition,
% 2.21/1.37 ( setminusSubset2
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( subset @ A @ B )
% 2.21/1.37 => ( ( setminus @ A @ B )
% 2.21/1.37 = emptyset ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusERneg_type,type,
% 2.21/1.37 setminusERneg: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusERneg,definition,
% 2.21/1.37 ( setminusERneg
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.21/1.37 => ( ( in @ Xx @ A )
% 2.21/1.37 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusELneg_type,type,
% 2.21/1.37 setminusELneg: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusELneg,definition,
% 2.21/1.37 ( setminusELneg
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusILneg_type,type,
% 2.21/1.37 setminusILneg: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusILneg,definition,
% 2.21/1.37 ( setminusILneg
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ~ ( in @ Xx @ A )
% 2.21/1.37 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusIRneg_type,type,
% 2.21/1.37 setminusIRneg: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusIRneg,definition,
% 2.21/1.37 ( setminusIRneg
% 2.21/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ B )
% 2.21/1.37 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusLsub_type,type,
% 2.21/1.37 setminusLsub: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusLsub,definition,
% 2.21/1.37 ( setminusLsub
% 2.21/1.37 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(setminusSubset1_type,type,
% 2.21/1.37 setminusSubset1: $o ).
% 2.21/1.37
% 2.21/1.37 thf(setminusSubset1,definition,
% 2.21/1.37 ( setminusSubset1
% 2.21/1.37 = ( ! [A: $i,B: $i] :
% 2.21/1.37 ( ( ( setminus @ A @ B )
% 2.21/1.37 = emptyset )
% 2.21/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(symdiff_type,type,
% 2.21/1.37 symdiff: $i > $i > $i ).
% 2.21/1.37
% 2.21/1.37 thf(symdiff,definition,
% 2.21/1.37 ( symdiff
% 2.21/1.37 = ( ^ [A: $i,B: $i] :
% 2.21/1.37 ( dsetconstr @ ( binunion @ A @ B )
% 2.21/1.37 @ ^ [Xx: $i] :
% 2.21/1.37 ( ~ ( in @ Xx @ A )
% 2.21/1.37 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 2.21/1.37
% 2.21/1.37 thf(symdiffE,conjecture,
% 2.21/1.37 ( setextAx
% 2.21/1.37 => ( emptysetAx
% 2.21/1.37 => ( setadjoinAx
% 2.21/1.37 => ( powersetAx
% 2.21/1.37 => ( setunionAx
% 2.21/1.37 => ( omega0Ax
% 2.21/1.37 => ( omegaSAx
% 2.21/1.37 => ( omegaIndAx
% 2.21/1.37 => ( replAx
% 2.21/1.37 => ( foundationAx
% 2.21/1.37 => ( wellorderingAx
% 2.21/1.37 => ( descrp
% 2.21/1.37 => ( dsetconstrI
% 2.21/1.37 => ( dsetconstrEL
% 2.21/1.37 => ( dsetconstrER
% 2.21/1.37 => ( exuE1
% 2.21/1.37 => ( prop2setE
% 2.21/1.37 => ( emptysetE
% 2.21/1.37 => ( emptysetimpfalse
% 2.21/1.37 => ( notinemptyset
% 2.21/1.37 => ( exuE3e
% 2.21/1.37 => ( setext
% 2.21/1.37 => ( emptyI
% 2.21/1.37 => ( noeltsimpempty
% 2.21/1.37 => ( setbeta
% 2.21/1.37 => ( nonemptyE1
% 2.21/1.37 => ( nonemptyI
% 2.21/1.37 => ( nonemptyI1
% 2.21/1.37 => ( setadjoinIL
% 2.21/1.37 => ( emptyinunitempty
% 2.21/1.37 => ( setadjoinIR
% 2.21/1.37 => ( setadjoinE
% 2.21/1.37 => ( setadjoinOr
% 2.21/1.37 => ( setoftrueEq
% 2.21/1.37 => ( powersetI
% 2.21/1.37 => ( emptyinPowerset
% 2.21/1.37 => ( emptyInPowerset
% 2.21/1.37 => ( powersetE
% 2.21/1.37 => ( setunionI
% 2.21/1.37 => ( setunionE
% 2.21/1.37 => ( subPowSU
% 2.21/1.37 => ( exuE2
% 2.21/1.37 => ( nonemptyImpWitness
% 2.21/1.37 => ( uniqinunit
% 2.21/1.37 => ( notinsingleton
% 2.21/1.37 => ( eqinunit
% 2.21/1.37 => ( singletonsswitch
% 2.21/1.37 => ( upairsetE
% 2.21/1.37 => ( upairsetIL
% 2.21/1.37 => ( upairsetIR
% 2.21/1.37 => ( emptyE1
% 2.21/1.37 => ( vacuousDall
% 2.21/1.37 => ( quantDeMorgan1
% 2.21/1.37 => ( quantDeMorgan2
% 2.21/1.37 => ( quantDeMorgan3
% 2.21/1.37 => ( quantDeMorgan4
% 2.21/1.37 => ( prop2setI
% 2.21/1.37 => ( prop2set2propI
% 2.21/1.37 => ( notdexE
% 2.21/1.37 => ( notdallE
% 2.21/1.37 => ( exuI1
% 2.21/1.37 => ( exuI3
% 2.21/1.37 => ( exuI2
% 2.21/1.37 => ( inCongP
% 2.21/1.37 => ( in__Cong
% 2.21/1.37 => ( exuE3u
% 2.21/1.37 => ( exu__Cong
% 2.21/1.37 => ( emptyset__Cong
% 2.21/1.37 => ( setadjoin__Cong
% 2.21/1.37 => ( powerset__Cong
% 2.21/1.37 => ( setunion__Cong
% 2.21/1.37 => ( omega__Cong
% 2.21/1.37 => ( exuEu
% 2.21/1.37 => ( descr__Cong
% 2.21/1.37 => ( dsetconstr__Cong
% 2.21/1.37 => ( subsetI1
% 2.21/1.37 => ( eqimpsubset2
% 2.21/1.37 => ( eqimpsubset1
% 2.21/1.37 => ( subsetI2
% 2.21/1.37 => ( emptysetsubset
% 2.21/1.37 => ( subsetE
% 2.21/1.37 => ( subsetE2
% 2.21/1.37 => ( notsubsetI
% 2.21/1.37 => ( notequalI1
% 2.21/1.37 => ( notequalI2
% 2.21/1.37 => ( subsetRefl
% 2.21/1.37 => ( subsetTrans
% 2.21/1.37 => ( setadjoinSub
% 2.21/1.37 => ( setadjoinSub2
% 2.21/1.37 => ( subset2powerset
% 2.21/1.37 => ( setextsub
% 2.21/1.37 => ( subsetemptysetimpeq
% 2.21/1.37 => ( powersetI1
% 2.21/1.37 => ( powersetE1
% 2.21/1.37 => ( inPowerset
% 2.21/1.37 => ( powersetsubset
% 2.21/1.37 => ( sepInPowerset
% 2.21/1.37 => ( sepSubset
% 2.21/1.37 => ( binunionIL
% 2.21/1.37 => ( upairset2IR
% 2.21/1.37 => ( binunionIR
% 2.21/1.37 => ( binunionEcases
% 2.21/1.37 => ( binunionE
% 2.21/1.37 => ( binunionLsub
% 2.21/1.37 => ( binunionRsub
% 2.21/1.37 => ( binintersectI
% 2.21/1.37 => ( binintersectSubset5
% 2.21/1.37 => ( binintersectEL
% 2.21/1.37 => ( binintersectLsub
% 2.21/1.37 => ( binintersectSubset2
% 2.21/1.37 => ( binintersectSubset3
% 2.21/1.37 => ( binintersectER
% 2.21/1.37 => ( disjointsetsI1
% 2.21/1.37 => ( binintersectRsub
% 2.21/1.37 => ( binintersectSubset4
% 2.21/1.37 => ( binintersectSubset1
% 2.21/1.37 => ( bs114d
% 2.21/1.37 => ( setminusI
% 2.21/1.37 => ( setminusEL
% 2.21/1.37 => ( setminusER
% 2.21/1.37 => ( setminusSubset2
% 2.21/1.37 => ( setminusERneg
% 2.21/1.37 => ( setminusELneg
% 2.21/1.37 => ( setminusILneg
% 2.21/1.37 => ( setminusIRneg
% 2.21/1.37 => ( setminusLsub
% 2.21/1.37 => ( setminusSubset1
% 2.21/1.37 => ! [A: $i,B: $i,Xx: $i] :
% 2.21/1.37 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.21/1.37 => ! [Xphi: $o] :
% 2.21/1.37 ( ( ( in @ Xx @ A )
% 2.21/1.37 => ( ~ ( in @ Xx @ B )
% 2.21/1.37 => Xphi ) )
% 2.21/1.37 => ( ( ~ ( in @ Xx @ A )
% 2.21/1.37 => ( ( in @ Xx @ B )
% 2.21/1.37 => Xphi ) )
% 2.21/1.37 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.21/1.37 ------------------------
% 2.21/1.39 % (10641)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/183Mi)
% 2.21/1.39 % (10647)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/18Mi)
% 2.21/1.39 % (10642)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_10434 for (2999ds/4Mi)
% 2.21/1.39 % (10643)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_10434 for (2999ds/27Mi)
% 2.21/1.39 % (10646)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_10434 for (2999ds/275Mi)
% 2.21/1.39 % (10642)Instruction limit reached!
% 2.21/1.39 % (10642)------------------------------
% 2.21/1.39 % (10642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (10642)Termination reason: Unknown
% 2.21/1.39 % (10642)Termination phase: shuffling
% 2.21/1.39
% 2.21/1.39 % (10642)Memory used [KB]: 1279
% 2.21/1.39 % (10642)Time elapsed: 0.003 s
% 2.21/1.39 % (10642)Instructions burned: 7 (million)
% 2.21/1.39 % (10642)------------------------------
% 2.21/1.39 % (10642)------------------------------
% 2.21/1.39 % (10647)Instruction limit reached!
% 2.21/1.39 % (10647)------------------------------
% 2.21/1.39 % (10647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (10647)Termination reason: Unknown
% 2.21/1.39 % (10647)Termination phase: Preprocessing 3
% 2.21/1.39
% 2.21/1.39 % (10647)Memory used [KB]: 1535
% 2.21/1.39 % (10647)Time elapsed: 0.007 s
% 2.21/1.39 % (10647)Instructions burned: 20 (million)
% 2.21/1.39 % (10647)------------------------------
% 2.21/1.39 % (10647)------------------------------
% 2.21/1.39 % (10644)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/2Mi)
% 2.21/1.39 % (10645)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_10434 for (2999ds/2Mi)
% 2.21/1.39 % (10643)Instruction limit reached!
% 2.21/1.39 % (10643)------------------------------
% 2.21/1.39 % (10643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (10643)Termination reason: Unknown
% 2.21/1.39 % (10643)Termination phase: Property scanning
% 2.21/1.39
% 2.21/1.39 % (10644)Instruction limit reached!
