%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU598^1 : 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 : n007.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 09:35:31 AM UTC 2026
% Result : Theorem 38.09s 6.97s
% Output : Refutation 38.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 2397 ( 671 equ; 0 cnn)
% Maximal formula atoms : 116 ( 28 avg)
% Number of connectives : 1485 ( 135 ~; 109 |; 384 &; 358 @)
% ( 18 <=>; 481 =>; 0 <=; 0 <~>)
% Maximal formula depth : 121 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 248 ( 245 usr; 135 con; 0-4 aty)
% Number of variables : 143 ( 0 ^; 110 !; 33 ?; 143 :)
% 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_145,type,
sP1: $i > $i > $o ).
thf(func_def_146,type,
sP2: $i > $o ).
thf(func_def_147,type,
sP3: $i > $i > $o ).
thf(func_def_148,type,
sP4: $i > $i > $o ).
thf(func_def_151,type,
sK7: $i > $i > $i ).
thf(func_def_154,type,
sK10: $i > $i > $i ).
thf(func_def_158,type,
sK14: $i > $o ).
thf(func_def_160,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK21: $i > $o ).
thf(func_def_167,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_169,type,
sK25: $i > $o ).
thf(func_def_179,type,
sK35: $i > $o ).
thf(func_def_182,type,
sK38: $i > $o ).
thf(func_def_183,type,
sK39: $i > $o ).
thf(func_def_184,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_185,type,
sK41: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK45: $i > $i > $o ).
thf(func_def_190,type,
sK46: $i > $i ).
thf(func_def_191,type,
sK47: $i > $i ).
thf(func_def_192,type,
sK48: ( $i > $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK49: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_194,type,
sK50: ( $i > $i > $o ) > $i > $i ).
thf(func_def_197,type,
sK53: $i > $i > $i ).
thf(func_def_198,type,
sK54: $i > $i > $i ).
thf(func_def_205,type,
sK61: $i > $o ).
thf(func_def_206,type,
sK62: $i > $o ).
thf(func_def_207,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_208,type,
sK64: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_217,type,
sK73: $i > $o ).
thf(func_def_224,type,
sK80: $i > $o ).
thf(func_def_225,type,
sK81: $i > $o ).
thf(func_def_228,type,
sK84: $i > ( $i > $o ) > $i ).
thf(func_def_231,type,
sK87: $i > $o ).
thf(func_def_234,type,
sK90: $i > ( $i > $o ) > $i ).
thf(func_def_242,type,
sK98: $i > $i > $i ).
thf(func_def_248,type,
sK104: $i > $i ).
thf(func_def_250,type,
sK106: $i > $i ).
thf(func_def_252,type,
sK108: $i > $i ).
thf(func_def_258,type,
sK114: $i > $o ).
thf(func_def_267,type,
sK123: $i > $o ).
thf(func_def_269,type,
sK125: $i > $i ).
thf(func_def_274,type,
sK130: $i > $o ).
thf(func_def_276,type,
sK132: ( $i > $o ) > $i > $i ).
thf(func_def_280,type,
sK136: $i > $i > $i ).
thf(func_def_287,type,
sK143: $i > $i > $i ).
thf(func_def_288,type,
sK144: $i > $i > $i ).
thf(func_def_289,type,
sK145: $i > $i > $i ).
thf(func_def_290,type,
sK146: $i > $i > $i ).
thf(func_def_291,type,
sK147: $i > $i > $i ).
thf(func_def_292,type,
sK148: $i > $i > $i > $i ).
thf(func_def_293,type,
sK149: $i > $i ).
thf(func_def_294,type,
sK150: $i > $i ).
thf(func_def_295,type,
sK151: $i > $i ).
thf(func_def_296,type,
sK152: $i > $i ).
thf(func_def_297,type,
sK153: $i > $i > $i ).
thf(func_def_298,type,
sK154: $i > $i > $i > $i ).
thf(func_def_299,type,
sK155: $i > $i > $i > $i ).
thf(func_def_300,type,
sK156: $i > $i > $i ).
thf(func_def_301,type,
sK157: $i > $i > $i ).
thf(func_def_303,type,
sK159: $i > $i ).
thf(func_def_304,type,
sK160: $i > $i ).
thf(func_def_305,type,
sK161: $i > $i ).
thf(func_def_310,type,
sK166: $i > $o ).
thf(func_def_314,type,
sK170: $i > $o ).
thf(func_def_318,type,
sK174: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_319,type,
sK175: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_322,type,
sK178: $i > $o ).
thf(func_def_323,type,
sK179: $i > $o ).
thf(func_def_324,type,
sK180: $i > $i > $i ).
thf(func_def_330,type,
sK186: $i > $o ).
thf(func_def_332,type,
sK188: ( $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK208: $i > $o ).
thf(func_def_355,type,
sK211: $i > $i ).
thf(func_def_359,type,
sK215: ( $i > $o ) > $i ).
thf(func_def_360,type,
sK216: $i > $o ).
thf(func_def_361,type,
sK217: $i > $i ).
thf(func_def_368,type,
sK224: $i > $i ).
thf(func_def_386,type,
sK242: $i > $i > $i ).
thf(func_def_389,type,
sK245: $o > $i > $i > $i ).
thf(func_def_394,type,
sK250: ( $i > $o ) > $i ).
thf(func_def_395,type,
sK251: $i > $o ).
thf(func_def_396,type,
sK252: $i > $o ).
thf(func_def_398,type,
sK254: $i > $o ).
thf(func_def_400,type,
sK256: $i > ( $i > $o ) > $i ).
thf(func_def_404,type,
sK260: $i > $o ).
thf(func_def_413,type,
sK269: $i > $i > $i ).
thf(func_def_417,type,
sK273: $i > $o ).
thf(func_def_419,type,
sK275: $i > ( $i > $o ) > $i ).
thf(func_def_431,type,
sK287: $i > $i ).
thf(func_def_445,type,
sK301: ( $i > $o ) > $i ).
thf(func_def_446,type,
sK302: ( $i > $o ) > $i ).
thf(func_def_447,type,
sK303: $i > $o ).
thf(func_def_452,type,
sK308: $i > $o ).
thf(func_def_453,type,
sK309: $i > $i ).
thf(func_def_454,type,
sK310: ( $i > $o ) > $i ).
thf(func_def_457,type,
sK313: $i > $o ).
thf(func_def_459,type,
ph315:
!>[X0: $tType] : X0 ).
thf(f23994,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1757,f1858,f2097,f2778,f2948,f3394,f4050,f4157,f23993]) ).
thf(f23993,plain,
( ~ spl314_5
| ~ spl314_98
| ~ spl314_236
| ~ spl314_501 ),
inference(avatar_contradiction_clause,[status(thm)],[f23992]) ).
thf(f23992,plain,
( $false
| ~ spl314_5
| ~ spl314_98
| ~ spl314_236
| ~ spl314_501 ),
inference(subsumption_resolution,[status(thm)],[f23960,f1506]) ).
thf(f1506,plain,
( sK262
!= ( binintersect @ sK261 @ sK262 ) ),
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f943,plain,
( ( replAx = $true )
& ( exuEu = $true )
& ( emptyset__Cong = $true )
& ( setadjoinE = $true )
& ( powersetE = $true )
& ( notsubsetI = $true )
& ( disjointsetsI1 = $true )
& ( setbeta = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( in__Cong = $true )
& ( eqinunit = $true )
& ( binunionEcases = $true )
& ( dsetconstrI = $true )
& ( powersetI1 = $true )
& ( sK262
!= ( binintersect @ sK261 @ sK262 ) )
& ( ( subset @ sK262 @ sK261 )
= $true )
& ( emptyInPowerset = $true )
& ( nonemptyI = $true )
& ( powersetE1 = $true )
& ( exuI3 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset5 = $true )
& ( descr__Cong = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( exu__Cong = $true )
& ( subsetE = $true )
& ( omega0Ax = $true )
& ( vacuousDall = $true )
& ( emptysetimpfalse = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( setadjoin__Cong = $true )
& ( notdallE = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( binunionIR = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinOr = $true )
& ( prop2setI = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( sepSubset = $true )
& ( setadjoinIL = $true )
& ( notequalI1 = $true )
& ( setadjoinSub2 = $true )
& ( upairset2IR = $true )
& ( powersetI = $true )
& ( setunion__Cong = $true )
& ( inPowerset = $true )
& ( powersetsubset = $true )
& ( subsetI2 = $true )
& ( upairsetIR = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( binintersectEL = $true )
& ( nonemptyI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectRsub = $true )
& ( setext = $true )
& ( binunionE = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( emptyI = $true )
& ( subsetTrans = $true )
& ( noeltsimpempty = $true )
& ( prop2set2propI = $true )
& ( setextsub = $true )
& ( notequalI2 = $true )
& ( exuE2 = $true )
& ( notinsingleton = $true )
& ( omega__Cong = $true )
& ( descrp = $true )
& ( subset2powerset = $true )
& ( binunionIL = $true )
& ( exuE3e = $true )
& ( binunionLsub = $true )
& ( omegaSAx = $true )
& ( emptyinPowerset = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( binintersectER = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( exuI2 = $true )
& ( binintersectSubset3 = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( notinemptyset = $true )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK261,sK262])],[f469,f942]) ).
thf(f942,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( sK262
!= ( binintersect @ sK261 @ sK262 ) )
& ( ( subset @ sK262 @ sK261 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f469,plain,
( ( replAx = $true )
& ( exuEu = $true )
& ( emptyset__Cong = $true )
& ( setadjoinE = $true )
& ( powersetE = $true )
& ( notsubsetI = $true )
& ( disjointsetsI1 = $true )
& ( setbeta = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( in__Cong = $true )
& ( eqinunit = $true )
& ( binunionEcases = $true )
& ( dsetconstrI = $true )
& ( powersetI1 = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( emptyInPowerset = $true )
& ( nonemptyI = $true )
& ( powersetE1 = $true )
& ( exuI3 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset5 = $true )
& ( descr__Cong = $true )
& ( notdexE = $true )
& ( exuE1 = $true )
& ( exu__Cong = $true )
& ( subsetE = $true )
& ( omega0Ax = $true )
& ( vacuousDall = $true )
& ( emptysetimpfalse = $true )
& ( singletonsswitch = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( setadjoin__Cong = $true )
& ( notdallE = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( eqimpsubset2 = $true )
& ( eqimpsubset1 = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( powerset__Cong = $true )
& ( binunionRsub = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( binunionIR = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinOr = $true )
& ( prop2setI = $true )
& ( subsetE2 = $true )
& ( powersetAx = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( sepSubset = $true )
& ( setadjoinIL = $true )
& ( notequalI1 = $true )
& ( setadjoinSub2 = $true )
& ( upairset2IR = $true )
& ( powersetI = $true )
& ( setunion__Cong = $true )
& ( inPowerset = $true )
& ( powersetsubset = $true )
& ( subsetI2 = $true )
& ( upairsetIR = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( binintersectEL = $true )
& ( nonemptyI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectRsub = $true )
& ( setext = $true )
& ( binunionE = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( emptyI = $true )
& ( subsetTrans = $true )
& ( noeltsimpempty = $true )
& ( prop2set2propI = $true )
& ( setextsub = $true )
& ( notequalI2 = $true )
& ( exuE2 = $true )
& ( notinsingleton = $true )
& ( omega__Cong = $true )
& ( descrp = $true )
& ( subset2powerset = $true )
& ( binunionIL = $true )
& ( exuE3e = $true )
& ( binunionLsub = $true )
& ( omegaSAx = $true )
& ( emptyinPowerset = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( binintersectER = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( exuI2 = $true )
& ( binintersectSubset3 = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( notinemptyset = $true )
& ( dsetconstrER = $true ) ),
inference(flattening,[status(thm)],[f468]) ).
thf(f468,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( 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)],[f311]) ).
thf(f311,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f310]) ).
thf(f310,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
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f118]) ).
thf(f118,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
=> ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
thf(f117,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
=> ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectSubset4) ).
thf(f23960,plain,
( ( sK262
= ( binintersect @ sK261 @ sK262 ) )
| ~ spl314_5
| ~ spl314_98
| ~ spl314_236
| ~ spl314_501 ),
inference(trivial_inequality_removal,[status(thm)],[f23936]) ).
thf(f23936,plain,
( ( $true != $true )
| ( sK262
= ( binintersect @ sK261 @ sK262 ) )
| ~ spl314_5
| ~ spl314_98
| ~ spl314_236
| ~ spl314_501 ),
inference(superposition,[status(thm)],[f4425,f23918]) ).
thf(f23918,plain,
( ( ( subset @ sK262 @ ( binintersect @ sK261 @ sK262 ) )
= $true )
| ~ spl314_5
| ~ spl314_98 ),
inference(trivial_inequality_removal,[status(thm)],[f23882]) ).
thf(f23882,plain,
( ( ( subset @ sK262 @ ( binintersect @ sK261 @ sK262 ) )
= $true )
| ( $true != $true )
| ~ spl314_5
| ~ spl314_98 ),
inference(superposition,[status(thm)],[f6852,f1505]) ).
thf(f1505,plain,
( ( subset @ sK262 @ sK261 )
= $true ),
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f6852,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true ) )
| ~ spl314_5
| ~ spl314_98 ),
inference(trivial_inequality_removal,[status(thm)],[f6834]) ).
thf(f6834,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( binintersect @ X1 @ X0 ) )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true != $true ) )
| ~ spl314_5
| ~ spl314_98 ),
inference(superposition,[status(thm)],[f1752,f2158]) ).
thf(f2158,plain,
( ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true )
| ~ spl314_98 ),
inference(avatar_component_clause,[status(thm)],[f2157]) ).
thf(f2157,definition,
( spl314_98
<=> ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl314_98])],[avatar_definition]) ).
thf(f1752,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ~ spl314_5 ),
inference(avatar_component_clause,[status(thm)],[f1751]) ).
thf(f1751,definition,
( spl314_5
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl314_5])],[avatar_definition]) ).
thf(f4425,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X1 ) )
!= $true )
| ( ( binintersect @ X0 @ X1 )
= X1 ) )
| ~ spl314_236
| ~ spl314_501 ),
inference(trivial_inequality_removal,[status(thm)],[f4411]) ).
thf(f4411,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( binintersect @ X0 @ X1 )
= X1 )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ~ spl314_236
| ~ spl314_501 ),
inference(superposition,[status(thm)],[f2777,f4049]) ).
thf(f4049,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true )
| ~ spl314_501 ),
inference(avatar_component_clause,[status(thm)],[f4048]) ).
thf(f4048,definition,
( spl314_501
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl314_501])],[avatar_definition]) ).
thf(f2777,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 ) )
| ~ spl314_236 ),
inference(avatar_component_clause,[status(thm)],[f2776]) ).
thf(f2776,definition,
( spl314_236
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl314_236])],[avatar_definition]) ).
thf(f4157,plain,
spl314_381,
inference(avatar_split_clause,[status(thm)],[f1440,f3468]) ).
thf(f3468,definition,
( spl314_381
<=> ( binintersectRsub = $true ) ),
introduced(definition,[new_symbols(naming,[spl314_381])],[avatar_definition]) ).
thf(f1440,plain,
binintersectRsub = $true,
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f4050,plain,
( ~ spl314_381
| spl314_501 ),
inference(avatar_split_clause,[status(thm)],[f1175,f4048,f3468]) ).
thf(f1175,plain,
! [X0: $i,X1: $i] :
( ( binintersectRsub != $true )
| ( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f674]) ).
thf(f674,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ( ( subset @ ( binintersect @ sK110 @ sK109 ) @ sK109 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110])],[f672,f673]) ).
thf(f673,plain,
( ? [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X2 )
!= $true )
=> ( ( subset @ ( binintersect @ sK110 @ sK109 ) @ sK109 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f672,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X2 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f671]) ).
thf(f671,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X0 )
= $true )
<=> ( binintersectRsub = $true ) ),
inference(fool_elimination,[status(thm)],[f156]) ).
thf(f156,plain,
( binintersectRsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X1 @ X0 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f116]) ).
thf(f116,axiom,
( binintersectRsub
= ( ! [X4: $i,X3: $i] : ( subset @ ( binintersect @ X3 @ X4 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectRsub) ).
thf(f3394,plain,
( spl314_98
| ~ spl314_260 ),
inference(avatar_split_clause,[status(thm)],[f1633,f2891,f2157]) ).
thf(f2891,definition,
( spl314_260
<=> ( notequalI1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl314_260])],[avatar_definition]) ).
thf(f1633,plain,
! [X3: $i] :
( ( notequalI1 != $true )
| ( ( subset @ X3 @ X3 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f1589]) ).
thf(f1589,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( X2 != X3 )
| ( notequalI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( ( notequalI1 = $true )
| ( ( ( subset @ sK306 @ sK305 )
!= $true )
& ( sK306 = sK305 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( X2 != X3 ) )
| ( notequalI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK305,sK306])],[f1018,f1019]) ).