% 2.21/1.39 % (10644)------------------------------
% 2.21/1.39 % (10644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (10644)Termination reason: Unknown
% 2.21/1.39 % (10644)Termination phase: shuffling
% 2.21/1.39
% 2.21/1.39 % (10644)Memory used [KB]: 1151
% 2.21/1.39 % (10644)Time elapsed: 0.003 s
% 2.21/1.39 % (10644)Instructions burned: 2 (million)
% 2.21/1.39 % (10644)------------------------------
% 2.21/1.39 % (10644)------------------------------
% 2.21/1.39 % (10643)Memory used [KB]: 1535
% 2.21/1.39 % (10643)Time elapsed: 0.009 s
% 2.21/1.39 % (10645)Instruction limit reached!
% 2.21/1.39 % (10645)------------------------------
% 2.21/1.39 % (10645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.39 % (10643)Instructions burned: 27 (million)
% 2.21/1.39 % (10643)------------------------------
% 2.21/1.39 % (10643)------------------------------
% 2.21/1.39 % (10645)Termination reason: Unknown
% 2.21/1.39 % (10645)Termination phase: shuffling
% 2.21/1.39
% 2.21/1.39 % (10645)Memory used [KB]: 1151
% 2.21/1.39 % (10645)Time elapsed: 0.003 s
% 2.21/1.39 % (10645)Instructions burned: 2 (million)
% 2.21/1.39 % (10645)------------------------------
% 2.21/1.39 % (10645)------------------------------
% 2.39/1.40 % (10648)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/3Mi)
% 2.39/1.40 % (10648)Instruction limit reached!
% 2.39/1.40 % (10648)------------------------------
% 2.39/1.40 % (10648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.40 % (10648)Termination reason: Unknown
% 2.39/1.40 % (10648)Termination phase: shuffling
% 2.39/1.40
% 2.39/1.40 % (10648)Memory used [KB]: 1279
% 2.39/1.40 % (10648)Time elapsed: 0.003 s
% 2.39/1.40 % (10648)Instructions burned: 4 (million)
% 2.39/1.40 % (10648)------------------------------
% 2.39/1.40 % (10648)------------------------------
% 2.39/1.40 % (10649)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_10434 for (2999ds/37Mi)
% 2.39/1.40 % (10650)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_10434 for (2999ds/15Mi)
% 2.39/1.41 % (10650)Instruction limit reached!
% 2.39/1.41 % (10650)------------------------------
% 2.39/1.41 % (10650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.41 % (10650)Termination reason: Unknown
% 2.39/1.41 % (10650)Termination phase: Preprocessing 1
% 2.39/1.41
% 2.39/1.41 % (10650)Memory used [KB]: 1407
% 2.39/1.41 % (10650)Time elapsed: 0.007 s
% 2.39/1.41 % (10650)Instructions burned: 17 (million)
% 2.39/1.41 % (10650)------------------------------
% 2.39/1.41 % (10650)------------------------------
% 2.39/1.41 % (10653)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/7Mi)
% 2.39/1.41 % (10649)Instruction limit reached!
% 2.39/1.41 % (10649)------------------------------
% 2.39/1.41 % (10649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.41 % (10649)Termination reason: Unknown
% 2.39/1.41 % (10649)Termination phase: Property scanning
% 2.39/1.41
% 2.39/1.41 % (10649)Memory used [KB]: 1663
% 2.39/1.41 % (10649)Time elapsed: 0.011 s
% 2.39/1.41 % (10649)Instructions burned: 40 (million)
% 2.39/1.41 % (10649)------------------------------
% 2.39/1.41 % (10649)------------------------------
% 2.39/1.41 % (10651)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_10434 for (2999ds/3Mi)
% 2.39/1.41 % (10652)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_10434 for (2999ds/1041Mi)
% 2.39/1.41 % (10653)Instruction limit reached!
% 2.39/1.41 % (10653)------------------------------
% 2.39/1.41 % (10653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.41 % (10653)Termination reason: Unknown
% 2.39/1.41 % (10653)Termination phase: shuffling
% 2.39/1.41
% 2.39/1.41 % (10653)Memory used [KB]: 1279
% 2.39/1.41 % (10653)Time elapsed: 0.004 s
% 2.39/1.41 % (10653)Instructions burned: 8 (million)
% 2.39/1.41 % (10653)------------------------------
% 2.39/1.41 % (10653)------------------------------
% 2.39/1.41 % (10651)Instruction limit reached!
% 2.39/1.41 % (10651)------------------------------
% 2.39/1.41 % (10651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.41 % (10651)Termination reason: Unknown
% 2.39/1.41 % (10651)Termination phase: shuffling
% 2.39/1.41
% 2.39/1.41 % (10651)Memory used [KB]: 1279
% 2.39/1.41 % (10651)Time elapsed: 0.004 s
% 2.39/1.41 % (10651)Instructions burned: 4 (million)
% 2.39/1.41 % (10651)------------------------------
% 2.39/1.41 % (10651)------------------------------
% 2.39/1.42 % (10654)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/16Mi)
% 2.39/1.42 % (10655)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_10434 for (2999ds/3Mi)
% 2.39/1.42 % (10655)Instruction limit reached!
% 2.39/1.42 % (10655)------------------------------
% 2.39/1.42 % (10655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.42 % (10655)Termination reason: Unknown
% 2.39/1.42 % (10655)Termination phase: shuffling
% 2.39/1.42
% 2.39/1.42 % (10655)Memory used [KB]: 1279
% 2.39/1.42 % (10655)Time elapsed: 0.002 s
% 2.39/1.42 % (10655)Instructions burned: 4 (million)
% 2.39/1.42 % (10655)------------------------------
% 2.39/1.42 % (10655)------------------------------
% 2.39/1.42 % (10656)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_10434 for (2999ds/3Mi)
% 2.39/1.42 % (10656)Instruction limit reached!
% 2.39/1.42 % (10656)------------------------------
% 2.39/1.42 % (10656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.42 % (10656)Termination reason: Unknown
% 2.39/1.42 % (10656)Termination phase: shuffling
% 2.39/1.42
% 2.39/1.42 % (10656)Memory used [KB]: 1279
% 2.39/1.42 % (10656)Time elapsed: 0.003 s
% 2.39/1.42 % (10656)Instructions burned: 5 (million)
% 2.39/1.42 % (10656)------------------------------
% 2.39/1.42 % (10656)------------------------------
% 2.39/1.42 % (10654)Instruction limit reached!
% 2.39/1.42 % (10654)------------------------------
% 2.39/1.42 % (10654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.42 % (10654)Termination reason: Unknown
% 2.39/1.42 % (10654)Termination phase: shuffling
% 2.39/1.42
% 2.39/1.42 % (10654)Memory used [KB]: 1535
% 2.39/1.42 % (10654)Time elapsed: 0.007 s
% 2.39/1.42 % (10654)Instructions burned: 18 (million)
% 2.39/1.42 % (10654)------------------------------
% 2.39/1.42 % (10654)------------------------------
% 2.39/1.43 % (10658)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/3Mi)
% 2.39/1.43 % (10657)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/7Mi)
% 2.39/1.43 % (10658)Instruction limit reached!
% 2.39/1.43 % (10658)------------------------------
% 2.39/1.43 % (10658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.43 % (10658)Termination reason: Unknown
% 2.39/1.43 % (10658)Termination phase: shuffling
% 2.39/1.43
% 2.39/1.43 % (10658)Memory used [KB]: 1279
% 2.39/1.43 % (10658)Time elapsed: 0.002 s
% 2.39/1.43 % (10658)Instructions burned: 4 (million)
% 2.39/1.43 % (10658)------------------------------
% 2.39/1.43 % (10658)------------------------------
% 2.39/1.43 % (10659)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/4Mi)
% 2.39/1.43 % (10659)Instruction limit reached!
% 2.39/1.43 % (10659)------------------------------
% 2.39/1.43 % (10659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.43 % (10659)Termination reason: Unknown
% 2.39/1.43 % (10659)Termination phase: shuffling
% 2.39/1.43
% 2.39/1.43 % (10659)Memory used [KB]: 1279
% 2.39/1.43 % (10659)Time elapsed: 0.003 s
% 2.39/1.43 % (10659)Instructions burned: 5 (million)
% 2.39/1.43 % (10659)------------------------------
% 2.39/1.43 % (10659)------------------------------
% 2.39/1.44 % (10660)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/18Mi)
% 2.39/1.44 % (10657)Instruction limit reached!
% 2.39/1.44 % (10657)------------------------------
% 2.39/1.44 % (10657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.44 % (10657)Termination reason: Unknown
% 2.39/1.44 % (10657)Termination phase: shuffling
% 2.39/1.44
% 2.39/1.44 % (10657)Memory used [KB]: 1407
% 2.39/1.44 % (10657)Time elapsed: 0.006 s
% 2.39/1.44 % (10657)Instructions burned: 8 (million)
% 2.39/1.44 % (10657)------------------------------
% 2.39/1.44 % (10657)------------------------------
% 2.39/1.44 % (10641)Instruction limit reached!
% 2.39/1.44 % (10641)------------------------------
% 2.39/1.44 % (10641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.44 % (10641)Termination reason: Unknown
% 2.39/1.44 % (10641)Termination phase: Saturation
% 2.39/1.44
% 2.39/1.44 % (10641)Memory used [KB]: 7036
% 2.39/1.44 % (10641)Time elapsed: 0.052 s
% 2.39/1.44 % (10641)Instructions burned: 183 (million)
% 2.39/1.44 % (10641)------------------------------
% 2.39/1.44 % (10641)------------------------------
% 2.39/1.44 % (10660)Instruction limit reached!
% 2.39/1.44 % (10660)------------------------------
% 2.39/1.44 % (10660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.44 % (10660)Termination reason: Unknown
% 2.39/1.44 % (10660)Termination phase: shuffling
% 2.39/1.44
% 2.39/1.44 % (10660)Memory used [KB]: 1535
% 2.39/1.44 % (10660)Time elapsed: 0.007 s
% 2.39/1.44 % (10660)Instructions burned: 18 (million)
% 2.39/1.44 % (10660)------------------------------
% 2.39/1.44 % (10660)------------------------------
% 2.39/1.44 % (10661)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/710Mi)
% 2.39/1.44 % (10662)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/6Mi)
% 2.39/1.45 % (10664)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_10434 for (2999ds/21Mi)
% 2.39/1.45 % (10662)Instruction limit reached!
% 2.39/1.45 % (10662)------------------------------
% 2.39/1.45 % (10662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.45 % (10662)Termination reason: Unknown
% 2.39/1.45 % (10662)Termination phase: shuffling
% 2.39/1.45
% 2.39/1.45 % (10662)Memory used [KB]: 1279
% 2.39/1.45 % (10662)Time elapsed: 0.004 s
% 2.39/1.45 % (10662)Instructions burned: 7 (million)
% 2.39/1.45 % (10662)------------------------------
% 2.39/1.45 % (10662)------------------------------
% 2.39/1.45 % (10665)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/5Mi)
% 2.39/1.45 % (10664)Instruction limit reached!
% 2.39/1.45 % (10664)------------------------------
% 2.39/1.45 % (10664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.45 % (10664)Termination reason: Unknown
% 2.39/1.45 % (10664)Termination phase: Property scanning
% 2.39/1.45
% 2.39/1.45 % (10664)Memory used [KB]: 1535
% 2.39/1.45 % (10664)Time elapsed: 0.007 s
% 2.39/1.45 % (10664)Instructions burned: 22 (million)
% 2.39/1.45 % (10664)------------------------------
% 2.39/1.45 % (10664)------------------------------
% 2.39/1.45 % (10665)Instruction limit reached!