thf(f1019,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( X0 = X1 ) )
=> ( ( ( subset @ sK306 @ sK305 )
!= $true )
& ( sK306 = sK305 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1018,plain,
( ( ( notequalI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( X0 = X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
| ( X2 != X3 ) )
| ( notequalI1 != $true ) ) ),
inference(rectify,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( ( notequalI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( X0 = X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f449]) ).
thf(f449,plain,
( ( notequalI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f367]) ).
thf(f367,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
=> ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(flattening,[status(thm)],[f317]) ).
thf(f317,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
=> ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f316]) ).
thf(f316,plain,
! [X0: $i,X1: $i] :
( ( ~ ( subset @ X1 @ X0 )
=> ( X0 != X1 ) )
= notequalI1 ),
inference(rectify,[status(thm)],[f86]) ).
thf(f86,axiom,
! [X4: $i,X3: $i] :
( ( ~ ( subset @ X3 @ X4 )
=> ( X3 != X4 ) )
= notequalI1 ),
file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',notequalI1) ).
thf(f2948,plain,
spl314_260,
inference(avatar_split_clause,[status(thm)],[f1456,f2891]) ).
thf(f1456,plain,
notequalI1 = $true,
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f2778,plain,
( ~ spl314_16
| spl314_236 ),
inference(avatar_split_clause,[status(thm)],[f1567,f2776,f1797]) ).
thf(f1797,definition,
( spl314_16
<=> ( setextsub = $true ) ),
introduced(definition,[new_symbols(naming,[spl314_16])],[avatar_definition]) ).
thf(f1567,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( setextsub != $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f997]) ).
thf(f997,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ( ( ( subset @ sK290 @ sK291 )
= $true )
& ( sK290 != sK291 )
& ( $true
= ( subset @ sK291 @ sK290 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK290,sK291])],[f995,f996]) ).
thf(f996,plain,
( ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( X2 != X3 )
& ( ( subset @ X3 @ X2 )
= $true ) )
=> ( ( ( subset @ sK290 @ sK291 )
= $true )
& ( sK290 != sK291 )
& ( $true
= ( subset @ sK291 @ sK290 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f995,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( X2 != X3 )
& ( ( subset @ X3 @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f994]) ).
thf(f994,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( X0 != X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f436]) ).
thf(f436,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
<=> ( setextsub = $true ) ),
inference(flattening,[status(thm)],[f435]) ).
thf(f435,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f147]) ).
thf(f147,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( $true
= ( subset @ X0 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f146]) ).
thf(f146,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
( setextsub
= ( ! [X4: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',setextsub) ).
thf(f2097,plain,
spl314_6,
inference(avatar_split_clause,[status(thm)],[f1499,f1754]) ).
thf(f1754,definition,
( spl314_6
<=> ( binintersectSubset5 = $true ) ),
introduced(definition,[new_symbols(naming,[spl314_6])],[avatar_definition]) ).
thf(f1499,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f1858,plain,
spl314_16,
inference(avatar_split_clause,[status(thm)],[f1430,f1797]) ).
thf(f1430,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f943]) ).
thf(f1757,plain,
( spl314_5
| ~ spl314_6 ),
inference(avatar_split_clause,[status(thm)],[f1309,f1754,f1751]) ).
thf(f1309,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true )
| ( binintersectSubset5 != $true )
| ( ( subset @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f821]) ).
thf(f821,plain,
( ( ( binintersectSubset5 = $true )
| ( ( ( subset @ sK199 @ sK200 )
= $true )
& ( $true
!= ( subset @ sK199 @ ( binintersect @ sK198 @ sK200 ) ) )
& ( $true
= ( subset @ sK199 @ sK198 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199,sK200])],[f819,f820]) ).
thf(f820,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( ( subset @ sK199 @ sK200 )
= $true )
& ( $true
!= ( subset @ sK199 @ ( binintersect @ sK198 @ sK200 ) ) )
& ( $true
= ( subset @ sK199 @ sK198 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f819,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(rectify,[status(thm)],[f818]) ).
thf(f818,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset5 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f422]) ).
thf(f422,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f171]) ).
thf(f171,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( subset @ X1 @ ( binintersect @ X0 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f170]) ).
thf(f170,plain,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f109]) ).
thf(f109,axiom,
( binintersectSubset5
= ( ! [X3: $i,X5: $i,X4: $i] :
( ( subset @ X5 @ X3 )
=> ( ( subset @ X5 @ X4 )
=> ( subset @ X5 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectSubset5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU598^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n007.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:27:23 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : SEU598^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.39 % Domain : Set Theory
% 0.19/0.39 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.19/0.39 % Version : Especial.
% 0.19/0.39 % English : (! A:i.! B:i.subset B A -> binintersect A B = B)
% 0.19/0.39
% 0.19/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.39 % Source : [Bro08]
% 0.19/0.39 % Names : ZFC100g [Bro08]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.19/0.39 % Syntax : Number of formulae : 248 ( 116 unt; 131 typ; 116 def)
% 0.19/0.39 % Number of atoms : 620 ( 169 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 116 ( 5 avg)
% 0.19/0.39 % Number of connectives : 971 ( 30 ~; 6 |; 28 &; 617 @)
% 0.19/0.39 % ( 14 <=>; 276 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 120 ( 2 avg)
% 0.19/0.39 % Number of types : 2 ( 0 usr)
% 0.19/0.39 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 134 ( 131 usr; 118 con; 0-2 aty)
% 0.19/0.39 % Number of variables : 338 ( 30 ^; 279 !; 29 ?; 338 :)
% 0.19/0.39 % SPC : TH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments : http://mathgate.info/detsetitem.php?id=365
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(in_type,type,
% 0.19/0.39 in: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(exu_type,type,
% 0.19/0.39 exu: ( $i > $o ) > $o ).
% 0.19/0.39
% 0.19/0.39 thf(exu,definition,
% 0.19/0.39 ( exu
% 0.19/0.39 = ( ^ [Xphi: $i > $o] :
% 0.19/0.39 ? [Xx: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 & ! [Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setextAx_type,type,
% 0.19/0.39 setextAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setextAx,definition,
% 0.19/0.39 ( setextAx
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 <=> ( in @ Xx @ B ) )
% 0.19/0.39 => ( A = B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyset_type,type,
% 0.19/0.39 emptyset: $i ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetAx_type,type,
% 0.19/0.39 emptysetAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetAx,definition,
% 0.19/0.39 ( emptysetAx
% 0.19/0.39 = ( ! [Xx: $i] :
% 0.19/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoin_type,type,
% 0.19/0.39 setadjoin: $i > $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinAx_type,type,
% 0.19/0.39 setadjoinAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinAx,definition,
% 0.19/0.39 ( setadjoinAx
% 0.19/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.39 <=> ( ( Xy = Xx )
% 0.19/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powerset_type,type,
% 0.19/0.39 powerset: $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(powersetAx_type,type,
% 0.19/0.39 powersetAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetAx,definition,
% 0.19/0.39 ( powersetAx
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.39 <=> ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setunion_type,type,
% 0.19/0.39 setunion: $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(setunionAx_type,type,
% 0.19/0.39 setunionAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setunionAx,definition,
% 0.19/0.39 ( setunionAx
% 0.19/0.39 = ( ! [A: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.39 <=> ? [B: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(omega_type,type,
% 0.19/0.39 omega: $i ).
% 0.19/0.39
% 0.19/0.39 thf(omega0Ax_type,type,
% 0.19/0.39 omega0Ax: $o ).
% 0.19/0.39
% 0.19/0.39 thf(omega0Ax,definition,
% 0.19/0.39 ( omega0Ax
% 0.19/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(omegaSAx_type,type,
% 0.19/0.39 omegaSAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(omegaSAx,definition,
% 0.19/0.39 ( omegaSAx
% 0.19/0.39 = ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ omega )
% 0.19/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(omegaIndAx_type,type,
% 0.19/0.39 omegaIndAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(omegaIndAx,definition,
% 0.19/0.39 ( omegaIndAx
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ( ( in @ emptyset @ A )
% 0.19/0.39 & ! [Xx: $i] :
% 0.19/0.39 ( ( ( in @ Xx @ omega )
% 0.19/0.39 & ( in @ Xx @ A ) )
% 0.19/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.19/0.39 => ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ omega )
% 0.19/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(replAx_type,type,
% 0.19/0.39 replAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(replAx,definition,
% 0.19/0.39 ( replAx
% 0.19/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( exu
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.19/0.39 => ? [B: $i] :
% 0.19/0.39 ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 <=> ? [Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ A )
% 0.19/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(foundationAx_type,type,
% 0.19/0.39 foundationAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(foundationAx,definition,
% 0.19/0.39 ( foundationAx
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.39 => ? [B: $i] :
% 0.19/0.39 ( ( in @ B @ A )
% 0.19/0.39 & ~ ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(wellorderingAx_type,type,
% 0.19/0.39 wellorderingAx: $o ).
% 0.19/0.39
% 0.19/0.39 thf(wellorderingAx,definition,
% 0.19/0.39 ( wellorderingAx
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ? [B: $i] :
% 0.19/0.39 ( ! [C: $i] :
% 0.19/0.39 ( ( in @ C @ B )
% 0.19/0.39 => ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ C )
% 0.19/0.39 => ( in @ Xx @ A ) ) )
% 0.19/0.39 & ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( ( in @ Xx @ A )
% 0.19/0.39 & ( in @ Xy @ A ) )
% 0.19/0.39 => ( ! [C: $i] :
% 0.19/0.39 ( ( in @ C @ B )
% 0.19/0.39 => ( ( in @ Xx @ C )
% 0.19/0.39 <=> ( in @ Xy @ C ) ) )
% 0.19/0.39 => ( Xx = Xy ) ) )
% 0.19/0.39 & ! [C: $i,D: $i] :
% 0.19/0.39 ( ( ( in @ C @ B )
% 0.19/0.39 & ( in @ D @ B ) )
% 0.19/0.39 => ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ C )
% 0.19/0.39 => ( in @ Xx @ D ) )
% 0.19/0.39 | ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ D )
% 0.19/0.39 => ( in @ Xx @ C ) ) ) )
% 0.19/0.39 & ! [C: $i] :
% 0.19/0.39 ( ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ C )
% 0.19/0.39 => ( in @ Xx @ A ) )
% 0.19/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.19/0.39 => ? [D: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ D @ B )
% 0.19/0.39 & ( in @ Xx @ C )
% 0.19/0.39 & ~ ? [Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ D )
% 0.19/0.39 & ( in @ Xy @ C ) )
% 0.19/0.39 & ! [E: $i] :
% 0.19/0.39 ( ( in @ E @ B )
% 0.19/0.39 => ( ! [Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ E )
% 0.19/0.39 => ( in @ Xy @ D ) )
% 0.19/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(descr_type,type,
% 0.19/0.39 descr: ( $i > $o ) > $i ).
% 0.19/0.39
% 0.19/0.39 thf(descrp_type,type,
% 0.19/0.39 descrp: $o ).
% 0.19/0.39
% 0.19/0.39 thf(descrp,definition,
% 0.19/0.39 ( descrp
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ( Xphi
% 0.19/0.39 @ ( descr
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstr_type,type,
% 0.19/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrI_type,type,
% 0.19/0.39 dsetconstrI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrI,definition,
% 0.19/0.39 ( dsetconstrI
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ( Xphi @ Xx )
% 0.19/0.39 => ( in @ Xx
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrEL_type,type,
% 0.19/0.39 dsetconstrEL: $o ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrEL,definition,
% 0.19/0.39 ( dsetconstrEL
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrER_type,type,
% 0.19/0.39 dsetconstrER: $o ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstrER,definition,
% 0.19/0.39 ( dsetconstrER
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuE1_type,type,
% 0.19/0.39 exuE1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuE1,definition,
% 0.19/0.39 ( exuE1
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 & ! [Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(prop2set_type,type,
% 0.19/0.39 prop2set: $o > $i ).
% 0.19/0.39
% 0.19/0.39 thf(prop2setE_type,type,
% 0.19/0.39 prop2setE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(prop2setE,definition,
% 0.19/0.39 ( prop2setE
% 0.19/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.19/0.39 => Xphi ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetE_type,type,
% 0.19/0.39 emptysetE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetE,definition,
% 0.19/0.39 ( emptysetE
% 0.19/0.39 = ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ emptyset )
% 0.19/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetimpfalse_type,type,
% 0.19/0.39 emptysetimpfalse: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetimpfalse,definition,
% 0.19/0.39 ( emptysetimpfalse
% 0.19/0.39 = ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ emptyset )
% 0.19/0.39 => $false ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notinemptyset_type,type,
% 0.19/0.39 notinemptyset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notinemptyset,definition,
% 0.19/0.39 ( notinemptyset
% 0.19/0.39 = ( ! [Xx: $i] :
% 0.19/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuE3e_type,type,
% 0.19/0.39 exuE3e: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuE3e,definition,
% 0.19/0.39 ( exuE3e
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setext_type,type,
% 0.19/0.39 setext: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setext,definition,
% 0.19/0.39 ( setext
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ B ) )
% 0.19/0.39 => ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ A ) )
% 0.19/0.39 => ( A = B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyI_type,type,
% 0.19/0.39 emptyI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyI,definition,
% 0.19/0.39 ( emptyI
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ~ ( in @ Xx @ A )
% 0.19/0.39 => ( A = emptyset ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(noeltsimpempty_type,type,
% 0.19/0.39 noeltsimpempty: $o ).
% 0.19/0.39
% 0.19/0.39 thf(noeltsimpempty,definition,
% 0.19/0.39 ( noeltsimpempty
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ~ ( in @ Xx @ A )
% 0.19/0.39 => ( A = emptyset ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setbeta_type,type,
% 0.19/0.39 setbeta: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setbeta,definition,
% 0.19/0.39 ( setbeta
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ( in @ Xx
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(nonempty_type,type,
% 0.19/0.39 nonempty: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonempty,definition,
% 0.19/0.39 ( nonempty
% 0.19/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyE1_type,type,
% 0.19/0.39 nonemptyE1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyE1,definition,
% 0.19/0.39 ( nonemptyE1
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ( nonempty @ A )
% 0.19/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyI_type,type,
% 0.19/0.39 nonemptyI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyI,definition,
% 0.19/0.39 ( nonemptyI
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ( Xphi @ Xx )
% 0.19/0.39 => ( nonempty
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyI1_type,type,
% 0.19/0.39 nonemptyI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyI1,definition,
% 0.19/0.39 ( nonemptyI1
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinIL_type,type,
% 0.19/0.39 setadjoinIL: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinIL,definition,
% 0.19/0.39 ( setadjoinIL
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyinunitempty_type,type,
% 0.19/0.39 emptyinunitempty: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyinunitempty,definition,
% 0.19/0.39 ( emptyinunitempty
% 0.19/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinIR_type,type,
% 0.19/0.39 setadjoinIR: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinIR,definition,
% 0.19/0.39 ( setadjoinIR
% 0.19/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ A )
% 0.19/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinE_type,type,
% 0.19/0.39 setadjoinE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinE,definition,
% 0.19/0.39 ( setadjoinE
% 0.19/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.39 => ! [Xphi: $o] :
% 0.19/0.39 ( ( ( Xy = Xx )
% 0.19/0.39 => Xphi )
% 0.19/0.39 => ( ( ( in @ Xy @ A )
% 0.19/0.39 => Xphi )
% 0.19/0.39 => Xphi ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinOr_type,type,
% 0.19/0.39 setadjoinOr: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinOr,definition,
% 0.19/0.39 ( setadjoinOr
% 0.19/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.39 => ( ( Xy = Xx )
% 0.19/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setoftrueEq_type,type,
% 0.19/0.39 setoftrueEq: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setoftrueEq,definition,
% 0.19/0.39 ( setoftrueEq
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xx: $i] : $true )
% 0.19/0.39 = A ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powersetI_type,type,
% 0.19/0.39 powersetI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetI,definition,
% 0.19/0.39 ( powersetI
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ A ) )
% 0.19/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyinPowerset_type,type,
% 0.19/0.39 emptyinPowerset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyinPowerset,definition,
% 0.19/0.39 ( emptyinPowerset
% 0.19/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyInPowerset_type,type,
% 0.19/0.39 emptyInPowerset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyInPowerset,definition,
% 0.19/0.39 ( emptyInPowerset
% 0.19/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powersetE_type,type,
% 0.19/0.39 powersetE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetE,definition,
% 0.19/0.39 ( powersetE
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.39 => ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setunionI_type,type,
% 0.19/0.39 setunionI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setunionI,definition,
% 0.19/0.39 ( setunionI
% 0.19/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( ( in @ B @ A )
% 0.19/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setunionE_type,type,
% 0.19/0.39 setunionE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setunionE,definition,
% 0.19/0.39 ( setunionE
% 0.19/0.39 = ( ! [A: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.39 => ! [Xphi: $o] :
% 0.19/0.39 ( ! [B: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( ( in @ B @ A )
% 0.19/0.39 => Xphi ) )
% 0.19/0.39 => Xphi ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subPowSU_type,type,
% 0.19/0.39 subPowSU: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subPowSU,definition,
% 0.19/0.39 ( subPowSU
% 0.19/0.39 = ( ! [A: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuE2_type,type,
% 0.19/0.39 exuE2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuE2,definition,
% 0.19/0.39 ( exuE2
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ! [Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xy )
% 0.19/0.39 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyImpWitness_type,type,
% 0.19/0.39 nonemptyImpWitness: $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonemptyImpWitness,definition,
% 0.19/0.39 ( nonemptyImpWitness
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ( nonempty @ A )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & $true ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(uniqinunit_type,type,
% 0.19/0.39 uniqinunit: $o ).
% 0.19/0.39
% 0.19/0.39 thf(uniqinunit,definition,
% 0.19/0.39 ( uniqinunit
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.39 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notinsingleton_type,type,
% 0.19/0.39 notinsingleton: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notinsingleton,definition,
% 0.19/0.39 ( notinsingleton
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx != Xy )
% 0.19/0.39 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(eqinunit_type,type,
% 0.19/0.39 eqinunit: $o ).
% 0.19/0.39
% 0.19/0.39 thf(eqinunit,definition,
% 0.19/0.39 ( eqinunit
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(singletonsswitch_type,type,
% 0.19/0.39 singletonsswitch: $o ).
% 0.19/0.39
% 0.19/0.39 thf(singletonsswitch,definition,
% 0.19/0.39 ( singletonsswitch
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetE_type,type,
% 0.19/0.39 upairsetE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetE,definition,
% 0.19/0.39 ( upairsetE
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.39 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.39 => ( ( Xz = Xx )
% 0.19/0.39 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetIL_type,type,
% 0.19/0.39 upairsetIL: $o ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetIL,definition,
% 0.19/0.39 ( upairsetIL
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetIR_type,type,
% 0.19/0.39 upairsetIR: $o ).
% 0.19/0.39
% 0.19/0.39 thf(upairsetIR,definition,
% 0.19/0.39 ( upairsetIR
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyE1_type,type,
% 0.19/0.39 emptyE1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyE1,definition,
% 0.19/0.39 ( emptyE1
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ( Xphi @ Xx ) )
% 0.19/0.39 => ( ( ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 = emptyset )
% 0.19/0.39 => $false ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(vacuousDall_type,type,
% 0.19/0.39 vacuousDall: $o ).
% 0.19/0.39
% 0.19/0.39 thf(vacuousDall,definition,
% 0.19/0.39 ( vacuousDall
% 0.19/0.39 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ emptyset )
% 0.19/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan1_type,type,
% 0.19/0.39 quantDeMorgan1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan1,definition,
% 0.19/0.39 ( quantDeMorgan1
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ~ ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( Xphi @ Xx ) )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan2_type,type,
% 0.19/0.39 quantDeMorgan2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan2,definition,
% 0.19/0.39 ( quantDeMorgan2
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ~ ( Xphi @ Xx ) )
% 0.19/0.39 => ~ ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan3_type,type,
% 0.19/0.39 quantDeMorgan3: $o ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan3,definition,
% 0.19/0.39 ( quantDeMorgan3
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ~ ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ( Xphi @ Xx ) )
% 0.19/0.39 => ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan4_type,type,
% 0.19/0.39 quantDeMorgan4: $o ).
% 0.19/0.39
% 0.19/0.39 thf(quantDeMorgan4,definition,
% 0.19/0.39 ( quantDeMorgan4
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ~ ( Xphi @ Xx ) )
% 0.19/0.39 => ~ ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(prop2setI_type,type,
% 0.19/0.39 prop2setI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(prop2setI,definition,
% 0.19/0.39 ( prop2setI
% 0.19/0.39 = ( ! [Xphi: $o] :
% 0.19/0.39 ( Xphi
% 0.19/0.39 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(set2prop_type,type,
% 0.19/0.39 set2prop: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(prop2set2propI_type,type,
% 0.19/0.39 prop2set2propI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(prop2set2propI,definition,
% 0.19/0.39 ( prop2set2propI
% 0.19/0.39 = ( ! [Xphi: $o] :
% 0.19/0.39 ( Xphi
% 0.19/0.39 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notdexE_type,type,
% 0.19/0.39 notdexE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notdexE,definition,
% 0.19/0.39 ( notdexE
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ~ ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ( Xphi @ Xx ) )
% 0.19/0.39 => ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notdallE_type,type,
% 0.19/0.39 notdallE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notdallE,definition,
% 0.19/0.39 ( notdallE
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( ~ ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( Xphi @ Xx ) )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuI1_type,type,
% 0.19/0.39 exuI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuI1,definition,
% 0.19/0.39 ( exuI1
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ? [Xx: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 & ! [Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) )
% 0.19/0.39 => ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuI3_type,type,
% 0.19/0.39 exuI3: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuI3,definition,
% 0.19/0.39 ( exuI3
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.19/0.39 => ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 => ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) )
% 0.19/0.39 => ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuI2_type,type,
% 0.19/0.39 exuI2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuI2,definition,
% 0.19/0.39 ( exuI2
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ? [Xx: $i] :
% 0.19/0.39 ! [Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xy )
% 0.19/0.39 <=> ( Xy = Xx ) )
% 0.19/0.39 => ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(inCongP_type,type,
% 0.19/0.39 inCongP: $o ).
% 0.19/0.39
% 0.19/0.39 thf(inCongP,definition,
% 0.19/0.39 ( inCongP
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(in__Cong_type,type,
% 0.19/0.39 in__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(in__Cong,definition,
% 0.19/0.39 ( in__Cong
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuE3u_type,type,
% 0.19/0.39 exuE3u: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuE3u,definition,
% 0.19/0.39 ( exuE3u
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 => ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exu__Cong_type,type,
% 0.19/0.39 exu__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exu__Cong,definition,
% 0.19/0.39 ( exu__Cong
% 0.19/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ( ( Xphi @ Xx )
% 0.19/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.39 => ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 <=> ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptyset__Cong_type,type,
% 0.19/0.39 emptyset__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyset__Cong,definition,
% 0.19/0.39 ( emptyset__Cong
% 0.19/0.39 = ( emptyset = emptyset ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoin__Cong_type,type,
% 0.19/0.39 setadjoin__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoin__Cong,definition,
% 0.19/0.39 ( setadjoin__Cong
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ! [Xz: $i,Xu: $i] :
% 0.19/0.39 ( ( Xz = Xu )
% 0.19/0.39 => ( ( setadjoin @ Xx @ Xz )
% 0.19/0.39 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powerset__Cong_type,type,
% 0.19/0.39 powerset__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powerset__Cong,definition,
% 0.19/0.39 ( powerset__Cong
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ( ( powerset @ A )
% 0.19/0.39 = ( powerset @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setunion__Cong_type,type,
% 0.19/0.39 setunion__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setunion__Cong,definition,
% 0.19/0.39 ( setunion__Cong
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ( ( setunion @ A )
% 0.19/0.39 = ( setunion @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(omega__Cong_type,type,
% 0.19/0.39 omega__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(omega__Cong,definition,
% 0.19/0.39 ( omega__Cong
% 0.19/0.39 = ( omega = omega ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(exuEu_type,type,
% 0.19/0.39 exuEu: $o ).
% 0.19/0.39
% 0.19/0.39 thf(exuEu,definition,
% 0.19/0.39 ( exuEu
% 0.19/0.39 = ( ! [Xphi: $i > $o] :
% 0.19/0.39 ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xphi @ Xx )
% 0.19/0.39 => ( ( Xphi @ Xy )
% 0.19/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(descr__Cong_type,type,
% 0.19/0.39 descr__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(descr__Cong,definition,
% 0.19/0.39 ( descr__Cong
% 0.19/0.39 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.39 ( ( Xx = Xy )
% 0.19/0.39 => ( ( Xphi @ Xx )
% 0.19/0.39 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.39 => ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 => ( ( exu
% 0.19/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.39 => ( ( descr
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 = ( descr
% 0.19/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstr__Cong_type,type,
% 0.19/0.39 dsetconstr__Cong: $o ).
% 0.19/0.39
% 0.19/0.39 thf(dsetconstr__Cong,definition,
% 0.19/0.39 ( dsetconstr__Cong
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ! [Xy: $i] :
% 0.19/0.39 ( ( in @ Xy @ B )
% 0.19/0.39 => ( ( Xx = Xy )
% 0.19/0.39 => ( ( Xphi @ Xx )
% 0.19/0.39 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.19/0.39 => ( ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 = ( dsetconstr @ B
% 0.19/0.39 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subset_type,type,
% 0.19/0.39 subset: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(disjoint_type,type,
% 0.19/0.39 disjoint: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(setsmeet_type,type,
% 0.19/0.39 setsmeet: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetI1_type,type,
% 0.19/0.39 subsetI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetI1,definition,
% 0.19/0.39 ( subsetI1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ B ) )
% 0.19/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(eqimpsubset2_type,type,
% 0.19/0.39 eqimpsubset2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(eqimpsubset2,definition,
% 0.19/0.39 ( eqimpsubset2
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(eqimpsubset1_type,type,
% 0.19/0.39 eqimpsubset1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(eqimpsubset1,definition,
% 0.19/0.39 ( eqimpsubset1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( A = B )
% 0.19/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetI2_type,type,
% 0.19/0.39 subsetI2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetI2,definition,
% 0.19/0.39 ( subsetI2
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ B ) )
% 0.19/0.39 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetsubset_type,type,
% 0.19/0.39 emptysetsubset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptysetsubset,definition,
% 0.19/0.39 ( emptysetsubset
% 0.19/0.39 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE_type,type,
% 0.19/0.39 subsetE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE,definition,
% 0.19/0.39 ( subsetE
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE2_type,type,
% 0.19/0.39 subsetE2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE2,definition,
% 0.19/0.39 ( subsetE2
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ~ ( in @ Xx @ B )
% 0.19/0.39 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notsubsetI_type,type,
% 0.19/0.39 notsubsetI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notsubsetI,definition,
% 0.19/0.39 ( notsubsetI
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ~ ( in @ Xx @ B )
% 0.19/0.39 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notequalI1_type,type,
% 0.19/0.39 notequalI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notequalI1,definition,
% 0.19/0.39 ( notequalI1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ~ ( subset @ A @ B )
% 0.19/0.39 => ( A != B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(notequalI2_type,type,
% 0.19/0.39 notequalI2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(notequalI2,definition,
% 0.19/0.39 ( notequalI2
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ~ ( in @ Xx @ B )
% 0.19/0.39 => ( A != B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetRefl_type,type,
% 0.19/0.39 subsetRefl: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetRefl,definition,
% 0.19/0.39 ( subsetRefl
% 0.19/0.39 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetTrans_type,type,
% 0.19/0.39 subsetTrans: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetTrans,definition,
% 0.19/0.39 ( subsetTrans
% 0.19/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ( subset @ B @ C )
% 0.19/0.39 => ( subset @ A @ C ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinSub_type,type,
% 0.19/0.39 setadjoinSub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinSub,definition,
% 0.19/0.39 ( setadjoinSub
% 0.19/0.39 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinSub2_type,type,
% 0.19/0.39 setadjoinSub2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setadjoinSub2,definition,
% 0.19/0.39 ( setadjoinSub2
% 0.19/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subset2powerset_type,type,
% 0.19/0.39 subset2powerset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subset2powerset,definition,
% 0.19/0.39 ( subset2powerset
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(setextsub_type,type,
% 0.19/0.39 setextsub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(setextsub,definition,
% 0.19/0.39 ( setextsub
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ( subset @ B @ A )
% 0.19/0.39 => ( A = B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subsetemptysetimpeq_type,type,
% 0.19/0.39 subsetemptysetimpeq: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetemptysetimpeq,definition,
% 0.19/0.39 ( subsetemptysetimpeq
% 0.19/0.39 = ( ! [A: $i] :
% 0.19/0.39 ( ( subset @ A @ emptyset )
% 0.19/0.39 => ( A = emptyset ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powersetI1_type,type,
% 0.19/0.39 powersetI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetI1,definition,
% 0.19/0.39 ( powersetI1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ B @ A )
% 0.19/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powersetE1_type,type,
% 0.19/0.39 powersetE1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetE1,definition,
% 0.19/0.39 ( powersetE1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(inPowerset_type,type,
% 0.19/0.39 inPowerset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(inPowerset,definition,
% 0.19/0.39 ( inPowerset
% 0.19/0.39 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(powersetsubset_type,type,
% 0.19/0.39 powersetsubset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(powersetsubset,definition,
% 0.19/0.39 ( powersetsubset
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(sepInPowerset_type,type,
% 0.19/0.39 sepInPowerset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(sepInPowerset,definition,
% 0.19/0.39 ( sepInPowerset
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( in
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 @ ( powerset @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(sepSubset_type,type,
% 0.19/0.39 sepSubset: $o ).
% 0.19/0.39
% 0.19/0.39 thf(sepSubset,definition,
% 0.19/0.39 ( sepSubset
% 0.19/0.39 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.39 ( subset
% 0.19/0.39 @ ( dsetconstr @ A
% 0.19/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.39 @ A ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunion_type,type,
% 0.19/0.39 binunion: $i > $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(binunionIL_type,type,
% 0.19/0.39 binunionIL: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionIL,definition,
% 0.19/0.39 ( binunionIL
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(upairset2IR_type,type,
% 0.19/0.39 upairset2IR: $o ).
% 0.19/0.39
% 0.19/0.39 thf(upairset2IR,definition,
% 0.19/0.39 ( upairset2IR
% 0.19/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunionIR_type,type,
% 0.19/0.39 binunionIR: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionIR,definition,
% 0.19/0.39 ( binunionIR
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunionEcases_type,type,
% 0.19/0.39 binunionEcases: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionEcases,definition,
% 0.19/0.39 ( binunionEcases
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.39 => ( ( ( in @ Xx @ A )
% 0.19/0.39 => Xphi )
% 0.19/0.39 => ( ( ( in @ Xx @ B )
% 0.19/0.39 => Xphi )
% 0.19/0.39 => Xphi ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunionE_type,type,
% 0.19/0.39 binunionE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionE,definition,
% 0.19/0.39 ( binunionE
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunionLsub_type,type,
% 0.19/0.39 binunionLsub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionLsub,definition,
% 0.19/0.39 ( binunionLsub
% 0.19/0.39 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binunionRsub_type,type,
% 0.19/0.39 binunionRsub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binunionRsub,definition,
% 0.19/0.39 ( binunionRsub
% 0.19/0.39 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersect_type,type,
% 0.19/0.39 binintersect: $i > $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectI_type,type,
% 0.19/0.39 binintersectI: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectI,definition,
% 0.19/0.39 ( binintersectI
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ( ( in @ Xx @ B )
% 0.19/0.39 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset5_type,type,
% 0.19/0.39 binintersectSubset5: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset5,definition,
% 0.19/0.39 ( binintersectSubset5
% 0.19/0.39 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.39 ( ( subset @ C @ A )
% 0.19/0.39 => ( ( subset @ C @ B )
% 0.19/0.39 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectEL_type,type,
% 0.19/0.39 binintersectEL: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectEL,definition,
% 0.19/0.39 ( binintersectEL
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectLsub_type,type,
% 0.19/0.39 binintersectLsub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectLsub,definition,
% 0.19/0.39 ( binintersectLsub
% 0.19/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset2_type,type,
% 0.19/0.39 binintersectSubset2: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset2,definition,
% 0.19/0.39 ( binintersectSubset2
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ( binintersect @ A @ B )
% 0.19/0.39 = A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset3_type,type,
% 0.19/0.39 binintersectSubset3: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset3,definition,
% 0.19/0.39 ( binintersectSubset3
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ( ( binintersect @ A @ B )
% 0.19/0.39 = B )
% 0.19/0.39 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectER_type,type,
% 0.19/0.39 binintersectER: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectER,definition,
% 0.19/0.39 ( binintersectER
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.39 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(disjointsetsI1_type,type,
% 0.19/0.39 disjointsetsI1: $o ).