% 2.39/1.45 % (10665)------------------------------
% 2.39/1.45 % (10665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.45 % (10665)Termination reason: Unknown
% 2.39/1.45 % (10665)Termination phase: shuffling
% 2.39/1.45
% 2.39/1.45 % (10665)Memory used [KB]: 1279
% 2.39/1.45 % (10665)Time elapsed: 0.003 s
% 2.39/1.45 % (10665)Instructions burned: 5 (million)
% 2.39/1.45 % (10665)------------------------------
% 2.39/1.45 % (10665)------------------------------
% 2.39/1.45 % (10663)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_10434 for (2999ds/902Mi)
% 2.39/1.46 % (10667)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_10434 for (2999ds/6Mi)
% 2.39/1.46 % (10667)Instruction limit reached!
% 2.39/1.46 % (10667)------------------------------
% 2.39/1.46 % (10667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.46 % (10667)Termination reason: Unknown
% 2.39/1.46 % (10667)Termination phase: shuffling
% 2.39/1.46
% 2.39/1.46 % (10667)Memory used [KB]: 1279
% 2.39/1.46 % (10667)Time elapsed: 0.004 s
% 2.39/1.46 % (10667)Instructions burned: 8 (million)
% 2.39/1.46 % (10667)------------------------------
% 2.39/1.46 % (10667)------------------------------
% 2.39/1.46 % (10670)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10434 for (2999ds/377Mi)
% 2.39/1.46 % (10671)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_10434 for (2999ds/779Mi)
% 2.39/1.47 % (10674)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_10434 for (2999ds/19Mi)
% 2.39/1.47 % (10646)Instruction limit reached!
% 2.39/1.47 % (10646)------------------------------
% 2.39/1.47 % (10646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.47 % (10646)Termination reason: Unknown
% 2.39/1.47 % (10646)Termination phase: Saturation
% 2.39/1.47
% 2.39/1.47 % (10646)Memory used [KB]: 7803
% 2.39/1.47 % (10646)Time elapsed: 0.089 s
% 2.39/1.47 % (10646)Instructions burned: 275 (million)
% 2.39/1.47 % (10646)------------------------------
% 2.39/1.47 % (10646)------------------------------
% 2.39/1.48 % (10674)Instruction limit reached!
% 2.39/1.48 % (10674)------------------------------
% 2.39/1.48 % (10674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.48 % (10674)Termination reason: Unknown
% 2.39/1.48 % (10674)Termination phase: Property scanning
% 2.39/1.48
% 2.39/1.48 % (10674)Memory used [KB]: 1535
% 2.39/1.48 % (10674)Time elapsed: 0.008 s
% 2.39/1.48 % (10674)Instructions burned: 22 (million)
% 2.39/1.48 % (10674)------------------------------
% 2.39/1.48 % (10674)------------------------------
% 2.39/1.48 % (10682)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10434 for (2998ds/879Mi)
% 2.39/1.49 % (10683)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10434 for (2998ds/17Mi)
% 2.39/1.49 % (10683)Instruction limit reached!
% 2.39/1.49 % (10683)------------------------------
% 2.39/1.49 % (10683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.49 % (10683)Termination reason: Unknown
% 2.39/1.49 % (10683)Termination phase: shuffling
% 2.39/1.49
% 2.39/1.49 % (10683)Memory used [KB]: 1535
% 2.39/1.49 % (10683)Time elapsed: 0.007 s
% 2.39/1.49 % (10683)Instructions burned: 18 (million)
% 2.39/1.49 % (10683)------------------------------
% 2.39/1.49 % (10683)------------------------------
% 2.39/1.50 % (10692)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10434 for (2998ds/3Mi)
% 2.39/1.50 % (10692)Instruction limit reached!
% 2.39/1.50 % (10692)------------------------------
% 2.39/1.50 % (10692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.50 % (10692)Termination reason: Unknown
% 2.39/1.50 % (10692)Termination phase: shuffling
% 2.39/1.50
% 2.39/1.50 % (10692)Memory used [KB]: 1279
% 2.39/1.50 % (10692)Time elapsed: 0.003 s
% 2.39/1.50 % (10692)Instructions burned: 4 (million)
% 2.39/1.50 % (10692)------------------------------
% 2.39/1.50 % (10692)------------------------------
% 2.39/1.51 % (10697)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10434 for (2998ds/30Mi)
% 2.39/1.52 % (10697)Instruction limit reached!
% 2.39/1.52 % (10697)------------------------------
% 2.39/1.52 % (10697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.52 % (10697)Termination reason: Unknown
% 2.39/1.52 % (10697)Termination phase: Property scanning
% 2.39/1.52
% 2.39/1.52 % (10697)Memory used [KB]: 1663
% 2.39/1.52 % (10697)Time elapsed: 0.011 s
% 2.39/1.52 % (10697)Instructions burned: 32 (million)
% 2.39/1.52 % (10697)------------------------------
% 2.39/1.52 % (10697)------------------------------
% 2.39/1.53 % (10709)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10434 for (2998ds/127Mi)
% 2.39/1.57 % (10709)Instruction limit reached!
% 2.39/1.57 % (10709)------------------------------
% 2.39/1.57 % (10709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.57 % (10709)Termination reason: Unknown
% 2.39/1.57 % (10709)Termination phase: Saturation
% 2.39/1.57
% 2.39/1.57 % (10709)Memory used [KB]: 6908
% 2.39/1.57 % (10709)Time elapsed: 0.039 s
% 2.39/1.57 % (10709)Instructions burned: 129 (million)
% 2.39/1.57 % (10709)------------------------------
% 2.39/1.57 % (10709)------------------------------
% 2.39/1.58 % (10670)Instruction limit reached!
% 2.39/1.58 % (10670)------------------------------
% 2.39/1.58 % (10670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.58 % (10670)Termination reason: Unknown
% 2.39/1.58 % (10670)Termination phase: Saturation
% 2.39/1.58
% 2.39/1.58 % (10670)Memory used [KB]: 7291
% 2.39/1.58 % (10670)Time elapsed: 0.138 s
% 2.39/1.58 % (10670)Instructions burned: 380 (million)
% 2.39/1.58 % (10670)------------------------------
% 2.39/1.58 % (10670)------------------------------
% 2.39/1.58 % (10728)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10434 for (2997ds/100Mi)
% 2.39/1.59 % (10731)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_10434 for (2997ds/3Mi)
% 2.39/1.59 % (10731)Instruction limit reached!
% 2.39/1.59 % (10731)------------------------------
% 2.39/1.59 % (10731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.59 % (10731)Termination reason: Unknown
% 2.39/1.59 % (10731)Termination phase: shuffling
% 2.39/1.59
% 2.39/1.59 % (10731)Memory used [KB]: 1151
% 2.39/1.59 % (10731)Time elapsed: 0.002 s
% 2.39/1.59 % (10731)Instructions burned: 3 (million)
% 2.39/1.59 % (10731)------------------------------
% 2.39/1.59 % (10731)------------------------------
% 2.39/1.60 % (10734)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_10434 for (2997ds/20Mi)
% 2.39/1.60 % (10734)Instruction limit reached!
% 2.39/1.60 % (10734)------------------------------
% 2.39/1.60 % (10734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.60 % (10734)Termination reason: Unknown
% 2.39/1.60 % (10734)Termination phase: SInE selection
% 2.39/1.60
% 2.39/1.60 % (10734)Memory used [KB]: 1407
% 2.39/1.60 % (10734)Time elapsed: 0.007 s
% 2.39/1.60 % (10734)Instructions burned: 21 (million)
% 2.39/1.60 % (10734)------------------------------
% 2.39/1.60 % (10734)------------------------------
% 2.39/1.61 % (10728)Instruction limit reached!
% 2.39/1.61 % (10728)------------------------------
% 2.39/1.61 % (10728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.61 % (10728)Termination reason: Unknown
% 2.39/1.61 % (10728)Termination phase: Saturation
% 2.39/1.61
% 2.39/1.61 % (10728)Memory used [KB]: 6396
% 2.39/1.61 % (10728)Time elapsed: 0.032 s
% 2.39/1.61 % (10728)Instructions burned: 101 (million)
% 2.39/1.61 % (10728)------------------------------
% 2.39/1.61 % (10728)------------------------------
% 2.39/1.61 % (10743)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_10434 for (2997ds/86Mi)
% 2.39/1.62 % (10745)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_10434 for (2997ds/107Mi)
% 2.39/1.63 % (10743)Instruction limit reached!
% 2.39/1.63 % (10743)------------------------------
% 2.39/1.63 % (10743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.63 % (10743)Termination reason: Unknown
% 2.39/1.63 % (10743)Termination phase: Saturation
% 2.39/1.63
% 2.39/1.63 % (10743)Memory used [KB]: 6396
% 2.39/1.63 % (10743)Time elapsed: 0.024 s
% 2.39/1.63 % (10743)Instructions burned: 88 (million)
% 2.39/1.63 % (10743)------------------------------
% 2.39/1.63 % (10743)------------------------------
% 2.39/1.64 % (10758)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_10434 for (2997ds/39Mi)
% 2.39/1.65 % (10745)Instruction limit reached!
% 2.39/1.65 % (10745)------------------------------
% 2.39/1.65 % (10745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.65 % (10745)Termination reason: Unknown
% 2.39/1.65 % (10745)Termination phase: Saturation
% 2.39/1.65
% 2.39/1.65 % (10745)Memory used [KB]: 6652
% 2.39/1.65 % (10745)Time elapsed: 0.033 s
% 2.39/1.65 % (10745)Instructions burned: 108 (million)
% 2.39/1.65 % (10745)------------------------------
% 2.39/1.65 % (10745)------------------------------
% 2.39/1.65 % (10671)Instruction limit reached!
% 2.39/1.65 % (10671)------------------------------
% 2.39/1.65 % (10671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.65 % (10671)Termination reason: Unknown
% 2.39/1.65 % (10671)Termination phase: Saturation
% 2.39/1.65
% 2.39/1.65 % (10671)Memory used [KB]: 6524
% 2.39/1.65 % (10671)Time elapsed: 0.194 s
% 2.39/1.65 % (10671)Instructions burned: 780 (million)
% 2.39/1.65 % (10671)------------------------------
% 2.39/1.65 % (10671)------------------------------
% 2.39/1.65 % (10758)Instruction limit reached!
% 2.39/1.65 % (10758)------------------------------
% 2.39/1.65 % (10758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.65 % (10758)Termination reason: Unknown
% 2.39/1.65 % (10758)Termination phase: Property scanning
% 2.39/1.65
% 2.39/1.65 % (10758)Memory used [KB]: 1663
% 2.39/1.65 % (10758)Time elapsed: 0.012 s
% 2.39/1.65 % (10758)Instructions burned: 42 (million)
% 2.39/1.65 % (10758)------------------------------
% 2.39/1.65 % (10758)------------------------------
% 2.39/1.66 % (10767)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_10434 for (2997ds/448Mi)
% 2.39/1.66 % (10661)Instruction limit reached!