% 0.19/0.39
% 0.19/0.39 thf(disjointsetsI1,definition,
% 0.19/0.39 ( disjointsetsI1
% 0.19/0.39 = ( ! [A: $i,B: $i] :
% 0.19/0.39 ( ~ ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 & ( in @ Xx @ B ) )
% 0.19/0.39 => ( ( binintersect @ A @ B )
% 0.19/0.39 = emptyset ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectRsub_type,type,
% 0.19/0.39 binintersectRsub: $o ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectRsub,definition,
% 0.19/0.39 ( binintersectRsub
% 0.19/0.39 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(binintersectSubset4,conjecture,
% 0.19/0.39 ( setextAx
% 0.19/0.39 => ( emptysetAx
% 0.19/0.39 => ( setadjoinAx
% 0.19/0.39 => ( powersetAx
% 0.19/0.39 => ( setunionAx
% 0.19/0.39 => ( omega0Ax
% 0.19/0.39 => ( omegaSAx
% 0.19/0.39 => ( omegaIndAx
% 0.19/0.39 => ( replAx
% 0.19/0.39 => ( foundationAx
% 0.19/0.39 => ( wellorderingAx
% 0.19/0.39 => ( descrp
% 0.19/0.39 => ( dsetconstrI
% 0.19/0.39 => ( dsetconstrEL
% 0.19/0.39 => ( dsetconstrER
% 0.19/0.39 => ( exuE1
% 0.19/0.39 => ( prop2setE
% 0.19/0.39 => ( emptysetE
% 0.19/0.39 => ( emptysetimpfalse
% 0.19/0.39 => ( notinemptyset
% 0.19/0.39 => ( exuE3e
% 0.19/0.39 => ( setext
% 0.19/0.39 => ( emptyI
% 0.19/0.39 => ( noeltsimpempty
% 0.19/0.39 => ( setbeta
% 0.19/0.39 => ( nonemptyE1
% 0.19/0.39 => ( nonemptyI
% 0.19/0.39 => ( nonemptyI1
% 0.19/0.39 => ( setadjoinIL
% 0.19/0.39 => ( emptyinunitempty
% 0.19/0.39 => ( setadjoinIR
% 0.19/0.39 => ( setadjoinE
% 0.19/0.39 => ( setadjoinOr
% 0.19/0.39 => ( setoftrueEq
% 0.19/0.39 => ( powersetI
% 0.19/0.39 => ( emptyinPowerset
% 0.19/0.39 => ( emptyInPowerset
% 0.19/0.39 => ( powersetE
% 0.19/0.39 => ( setunionI
% 0.19/0.39 => ( setunionE
% 0.19/0.39 => ( subPowSU
% 0.19/0.39 => ( exuE2
% 0.19/0.39 => ( nonemptyImpWitness
% 0.19/0.39 => ( uniqinunit
% 0.19/0.39 => ( notinsingleton
% 0.19/0.39 => ( eqinunit
% 0.19/0.39 => ( singletonsswitch
% 0.19/0.39 => ( upairsetE
% 0.19/0.39 => ( upairsetIL
% 0.19/0.39 => ( upairsetIR
% 0.19/0.39 => ( emptyE1
% 0.19/0.39 => ( vacuousDall
% 0.19/0.39 => ( quantDeMorgan1
% 0.19/0.39 => ( quantDeMorgan2
% 0.19/0.39 => ( quantDeMorgan3
% 0.19/0.39 => ( quantDeMorgan4
% 0.19/0.39 => ( prop2setI
% 0.19/0.39 => ( prop2set2propI
% 0.19/0.39 => ( notdexE
% 0.19/0.39 => ( notdallE
% 0.19/0.39 => ( exuI1
% 0.19/0.39 => ( exuI3
% 0.19/0.39 => ( exuI2
% 0.19/0.39 => ( inCongP
% 0.19/0.39 => ( in__Cong
% 0.19/0.39 => ( exuE3u
% 0.19/0.39 => ( exu__Cong
% 0.19/0.39 => ( emptyset__Cong
% 0.19/0.39 => ( setadjoin__Cong
% 0.19/0.39 => ( powerset__Cong
% 0.19/0.39 => ( setunion__Cong
% 0.19/0.39 => ( omega__Cong
% 0.19/0.39 => ( exuEu
% 0.19/0.39 => ( descr__Cong
% 0.19/0.39 => ( dsetconstr__Cong
% 0.19/0.39 => ( subsetI1
% 0.19/0.39 => ( eqimpsubset2
% 0.19/0.39 => ( eqimpsubset1
% 0.19/0.39 => ( subsetI2
% 0.19/0.39 => ( emptysetsubset
% 0.19/0.39 => ( subsetE
% 0.19/0.39 => ( subsetE2
% 0.19/0.39 => ( notsubsetI
% 0.19/0.39 => ( notequalI1
% 0.19/0.39 => ( notequalI2
% 0.19/0.39 => ( subsetRefl
% 0.19/0.39 => ( subsetTrans
% 0.19/0.39 => ( setadjoinSub
% 0.19/0.39 => ( setadjoinSub2
% 0.19/0.39 => ( subset2powerset
% 0.19/0.39 => ( setextsub
% 0.19/0.39 => ( subsetemptysetimpeq
% 0.19/0.39 => ( powersetI1
% 0.19/0.39 => ( powersetE1
% 0.19/0.39 => ( inPowerset
% 0.19/0.39 => ( powersetsubset
% 0.19/0.39 => ( sepInPowerset
% 0.19/0.39 => ( sepSubset
% 0.19/0.39 => ( binunionIL
% 0.19/0.39 => ( upairset2IR
% 0.19/0.39 => ( binunionIR
% 0.19/0.39 => ( binunionEcases
% 0.19/0.39 => ( binunionE
% 0.19/0.39 => ( binunionLsub
% 0.19/0.39 => ( binunionRsub
% 0.19/0.39 => ( binintersectI
% 0.19/0.39 => ( binintersectSubset5
% 0.19/0.39 => ( binintersectEL
% 0.19/0.39 => ( binintersectLsub
% 0.19/0.39 => ( binintersectSubset2
% 0.19/0.39 => ( binintersectSubset3
% 0.19/0.39 => ( binintersectER
% 0.19/0.39 => ( disjointsetsI1
% 0.19/0.39 => ( binintersectRsub
% 0.19/0.39 => ! [A: $i,B: $i] :
% 0.19/0.39 ( ( subset @ B @ A )
% 0.19/0.39 => ( ( binintersect @ A @ B )
% 0.19/0.39 = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 2.48/1.53 ---- Embedded in THF ---
% 2.48/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.48/1.53 %%% Generated on Tue Feb 24 12:27:24 EST 2026
% 2.48/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.48/1.53 %%% Logic specification used:
% 2.48/1.53 %%% thf(spec, logic, $$dhol).
% 2.48/1.53
% 2.48/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2DTF29850.p
% See solution above
% 2.48/1.53 ------------------------
% 2.48/1.55 ---- Cleaned THF ---
% 2.48/1.55 thf(in_type,type,
% 2.48/1.55 in: $i > $i > $o ).
% 2.48/1.55
% 2.48/1.55 thf(exu_type,type,
% 2.48/1.55 exu: ( $i > $o ) > $o ).
% 2.48/1.55
% 2.48/1.55 thf(exu,definition,
% 2.48/1.55 ( exu
% 2.48/1.55 = ( ^ [Xphi: $i > $o] :
% 2.48/1.55 ? [Xx: $i] :
% 2.48/1.55 ( ( Xphi @ Xx )
% 2.48/1.55 & ! [Xy: $i] :
% 2.48/1.55 ( ( Xphi @ Xy )
% 2.48/1.55 => ( Xx = Xy ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setextAx_type,type,
% 2.48/1.55 setextAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setextAx,definition,
% 2.48/1.55 ( setextAx
% 2.48/1.55 = ( ! [A: $i,B: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 <=> ( in @ Xx @ B ) )
% 2.48/1.55 => ( A = B ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptyset_type,type,
% 2.48/1.55 emptyset: $i ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetAx_type,type,
% 2.48/1.55 emptysetAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetAx,definition,
% 2.48/1.55 ( emptysetAx
% 2.48/1.55 = ( ! [Xx: $i] :
% 2.48/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoin_type,type,
% 2.48/1.55 setadjoin: $i > $i > $i ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinAx_type,type,
% 2.48/1.55 setadjoinAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinAx,definition,
% 2.48/1.55 ( setadjoinAx
% 2.48/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.55 <=> ( ( Xy = Xx )
% 2.48/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(powerset_type,type,
% 2.48/1.55 powerset: $i > $i ).
% 2.48/1.55
% 2.48/1.55 thf(powersetAx_type,type,
% 2.48/1.55 powersetAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(powersetAx,definition,
% 2.48/1.55 ( powersetAx
% 2.48/1.55 = ( ! [A: $i,B: $i] :
% 2.48/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.55 <=> ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setunion_type,type,
% 2.48/1.55 setunion: $i > $i ).
% 2.48/1.55
% 2.48/1.55 thf(setunionAx_type,type,
% 2.48/1.55 setunionAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setunionAx,definition,
% 2.48/1.55 ( setunionAx
% 2.48/1.55 = ( ! [A: $i,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.48/1.55 <=> ? [B: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 & ( in @ B @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(omega_type,type,
% 2.48/1.55 omega: $i ).
% 2.48/1.55
% 2.48/1.55 thf(omega0Ax_type,type,
% 2.48/1.55 omega0Ax: $o ).
% 2.48/1.55
% 2.48/1.55 thf(omega0Ax,definition,
% 2.48/1.55 ( omega0Ax
% 2.48/1.55 = ( in @ emptyset @ omega ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(omegaSAx_type,type,
% 2.48/1.55 omegaSAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(omegaSAx,definition,
% 2.48/1.55 ( omegaSAx
% 2.48/1.55 = ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ omega )
% 2.48/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(omegaIndAx_type,type,
% 2.48/1.55 omegaIndAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(omegaIndAx,definition,
% 2.48/1.55 ( omegaIndAx
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ( ( in @ emptyset @ A )
% 2.48/1.55 & ! [Xx: $i] :
% 2.48/1.55 ( ( ( in @ Xx @ omega )
% 2.48/1.55 & ( in @ Xx @ A ) )
% 2.48/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.48/1.55 => ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ omega )
% 2.48/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(replAx_type,type,
% 2.48/1.55 replAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(replAx,definition,
% 2.48/1.55 ( replAx
% 2.48/1.55 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( exu
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.48/1.55 => ? [B: $i] :
% 2.48/1.55 ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 <=> ? [Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ A )
% 2.48/1.55 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(foundationAx_type,type,
% 2.48/1.55 foundationAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(foundationAx,definition,
% 2.48/1.55 ( foundationAx
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.48/1.55 => ? [B: $i] :
% 2.48/1.55 ( ( in @ B @ A )
% 2.48/1.55 & ~ ? [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(wellorderingAx_type,type,
% 2.48/1.55 wellorderingAx: $o ).
% 2.48/1.55
% 2.48/1.55 thf(wellorderingAx,definition,
% 2.48/1.55 ( wellorderingAx
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ? [B: $i] :
% 2.48/1.55 ( ! [C: $i] :
% 2.48/1.55 ( ( in @ C @ B )
% 2.48/1.55 => ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ C )
% 2.48/1.55 => ( in @ Xx @ A ) ) )
% 2.48/1.55 & ! [Xx: $i,Xy: $i] :
% 2.48/1.55 ( ( ( in @ Xx @ A )
% 2.48/1.55 & ( in @ Xy @ A ) )
% 2.48/1.55 => ( ! [C: $i] :
% 2.48/1.55 ( ( in @ C @ B )
% 2.48/1.55 => ( ( in @ Xx @ C )
% 2.48/1.55 <=> ( in @ Xy @ C ) ) )
% 2.48/1.55 => ( Xx = Xy ) ) )
% 2.48/1.55 & ! [C: $i,D: $i] :
% 2.48/1.55 ( ( ( in @ C @ B )
% 2.48/1.55 & ( in @ D @ B ) )
% 2.48/1.55 => ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ C )
% 2.48/1.55 => ( in @ Xx @ D ) )
% 2.48/1.55 | ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ D )
% 2.48/1.55 => ( in @ Xx @ C ) ) ) )
% 2.48/1.55 & ! [C: $i] :
% 2.48/1.55 ( ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ C )
% 2.48/1.55 => ( in @ Xx @ A ) )
% 2.48/1.55 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.48/1.55 => ? [D: $i,Xx: $i] :
% 2.48/1.55 ( ( in @ D @ B )
% 2.48/1.55 & ( in @ Xx @ C )
% 2.48/1.55 & ~ ? [Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ D )
% 2.48/1.55 & ( in @ Xy @ C ) )
% 2.48/1.55 & ! [E: $i] :
% 2.48/1.55 ( ( in @ E @ B )
% 2.48/1.55 => ( ! [Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ E )
% 2.48/1.55 => ( in @ Xy @ D ) )
% 2.48/1.55 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(descr_type,type,
% 2.48/1.55 descr: ( $i > $o ) > $i ).
% 2.48/1.55
% 2.48/1.55 thf(descrp_type,type,
% 2.48/1.55 descrp: $o ).
% 2.48/1.55
% 2.48/1.55 thf(descrp,definition,
% 2.48/1.55 ( descrp
% 2.48/1.55 = ( ! [Xphi: $i > $o] :
% 2.48/1.55 ( ( exu
% 2.48/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.55 => ( Xphi
% 2.48/1.55 @ ( descr
% 2.48/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstr_type,type,
% 2.48/1.55 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrI_type,type,
% 2.48/1.55 dsetconstrI: $o ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrI,definition,
% 2.48/1.55 ( dsetconstrI
% 2.48/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( ( Xphi @ Xx )
% 2.48/1.55 => ( in @ Xx
% 2.48/1.55 @ ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrEL_type,type,
% 2.48/1.55 dsetconstrEL: $o ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrEL,definition,
% 2.48/1.55 ( dsetconstrEL
% 2.48/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx
% 2.48/1.55 @ ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrER_type,type,
% 2.48/1.55 dsetconstrER: $o ).
% 2.48/1.55
% 2.48/1.55 thf(dsetconstrER,definition,
% 2.48/1.55 ( dsetconstrER
% 2.48/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx
% 2.48/1.55 @ ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(exuE1_type,type,
% 2.48/1.55 exuE1: $o ).
% 2.48/1.55
% 2.48/1.55 thf(exuE1,definition,
% 2.48/1.55 ( exuE1
% 2.48/1.55 = ( ! [Xphi: $i > $o] :
% 2.48/1.55 ( ( exu
% 2.48/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.55 => ? [Xx: $i] :
% 2.48/1.55 ( ( Xphi @ Xx )
% 2.48/1.55 & ! [Xy: $i] :
% 2.48/1.55 ( ( Xphi @ Xy )
% 2.48/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(prop2set_type,type,
% 2.48/1.55 prop2set: $o > $i ).
% 2.48/1.55
% 2.48/1.55 thf(prop2setE_type,type,
% 2.48/1.55 prop2setE: $o ).
% 2.48/1.55
% 2.48/1.55 thf(prop2setE,definition,
% 2.48/1.55 ( prop2setE
% 2.48/1.55 = ( ! [Xphi: $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.48/1.55 => Xphi ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetE_type,type,
% 2.48/1.55 emptysetE: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetE,definition,
% 2.48/1.55 ( emptysetE
% 2.48/1.55 = ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ emptyset )
% 2.48/1.55 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetimpfalse_type,type,
% 2.48/1.55 emptysetimpfalse: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptysetimpfalse,definition,
% 2.48/1.55 ( emptysetimpfalse
% 2.48/1.55 = ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ emptyset )
% 2.48/1.55 => $false ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(notinemptyset_type,type,
% 2.48/1.55 notinemptyset: $o ).
% 2.48/1.55
% 2.48/1.55 thf(notinemptyset,definition,
% 2.48/1.55 ( notinemptyset
% 2.48/1.55 = ( ! [Xx: $i] :
% 2.48/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(exuE3e_type,type,
% 2.48/1.55 exuE3e: $o ).
% 2.48/1.55
% 2.48/1.55 thf(exuE3e,definition,
% 2.48/1.55 ( exuE3e
% 2.48/1.55 = ( ! [Xphi: $i > $o] :
% 2.48/1.55 ( ( exu
% 2.48/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.55 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setext_type,type,
% 2.48/1.55 setext: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setext,definition,
% 2.48/1.55 ( setext
% 2.48/1.55 = ( ! [A: $i,B: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( in @ Xx @ B ) )
% 2.48/1.55 => ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 => ( in @ Xx @ A ) )
% 2.48/1.55 => ( A = B ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptyI_type,type,
% 2.48/1.55 emptyI: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptyI,definition,
% 2.48/1.55 ( emptyI
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ~ ( in @ Xx @ A )
% 2.48/1.55 => ( A = emptyset ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(noeltsimpempty_type,type,
% 2.48/1.55 noeltsimpempty: $o ).
% 2.48/1.55
% 2.48/1.55 thf(noeltsimpempty,definition,
% 2.48/1.55 ( noeltsimpempty
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ~ ( in @ Xx @ A )
% 2.48/1.55 => ( A = emptyset ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setbeta_type,type,
% 2.48/1.55 setbeta: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setbeta,definition,
% 2.48/1.55 ( setbeta
% 2.48/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( ( in @ Xx
% 2.48/1.55 @ ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.48/1.55 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(nonempty_type,type,
% 2.48/1.55 nonempty: $i > $o ).