% 2.39/1.66 % (10661)------------------------------
% 2.39/1.66 % (10661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.66 % (10661)Termination reason: Unknown
% 2.39/1.66 % (10661)Termination phase: Saturation
% 2.39/1.66
% 2.39/1.66 % (10661)Memory used [KB]: 8827
% 2.39/1.66 % (10661)Time elapsed: 0.223 s
% 2.39/1.66 % (10661)Instructions burned: 713 (million)
% 2.39/1.66 % (10661)------------------------------
% 2.39/1.66 % (10661)------------------------------
% 2.39/1.66 % (10768)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_10434 for (2997ds/46Mi)
% 2.39/1.66 % (10769)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_10434 for (2997ds/98Mi)
% 2.39/1.67 % (10772)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_10434 for (2997ds/507Mi)
% 2.39/1.68 % (10768)Instruction limit reached!
% 2.39/1.68 % (10768)------------------------------
% 2.39/1.68 % (10768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.68 % (10768)Termination reason: Unknown
% 2.39/1.68 % (10768)Termination phase: Property scanning
% 2.39/1.68
% 2.39/1.68 % (10768)Memory used [KB]: 1663
% 2.39/1.68 % (10768)Time elapsed: 0.014 s
% 2.39/1.68 % (10768)Instructions burned: 49 (million)
% 2.39/1.68 % (10768)------------------------------
% 2.39/1.68 % (10768)------------------------------
% 2.39/1.69 % (10786)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_10434 for (2996ds/149Mi)
% 2.39/1.69 % (10769)Instruction limit reached!
% 2.39/1.69 % (10769)------------------------------
% 2.39/1.69 % (10769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.69 % (10769)Termination reason: Unknown
% 2.39/1.69 % (10769)Termination phase: Saturation
% 2.39/1.69
% 2.39/1.69 % (10769)Memory used [KB]: 1791
% 2.39/1.69 % (10769)Time elapsed: 0.026 s
% 2.39/1.69 % (10769)Instructions burned: 99 (million)
% 2.39/1.69 % (10769)------------------------------
% 2.39/1.69 % (10769)------------------------------
% 2.39/1.69 % (10652)Instruction limit reached!
% 2.39/1.69 % (10652)------------------------------
% 2.39/1.69 % (10652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.69 % (10652)Termination reason: Unknown
% 2.39/1.69 % (10652)Termination phase: Saturation
% 2.39/1.69
% 2.39/1.69 % (10652)Memory used [KB]: 8699
% 2.39/1.69 % (10652)Time elapsed: 0.282 s
% 2.39/1.69 % (10652)Instructions burned: 1044 (million)
% 2.39/1.69 % (10652)------------------------------
% 2.39/1.69 % (10652)------------------------------
% 2.39/1.70 % (10794)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10434 for (2996ds/39Mi)
% 2.39/1.70 % (10797)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_10434 for (2996ds/6Mi)
% 2.39/1.70 % (10797)Instruction limit reached!
% 2.39/1.70 % (10797)------------------------------
% 2.39/1.70 % (10797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.70 % (10797)Termination reason: Unknown
% 2.39/1.70 % (10797)Termination phase: shuffling
% 2.39/1.70
% 2.39/1.70 % (10797)Memory used [KB]: 1279
% 2.39/1.70 % (10797)Time elapsed: 0.004 s
% 2.39/1.70 % (10797)Instructions burned: 7 (million)
% 2.39/1.70 % (10797)------------------------------
% 2.39/1.70 % (10797)------------------------------
% 2.39/1.71 % (10794)Instruction limit reached!
% 2.39/1.71 % (10794)------------------------------
% 2.39/1.71 % (10794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.71 % (10794)Termination reason: Unknown
% 2.39/1.71 % (10794)Termination phase: Function definition elimination
% 2.39/1.71
% 2.39/1.71 % (10794)Memory used [KB]: 1663
% 2.39/1.71 % (10794)Time elapsed: 0.012 s
% 2.39/1.71 % (10794)Instructions burned: 43 (million)
% 2.39/1.71 % (10794)------------------------------
% 2.39/1.71 % (10794)------------------------------
% 2.39/1.71 % (10798)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_10434 for (2996ds/1087Mi)
% 2.39/1.72 % (10799)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10434 for (2996ds/47Mi)
% 2.39/1.73 % (10786)Instruction limit reached!
% 2.39/1.73 % (10786)------------------------------
% 2.39/1.73 % (10786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.73 % (10786)Termination reason: Unknown
% 2.39/1.73 % (10786)Termination phase: Saturation
% 2.39/1.73
% 2.39/1.73 % (10786)Memory used [KB]: 6908
% 2.39/1.73 % (10786)Time elapsed: 0.045 s
% 2.39/1.73 % (10786)Instructions burned: 149 (million)
% 2.39/1.73 % (10786)------------------------------
% 2.39/1.73 % (10786)------------------------------
% 2.39/1.73 % (10799)Instruction limit reached!
% 2.39/1.73 % (10799)------------------------------
% 2.39/1.73 % (10799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.73 % (10799)Termination reason: Unknown
% 2.39/1.73 % (10799)Termination phase: Property scanning
% 2.39/1.73
% 2.39/1.73 % (10799)Memory used [KB]: 1791
% 2.39/1.73 % (10799)Time elapsed: 0.014 s
% 2.39/1.73 % (10799)Instructions burned: 48 (million)
% 2.39/1.73 % (10799)------------------------------
% 2.39/1.73 % (10799)------------------------------
% 2.39/1.74 % (10815)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_10434 for (2996ds/44Mi)
% 2.39/1.74 % (10816)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_10434 for (2996ds/432Mi)
% 2.39/1.75 % (10815)Instruction limit reached!
% 2.39/1.75 % (10815)------------------------------
% 2.39/1.75 % (10815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.75 % (10815)Termination reason: Unknown
% 2.39/1.75 % (10815)Termination phase: Property scanning
% 2.39/1.75
% 2.39/1.75 % (10815)Memory used [KB]: 1663
% 2.39/1.75 % (10815)Time elapsed: 0.012 s
% 2.39/1.75 % (10815)Instructions burned: 44 (million)
% 2.39/1.75 % (10815)------------------------------
% 2.39/1.75 % (10815)------------------------------
% 2.39/1.76 % (10826)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10434 for (2996ds/62Mi)
% 2.39/1.76 % (10682)Instruction limit reached!
% 2.39/1.76 % (10682)------------------------------
% 2.39/1.76 % (10682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.76 % (10682)Termination reason: Unknown
% 2.39/1.76 % (10682)Termination phase: Saturation
% 2.39/1.76
% 2.39/1.76 % (10682)Memory used [KB]: 7803
% 2.39/1.76 % (10682)Time elapsed: 0.277 s
% 2.39/1.76 % (10682)Instructions burned: 880 (million)
% 2.39/1.76 % (10682)------------------------------
% 2.39/1.76 % (10682)------------------------------
% 2.39/1.76 % (10663)Instruction limit reached!
% 2.39/1.76 % (10663)------------------------------
% 2.39/1.76 % (10663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.76 % (10663)Termination reason: Unknown
% 2.39/1.76 % (10663)Termination phase: Saturation
% 2.39/1.76
% 2.39/1.76 % (10663)Memory used [KB]: 9850
% 2.39/1.76 % (10663)Time elapsed: 0.311 s
% 2.39/1.76 % (10663)Instructions burned: 904 (million)
% 2.39/1.76 % (10663)------------------------------
% 2.39/1.76 % (10663)------------------------------
% 2.39/1.77 % (10767)Instruction limit reached!
% 2.39/1.77 % (10767)------------------------------
% 2.39/1.77 % (10767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.77 % (10767)Termination reason: Unknown
% 2.39/1.77 % (10767)Termination phase: Saturation
% 2.39/1.77
% 2.39/1.77 % (10767)Memory used [KB]: 6524
% 2.39/1.77 % (10767)Time elapsed: 0.110 s
% 2.39/1.77 % (10767)Instructions burned: 449 (million)
% 2.39/1.77 % (10767)------------------------------
% 2.39/1.77 % (10767)------------------------------
% 2.39/1.77 % (10833)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_10434 for (2996ds/31Mi)
% 2.39/1.77 % (10834)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10434 for (2996ds/96Mi)
% 2.39/1.78 % (10826)Instruction limit reached!
% 2.39/1.78 % (10826)------------------------------
% 2.39/1.78 % (10826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.78 % (10826)Termination reason: Unknown
% 2.39/1.78 % (10826)Termination phase: Saturation
% 2.39/1.78
% 2.39/1.78 % (10826)Memory used [KB]: 6268
% 2.39/1.78 % (10826)Time elapsed: 0.017 s
% 2.39/1.78 % (10826)Instructions burned: 64 (million)
% 2.39/1.78 % (10826)------------------------------
% 2.39/1.78 % (10826)------------------------------
% 2.39/1.78 % (10833)Instruction limit reached!
% 2.39/1.78 % (10833)------------------------------
% 2.39/1.78 % (10833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.78 % (10833)Termination reason: Unknown
% 2.39/1.78 % (10833)Termination phase: Property scanning
% 2.39/1.78
% 2.39/1.78 % (10833)Memory used [KB]: 1663
% 2.39/1.78 % (10833)Time elapsed: 0.010 s
% 2.39/1.78 % (10833)Instructions burned: 34 (million)
% 2.39/1.78 % (10833)------------------------------
% 2.39/1.78 % (10833)------------------------------
% 2.39/1.78 % (10836)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_10434 for (2996ds/453Mi)
% 2.39/1.79 % (10840)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_10434 for (2995ds/71Mi)
% 2.39/1.79 % (10842)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/83Mi)
% 2.39/1.80 % (10834)Instruction limit reached!
% 2.39/1.80 % (10834)------------------------------
% 2.39/1.80 % (10834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.80 % (10834)Termination reason: Unknown
% 2.39/1.80 % (10834)Termination phase: Saturation
% 2.39/1.80
% 2.39/1.80 % (10834)Memory used [KB]: 6652
% 2.39/1.80 % (10834)Time elapsed: 0.030 s
% 2.39/1.80 % (10834)Instructions burned: 98 (million)
% 2.39/1.80 % (10834)------------------------------
% 2.39/1.80 % (10834)------------------------------
% 2.39/1.80 % (10840)Instruction limit reached!
% 2.39/1.80 % (10840)------------------------------
% 2.39/1.80 % (10840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.80 % (10840)Termination reason: Unknown
% 2.39/1.80 % (10840)Termination phase: Saturation
% 2.39/1.80
% 2.39/1.80 % (10840)Memory used [KB]: 6268
% 2.39/1.80 % (10840)Time elapsed: 0.020 s
% 2.39/1.80 % (10840)Instructions burned: 72 (million)
% 2.39/1.80 % (10840)------------------------------
% 2.39/1.80 % (10840)------------------------------
% 2.39/1.81 % (10842)Instruction limit reached!
% 2.39/1.81 % (10842)------------------------------
% 2.39/1.81 % (10842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.81 % (10842)Termination reason: Unknown
% 2.39/1.81 % (10842)Termination phase: Saturation
% 2.39/1.81
% 2.39/1.81 % (10842)Memory used [KB]: 6396
% 2.39/1.81 % (10842)Time elapsed: 0.023 s
% 2.39/1.81 % (10842)Instructions burned: 84 (million)
% 2.39/1.81 % (10842)------------------------------
% 2.39/1.81 % (10842)------------------------------
% 2.39/1.81 % (10849)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/11Mi)
% 2.39/1.81 % (10851)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_10434 for (2995ds/41Mi)
% 2.39/1.81 % (10849)Instruction limit reached!
% 2.39/1.81 % (10849)------------------------------
% 2.39/1.81 % (10849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.81 % (10849)Termination reason: Unknown
% 2.39/1.81 % (10849)Termination phase: shuffling
% 2.39/1.81
% 2.39/1.81 % (10849)Memory used [KB]: 1407
% 2.39/1.81 % (10849)Time elapsed: 0.005 s
% 2.39/1.81 % (10849)Instructions burned: 12 (million)
% 2.39/1.81 % (10849)------------------------------
% 2.39/1.81 % (10849)------------------------------
% 2.39/1.82 % (10854)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/6Mi)
% 2.39/1.82 % (10854)Instruction limit reached!
% 2.39/1.82 % (10854)------------------------------
% 2.39/1.82 % (10854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.82 % (10854)Termination reason: Unknown
% 2.39/1.82 % (10854)Termination phase: shuffling
% 2.39/1.82
% 2.39/1.82 % (10854)Memory used [KB]: 1279
% 2.39/1.82 % (10854)Time elapsed: 0.003 s
% 2.39/1.82 % (10854)Instructions burned: 7 (million)
% 2.39/1.82 % (10854)------------------------------
% 2.39/1.82 % (10854)------------------------------
% 2.39/1.82 % (10772)Instruction limit reached!
% 2.39/1.82 % (10772)------------------------------
% 2.39/1.82 % (10772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.82 % (10772)Termination reason: Unknown
% 2.39/1.82 % (10772)Termination phase: Saturation
% 2.39/1.82
% 2.39/1.82 % (10772)Memory used [KB]: 7164
% 2.39/1.82 % (10772)Time elapsed: 0.151 s
% 2.39/1.82 % (10772)Instructions burned: 509 (million)
% 2.39/1.82 % (10772)------------------------------
% 2.39/1.82 % (10772)------------------------------
% 2.39/1.82 % (10857)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/150Mi)
% 2.39/1.82 % (10851)Instruction limit reached!
% 2.39/1.82 % (10851)------------------------------
% 2.39/1.82 % (10851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.82 % (10851)Termination reason: Unknown
% 2.39/1.82 % (10851)Termination phase: Property scanning
% 2.39/1.82
% 2.39/1.82 % (10851)Memory used [KB]: 1663
% 2.39/1.82 % (10851)Time elapsed: 0.012 s
% 2.39/1.82 % (10851)Instructions burned: 42 (million)
% 2.39/1.82 % (10851)------------------------------
% 2.39/1.82 % (10851)------------------------------
% 2.39/1.83 % (10861)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/343Mi)
% 2.39/1.83 % (10863)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_10434 for (2995ds/109Mi)
% 2.39/1.83 % (10864)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_10434 for (2995ds/253Mi)
% 2.39/1.85 % (10816)Instruction limit reached!
% 2.39/1.85 % (10816)------------------------------
% 2.39/1.85 % (10816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.85 % (10816)Termination reason: Unknown
% 2.39/1.85 % (10816)Termination phase: Saturation
% 2.39/1.85
% 2.39/1.85 % (10816)Memory used [KB]: 2942
% 2.39/1.85 % (10816)Time elapsed: 0.108 s
% 2.39/1.85 % (10816)Instructions burned: 432 (million)
% 2.39/1.85 % (10816)------------------------------
% 2.39/1.85 % (10816)------------------------------
% 2.39/1.86 % (10872)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/140Mi)
% 2.39/1.86 % (10863)Instruction limit reached!
% 2.39/1.86 % (10863)------------------------------
% 2.39/1.86 % (10863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.86 % (10863)Termination reason: Unknown
% 2.39/1.86 % (10863)Termination phase: Saturation
% 2.39/1.86
% 2.39/1.86 % (10863)Memory used [KB]: 6652
% 2.39/1.86 % (10863)Time elapsed: 0.030 s
% 2.39/1.86 % (10863)Instructions burned: 109 (million)
% 2.39/1.86 % (10863)------------------------------
% 2.39/1.86 % (10863)------------------------------
% 2.39/1.87 % (10857)Instruction limit reached!
% 2.39/1.87 % (10857)------------------------------
% 2.39/1.87 % (10857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.87 % (10857)Termination reason: Unknown
% 2.39/1.87 % (10857)Termination phase: Saturation
% 2.39/1.87
% 2.39/1.87 % (10857)Memory used [KB]: 7547
% 2.39/1.87 % (10857)Time elapsed: 0.047 s
% 2.39/1.87 % (10857)Instructions burned: 152 (million)
% 2.39/1.87 % (10857)------------------------------
% 2.39/1.87 % (10857)------------------------------
% 2.39/1.87 % (10877)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/614Mi)
% 2.39/1.88 % (10881)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_10434 for (2995ds/202Mi)
% 2.39/1.89 % (10836)Instruction limit reached!
% 2.39/1.89 % (10836)------------------------------
% 2.39/1.89 % (10836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.89 % (10836)Termination reason: Unknown
% 2.39/1.89 % (10836)Termination phase: Saturation
% 2.39/1.89
% 2.39/1.89 % (10836)Memory used [KB]: 6524
% 2.39/1.89 % (10836)Time elapsed: 0.111 s
% 2.39/1.89 % (10836)Instructions burned: 456 (million)
% 2.39/1.89 % (10836)------------------------------
% 2.39/1.89 % (10836)------------------------------
% 2.39/1.90 % (10872)Instruction limit reached!
% 2.39/1.90 % (10872)------------------------------
% 2.39/1.90 % (10872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.90 % (10872)Termination reason: Unknown
% 2.39/1.90 % (10872)Termination phase: Saturation
% 2.39/1.90
% 2.39/1.90 % (10872)Memory used [KB]: 6524
% 2.39/1.90 % (10872)Time elapsed: 0.039 s
% 2.39/1.90 % (10872)Instructions burned: 140 (million)
% 2.39/1.90 % (10872)------------------------------
% 2.39/1.90 % (10872)------------------------------
% 2.39/1.90 % (10886)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_10434 for (2994ds/339Mi)
% 2.39/1.90 % (10891)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_10434 for (2994ds/283Mi)
% 2.39/1.91 % (10864)Instruction limit reached!
% 2.39/1.91 % (10864)------------------------------
% 2.39/1.91 % (10864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.91 % (10864)Termination reason: Unknown
% 2.39/1.91 % (10864)Termination phase: Saturation
% 2.39/1.91
% 2.39/1.91 % (10864)Memory used [KB]: 7803
% 2.39/1.91 % (10864)Time elapsed: 0.080 s
% 2.39/1.91 % (10864)Instructions burned: 253 (million)
% 2.39/1.91 % (10864)------------------------------
% 2.39/1.91 % (10864)------------------------------
% 2.39/1.92 % (10798)First to succeed.
% 2.39/1.92 % (10897)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_10434 for (2994ds/134Mi)
% 2.39/1.92 % (10798)Refutation found. Thanks to Tanya!
% 2.39/1.92 % SZS status Theorem for DTF2THF_10434
% 2.39/1.92 % SZS output start Proof for DTF2THF_10434
% 2.39/1.92 thf(func_def_0, type, in: $i > $i > $o).
% 2.39/1.92 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.39/1.92 thf(func_def_8, type, powerset: $i > $i).
% 2.39/1.92 thf(func_def_10, type, setunion: $i > $i).
% 2.39/1.92 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_26, type, prop2set: $o > $i).
% 2.39/1.92 thf(func_def_36, type, nonempty: $i > $o).
% 2.39/1.92 thf(func_def_69, type, set2prop: $i > $o).
% 2.39/1.92 thf(func_def_88, type, subset: $i > $i > $o).
% 2.39/1.92 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.39/1.92 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.39/1.92 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.39/1.92 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.39/1.92 thf(func_def_135, type, regular: $i > $o).
% 2.39/1.92 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.39/1.92 thf(func_def_147, type, symdiff: $i > $i > $i).
% 2.39/1.92 thf(func_def_161, type, sP0: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_162, type, sP1: $i > $i > $i > $o).
% 2.39/1.92 thf(func_def_163, type, sP2: $i > $i > $o).
% 2.39/1.92 thf(func_def_164, type, sP3: $i > $i > $o).
% 2.39/1.92 thf(func_def_165, type, sP4: $i > $i > $o).
% 2.39/1.92 thf(func_def_166, type, sP5: $i > $o).
% 2.39/1.92 thf(func_def_167, type, sP6: $i > $i > $o).
% 2.39/1.92 thf(func_def_168, type, sP7: $i > $i > $o).
% 2.39/1.92 thf(func_def_170, type, sP9: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_171, type, sP10: $i > ($i > $o) > $o).
% 2.39/1.92 thf(func_def_173, type, sP12: $i > ($i > $i > $o) > $i > $o).
% 2.39/1.92 thf(func_def_174, type, sP13: $i > ($i > $i > $o) > $o).
% 2.39/1.92 thf(func_def_177, type, sP16: $i > $i > ($i > $o) > ($i > $o) > $o).
% 2.39/1.92 thf(func_def_178, type, sP17: $i > $o).
% 2.39/1.92 thf(func_def_179, type, sP18: $i > $i > $o).
% 2.39/1.92 thf(func_def_183, type, sP22: $i > $i > $o > $o).
% 2.39/1.92 thf(func_def_184, type, sP23: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_185, type, sP24: $i > $i > $o).
% 2.39/1.92 thf(func_def_187, type, sP26: $i > $i > $i > $o).
% 2.39/1.92 thf(func_def_191, type, sP30: $o > $i > $i > $o).
% 2.39/1.92 thf(func_def_193, type, sP32: $i > $o).
% 2.39/1.92 thf(func_def_194, type, sP33: $i > $o).
% 2.39/1.92 thf(func_def_195, type, sP34: ($i > $o) > $i > $o).
% 2.39/1.92 thf(func_def_197, type, sP36: $o > $i > $i > $o).
% 2.39/1.92 thf(func_def_198, type, sP37: $i > $i > $i > $o).
% 2.39/1.92 thf(func_def_199, type, sP38: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_200, type, sP39: $i > ($i > $o) > $o).
% 2.39/1.92 thf(func_def_202, type, sP41: $i > ($i > $o) > $o).
% 2.39/1.92 thf(func_def_204, type, sP43: ($i > $o) > $i > $o).
% 2.39/1.92 thf(func_def_206, type, sP45: $i > ($i > $o) > $o).
% 2.39/1.92 thf(func_def_209, type, sP48: ($i > $o) > $o).
% 2.39/1.92 thf(func_def_224, type, sK63: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_225, type, sK64: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_226, type, sK65: $i > $o).
% 2.39/1.92 thf(func_def_227, type, sK66: $i > $i > $i).
% 2.39/1.92 thf(func_def_228, type, sK67: $i > $i > $i).
% 2.39/1.92 thf(func_def_229, type, sK68: $i > $i > $i > $i).
% 2.39/1.92 thf(func_def_230, type, sK69: $i > $i).
% 2.39/1.92 thf(func_def_231, type, sK70: $i > $i).
% 2.39/1.92 thf(func_def_232, type, sK71: $i > $i).
% 2.39/1.92 thf(func_def_233, type, sK72: $i > $i).
% 2.39/1.92 thf(func_def_234, type, sK73: $i > $i > $i).
% 2.39/1.92 thf(func_def_235, type, sK74: $i > $i > $i).
% 2.39/1.92 thf(func_def_236, type, sK75: $i > $i > $i).
% 2.39/1.92 thf(func_def_237, type, sK76: $i > $i > $i).