% 2.48/1.55
% 2.48/1.55 thf(nonempty,definition,
% 2.48/1.55 ( nonempty
% 2.48/1.55 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyE1_type,type,
% 2.48/1.55 nonemptyE1: $o ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyE1,definition,
% 2.48/1.55 ( nonemptyE1
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ( nonempty @ A )
% 2.48/1.55 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyI_type,type,
% 2.48/1.55 nonemptyI: $o ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyI,definition,
% 2.48/1.55 ( nonemptyI
% 2.48/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( ( Xphi @ Xx )
% 2.48/1.55 => ( nonempty
% 2.48/1.55 @ ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyI1_type,type,
% 2.48/1.55 nonemptyI1: $o ).
% 2.48/1.55
% 2.48/1.55 thf(nonemptyI1,definition,
% 2.48/1.55 ( nonemptyI1
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.48/1.55 => ( nonempty @ A ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinIL_type,type,
% 2.48/1.55 setadjoinIL: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinIL,definition,
% 2.48/1.55 ( setadjoinIL
% 2.48/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptyinunitempty_type,type,
% 2.48/1.55 emptyinunitempty: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptyinunitempty,definition,
% 2.48/1.55 ( emptyinunitempty
% 2.48/1.55 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinIR_type,type,
% 2.48/1.55 setadjoinIR: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinIR,definition,
% 2.48/1.55 ( setadjoinIR
% 2.48/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ A )
% 2.48/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinE_type,type,
% 2.48/1.55 setadjoinE: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinE,definition,
% 2.48/1.55 ( setadjoinE
% 2.48/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.55 => ! [Xphi: $o] :
% 2.48/1.55 ( ( ( Xy = Xx )
% 2.48/1.55 => Xphi )
% 2.48/1.55 => ( ( ( in @ Xy @ A )
% 2.48/1.55 => Xphi )
% 2.48/1.55 => Xphi ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinOr_type,type,
% 2.48/1.55 setadjoinOr: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setadjoinOr,definition,
% 2.48/1.55 ( setadjoinOr
% 2.48/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.48/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.48/1.55 => ( ( Xy = Xx )
% 2.48/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setoftrueEq_type,type,
% 2.48/1.55 setoftrueEq: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setoftrueEq,definition,
% 2.48/1.55 ( setoftrueEq
% 2.48/1.55 = ( ! [A: $i] :
% 2.48/1.55 ( ( dsetconstr @ A
% 2.48/1.55 @ ^ [Xx: $i] : $true )
% 2.48/1.55 = A ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(powersetI_type,type,
% 2.48/1.55 powersetI: $o ).
% 2.48/1.55
% 2.48/1.55 thf(powersetI,definition,
% 2.48/1.55 ( powersetI
% 2.48/1.55 = ( ! [A: $i,B: $i] :
% 2.48/1.55 ( ! [Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 => ( in @ Xx @ A ) )
% 2.48/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptyinPowerset_type,type,
% 2.48/1.55 emptyinPowerset: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptyinPowerset,definition,
% 2.48/1.55 ( emptyinPowerset
% 2.48/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(emptyInPowerset_type,type,
% 2.48/1.55 emptyInPowerset: $o ).
% 2.48/1.55
% 2.48/1.55 thf(emptyInPowerset,definition,
% 2.48/1.55 ( emptyInPowerset
% 2.48/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(powersetE_type,type,
% 2.48/1.55 powersetE: $o ).
% 2.48/1.55
% 2.48/1.55 thf(powersetE,definition,
% 2.48/1.55 ( powersetE
% 2.48/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.55 => ( ( in @ Xx @ B )
% 2.48/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setunionI_type,type,
% 2.48/1.55 setunionI: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setunionI,definition,
% 2.48/1.55 ( setunionI
% 2.48/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 => ( ( in @ B @ A )
% 2.48/1.55 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(setunionE_type,type,
% 2.48/1.55 setunionE: $o ).
% 2.48/1.55
% 2.48/1.55 thf(setunionE,definition,
% 2.48/1.55 ( setunionE
% 2.48/1.55 = ( ! [A: $i,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.48/1.55 => ! [Xphi: $o] :
% 2.48/1.55 ( ! [B: $i] :
% 2.48/1.55 ( ( in @ Xx @ B )
% 2.48/1.55 => ( ( in @ B @ A )
% 2.48/1.55 => Xphi ) )
% 2.48/1.55 => Xphi ) ) ) ) ).
% 2.48/1.55
% 2.48/1.55 thf(subPowSU_type,type,
% 2.48/1.55 subPowSU: $o ).
% 2.48/1.55
% 2.48/1.55 thf(subPowSU,definition,
% 2.48/1.55 ( subPowSU
% 2.48/1.55 = ( ! [A: $i,Xx: $i] :
% 2.48/1.55 ( ( in @ Xx @ A )
% 2.48/1.55 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuE2_type,type,
% 2.48/1.56 exuE2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuE2,definition,
% 2.48/1.56 ( exuE2
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 => ? [Xx: $i] :
% 2.48/1.56 ! [Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xy )
% 2.48/1.56 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(nonemptyImpWitness_type,type,
% 2.48/1.56 nonemptyImpWitness: $o ).
% 2.48/1.56
% 2.48/1.56 thf(nonemptyImpWitness,definition,
% 2.48/1.56 ( nonemptyImpWitness
% 2.48/1.56 = ( ! [A: $i] :
% 2.48/1.56 ( ( nonempty @ A )
% 2.48/1.56 => ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & $true ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(uniqinunit_type,type,
% 2.48/1.56 uniqinunit: $o ).
% 2.48/1.56
% 2.48/1.56 thf(uniqinunit,definition,
% 2.48/1.56 ( uniqinunit
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.48/1.56 => ( Xx = Xy ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notinsingleton_type,type,
% 2.48/1.56 notinsingleton: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notinsingleton,definition,
% 2.48/1.56 ( notinsingleton
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx != Xy )
% 2.48/1.56 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(eqinunit_type,type,
% 2.48/1.56 eqinunit: $o ).
% 2.48/1.56
% 2.48/1.56 thf(eqinunit,definition,
% 2.48/1.56 ( eqinunit
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(singletonsswitch_type,type,
% 2.48/1.56 singletonsswitch: $o ).
% 2.48/1.56
% 2.48/1.56 thf(singletonsswitch,definition,
% 2.48/1.56 ( singletonsswitch
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.48/1.56 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetE_type,type,
% 2.48/1.56 upairsetE: $o ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetE,definition,
% 2.48/1.56 ( upairsetE
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.48/1.56 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.48/1.56 => ( ( Xz = Xx )
% 2.48/1.56 | ( Xz = Xy ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetIL_type,type,
% 2.48/1.56 upairsetIL: $o ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetIL,definition,
% 2.48/1.56 ( upairsetIL
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetIR_type,type,
% 2.48/1.56 upairsetIR: $o ).
% 2.48/1.56
% 2.48/1.56 thf(upairsetIR,definition,
% 2.48/1.56 ( upairsetIR
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(emptyE1_type,type,
% 2.48/1.56 emptyE1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(emptyE1,definition,
% 2.48/1.56 ( emptyE1
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ( Xphi @ Xx ) )
% 2.48/1.56 => ( ( ( dsetconstr @ A
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 = emptyset )
% 2.48/1.56 => $false ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(vacuousDall_type,type,
% 2.48/1.56 vacuousDall: $o ).
% 2.48/1.56
% 2.48/1.56 thf(vacuousDall,definition,
% 2.48/1.56 ( vacuousDall
% 2.48/1.56 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ emptyset )
% 2.48/1.56 => ( Xphi @ Xx ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan1_type,type,
% 2.48/1.56 quantDeMorgan1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan1,definition,
% 2.48/1.56 ( quantDeMorgan1
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ~ ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( Xphi @ Xx ) )
% 2.48/1.56 => ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan2_type,type,
% 2.48/1.56 quantDeMorgan2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan2,definition,
% 2.48/1.56 ( quantDeMorgan2
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ~ ( Xphi @ Xx ) )
% 2.48/1.56 => ~ ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan3_type,type,
% 2.48/1.56 quantDeMorgan3: $o ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan3,definition,
% 2.48/1.56 ( quantDeMorgan3
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ~ ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ( Xphi @ Xx ) )
% 2.48/1.56 => ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan4_type,type,
% 2.48/1.56 quantDeMorgan4: $o ).
% 2.48/1.56
% 2.48/1.56 thf(quantDeMorgan4,definition,
% 2.48/1.56 ( quantDeMorgan4
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ~ ( Xphi @ Xx ) )
% 2.48/1.56 => ~ ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(prop2setI_type,type,
% 2.48/1.56 prop2setI: $o ).
% 2.48/1.56
% 2.48/1.56 thf(prop2setI,definition,
% 2.48/1.56 ( prop2setI
% 2.48/1.56 = ( ! [Xphi: $o] :
% 2.48/1.56 ( Xphi
% 2.48/1.56 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(set2prop_type,type,
% 2.48/1.56 set2prop: $i > $o ).
% 2.48/1.56
% 2.48/1.56 thf(prop2set2propI_type,type,
% 2.48/1.56 prop2set2propI: $o ).
% 2.48/1.56
% 2.48/1.56 thf(prop2set2propI,definition,
% 2.48/1.56 ( prop2set2propI
% 2.48/1.56 = ( ! [Xphi: $o] :
% 2.48/1.56 ( Xphi
% 2.48/1.56 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notdexE_type,type,
% 2.48/1.56 notdexE: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notdexE,definition,
% 2.48/1.56 ( notdexE
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ~ ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ( Xphi @ Xx ) )
% 2.48/1.56 => ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notdallE_type,type,
% 2.48/1.56 notdallE: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notdallE,definition,
% 2.48/1.56 ( notdallE
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( ~ ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( Xphi @ Xx ) )
% 2.48/1.56 => ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuI1_type,type,
% 2.48/1.56 exuI1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuI1,definition,
% 2.48/1.56 ( exuI1
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ? [Xx: $i] :
% 2.48/1.56 ( ( Xphi @ Xx )
% 2.48/1.56 & ! [Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xy )
% 2.48/1.56 => ( Xx = Xy ) ) )
% 2.48/1.56 => ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuI3_type,type,
% 2.48/1.56 exuI3: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuI3,definition,
% 2.48/1.56 ( exuI3
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.48/1.56 => ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xx )
% 2.48/1.56 => ( ( Xphi @ Xy )
% 2.48/1.56 => ( Xx = Xy ) ) )
% 2.48/1.56 => ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuI2_type,type,
% 2.48/1.56 exuI2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuI2,definition,
% 2.48/1.56 ( exuI2
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ? [Xx: $i] :
% 2.48/1.56 ! [Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xy )
% 2.48/1.56 <=> ( Xy = Xx ) )
% 2.48/1.56 => ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(inCongP_type,type,
% 2.48/1.56 inCongP: $o ).
% 2.48/1.56
% 2.48/1.56 thf(inCongP,definition,
% 2.48/1.56 ( inCongP
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ( ( in @ Xx @ A )
% 2.48/1.56 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(in__Cong_type,type,
% 2.48/1.56 in__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(in__Cong,definition,
% 2.48/1.56 ( in__Cong
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ( ( in @ Xx @ A )
% 2.48/1.56 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuE3u_type,type,
% 2.48/1.56 exuE3u: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuE3u,definition,
% 2.48/1.56 ( exuE3u
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 => ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xx )
% 2.48/1.56 => ( ( Xphi @ Xy )
% 2.48/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exu__Cong_type,type,
% 2.48/1.56 exu__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exu__Cong,definition,
% 2.48/1.56 ( exu__Cong
% 2.48/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ( ( Xphi @ Xx )
% 2.48/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.48/1.56 => ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 <=> ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(emptyset__Cong_type,type,
% 2.48/1.56 emptyset__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(emptyset__Cong,definition,
% 2.48/1.56 ( emptyset__Cong
% 2.48/1.56 = ( emptyset = emptyset ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoin__Cong_type,type,
% 2.48/1.56 setadjoin__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoin__Cong,definition,
% 2.48/1.56 ( setadjoin__Cong
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ! [Xz: $i,Xu: $i] :
% 2.48/1.56 ( ( Xz = Xu )
% 2.48/1.56 => ( ( setadjoin @ Xx @ Xz )
% 2.48/1.56 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(powerset__Cong_type,type,
% 2.48/1.56 powerset__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(powerset__Cong,definition,
% 2.48/1.56 ( powerset__Cong
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ( ( powerset @ A )
% 2.48/1.56 = ( powerset @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(setunion__Cong_type,type,
% 2.48/1.56 setunion__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(setunion__Cong,definition,
% 2.48/1.56 ( setunion__Cong
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ( ( setunion @ A )
% 2.48/1.56 = ( setunion @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(omega__Cong_type,type,
% 2.48/1.56 omega__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(omega__Cong,definition,
% 2.48/1.56 ( omega__Cong
% 2.48/1.56 = ( omega = omega ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(exuEu_type,type,
% 2.48/1.56 exuEu: $o ).
% 2.48/1.56
% 2.48/1.56 thf(exuEu,definition,
% 2.48/1.56 ( exuEu
% 2.48/1.56 = ( ! [Xphi: $i > $o] :
% 2.48/1.56 ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 => ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xphi @ Xx )
% 2.48/1.56 => ( ( Xphi @ Xy )
% 2.48/1.56 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(descr__Cong_type,type,
% 2.48/1.56 descr__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(descr__Cong,definition,
% 2.48/1.56 ( descr__Cong
% 2.48/1.56 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.56 ( ! [Xx: $i,Xy: $i] :
% 2.48/1.56 ( ( Xx = Xy )
% 2.48/1.56 => ( ( Xphi @ Xx )
% 2.48/1.56 <=> ( Xpsi @ Xy ) ) )
% 2.48/1.56 => ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 => ( ( exu
% 2.48/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.48/1.56 => ( ( descr
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 = ( descr
% 2.48/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(dsetconstr__Cong_type,type,
% 2.48/1.56 dsetconstr__Cong: $o ).
% 2.48/1.56
% 2.48/1.56 thf(dsetconstr__Cong,definition,
% 2.48/1.56 ( dsetconstr__Cong
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.48/1.56 ( ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ! [Xy: $i] :
% 2.48/1.56 ( ( in @ Xy @ B )
% 2.48/1.56 => ( ( Xx = Xy )
% 2.48/1.56 => ( ( Xphi @ Xx )
% 2.48/1.56 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.48/1.56 => ( ( dsetconstr @ A
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 = ( dsetconstr @ B
% 2.48/1.56 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subset_type,type,
% 2.48/1.56 subset: $i > $i > $o ).
% 2.48/1.56
% 2.48/1.56 thf(disjoint_type,type,
% 2.48/1.56 disjoint: $i > $i > $o ).
% 2.48/1.56
% 2.48/1.56 thf(setsmeet_type,type,
% 2.48/1.56 setsmeet: $i > $i > $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetI1_type,type,
% 2.48/1.56 subsetI1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetI1,definition,
% 2.48/1.56 ( subsetI1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( in @ Xx @ B ) )
% 2.48/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(eqimpsubset2_type,type,
% 2.48/1.56 eqimpsubset2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(eqimpsubset2,definition,
% 2.48/1.56 ( eqimpsubset2
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(eqimpsubset1_type,type,
% 2.48/1.56 eqimpsubset1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(eqimpsubset1,definition,
% 2.48/1.56 ( eqimpsubset1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( A = B )
% 2.48/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetI2_type,type,
% 2.48/1.56 subsetI2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetI2,definition,
% 2.48/1.56 ( subsetI2
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ! [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( in @ Xx @ B ) )
% 2.48/1.56 => ( subset @ A @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(emptysetsubset_type,type,
% 2.48/1.56 emptysetsubset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(emptysetsubset,definition,
% 2.48/1.56 ( emptysetsubset
% 2.48/1.56 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetE_type,type,
% 2.48/1.56 subsetE: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetE,definition,
% 2.48/1.56 ( subsetE
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( ( in @ Xx @ A )
% 2.48/1.56 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetE2_type,type,
% 2.48/1.56 subsetE2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetE2,definition,
% 2.48/1.56 ( subsetE2
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( ~ ( in @ Xx @ B )
% 2.48/1.56 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notsubsetI_type,type,
% 2.48/1.56 notsubsetI: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notsubsetI,definition,
% 2.48/1.56 ( notsubsetI
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( ~ ( in @ Xx @ B )
% 2.48/1.56 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notequalI1_type,type,
% 2.48/1.56 notequalI1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notequalI1,definition,
% 2.48/1.56 ( notequalI1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ~ ( subset @ A @ B )
% 2.48/1.56 => ( A != B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(notequalI2_type,type,
% 2.48/1.56 notequalI2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(notequalI2,definition,
% 2.48/1.56 ( notequalI2
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( ~ ( in @ Xx @ B )
% 2.48/1.56 => ( A != B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetRefl_type,type,
% 2.48/1.56 subsetRefl: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetRefl,definition,
% 2.48/1.56 ( subsetRefl
% 2.48/1.56 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetTrans_type,type,
% 2.48/1.56 subsetTrans: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetTrans,definition,
% 2.48/1.56 ( subsetTrans
% 2.48/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( ( subset @ B @ C )
% 2.48/1.56 => ( subset @ A @ C ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoinSub_type,type,
% 2.48/1.56 setadjoinSub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoinSub,definition,
% 2.48/1.56 ( setadjoinSub
% 2.48/1.56 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoinSub2_type,type,
% 2.48/1.56 setadjoinSub2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(setadjoinSub2,definition,
% 2.48/1.56 ( setadjoinSub2
% 2.48/1.56 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subset2powerset_type,type,
% 2.48/1.56 subset2powerset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subset2powerset,definition,
% 2.48/1.56 ( subset2powerset
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(setextsub_type,type,
% 2.48/1.56 setextsub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(setextsub,definition,
% 2.48/1.56 ( setextsub
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( ( subset @ B @ A )
% 2.48/1.56 => ( A = B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(subsetemptysetimpeq_type,type,
% 2.48/1.56 subsetemptysetimpeq: $o ).