% 2.39/1.92 thf(func_def_238, type, sK77: $i > $i > $i).
% 2.39/1.92 thf(func_def_239, type, sK78: $i > $i > $i).
% 2.39/1.92 thf(func_def_240, type, sK79: $i > $i > $i).
% 2.39/1.92 thf(func_def_241, type, sK80: $i > $i > $i).
% 2.39/1.92 thf(func_def_242, type, sK81: $i > $i > $i > $i).
% 2.39/1.92 thf(func_def_243, type, sK82: $i > $i > $i > $i).
% 2.39/1.92 thf(func_def_245, type, sK84: $i > $i).
% 2.39/1.92 thf(func_def_250, type, sK89: $i > $i > $i).
% 2.39/1.92 thf(func_def_251, type, sK90: $i > $i > $i).
% 2.39/1.92 thf(func_def_252, type, sK91: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_253, type, sK92: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_254, type, sK93: $i > $o).
% 2.39/1.92 thf(func_def_265, type, sK104: $i > $i).
% 2.39/1.92 thf(func_def_267, type, sK106: $i > $o).
% 2.39/1.92 thf(func_def_268, type, sK107: ($i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_269, type, sK108: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_272, type, sK111: $i > $i > $i).
% 2.39/1.92 thf(func_def_275, type, sK114: $i > $o).
% 2.39/1.92 thf(func_def_283, type, sK122: $i > $i > $o).
% 2.39/1.92 thf(func_def_285, type, sK124: $i > ($i > $i > $o) > $i).
% 2.39/1.92 thf(func_def_286, type, sK125: $i > $i > ($i > $i > $o) > $i).
% 2.39/1.92 thf(func_def_287, type, sK126: $i > ($i > $i > $o) > $i).
% 2.39/1.92 thf(func_def_288, type, sK127: $i > ($i > $i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_291, type, sK130: $i > $i > $i).
% 2.39/1.92 thf(func_def_302, type, sK141: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_303, type, sK142: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_306, type, sK145: $i > $o).
% 2.39/1.92 thf(func_def_307, type, sK146: $i > $o).
% 2.39/1.92 thf(func_def_323, type, sK162: $i > $i > $i).
% 2.39/1.92 thf(func_def_324, type, sK163: $i > $i).
% 2.39/1.92 thf(func_def_329, type, sK168: $i > $i > $i).
% 2.39/1.92 thf(func_def_331, type, sK170: $i > $o).
% 2.39/1.92 thf(func_def_332, type, sK171: $i > $o).
% 2.39/1.92 thf(func_def_333, type, sK172: ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_334, type, sK173: ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_341, type, sK180: $i > $o).
% 2.39/1.92 thf(func_def_349, type, sK188: $i > $o).
% 2.39/1.92 thf(func_def_362, type, sK201: $i > $i > $i).
% 2.39/1.92 thf(func_def_363, type, sK202: $i > $o).
% 2.39/1.92 thf(func_def_372, type, sK211: $i > $i > $o > $i).
% 2.39/1.92 thf(func_def_381, type, sK220: $i > $i).
% 2.39/1.92 thf(func_def_382, type, sK221: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_383, type, sK222: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_384, type, sK223: $i > $o).
% 2.39/1.92 thf(func_def_387, type, sK226: $i > $i > $i).
% 2.39/1.92 thf(func_def_403, type, sK242: $i > $i > $i).
% 2.39/1.92 thf(func_def_405, type, sK244: $i > $o).
% 2.39/1.92 thf(func_def_410, type, sK249: $i > $i).
% 2.39/1.92 thf(func_def_414, type, sK253: $i > $i > $i).
% 2.39/1.92 thf(func_def_418, type, sK257: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_419, type, sK258: $i > $o).
% 2.39/1.92 thf(func_def_432, type, sK271: $i > $o).
% 2.39/1.92 thf(func_def_433, type, sK272: $i > $i).
% 2.39/1.92 thf(func_def_434, type, sK273: $i > $i).
% 2.39/1.92 thf(func_def_437, type, sK276: $i > $i).
% 2.39/1.92 thf(func_def_443, type, sK282: $i > $o).
% 2.39/1.92 thf(func_def_445, type, sK284: $i > $o).
% 2.39/1.92 thf(func_def_448, type, sK287: $i > $o).
% 2.39/1.92 thf(func_def_450, type, sK289: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_451, type, sK290: ($i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_458, type, sK297: $i > $i > $i > $o).
% 2.39/1.92 thf(func_def_475, type, sK314: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_476, type, sK315: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_477, type, sK316: $i > $o).
% 2.39/1.92 thf(func_def_481, type, sK320: $i > $o).
% 2.39/1.92 thf(func_def_483, type, sK322: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_484, type, sK323: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_487, type, sK326: $i > $o).
% 2.39/1.92 thf(func_def_489, type, sK328: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_490, type, sK329: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_498, type, sK337: $i > $o).
% 2.39/1.92 thf(func_def_499, type, sK338: ($i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_500, type, sK339: ($i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_502, type, sK341: $i > $o).
% 2.39/1.92 thf(func_def_503, type, sK342: ($i > $o) > $i > $i).
% 2.39/1.92 thf(func_def_504, type, sK343: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_518, type, sK357: $i > $o).
% 2.39/1.92 thf(func_def_521, type, sK360: $i > $o).
% 2.39/1.92 thf(func_def_522, type, sK361: $i > $o).
% 2.39/1.92 thf(func_def_523, type, sK362: ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_524, type, sK363: ($i > $o) > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_525, type, sK364: ($i > $o) > $i).
% 2.39/1.92 thf(func_def_526, type, sK365: $i > ($i > $o) > $i).
% 2.39/1.92 thf(func_def_527, type, sK366: $i > $o).
% 2.39/1.92 thf(func_def_532, type, sK371: $i > $o).
% 2.39/1.92 thf(func_def_538, type, sK377: $i > $o).
% 2.39/1.92 thf(func_def_547, type, sK386: $i > $o).
% 2.39/1.92 thf(func_def_553, type, ph392: !>[X0: $tType]:(X0)).
% 2.39/1.92 thf(f5229,plain,(
% 2.39/1.92 $false),
% 2.39/1.92 inference(avatar_sat_refutation,[status(thm)],[f2909,f2999,f3960,f4030,f4036,f4037,f5218])).
% 2.39/1.92 thf(f5218,plain,(
% 2.39/1.92 ~spl391_80 | ~spl391_132),
% 2.39/1.92 inference(avatar_contradiction_clause,[status(thm)],[f5217])).
% 2.39/1.92 thf(f5217,plain,(
% 2.39/1.92 $false | (~spl391_80 | ~spl391_132)),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f5207])).
% 2.39/1.92 thf(f5207,plain,(
% 2.39/1.92 ($false = $true) | (~spl391_80 | ~spl391_132)),
% 2.39/1.92 inference(backward_demodulation,[status(thm)],[f2908,f3959])).
% 2.39/1.92 thf(f3959,plain,(
% 2.39/1.92 ($false = (in @ sK190 @ sK189)) | ~spl391_132),
% 2.39/1.92 inference(avatar_component_clause,[status(thm)],[f3958])).
% 2.39/1.92 thf(f3958,definition,(
% 2.39/1.92 spl391_132 <=> ($false = (in @ sK190 @ sK189))),
% 2.39/1.92 introduced(definition,[new_symbols(naming,[spl391_132])],[avatar_definition])).
% 2.39/1.92 thf(f2908,plain,(
% 2.39/1.92 ((in @ sK190 @ sK189) = $true) | ~spl391_80),
% 2.39/1.92 inference(avatar_component_clause,[status(thm)],[f2907])).
% 2.39/1.92 thf(f2907,definition,(
% 2.39/1.92 spl391_80 <=> ((in @ sK190 @ sK189) = $true)),
% 2.39/1.92 introduced(definition,[new_symbols(naming,[spl391_80])],[avatar_definition])).
% 2.39/1.92 thf(f4037,plain,(
% 2.39/1.92 spl391_79 | spl391_80),
% 2.39/1.92 inference(avatar_split_clause,[status(thm)],[f4022,f2907,f2904])).
% 2.39/1.92 thf(f2904,definition,(
% 2.39/1.92 spl391_79 <=> ((in @ sK190 @ sK191) = $true)),
% 2.39/1.92 introduced(definition,[new_symbols(naming,[spl391_79])],[avatar_definition])).
% 2.39/1.92 thf(f4022,plain,(
% 2.39/1.92 ((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) = $true)),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f4017])).
% 2.39/1.92 thf(f4017,plain,(
% 2.39/1.92 ((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) = $true) | ($true != $true)),
% 2.39/1.92 inference(superposition,[status(thm)],[f2423,f3953])).
% 2.39/1.92 thf(f3953,plain,(
% 2.39/1.92 ((in @ sK190 @ (binunion @ sK189 @ sK191)) = $true)),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f3940])).
% 2.39/1.92 thf(f3940,plain,(
% 2.39/1.92 ($true != $true) | ((in @ sK190 @ (binunion @ sK189 @ sK191)) = $true)),
% 2.39/1.92 inference(superposition,[status(thm)],[f2569,f2536])).
% 2.39/1.92 thf(f2536,plain,(
% 2.39/1.92 ((in @ sK190 @ (dsetconstr @ (binunion @ sK189 @ sK191) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK191)) | (~ (in @ Y0 @ sK189)))))) = $true)),
% 2.39/1.92 inference(beta_eta_normalization,[status(thm)],[f2148])).
% 2.39/1.92 thf(f2148,plain,(
% 2.39/1.92 ((in @ sK190 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))) @ sK189 @ sK191)) = $true)),
% 2.39/1.92 inference(definition_unfolding,[status(thm)],[f1650,f1895])).
% 2.39/1.92 thf(f1895,plain,(
% 2.39/1.92 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f359])).
% 2.39/1.92 thf(f359,plain,(
% 2.39/1.92 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 2.39/1.92 inference(fool_elimination,[status(thm)],[f358])).
% 2.39/1.92 thf(f358,plain,(
% 2.39/1.92 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X0) | ~(in @ X2 @ X1))))) = symdiff)),
% 2.39/1.92 inference(rectify,[status(thm)],[f130])).
% 2.39/1.92 thf(f130,axiom,(
% 2.39/1.92 ((^[X3 : $i, X4 : $i] : (dsetconstr @ (binunion @ X3 @ X4) @ (^[X1 : $i] : (~(in @ X1 @ X3) | ~(in @ X1 @ X4))))) = symdiff)),
% 2.39/1.92 file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',symdiff)).
% 2.39/1.92 thf(f1650,plain,(
% 2.39/1.92 ($true = (in @ sK190 @ (symdiff @ sK189 @ sK191)))),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f907,plain,(
% 2.39/1.92 (notsubsetI = $true) & (sepSubset = $true) & (subsetE = $true) & (nonemptyE1 = $true) & (setunionI = $true) & (notdallE = $true) & (powersetI = $true) & (powersetE = $true) & (setminusER = $true) & (exuI3 = $true) & (prop2set2propI = $true) & (powersetsubset = $true) & (inCongP = $true) & (setadjoinSub = $true) & (bs114d = $true) & (setadjoinIL = $true) & (subsetE2 = $true) & (setextAx = $true) & (((sK192 != $true) & (((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) != $true) | (sK192 = $true)) & ((sK192 = $true) | ((in @ sK190 @ sK189) != $true) | ((in @ sK190 @ sK191) = $true))) & ($true = (in @ sK190 @ (symdiff @ sK189 @ sK191)))) & (powerset__Cong = $true) & (wellorderingAx = $true) & (exu__Cong = $true) & (quantDeMorgan1 = $true) & (binintersectSubset1 = $true) & (binintersectSubset5 = $true) & (exuE3u = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (subsetRefl = $true) & (setminusSubset2 = $true) & (binunionEcases = $true) & (binintersectER = $true) & (subsetTrans = $true) & (descr__Cong = $true) & (subsetI2 = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (upairset2IR = $true) & (setunion__Cong = $true) & (setunionAx = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (quantDeMorgan2 = $true) & (descrp = $true) & (nonemptyI = $true) & (nonemptyI1 = $true) & (setminusIRneg = $true) & (notdexE = $true) & (binintersectSubset4 = $true) & (exuI1 = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (setminusI = $true) & (subsetI1 = $true) & (setadjoinAx = $true) & (notequalI1 = $true) & (binunionIL = $true) & (setextsub = $true) & (setunionE = $true) & (binunionE = $true) & (powersetI1 = $true) & (notinsingleton = $true) & (inPowerset = $true) & (binintersectSubset3 = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (disjointsetsI1 = $true) & (powersetE1 = $true) & (setadjoin__Cong = $true) & (setminusEL = $true) & (binintersectSubset2 = $true) & (upairsetE = $true) & (setminusLsub = $true) & (emptyE1 = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (exuEu = $true) & (omega__Cong = $true) & (notinemptyset = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (dsetconstr__Cong = $true) & (setadjoinIR = $true) & (in__Cong = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (exuI2 = $true) & (noeltsimpempty = $true) & (binintersectEL = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (emptyinPowerset = $true) & (uniqinunit = $true) & (subPowSU = $true) & (notequalI2 = $true) & (setadjoinOr = $true) & (prop2setE = $true) & (emptysetAx = $true) & (emptyset__Cong = $true) & (replAx = $true) & (binintersectI = $true) & (setext = $true) & (setoftrueEq = $true) & (emptysetE = $true) & (sepInPowerset = $true) & (setminusILneg = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (binunionLsub = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (emptysetsubset = $true) & (dsetconstrEL = $true) & (setadjoinSub2 = $true) & (prop2setI = $true) & (subset2powerset = $true) & (powersetAx = $true) & (eqinunit = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (binintersectLsub = $true) & (setminusELneg = $true)),
% 2.39/1.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK189,sK190,sK191,sK192])],[f447,f906,f905])).
% 2.39/1.92 thf(f905,plain,(
% 2.39/1.92 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true) | ($true = X3)) & (($true = X3) | ($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true))) & ((in @ X1 @ (symdiff @ X0 @ X2)) = $true)) => (? [X3 : $o] : (($true != X3) & (((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) != $true) | ($true = X3)) & (($true = X3) | ((in @ sK190 @ sK189) != $true) | ((in @ sK190 @ sK191) = $true))) & ($true = (in @ sK190 @ (symdiff @ sK189 @ sK191))))),
% 2.39/1.92 introduced(definition,[],[choice_axiom])).
% 2.39/1.92 thf(f906,plain,(
% 2.39/1.92 ? [X3 : $o] : (($true != X3) & (((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) != $true) | ($true = X3)) & (($true = X3) | ((in @ sK190 @ sK189) != $true) | ((in @ sK190 @ sK191) = $true))) => ((sK192 != $true) & (((in @ sK190 @ sK189) = $true) | ((in @ sK190 @ sK191) != $true) | (sK192 = $true)) & ((sK192 = $true) | ((in @ sK190 @ sK189) != $true) | ((in @ sK190 @ sK191) = $true)))),
% 2.39/1.92 introduced(definition,[],[choice_axiom])).
% 2.39/1.92 thf(f447,plain,(
% 2.39/1.92 (notsubsetI = $true) & (sepSubset = $true) & (subsetE = $true) & (nonemptyE1 = $true) & (setunionI = $true) & (notdallE = $true) & (powersetI = $true) & (powersetE = $true) & (setminusER = $true) & (exuI3 = $true) & (prop2set2propI = $true) & (powersetsubset = $true) & (inCongP = $true) & (setadjoinSub = $true) & (bs114d = $true) & (setadjoinIL = $true) & (subsetE2 = $true) & (setextAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = (in @ X1 @ X0)) | ((in @ X1 @ X2) != $true) | ($true = X3)) & (($true = X3) | ($true != (in @ X1 @ X0)) | ((in @ X1 @ X2) = $true))) & ((in @ X1 @ (symdiff @ X0 @ X2)) = $true)) & (powerset__Cong = $true) & (wellorderingAx = $true) & (exu__Cong = $true) & (quantDeMorgan1 = $true) & (binintersectSubset1 = $true) & (binintersectSubset5 = $true) & (exuE3u = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (subsetRefl = $true) & (setminusSubset2 = $true) & (binunionEcases = $true) & (binintersectER = $true) & (subsetTrans = $true) & (descr__Cong = $true) & (subsetI2 = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (upairset2IR = $true) & (setunion__Cong = $true) & (setunionAx = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (quantDeMorgan2 = $true) & (descrp = $true) & (nonemptyI = $true) & (nonemptyI1 = $true) & (setminusIRneg = $true) & (notdexE = $true) & (binintersectSubset4 = $true) & (exuI1 = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (setminusI = $true) & (subsetI1 = $true) & (setadjoinAx = $true) & (notequalI1 = $true) & (binunionIL = $true) & (setextsub = $true) & (setunionE = $true) & (binunionE = $true) & (powersetI1 = $true) & (notinsingleton = $true) & (inPowerset = $true) & (binintersectSubset3 = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (disjointsetsI1 = $true) & (powersetE1 = $true) & (setadjoin__Cong = $true) & (setminusEL = $true) & (binintersectSubset2 = $true) & (upairsetE = $true) & (setminusLsub = $true) & (emptyE1 = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (exuEu = $true) & (omega__Cong = $true) & (notinemptyset = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (dsetconstr__Cong = $true) & (setadjoinIR = $true) & (in__Cong = $true) & (emptyI = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (exuI2 = $true) & (noeltsimpempty = $true) & (binintersectEL = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (emptyinPowerset = $true) & (uniqinunit = $true) & (subPowSU = $true) & (notequalI2 = $true) & (setadjoinOr = $true) & (prop2setE = $true) & (emptysetAx = $true) & (emptyset__Cong = $true) & (replAx = $true) & (binintersectI = $true) & (setext = $true) & (setoftrueEq = $true) & (emptysetE = $true) & (sepInPowerset = $true) & (setminusILneg = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (binunionLsub = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (emptysetsubset = $true) & (dsetconstrEL = $true) & (setadjoinSub2 = $true) & (prop2setI = $true) & (subset2powerset = $true) & (powersetAx = $true) & (eqinunit = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (binintersectLsub = $true) & (setminusELneg = $true)),
% 2.39/1.92 inference(flattening,[status(thm)],[f446])).
% 2.39/1.92 thf(f446,plain,(
% 2.39/1.92 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [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)))) & ((in @ X1 @ (symdiff @ X0 @ X2)) = $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)),
% 2.39/1.92 inference(ennf_transformation,[status(thm)],[f390])).
% 2.39/1.92 thf(f390,plain,(
% 2.39/1.92 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (symdiff @ X0 @ X2)) = $true) => ! [X3 : $o] : ((($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) != $true) => ($true = X3))) => ((($true != (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ($true = X3))) => ($true = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.39/1.92 inference(flattening,[status(thm)],[f180])).
% 2.39/1.92 thf(f180,plain,(
% 2.39/1.92 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (symdiff @ X0 @ X2)) = $true) => ! [X3 : $o] : ((($true = (in @ X1 @ X0)) => (~((in @ X1 @ X2) = $true) => ($true = X3))) => ((~($true = (in @ X1 @ X0)) => (((in @ X1 @ X2) = $true) => ($true = X3))) => ($true = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.39/1.92 inference(fool_elimination,[status(thm)],[f179])).
% 2.39/1.92 thf(f179,plain,(
% 2.39/1.92 ~(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 => ! [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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.39/1.92 inference(rectify,[status(thm)],[f132])).
% 2.39/1.92 thf(f132,negated_conjecture,(
% 2.39/1.92 ~(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 => ! [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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.39/1.92 inference(negated_conjecture,[status(cth)],[f131])).
% 2.39/1.92 thf(f131,conjecture,(
% 2.39/1.92 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 => ! [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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.39/1.92 file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',symdiffE)).
% 2.39/1.92 thf(f2569,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ X1)) != $true) | ((in @ X0 @ X2) = $true)) )),
% 2.39/1.92 inference(beta_eta_normalization,[status(thm)],[f2568])).
% 2.39/1.92 thf(f2568,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true)) )),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f2208])).
% 2.39/1.92 thf(f2208,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != $true) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) )),
% 2.39/1.92 inference(definition_unfolding,[status(thm)],[f1763,f1550])).
% 2.39/1.92 thf(f1550,plain,(
% 2.39/1.92 (dsetconstrEL = $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f1763,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true) | (dsetconstrEL != $true)) )),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f1020])).
% 2.39/1.92 thf(f1020,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK243 @ (dsetconstr @ sK245 @ (^[Y0 : $i]: (sK244 @ Y0)))) = $true) & ($true != (in @ sK243 @ sK245))))),
% 2.39/1.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f1018,f1019])).
% 2.39/1.92 thf(f1019,plain,(
% 2.39/1.92 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true) & ((in @ X3 @ X5) != $true)) => (((in @ sK243 @ (dsetconstr @ sK245 @ (^[Y0 : $i]: (sK244 @ Y0)))) = $true) & ($true != (in @ sK243 @ sK245)))),
% 2.39/1.92 introduced(definition,[],[choice_axiom])).
% 2.39/1.92 thf(f1018,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((in @ X3 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true) & ((in @ X3 @ X5) != $true)))),
% 2.39/1.92 inference(rectify,[status(thm)],[f1017])).
% 2.39/1.92 thf(f1017,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) & ((in @ X0 @ X2) != $true)))),
% 2.39/1.92 inference(nnf_transformation,[status(thm)],[f462])).
% 2.39/1.92 thf(f462,plain,(
% 2.39/1.92 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X0 @ X2) = $true)) <=> (dsetconstrEL = $true)),
% 2.39/1.92 inference(ennf_transformation,[status(thm)],[f238])).
% 2.39/1.92 thf(f238,plain,(
% 2.39/1.92 (dsetconstrEL = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((in @ X0 @ X2) = $true))),
% 2.39/1.92 inference(fool_elimination,[status(thm)],[f237])).
% 2.39/1.92 thf(f237,plain,(
% 2.39/1.92 (dsetconstrEL = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)))),
% 2.39/1.92 inference(rectify,[status(thm)],[f15])).
% 2.39/1.92 thf(f15,axiom,(
% 2.39/1.92 (dsetconstrEL = ! [X1 : $i,X0 : $i > $o,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)))),
% 2.39/1.92 file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',dsetconstrEL)).
% 2.39/1.92 thf(f2423,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) )),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f2107])).
% 2.39/1.92 thf(f2107,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ($true != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) )),
% 2.39/1.92 inference(definition_unfolding,[status(thm)],[f1488,f1608])).