% 2.48/1.56
% 2.48/1.56 thf(subsetemptysetimpeq,definition,
% 2.48/1.56 ( subsetemptysetimpeq
% 2.48/1.56 = ( ! [A: $i] :
% 2.48/1.56 ( ( subset @ A @ emptyset )
% 2.48/1.56 => ( A = emptyset ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(powersetI1_type,type,
% 2.48/1.56 powersetI1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(powersetI1,definition,
% 2.48/1.56 ( powersetI1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ B @ A )
% 2.48/1.56 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(powersetE1_type,type,
% 2.48/1.56 powersetE1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(powersetE1,definition,
% 2.48/1.56 ( powersetE1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( in @ B @ ( powerset @ A ) )
% 2.48/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(inPowerset_type,type,
% 2.48/1.56 inPowerset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(inPowerset,definition,
% 2.48/1.56 ( inPowerset
% 2.48/1.56 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(powersetsubset_type,type,
% 2.48/1.56 powersetsubset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(powersetsubset,definition,
% 2.48/1.56 ( powersetsubset
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(sepInPowerset_type,type,
% 2.48/1.56 sepInPowerset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(sepInPowerset,definition,
% 2.48/1.56 ( sepInPowerset
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( in
% 2.48/1.56 @ ( dsetconstr @ A
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 @ ( powerset @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(sepSubset_type,type,
% 2.48/1.56 sepSubset: $o ).
% 2.48/1.56
% 2.48/1.56 thf(sepSubset,definition,
% 2.48/1.56 ( sepSubset
% 2.48/1.56 = ( ! [A: $i,Xphi: $i > $o] :
% 2.48/1.56 ( subset
% 2.48/1.56 @ ( dsetconstr @ A
% 2.48/1.56 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.48/1.56 @ A ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunion_type,type,
% 2.48/1.56 binunion: $i > $i > $i ).
% 2.48/1.56
% 2.48/1.56 thf(binunionIL_type,type,
% 2.48/1.56 binunionIL: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionIL,definition,
% 2.48/1.56 ( binunionIL
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(upairset2IR_type,type,
% 2.48/1.56 upairset2IR: $o ).
% 2.48/1.56
% 2.48/1.56 thf(upairset2IR,definition,
% 2.48/1.56 ( upairset2IR
% 2.48/1.56 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunionIR_type,type,
% 2.48/1.56 binunionIR: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionIR,definition,
% 2.48/1.56 ( binunionIR
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ B )
% 2.48/1.56 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunionEcases_type,type,
% 2.48/1.56 binunionEcases: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionEcases,definition,
% 2.48/1.56 ( binunionEcases
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.48/1.56 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.48/1.56 => ( ( ( in @ Xx @ A )
% 2.48/1.56 => Xphi )
% 2.48/1.56 => ( ( ( in @ Xx @ B )
% 2.48/1.56 => Xphi )
% 2.48/1.56 => Xphi ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunionE_type,type,
% 2.48/1.56 binunionE: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionE,definition,
% 2.48/1.56 ( binunionE
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.48/1.56 => ( ( in @ Xx @ A )
% 2.48/1.56 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunionLsub_type,type,
% 2.48/1.56 binunionLsub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionLsub,definition,
% 2.48/1.56 ( binunionLsub
% 2.48/1.56 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binunionRsub_type,type,
% 2.48/1.56 binunionRsub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binunionRsub,definition,
% 2.48/1.56 ( binunionRsub
% 2.48/1.56 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersect_type,type,
% 2.48/1.56 binintersect: $i > $i > $i ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectI_type,type,
% 2.48/1.56 binintersectI: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectI,definition,
% 2.48/1.56 ( binintersectI
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 => ( ( in @ Xx @ B )
% 2.48/1.56 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset5_type,type,
% 2.48/1.56 binintersectSubset5: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset5,definition,
% 2.48/1.56 ( binintersectSubset5
% 2.48/1.56 = ( ! [A: $i,B: $i,C: $i] :
% 2.48/1.56 ( ( subset @ C @ A )
% 2.48/1.56 => ( ( subset @ C @ B )
% 2.48/1.56 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectEL_type,type,
% 2.48/1.56 binintersectEL: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectEL,definition,
% 2.48/1.56 ( binintersectEL
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.48/1.56 => ( in @ Xx @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectLsub_type,type,
% 2.48/1.56 binintersectLsub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectLsub,definition,
% 2.48/1.56 ( binintersectLsub
% 2.48/1.56 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset2_type,type,
% 2.48/1.56 binintersectSubset2: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset2,definition,
% 2.48/1.56 ( binintersectSubset2
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ A @ B )
% 2.48/1.56 => ( ( binintersect @ A @ B )
% 2.48/1.56 = A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset3_type,type,
% 2.48/1.56 binintersectSubset3: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset3,definition,
% 2.48/1.56 ( binintersectSubset3
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ( ( binintersect @ A @ B )
% 2.48/1.56 = B )
% 2.48/1.56 => ( subset @ B @ A ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectER_type,type,
% 2.48/1.56 binintersectER: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectER,definition,
% 2.48/1.56 ( binintersectER
% 2.48/1.56 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.48/1.56 => ( in @ Xx @ B ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(disjointsetsI1_type,type,
% 2.48/1.56 disjointsetsI1: $o ).
% 2.48/1.56
% 2.48/1.56 thf(disjointsetsI1,definition,
% 2.48/1.56 ( disjointsetsI1
% 2.48/1.56 = ( ! [A: $i,B: $i] :
% 2.48/1.56 ( ~ ? [Xx: $i] :
% 2.48/1.56 ( ( in @ Xx @ A )
% 2.48/1.56 & ( in @ Xx @ B ) )
% 2.48/1.56 => ( ( binintersect @ A @ B )
% 2.48/1.56 = emptyset ) ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectRsub_type,type,
% 2.48/1.56 binintersectRsub: $o ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectRsub,definition,
% 2.48/1.56 ( binintersectRsub
% 2.48/1.56 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.48/1.56
% 2.48/1.56 thf(binintersectSubset4,conjecture,
% 2.48/1.56 ( setextAx
% 2.48/1.56 => ( emptysetAx
% 2.48/1.56 => ( setadjoinAx
% 2.48/1.56 => ( powersetAx
% 2.48/1.56 => ( setunionAx
% 2.48/1.56 => ( omega0Ax
% 2.48/1.56 => ( omegaSAx
% 2.48/1.56 => ( omegaIndAx
% 2.48/1.56 => ( replAx
% 2.48/1.56 => ( foundationAx
% 2.48/1.56 => ( wellorderingAx
% 2.48/1.56 => ( descrp
% 2.48/1.56 => ( dsetconstrI
% 2.48/1.56 => ( dsetconstrEL
% 2.48/1.56 => ( dsetconstrER
% 2.48/1.56 => ( exuE1
% 2.48/1.56 => ( prop2setE
% 2.48/1.56 => ( emptysetE
% 2.48/1.56 => ( emptysetimpfalse
% 2.48/1.56 => ( notinemptyset
% 2.48/1.56 => ( exuE3e
% 2.48/1.56 => ( setext
% 2.48/1.56 => ( emptyI
% 2.48/1.56 => ( noeltsimpempty
% 2.48/1.56 => ( setbeta
% 2.48/1.56 => ( nonemptyE1
% 2.48/1.56 => ( nonemptyI
% 2.48/1.56 => ( nonemptyI1
% 2.48/1.56 => ( setadjoinIL
% 2.48/1.56 => ( emptyinunitempty
% 2.48/1.56 => ( setadjoinIR
% 2.48/1.56 => ( setadjoinE
% 2.48/1.56 => ( setadjoinOr
% 2.48/1.56 => ( setoftrueEq
% 2.48/1.56 => ( powersetI
% 2.48/1.56 => ( emptyinPowerset
% 2.48/1.56 => ( emptyInPowerset
% 2.48/1.56 => ( powersetE
% 2.48/1.56 => ( setunionI
% 2.48/1.56 => ( setunionE
% 2.48/1.56 => ( subPowSU
% 2.48/1.56 => ( exuE2
% 2.48/1.56 => ( nonemptyImpWitness
% 2.48/1.56 => ( uniqinunit
% 2.48/1.56 => ( notinsingleton
% 2.48/1.56 => ( eqinunit
% 2.48/1.56 => ( singletonsswitch
% 2.48/1.56 => ( upairsetE
% 2.48/1.56 => ( upairsetIL
% 2.48/1.56 => ( upairsetIR
% 2.48/1.56 => ( emptyE1
% 2.48/1.56 => ( vacuousDall
% 2.48/1.56 => ( quantDeMorgan1
% 2.48/1.56 => ( quantDeMorgan2
% 2.48/1.56 => ( quantDeMorgan3
% 2.48/1.56 => ( quantDeMorgan4
% 2.48/1.56 => ( prop2setI
% 2.48/1.56 => ( prop2set2propI
% 2.48/1.56 => ( notdexE
% 2.48/1.56 => ( notdallE
% 2.48/1.56 => ( exuI1
% 2.48/1.56 => ( exuI3
% 2.48/1.56 => ( exuI2
% 2.48/1.56 => ( inCongP
% 2.48/1.56 => ( in__Cong
% 2.48/1.56 => ( exuE3u
% 2.48/1.56 => ( exu__Cong
% 2.48/1.56 => ( emptyset__Cong
% 2.48/1.56 => ( setadjoin__Cong
% 2.48/1.56 => ( powerset__Cong
% 2.48/1.56 => ( setunion__Cong
% 2.48/1.56 => ( omega__Cong
% 2.48/1.56 => ( exuEu
% 2.48/1.56 => ( descr__Cong
% 2.48/1.56 => ( dsetconstr__Cong
% 2.48/1.56 => ( subsetI1
% 2.48/1.56 => ( eqimpsubset2
% 2.48/1.56 => ( eqimpsubset1
% 2.48/1.56 => ( subsetI2
% 2.48/1.56 => ( emptysetsubset
% 2.48/1.56 => ( subsetE
% 2.48/1.56 => ( subsetE2
% 2.48/1.56 => ( notsubsetI
% 2.48/1.56 => ( notequalI1
% 2.48/1.56 => ( notequalI2
% 2.48/1.56 => ( subsetRefl
% 2.48/1.56 => ( subsetTrans
% 2.48/1.56 => ( setadjoinSub
% 2.48/1.56 => ( setadjoinSub2
% 2.48/1.56 => ( subset2powerset
% 2.48/1.56 => ( setextsub
% 2.48/1.56 => ( subsetemptysetimpeq
% 2.48/1.56 => ( powersetI1
% 2.48/1.56 => ( powersetE1
% 2.48/1.56 => ( inPowerset
% 2.48/1.56 => ( powersetsubset
% 2.48/1.56 => ( sepInPowerset
% 2.48/1.56 => ( sepSubset
% 2.48/1.56 => ( binunionIL
% 2.48/1.56 => ( upairset2IR
% 2.48/1.56 => ( binunionIR
% 2.48/1.56 => ( binunionEcases
% 2.48/1.56 => ( binunionE
% 2.48/1.56 => ( binunionLsub
% 2.48/1.56 => ( binunionRsub
% 2.48/1.56 => ( binintersectI
% 2.48/1.56 => ( binintersectSubset5
% 2.48/1.56 => ( binintersectEL
% 2.48/1.56 => ( binintersectLsub
% 2.48/1.56 => ( binintersectSubset2
% 2.48/1.56 => ( binintersectSubset3
% 2.48/1.56 => ( binintersectER
% 2.48/1.56 => ( disjointsetsI1
% 2.48/1.56 => ( binintersectRsub
% 2.48/1.56 => ! [A: $i,B: $i] :
% 2.48/1.56 ( ( subset @ B @ A )
% 2.48/1.56 => ( ( binintersect @ A @ B )
% 2.48/1.56 = B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.48/1.56 ------------------------
% 2.48/1.58 % (29950)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_29850 for (2999ds/27Mi)
% 2.48/1.58 % (29951)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/2Mi)
% 2.48/1.58 % (29949)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_29850 for (2999ds/4Mi)
% 2.48/1.58 % (29948)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/183Mi)
% 2.48/1.58 % (29952)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_29850 for (2999ds/2Mi)
% 2.48/1.58 % (29953)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_29850 for (2999ds/275Mi)
% 2.48/1.58 % (29954)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/18Mi)
% 2.48/1.58 % (29951)Instruction limit reached!
% 2.48/1.58 % (29951)------------------------------
% 2.48/1.58 % (29951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.58 % (29951)Termination reason: Unknown
% 2.48/1.58 % (29951)Termination phase: shuffling
% 2.48/1.58
% 2.48/1.58 % (29951)Memory used [KB]: 1151
% 2.48/1.58 % (29951)Time elapsed: 0.002 s
% 2.48/1.58 % (29951)Instructions burned: 2 (million)
% 2.48/1.58 % (29951)------------------------------
% 2.48/1.58 % (29951)------------------------------
% 2.48/1.58 % (29952)Instruction limit reached!
% 2.48/1.58 % (29952)------------------------------
% 2.48/1.58 % (29952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.58 % (29952)Termination reason: Unknown
% 2.48/1.58 % (29952)Termination phase: shuffling
% 2.48/1.58
% 2.48/1.58 % (29952)Memory used [KB]: 1151
% 2.48/1.58 % (29952)Time elapsed: 0.003 s
% 2.48/1.58 % (29952)Instructions burned: 4 (million)
% 2.48/1.58 % (29952)------------------------------
% 2.48/1.58 % (29952)------------------------------
% 2.48/1.58 % (29949)Instruction limit reached!
% 2.48/1.58 % (29949)------------------------------
% 2.48/1.58 % (29949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.58 % (29949)Termination reason: Unknown
% 2.48/1.58 % (29949)Termination phase: shuffling
% 2.48/1.58
% 2.48/1.58 % (29949)Memory used [KB]: 1279
% 2.48/1.58 % (29949)Time elapsed: 0.004 s
% 2.48/1.58 % (29949)Instructions burned: 5 (million)
% 2.48/1.58 % (29949)------------------------------
% 2.48/1.58 % (29949)------------------------------
% 2.48/1.59 % (29954)Instruction limit reached!
% 2.48/1.59 % (29954)------------------------------
% 2.48/1.59 % (29954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.59 % (29954)Termination reason: Unknown
% 2.48/1.59 % (29954)Termination phase: Preprocessing 3
% 2.48/1.59
% 2.48/1.59 % (29954)Memory used [KB]: 1535
% 2.48/1.59 % (29954)Time elapsed: 0.011 s
% 2.48/1.59 % (29954)Instructions burned: 19 (million)
% 2.48/1.59 % (29954)------------------------------
% 2.48/1.59 % (29954)------------------------------
% 2.48/1.59 % (29950)Instruction limit reached!
% 2.48/1.59 % (29950)------------------------------
% 2.48/1.59 % (29950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.48/1.59 % (29950)Termination reason: Unknown
% 2.48/1.59 % (29950)Termination phase: Property scanning
% 2.48/1.59
% 2.48/1.59 % (29950)Memory used [KB]: 1535
% 2.48/1.59 % (29950)Time elapsed: 0.014 s
% 2.48/1.59 % (29950)Instructions burned: 29 (million)
% 2.48/1.59 % (29950)------------------------------
% 2.48/1.59 % (29950)------------------------------
% 2.54/1.60 % (29955)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/3Mi)
% 2.54/1.60 % (29956)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_29850 for (2999ds/37Mi)
% 2.54/1.60 % (29957)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_29850 for (2999ds/15Mi)
% 2.54/1.60 % (29955)Instruction limit reached!