% 2.39/1.92 thf(f1608,plain,(
% 2.39/1.92 (binunionE = $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f1488,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true) | (binunionE != $true)) )),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f841])).
% 2.39/1.92 thf(f841,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) | (binunionE != $true)) & ((binunionE = $true) | (((in @ sK151 @ (binunion @ sK153 @ sK152)) = $true) & ((in @ sK151 @ sK152) != $true) & ((in @ sK151 @ sK153) != $true)))),
% 2.39/1.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK151,sK152,sK153])],[f839,f840])).
% 2.39/1.92 thf(f840,plain,(
% 2.39/1.92 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ (binunion @ X5 @ X4))) & ((in @ X3 @ X4) != $true) & ((in @ X3 @ X5) != $true)) => (((in @ sK151 @ (binunion @ sK153 @ sK152)) = $true) & ((in @ sK151 @ sK152) != $true) & ((in @ sK151 @ sK153) != $true))),
% 2.39/1.92 introduced(definition,[],[choice_axiom])).
% 2.39/1.92 thf(f839,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) | (binunionE != $true)) & ((binunionE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ (binunion @ X5 @ X4))) & ((in @ X3 @ X4) != $true) & ((in @ X3 @ X5) != $true)))),
% 2.39/1.92 inference(rectify,[status(thm)],[f838])).
% 2.39/1.92 thf(f838,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) | (binunionE != $true)) & ((binunionE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) = $true) & ((in @ X0 @ X1) != $true) & ((in @ X0 @ X2) != $true)))),
% 2.39/1.92 inference(nnf_transformation,[status(thm)],[f537])).
% 2.39/1.92 thf(f537,plain,(
% 2.39/1.92 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) <=> (binunionE = $true)),
% 2.39/1.92 inference(flattening,[status(thm)],[f536])).
% 2.39/1.92 thf(f536,plain,(
% 2.39/1.92 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) = $true)) | ((in @ X0 @ (binunion @ X2 @ X1)) != $true)) <=> (binunionE = $true)),
% 2.39/1.92 inference(ennf_transformation,[status(thm)],[f375])).
% 2.39/1.92 thf(f375,plain,(
% 2.39/1.92 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (binunion @ X2 @ X1)) = $true) => (((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) = $true))) <=> (binunionE = $true)),
% 2.39/1.92 inference(fool_elimination,[status(thm)],[f374])).
% 2.39/1.92 thf(f374,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binunion @ X2 @ X1)) => ((in @ X0 @ X1) | (in @ X0 @ X2))) = binunionE)),
% 2.39/1.92 inference(rectify,[status(thm)],[f105])).
% 2.39/1.92 thf(f105,axiom,(
% 2.39/1.92 (! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ (binunion @ X3 @ X4)) => ((in @ X1 @ X4) | (in @ X1 @ X3))) = binunionE)),
% 2.39/1.92 file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',binunionE)).
% 2.39/1.92 thf(f4036,plain,(
% 2.39/1.92 ~spl391_79 | ~spl391_131),
% 2.39/1.92 inference(avatar_contradiction_clause,[status(thm)],[f4035])).
% 2.39/1.92 thf(f4035,plain,(
% 2.39/1.92 $false | (~spl391_79 | ~spl391_131)),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f4034])).
% 2.39/1.92 thf(f4034,plain,(
% 2.39/1.92 ($false = $true) | (~spl391_79 | ~spl391_131)),
% 2.39/1.92 inference(forward_demodulation,[status(thm)],[f2997,f3956])).
% 2.39/1.92 thf(f3956,plain,(
% 2.39/1.92 ($false = (in @ sK190 @ sK191)) | ~spl391_131),
% 2.39/1.92 inference(avatar_component_clause,[status(thm)],[f3955])).
% 2.39/1.92 thf(f3955,definition,(
% 2.39/1.92 spl391_131 <=> ($false = (in @ sK190 @ sK191))),
% 2.39/1.92 introduced(definition,[new_symbols(naming,[spl391_131])],[avatar_definition])).
% 2.39/1.92 thf(f2997,plain,(
% 2.39/1.92 ((in @ sK190 @ sK191) = $true) | ~spl391_79),
% 2.39/1.92 inference(avatar_component_clause,[status(thm)],[f2904])).
% 2.39/1.92 thf(f4030,plain,(
% 2.39/1.92 ~spl391_78),
% 2.39/1.92 inference(avatar_contradiction_clause,[status(thm)],[f4029])).
% 2.39/1.92 thf(f4029,plain,(
% 2.39/1.92 $false | ~spl391_78),
% 2.39/1.92 inference(subsumption_resolution,[status(thm)],[f2902,f1653])).
% 2.39/1.92 thf(f1653,plain,(
% 2.39/1.92 (sK192 != $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f2902,plain,(
% 2.39/1.92 (sK192 = $true) | ~spl391_78),
% 2.39/1.92 inference(avatar_component_clause,[status(thm)],[f2901])).
% 2.39/1.92 thf(f2901,definition,(
% 2.39/1.92 spl391_78 <=> (sK192 = $true)),
% 2.39/1.92 introduced(definition,[new_symbols(naming,[spl391_78])],[avatar_definition])).
% 2.39/1.92 thf(f3960,plain,(
% 2.39/1.92 spl391_131 | spl391_132),
% 2.39/1.92 inference(avatar_split_clause,[status(thm)],[f3952,f3958,f3955])).
% 2.39/1.92 thf(f3952,plain,(
% 2.39/1.92 ($false = (in @ sK190 @ sK189)) | ($false = (in @ sK190 @ sK191))),
% 2.39/1.92 inference(not_proxy_clausification,[status(thm)],[f3951])).
% 2.39/1.92 thf(f3951,plain,(
% 2.39/1.92 ($false = (in @ sK190 @ sK191)) | ((~ (in @ sK190 @ sK189)) = $true)),
% 2.39/1.92 inference(not_proxy_clausification,[status(thm)],[f3950])).
% 2.39/1.92 thf(f3950,plain,(
% 2.39/1.92 ((~ (in @ sK190 @ sK191)) = $true) | ((~ (in @ sK190 @ sK189)) = $true)),
% 2.39/1.92 inference(binary_proxy_clausification,[status(thm)],[f3949])).
% 2.39/1.92 thf(f3949,plain,(
% 2.39/1.92 (((~ (in @ sK190 @ sK191)) | (~ (in @ sK190 @ sK189))) = $true)),
% 2.39/1.92 inference(beta_eta_normalization,[status(thm)],[f3948])).
% 2.39/1.92 thf(f3948,plain,(
% 2.39/1.92 (((^[Y0 : $i]: ((~ (in @ Y0 @ sK191)) | (~ (in @ Y0 @ sK189)))) @ sK190) = $true)),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f3941])).
% 2.39/1.92 thf(f3941,plain,(
% 2.39/1.92 ($true != $true) | (((^[Y0 : $i]: ((~ (in @ Y0 @ sK191)) | (~ (in @ Y0 @ sK189)))) @ sK190) = $true)),
% 2.39/1.92 inference(superposition,[status(thm)],[f2452,f2536])).
% 2.39/1.92 thf(f2452,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X0 @ X1)) != $true) | ((X1 @ X2) = $true)) )),
% 2.39/1.92 inference(beta_eta_normalization,[status(thm)],[f2451])).
% 2.39/1.92 thf(f2451,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) )),
% 2.39/1.92 inference(trivial_inequality_removal,[status(thm)],[f2375])).
% 2.39/1.92 thf(f2375,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((X1 @ X2) = $true) | ($true != $true)) )),
% 2.39/1.92 inference(definition_unfolding,[status(thm)],[f2008,f1552])).
% 2.39/1.92 thf(f1552,plain,(
% 2.39/1.92 (dsetconstrER = $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f2008,plain,(
% 2.39/1.92 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | (dsetconstrER != $true)) )),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f1310])).
% 2.39/1.92 thf(f1310,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (((sK386 @ sK387) != $true) & ((in @ sK387 @ (dsetconstr @ sK385 @ (^[Y0 : $i]: (sK386 @ Y0)))) = $true)))),
% 2.39/1.92 inference(skolemisation,[status(esa),new_symbols(skolem,[sK385,sK386,sK387])],[f1308,f1309])).
% 2.39/1.92 thf(f1309,plain,(
% 2.39/1.92 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) != $true) & ((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true)) => (((sK386 @ sK387) != $true) & ((in @ sK387 @ (dsetconstr @ sK385 @ (^[Y0 : $i]: (sK386 @ Y0)))) = $true))),
% 2.39/1.92 introduced(definition,[],[choice_axiom])).
% 2.39/1.92 thf(f1308,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) != $true) & ((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true)))),
% 2.39/1.92 inference(rectify,[status(thm)],[f1307])).
% 2.39/1.92 thf(f1307,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) != $true) & ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)))),
% 2.39/1.92 inference(nnf_transformation,[status(thm)],[f425])).
% 2.39/1.92 thf(f425,plain,(
% 2.39/1.92 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((X1 @ X2) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) <=> (dsetconstrER = $true)),
% 2.39/1.92 inference(ennf_transformation,[status(thm)],[f280])).
% 2.39/1.92 thf(f280,plain,(
% 2.39/1.92 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((X1 @ X2) = $true))),
% 2.39/1.92 inference(fool_elimination,[status(thm)],[f279])).
% 2.39/1.92 thf(f279,plain,(
% 2.39/1.92 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 2.39/1.92 inference(rectify,[status(thm)],[f16])).
% 2.39/1.92 thf(f16,axiom,(
% 2.39/1.92 (! [X3 : $i,X0 : $i > $o,X1 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 2.39/1.92 file('/export/starexec/sandbox/tmp/tmp.LRgESb0Okx/DTF2THF_10434.p',dsetconstrER)).
% 2.39/1.92 thf(f2999,plain,(
% 2.39/1.92 spl391_79 | ~spl391_80 | spl391_78),
% 2.39/1.92 inference(avatar_split_clause,[status(thm)],[f1651,f2901,f2907,f2904])).
% 2.39/1.92 thf(f1651,plain,(
% 2.39/1.92 (sK192 = $true) | ((in @ sK190 @ sK189) != $true) | ((in @ sK190 @ sK191) = $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 thf(f2909,plain,(
% 2.39/1.92 spl391_78 | ~spl391_79 | spl391_80),
% 2.39/1.92 inference(avatar_split_clause,[status(thm)],[f1652,f2907,f2904,f2901])).
% 2.39/1.92 thf(f1652,plain,(
% 2.39/1.92 (sK192 = $true) | ((in @ sK190 @ sK191) != $true) | ((in @ sK190 @ sK189) = $true)),
% 2.39/1.92 inference(cnf_transformation,[status(thm)],[f907])).
% 2.39/1.92 % SZS output end Proof for DTF2THF_10434
% 2.39/1.92 % (10798)------------------------------
% 2.39/1.92 % (10798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.92 % (10798)Termination reason: Refutation
% 2.39/1.92
% 2.39/1.92 % (10798)Memory used [KB]: 9466
% 2.39/1.92 % (10798)Time elapsed: 0.208 s
% 2.39/1.92 % (10798)Instructions burned: 618 (million)
% 2.39/1.92 % (10798)------------------------------
% 2.39/1.92 % (10798)------------------------------
% 2.39/1.92 % (10640)Success in time 0.54 s
%------------------------------------------------------------------------------