% 2.54/1.60 % (29955)------------------------------
% 2.54/1.60 % (29955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.60 % (29955)Termination reason: Unknown
% 2.54/1.60 % (29955)Termination phase: shuffling
% 2.54/1.60
% 2.54/1.60 % (29955)Memory used [KB]: 1279
% 2.54/1.60 % (29955)Time elapsed: 0.004 s
% 2.54/1.60 % (29955)Instructions burned: 5 (million)
% 2.54/1.60 % (29955)------------------------------
% 2.54/1.60 % (29955)------------------------------
% 2.54/1.60 % (29959)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_29850 for (2999ds/1041Mi)
% 2.54/1.60 % (29957)Instruction limit reached!
% 2.54/1.60 % (29957)------------------------------
% 2.54/1.60 % (29957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (29957)Termination reason: Unknown
% 2.54/1.61 % (29957)Termination phase: Preprocessing 1
% 2.54/1.61
% 2.54/1.61 % (29957)Memory used [KB]: 1407
% 2.54/1.61 % (29957)Time elapsed: 0.008 s
% 2.54/1.61 % (29957)Instructions burned: 15 (million)
% 2.54/1.61 % (29957)------------------------------
% 2.54/1.61 % (29957)------------------------------
% 2.54/1.61 % (29958)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_29850 for (2999ds/3Mi)
% 2.54/1.61 % (29958)Instruction limit reached!
% 2.54/1.61 % (29958)------------------------------
% 2.54/1.61 % (29958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (29958)Termination reason: Unknown
% 2.54/1.61 % (29958)Termination phase: shuffling
% 2.54/1.61
% 2.54/1.61 % (29958)Memory used [KB]: 1151
% 2.54/1.61 % (29958)Time elapsed: 0.003 s
% 2.54/1.61 % (29958)Instructions burned: 4 (million)
% 2.54/1.61 % (29958)------------------------------
% 2.54/1.61 % (29958)------------------------------
% 2.54/1.61 % (29960)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/7Mi)
% 2.54/1.61 % (29960)Instruction limit reached!
% 2.54/1.61 % (29960)------------------------------
% 2.54/1.61 % (29960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (29960)Termination reason: Unknown
% 2.54/1.61 % (29960)Termination phase: shuffling
% 2.54/1.61
% 2.54/1.61 % (29960)Memory used [KB]: 1279
% 2.54/1.61 % (29960)Time elapsed: 0.004 s
% 2.54/1.61 % (29960)Instructions burned: 10 (million)
% 2.54/1.61 % (29960)------------------------------
% 2.54/1.61 % (29960)------------------------------
% 2.54/1.61 % (29956)Instruction limit reached!
% 2.54/1.61 % (29956)------------------------------
% 2.54/1.61 % (29956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.61 % (29956)Termination reason: Unknown
% 2.54/1.61 % (29956)Termination phase: Property scanning
% 2.54/1.61
% 2.54/1.61 % (29956)Memory used [KB]: 1535
% 2.54/1.61 % (29956)Time elapsed: 0.018 s
% 2.54/1.61 % (29956)Instructions burned: 38 (million)
% 2.54/1.61 % (29956)------------------------------
% 2.54/1.61 % (29956)------------------------------
% 2.54/1.62 % (29961)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/16Mi)
% 2.54/1.62 % (29963)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_29850 for (2999ds/3Mi)
% 2.54/1.62 % (29963)Instruction limit reached!
% 2.54/1.62 % (29963)------------------------------
% 2.54/1.62 % (29963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.62 % (29963)Termination reason: Unknown
% 2.54/1.62 % (29963)Termination phase: shuffling
% 2.54/1.62
% 2.54/1.62 % (29963)Memory used [KB]: 1279
% 2.54/1.62 % (29963)Time elapsed: 0.002 s
% 2.54/1.62 % (29963)Instructions burned: 4 (million)
% 2.54/1.62 % (29963)------------------------------
% 2.54/1.62 % (29963)------------------------------
% 2.54/1.63 % (29962)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_29850 for (2999ds/3Mi)
% 2.54/1.63 % (29962)Instruction limit reached!
% 2.54/1.63 % (29962)------------------------------
% 2.54/1.63 % (29962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.63 % (29962)Termination reason: Unknown
% 2.54/1.63 % (29962)Termination phase: shuffling
% 2.54/1.63
% 2.54/1.63 % (29962)Memory used [KB]: 1151
% 2.54/1.63 % (29962)Time elapsed: 0.003 s
% 2.54/1.63 % (29962)Instructions burned: 3 (million)
% 2.54/1.63 % (29962)------------------------------
% 2.54/1.63 % (29962)------------------------------
% 2.54/1.63 % (29961)Instruction limit reached!
% 2.54/1.63 % (29961)------------------------------
% 2.54/1.63 % (29961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.63 % (29961)Termination reason: Unknown
% 2.54/1.63 % (29961)Termination phase: Property scanning
% 2.54/1.63
% 2.54/1.63 % (29961)Memory used [KB]: 1535
% 2.54/1.63 % (29961)Time elapsed: 0.010 s
% 2.54/1.63 % (29961)Instructions burned: 18 (million)
% 2.54/1.63 % (29961)------------------------------
% 2.54/1.63 % (29961)------------------------------
% 2.54/1.63 % (29964)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/7Mi)
% 2.54/1.63 % (29964)Instruction limit reached!
% 2.54/1.63 % (29964)------------------------------
% 2.54/1.63 % (29964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.63 % (29964)Termination reason: Unknown
% 2.54/1.63 % (29964)Termination phase: shuffling
% 2.54/1.63
% 2.54/1.63 % (29964)Memory used [KB]: 1279
% 2.54/1.63 % (29964)Time elapsed: 0.005 s
% 2.54/1.63 % (29964)Instructions burned: 8 (million)
% 2.54/1.63 % (29964)------------------------------
% 2.54/1.63 % (29964)------------------------------
% 2.54/1.64 % (29965)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/3Mi)
% 2.54/1.64 % (29965)Instruction limit reached!
% 2.54/1.64 % (29965)------------------------------
% 2.54/1.64 % (29965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.64 % (29965)Termination reason: Unknown
% 2.54/1.64 % (29965)Termination phase: shuffling
% 2.54/1.64
% 2.54/1.64 % (29965)Memory used [KB]: 1151
% 2.54/1.64 % (29965)Time elapsed: 0.003 s
% 2.54/1.64 % (29965)Instructions burned: 3 (million)
% 2.54/1.64 % (29965)------------------------------
% 2.54/1.64 % (29965)------------------------------
% 2.54/1.64 % (29967)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/18Mi)
% 2.54/1.64 % (29966)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/4Mi)
% 2.54/1.65 % (29966)Instruction limit reached!
% 2.54/1.65 % (29966)------------------------------
% 2.54/1.65 % (29966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.65 % (29966)Termination reason: Unknown
% 2.54/1.65 % (29966)Termination phase: shuffling
% 2.54/1.65
% 2.54/1.65 % (29966)Memory used [KB]: 1279
% 2.54/1.65 % (29966)Time elapsed: 0.004 s
% 2.54/1.65 % (29966)Instructions burned: 6 (million)
% 2.54/1.65 % (29966)------------------------------
% 2.54/1.65 % (29966)------------------------------
% 2.54/1.65 % (29968)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/710Mi)
% 2.54/1.65 % (29967)Instruction limit reached!
% 2.54/1.65 % (29967)------------------------------
% 2.54/1.65 % (29967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.65 % (29967)Termination reason: Unknown
% 2.54/1.65 % (29967)Termination phase: Property scanning
% 2.54/1.65
% 2.54/1.65 % (29967)Memory used [KB]: 1535
% 2.54/1.65 % (29967)Time elapsed: 0.010 s
% 2.54/1.65 % (29967)Instructions burned: 18 (million)
% 2.54/1.65 % (29967)------------------------------
% 2.54/1.65 % (29967)------------------------------
% 2.54/1.66 % (29969)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/6Mi)
% 2.54/1.66 % (29969)Instruction limit reached!
% 2.54/1.66 % (29969)------------------------------
% 2.54/1.66 % (29969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.66 % (29969)Termination reason: Unknown
% 2.54/1.66 % (29969)Termination phase: shuffling
% 2.54/1.66
% 2.54/1.66 % (29969)Memory used [KB]: 1279
% 2.54/1.66 % (29969)Time elapsed: 0.005 s
% 2.54/1.66 % (29969)Instructions burned: 8 (million)
% 2.54/1.66 % (29969)------------------------------
% 2.54/1.66 % (29969)------------------------------
% 2.54/1.66 % (29970)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_29850 for (2999ds/902Mi)
% 2.54/1.67 % (29948)Instruction limit reached!
% 2.54/1.67 % (29948)------------------------------
% 2.54/1.67 % (29948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.67 % (29948)Termination reason: Unknown
% 2.54/1.67 % (29948)Termination phase: Saturation
% 2.54/1.67
% 2.54/1.67 % (29948)Memory used [KB]: 7036
% 2.54/1.67 % (29948)Time elapsed: 0.087 s
% 2.54/1.67 % (29948)Instructions burned: 183 (million)
% 2.54/1.67 % (29948)------------------------------
% 2.54/1.67 % (29948)------------------------------
% 2.54/1.67 % (29971)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_29850 for (2999ds/21Mi)
% 2.54/1.68 % (29971)Instruction limit reached!
% 2.54/1.68 % (29971)------------------------------
% 2.54/1.68 % (29971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.68 % (29971)Termination reason: Unknown
% 2.54/1.68 % (29971)Termination phase: Property scanning
% 2.54/1.68
% 2.54/1.68 % (29971)Memory used [KB]: 1535
% 2.54/1.68 % (29971)Time elapsed: 0.011 s
% 2.54/1.68 % (29971)Instructions burned: 22 (million)
% 2.54/1.68 % (29971)------------------------------
% 2.54/1.68 % (29971)------------------------------
% 2.54/1.68 % (29972)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29850 for (2999ds/5Mi)
% 2.54/1.68 % (29972)Instruction limit reached!
% 2.54/1.68 % (29972)------------------------------
% 2.54/1.68 % (29972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.68 % (29972)Termination reason: Unknown
% 2.54/1.68 % (29972)Termination phase: shuffling
% 2.54/1.68
% 2.54/1.68 % (29972)Memory used [KB]: 1279
% 2.54/1.68 % (29972)Time elapsed: 0.004 s
% 2.54/1.68 % (29972)Instructions burned: 6 (million)
% 2.54/1.68 % (29972)------------------------------
% 2.54/1.68 % (29972)------------------------------
% 2.54/1.68 % (29973)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_29850 for (2999ds/6Mi)
% 2.54/1.68 % (29973)Instruction limit reached!
% 2.54/1.68 % (29973)------------------------------
% 2.54/1.68 % (29973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.68 % (29973)Termination reason: Unknown
% 2.54/1.68 % (29973)Termination phase: shuffling
% 2.54/1.68
% 2.54/1.68 % (29973)Memory used [KB]: 1279
% 2.54/1.68 % (29973)Time elapsed: 0.004 s
% 2.54/1.68 % (29973)Instructions burned: 6 (million)
% 2.54/1.68 % (29973)------------------------------
% 2.54/1.68 % (29973)------------------------------
% 2.54/1.69 % (29974)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29850 for (2998ds/377Mi)
% 2.54/1.70 % (29975)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_29850 for (2998ds/779Mi)
% 2.54/1.70 % (29976)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_29850 for (2998ds/19Mi)
% 2.54/1.71 % (29976)Instruction limit reached!
% 2.54/1.71 % (29976)------------------------------
% 2.54/1.71 % (29976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (29976)Termination reason: Unknown
% 2.54/1.71 % (29976)Termination phase: Property scanning
% 2.54/1.71
% 2.54/1.71 % (29976)Memory used [KB]: 1535
% 2.54/1.71 % (29976)Time elapsed: 0.010 s
% 2.54/1.71 % (29976)Instructions burned: 19 (million)
% 2.54/1.71 % (29976)------------------------------
% 2.54/1.71 % (29976)------------------------------
% 2.54/1.72 % (29953)Instruction limit reached!
% 2.54/1.72 % (29953)------------------------------
% 2.54/1.72 % (29953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.72 % (29953)Termination reason: Unknown
% 2.54/1.72 % (29953)Termination phase: Saturation
% 2.54/1.72
% 2.54/1.72 % (29953)Memory used [KB]: 7803
% 2.54/1.72 % (29953)Time elapsed: 0.140 s
% 2.54/1.72 % (29953)Instructions burned: 276 (million)
% 2.54/1.72 % (29953)------------------------------
% 2.54/1.72 % (29953)------------------------------
% 2.54/1.72 % (29977)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29850 for (2998ds/879Mi)
% 2.54/1.73 % (29978)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29850 for (2998ds/17Mi)
% 2.54/1.74 % (29978)Instruction limit reached!
% 2.54/1.74 % (29978)------------------------------
% 2.54/1.74 % (29978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.74 % (29978)Termination reason: Unknown
% 2.54/1.74 % (29978)Termination phase: Property scanning
% 2.54/1.74
% 2.54/1.74 % (29978)Memory used [KB]: 1535
% 2.54/1.74 % (29978)Time elapsed: 0.009 s
% 2.54/1.74 % (29978)Instructions burned: 17 (million)
% 2.54/1.74 % (29978)------------------------------
% 2.54/1.74 % (29978)------------------------------
% 2.54/1.76 % (29979)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29850 for (2998ds/3Mi)
% 2.54/1.76 % (29979)Instruction limit reached!
% 2.54/1.76 % (29979)------------------------------
% 2.54/1.76 % (29979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.76 % (29979)Termination reason: Unknown
% 2.54/1.76 % (29979)Termination phase: shuffling
% 2.54/1.76
% 2.54/1.76 % (29979)Memory used [KB]: 1151
% 2.54/1.76 % (29979)Time elapsed: 0.003 s
% 2.54/1.76 % (29979)Instructions burned: 4 (million)
% 2.54/1.76 % (29979)------------------------------
% 2.54/1.76 % (29979)------------------------------
% 2.54/1.78 % (29980)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29850 for (2998ds/30Mi)
% 2.54/1.79 % (29980)Instruction limit reached!
% 2.54/1.79 % (29980)------------------------------
% 2.54/1.79 % (29980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (29980)Termination reason: Unknown
% 2.54/1.79 % (29980)Termination phase: Property scanning
% 2.54/1.79
% 2.54/1.79 % (29980)Memory used [KB]: 1535
% 2.54/1.79 % (29980)Time elapsed: 0.015 s
% 2.54/1.79 % (29980)Instructions burned: 31 (million)
% 2.54/1.79 % (29980)------------------------------
% 2.54/1.79 % (29980)------------------------------
% 2.54/1.81 % (29981)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29850 for (2997ds/127Mi)
% 2.54/1.86 % (29981)Instruction limit reached!
% 2.54/1.86 % (29981)------------------------------
% 2.54/1.86 % (29981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.86 % (29981)Termination reason: Unknown
% 2.54/1.86 % (29981)Termination phase: Saturation
% 2.54/1.86
% 2.54/1.86 % (29981)Memory used [KB]: 6780
% 2.54/1.86 % (29981)Time elapsed: 0.059 s
% 2.54/1.86 % (29981)Instructions burned: 127 (million)
% 2.54/1.86 % (29981)------------------------------
% 2.54/1.86 % (29981)------------------------------
% 2.54/1.88 % (29974)Instruction limit reached!
% 2.54/1.88 % (29974)------------------------------
% 2.54/1.88 % (29974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (29974)Termination reason: Unknown
% 2.54/1.88 % (29974)Termination phase: Saturation
% 2.54/1.88
% 2.54/1.88 % (29974)Memory used [KB]: 7291
% 2.54/1.88 % (29974)Time elapsed: 0.184 s
% 2.54/1.88 % (29974)Instructions burned: 378 (million)
% 2.54/1.88 % (29974)------------------------------
% 2.54/1.88 % (29974)------------------------------
% 2.54/1.88 % (29982)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29850 for (2997ds/100Mi)
% 2.54/1.89 % (29983)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_29850 for (2996ds/3Mi)
% 2.54/1.89 % (29983)Instruction limit reached!
% 2.54/1.89 % (29983)------------------------------
% 2.54/1.89 % (29983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.90 % (29983)Termination reason: Unknown
% 2.54/1.90 % (29983)Termination phase: shuffling
% 2.54/1.90
% 2.54/1.90 % (29983)Memory used [KB]: 1279
% 2.54/1.90 % (29983)Time elapsed: 0.004 s
% 2.54/1.90 % (29983)Instructions burned: 5 (million)
% 2.54/1.90 % (29983)------------------------------
% 2.54/1.90 % (29983)------------------------------
% 2.54/1.91 % (29984)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_29850 for (2996ds/20Mi)
% 2.54/1.92 % (29984)Instruction limit reached!
% 2.54/1.92 % (29984)------------------------------
% 2.54/1.92 % (29984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (29984)Termination reason: Unknown
% 2.54/1.92 % (29984)Termination phase: Preprocessing 1
% 2.54/1.92
% 2.54/1.92 % (29984)Memory used [KB]: 1407
% 2.54/1.92 % (29984)Time elapsed: 0.011 s
% 2.54/1.92 % (29984)Instructions burned: 21 (million)
% 2.54/1.92 % (29984)------------------------------
% 2.54/1.92 % (29984)------------------------------
% 2.54/1.93 % (29982)Instruction limit reached!
% 2.54/1.93 % (29982)------------------------------
% 2.54/1.93 % (29982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (29982)Termination reason: Unknown
% 2.54/1.93 % (29982)Termination phase: Saturation
% 2.54/1.93
% 2.54/1.93 % (29982)Memory used [KB]: 6268
% 2.54/1.93 % (29982)Time elapsed: 0.048 s
% 2.54/1.93 % (29982)Instructions burned: 101 (million)
% 2.54/1.93 % (29982)------------------------------
% 2.54/1.93 % (29982)------------------------------
% 2.54/1.94 % (29985)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_29850 for (2996ds/86Mi)
% 2.54/1.94 % (29986)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_29850 for (2996ds/107Mi)
% 2.54/1.98 % (29985)Instruction limit reached!
% 2.54/1.98 % (29985)------------------------------
% 2.54/1.98 % (29985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (29985)Termination reason: Unknown
% 2.54/1.98 % (29985)Termination phase: Saturation
% 2.54/1.98
% 2.54/1.98 % (29985)Memory used [KB]: 6396
% 2.54/1.98 % (29985)Time elapsed: 0.040 s
% 2.54/1.98 % (29985)Instructions burned: 86 (million)
% 2.54/1.98 % (29985)------------------------------
% 2.54/1.98 % (29985)------------------------------
% 2.54/1.98 % (29975)Instruction limit reached!
% 2.54/1.98 % (29975)------------------------------
% 2.54/1.98 % (29975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (29975)Termination reason: Unknown
% 2.54/1.98 % (29975)Termination phase: Saturation
% 2.54/1.98
% 2.54/1.98 % (29975)Memory used [KB]: 6524
% 2.54/1.98 % (29975)Time elapsed: 0.285 s
% 2.54/1.98 % (29975)Instructions burned: 779 (million)
% 2.54/1.98 % (29975)------------------------------
% 2.54/1.98 % (29975)------------------------------
% 2.54/1.99 % (29959)Instruction limit reached!
% 2.54/1.99 % (29959)------------------------------
% 2.54/1.99 % (29959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (29959)Termination reason: Unknown
% 2.54/1.99 % (29959)Termination phase: Saturation
% 2.54/1.99
% 2.54/1.99 % (29959)Memory used [KB]: 8187
% 2.54/1.99 % (29959)Time elapsed: 0.383 s
% 2.54/1.99 % (29959)Instructions burned: 1042 (million)
% 2.54/1.99 % (29959)------------------------------
% 2.54/1.99 % (29959)------------------------------
% 2.54/1.99 % (29986)Instruction limit reached!
% 2.54/1.99 % (29986)------------------------------
% 2.54/1.99 % (29986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.99 % (29986)Termination reason: Unknown
% 2.54/1.99 % (29986)Termination phase: Saturation
% 2.54/1.99
% 2.54/1.99 % (29986)Memory used [KB]: 6652
% 2.54/1.99 % (29986)Time elapsed: 0.049 s
% 2.54/1.99 % (29986)Instructions burned: 108 (million)
% 2.54/1.99 % (29986)------------------------------
% 2.54/1.99 % (29986)------------------------------
% 2.54/1.99 % (29987)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_29850 for (2995ds/39Mi)
% 2.54/2.00 % (29988)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_29850 for (2995ds/448Mi)
% 2.54/2.00 % (29968)Instruction limit reached!
% 2.54/2.00 % (29968)------------------------------
% 2.54/2.00 % (29968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.00 % (29968)Termination reason: Unknown
% 2.54/2.00 % (29968)Termination phase: Saturation
% 2.54/2.00
% 2.54/2.00 % (29968)Memory used [KB]: 8699
% 2.54/2.00 % (29968)Time elapsed: 0.354 s
% 2.54/2.00 % (29989)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_29850 for (2995ds/46Mi)
% 2.54/2.00 % (29968)Instructions burned: 710 (million)
% 2.54/2.00 % (29968)------------------------------
% 2.54/2.00 % (29968)------------------------------
% 2.54/2.01 % (29990)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_29850 for (2995ds/98Mi)
% 2.54/2.01 % (29987)Instruction limit reached!
% 2.54/2.01 % (29987)------------------------------
% 2.54/2.01 % (29987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.01 % (29987)Termination reason: Unknown
% 2.54/2.01 % (29987)Termination phase: Function definition elimination
% 2.54/2.01
% 2.54/2.01 % (29987)Memory used [KB]: 1535
% 2.54/2.01 % (29987)Time elapsed: 0.019 s
% 2.54/2.01 % (29987)Instructions burned: 39 (million)
% 2.54/2.01 % (29987)------------------------------
% 2.54/2.01 % (29987)------------------------------
% 2.54/2.02 % (29991)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_29850 for (2995ds/507Mi)
% 2.54/2.02 % (29989)Instruction limit reached!
% 2.54/2.02 % (29989)------------------------------
% 2.54/2.02 % (29989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.02 % (29989)Termination reason: Unknown
% 2.54/2.02 % (29989)Termination phase: Twee Goal Transformation
% 2.54/2.02
% 2.54/2.02 % (29989)Memory used [KB]: 1535
% 2.54/2.02 % (29989)Time elapsed: 0.021 s
% 2.54/2.02 % (29989)Instructions burned: 47 (million)
% 2.54/2.02 % (29989)------------------------------
% 2.54/2.02 % (29989)------------------------------
% 5.68/2.03 % (29992)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_29850 for (2995ds/149Mi)
% 5.68/2.04 % (29993)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29850 for (2995ds/39Mi)
% 5.68/2.05 % (29990)Instruction limit reached!
% 5.68/2.05 % (29990)------------------------------
% 5.68/2.05 % (29990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.05 % (29990)Termination reason: Unknown
% 5.68/2.05 % (29990)Termination phase: Saturation
% 5.68/2.05
% 5.68/2.05 % (29990)Memory used [KB]: 1663
% 5.68/2.05 % (29990)Time elapsed: 0.043 s
% 5.68/2.05 % (29990)Instructions burned: 99 (million)
% 5.68/2.05 % (29990)------------------------------
% 5.68/2.05 % (29990)------------------------------
% 5.68/2.05 % (29993)Instruction limit reached!
% 5.68/2.05 % (29993)------------------------------
% 5.68/2.05 % (29993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.05 % (29993)Termination reason: Unknown
% 5.68/2.05 % (29993)Termination phase: Function definition elimination
% 5.68/2.05
% 5.68/2.05 % (29993)Memory used [KB]: 1535
% 5.68/2.05 % (29993)Time elapsed: 0.020 s
% 5.68/2.05 % (29993)Instructions burned: 40 (million)
% 5.68/2.05 % (29993)------------------------------
% 5.68/2.05 % (29993)------------------------------
% 5.68/2.06 % (29994)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_29850 for (2995ds/6Mi)
% 5.68/2.07 % (29994)Instruction limit reached!
% 5.68/2.07 % (29994)------------------------------
% 5.68/2.07 % (29994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.07 % (29994)Termination reason: Unknown
% 5.68/2.07 % (29994)Termination phase: shuffling
% 5.68/2.07
% 5.68/2.07 % (29994)Memory used [KB]: 1279
% 5.68/2.07 % (29994)Time elapsed: 0.005 s
% 5.68/2.07 % (29994)Instructions burned: 7 (million)
% 5.68/2.07 % (29994)------------------------------
% 5.68/2.07 % (29994)------------------------------
% 5.68/2.07 % (29995)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_29850 for (2995ds/1087Mi)
% 5.68/2.08 % (29996)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29850 for (2994ds/47Mi)
% 5.68/2.10 % (29992)Instruction limit reached!
% 5.68/2.10 % (29992)------------------------------
% 5.68/2.10 % (29992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.10 % (29992)Termination reason: Unknown
% 5.68/2.10 % (29992)Termination phase: Saturation
% 5.68/2.10
% 5.68/2.10 % (29992)Memory used [KB]: 6652
% 5.68/2.10 % (29992)Time elapsed: 0.075 s
% 5.68/2.10 % (29992)Instructions burned: 150 (million)
% 5.68/2.10 % (29992)------------------------------
% 5.68/2.10 % (29992)------------------------------
% 5.68/2.10 % (29996)Instruction limit reached!
% 5.68/2.10 % (29996)------------------------------
% 5.68/2.10 % (29996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.10 % (29996)Termination reason: Unknown
% 5.68/2.10 % (29996)Termination phase: Property scanning
% 5.68/2.10
% 5.68/2.10 % (29996)Memory used [KB]: 1535
% 5.68/2.10 % (29996)Time elapsed: 0.023 s
% 5.68/2.10 % (29996)Instructions burned: 48 (million)
% 5.68/2.10 % (29996)------------------------------
% 5.68/2.10 % (29996)------------------------------
% 5.68/2.12 % (29997)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_29850 for (2994ds/44Mi)
% 5.68/2.12 % (29970)Instruction limit reached!
% 5.68/2.12 % (29970)------------------------------
% 5.68/2.12 % (29970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.68/2.12 % (29970)Termination reason: Unknown
% 5.68/2.12 % (29970)Termination phase: Saturation
% 5.68/2.12
% 5.68/2.12 % (29970)Memory used [KB]: 10874
% 5.68/2.12 % (29970)Time elapsed: 0.458 s
% 5.68/2.12 % (29970)Instructions burned: 903 (million)
% 5.68/2.12 % (29970)------------------------------
% 5.68/2.12 % (29970)------------------------------
% 5.68/2.12 % (29998)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_29850 for (2994ds/432Mi)
% 6.19/2.14 % (29997)Instruction limit reached!
% 6.19/2.14 % (29997)------------------------------
% 6.19/2.14 % (29997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.14 % (29997)Termination reason: Unknown
% 6.19/2.14 % (29997)Termination phase: Property scanning
% 6.19/2.14
% 6.19/2.14 % (29997)Memory used [KB]: 1663
% 6.19/2.14 % (29997)Time elapsed: 0.021 s
% 6.19/2.14 % (29997)Instructions burned: 44 (million)
% 6.19/2.14 % (29997)------------------------------
% 6.19/2.14 % (29997)------------------------------
% 6.19/2.14 % (29999)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29850 for (2994ds/62Mi)
% 6.19/2.15 % (30000)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_29850 for (2994ds/31Mi)
% 6.19/2.16 % (29977)Instruction limit reached!
% 6.19/2.16 % (29977)------------------------------
% 6.19/2.16 % (29977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.16 % (29977)Termination reason: Unknown
% 6.19/2.16 % (29977)Termination phase: Saturation
% 6.19/2.16
% 6.19/2.16 % (29977)Memory used [KB]: 7931
% 6.19/2.16 % (29977)Time elapsed: 0.433 s
% 6.19/2.16 % (29977)Instructions burned: 879 (million)
% 6.19/2.16 % (29977)------------------------------
% 6.19/2.16 % (29977)------------------------------
% 6.19/2.16 % (29988)Instruction limit reached!
% 6.19/2.16 % (29988)------------------------------
% 6.19/2.16 % (29988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.16 % (29988)Termination reason: Unknown
% 6.19/2.16 % (29988)Termination phase: Saturation
% 6.19/2.16
% 6.19/2.16 % (29988)Memory used [KB]: 6396
% 6.19/2.16 % (29988)Time elapsed: 0.169 s
% 6.19/2.16 % (29988)Instructions burned: 450 (million)
% 6.19/2.16 % (29988)------------------------------
% 6.19/2.16 % (29988)------------------------------
% 6.19/2.16 % (29999)Instruction limit reached!
% 6.19/2.16 % (29999)------------------------------
% 6.19/2.16 % (29999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.16 % (29999)Termination reason: Unknown
% 6.19/2.16 % (29999)Termination phase: Saturation
% 6.19/2.16
% 6.19/2.16 % (29999)Memory used [KB]: 6140
% 6.19/2.16 % (29999)Time elapsed: 0.029 s
% 6.19/2.16 % (29999)Instructions burned: 62 (million)
% 6.19/2.16 % (29999)------------------------------
% 6.19/2.16 % (29999)------------------------------
% 6.19/2.17 % (30000)Instruction limit reached!
% 6.19/2.17 % (30000)------------------------------
% 6.19/2.17 % (30000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.17 % (30000)Termination reason: Unknown
% 6.19/2.17 % (30000)Termination phase: Property scanning
% 6.19/2.17
% 6.19/2.17 % (30000)Memory used [KB]: 1535
% 6.19/2.17 % (30000)Time elapsed: 0.016 s
% 6.19/2.17 % (30000)Instructions burned: 31 (million)
% 6.19/2.17 % (30000)------------------------------
% 6.19/2.17 % (30000)------------------------------
% 6.19/2.17 % (30001)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29850 for (2994ds/96Mi)
% 6.19/2.18 % (30002)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_29850 for (2993ds/453Mi)
% 6.19/2.18 % (30003)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_29850 for (2993ds/71Mi)
% 6.19/2.18 % (30004)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_29850 for (2993ds/83Mi)
% 6.38/2.21 % (30003)Instruction limit reached!
% 6.38/2.21 % (30003)------------------------------
% 6.38/2.21 % (30003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.21 % (30003)Termination reason: Unknown
% 6.38/2.21 % (30003)Termination phase: Saturation
% 6.38/2.21
% 6.38/2.21 % (30003)Memory used [KB]: 6268
% 6.38/2.21 % (30003)Time elapsed: 0.034 s
% 6.38/2.21 % (30003)Instructions burned: 72 (million)
% 6.38/2.21 % (30003)------------------------------
% 6.38/2.21 % (30003)------------------------------
% 6.38/2.22 % (30001)Instruction limit reached!
% 6.38/2.22 % (30001)------------------------------
% 6.38/2.22 % (30001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.22 % (30001)Termination reason: Unknown
% 6.38/2.22 % (30001)Termination phase: Saturation
% 6.38/2.22
% 6.38/2.22 % (30001)Memory used [KB]: 6524
% 6.38/2.22 % (30001)Time elapsed: 0.045 s
% 6.38/2.22 % (30001)Instructions burned: 97 (million)
% 6.38/2.22 % (30001)------------------------------
% 6.38/2.22 % (30001)------------------------------
% 6.38/2.22 % (30004)Instruction limit reached!
% 6.38/2.22 % (30004)------------------------------
% 6.38/2.22 % (30004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.22 % (30004)Termination reason: Unknown
% 6.38/2.22 % (30004)Termination phase: Saturation
% 6.38/2.22
% 6.38/2.22 % (30004)Memory used [KB]: 6268
% 6.38/2.22 % (30004)Time elapsed: 0.038 s
% 6.38/2.22 % (30004)Instructions burned: 84 (million)
% 6.38/2.22 % (30004)------------------------------
% 6.38/2.22 % (30004)------------------------------
% 6.38/2.23 % (30005)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_29850 for (2993ds/11Mi)
% 6.38/2.23 % (30006)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_29850 for (2993ds/41Mi)
% 6.38/2.23 % (30005)Instruction limit reached!
% 6.38/2.23 % (30005)------------------------------
% 6.38/2.23 % (30005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.23 % (30005)Termination reason: Unknown
% 6.38/2.23 % (30005)Termination phase: shuffling
% 6.38/2.23
% 6.38/2.23 % (30005)Memory used [KB]: 1407
% 6.38/2.23 % (30005)Time elapsed: 0.007 s
% 6.38/2.23 % (30005)Instructions burned: 12 (million)
% 6.38/2.23 % (30005)------------------------------
% 6.38/2.23 % (30005)------------------------------
% 6.38/2.23 % (30007)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29850 for (2993ds/6Mi)
% 6.38/2.24 % (30007)Instruction limit reached!
% 6.38/2.24 % (30007)------------------------------
% 6.38/2.24 % (30007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.24 % (30007)Termination reason: Unknown
% 6.38/2.24 % (30007)Termination phase: shuffling
% 6.38/2.24
% 6.38/2.24 % (30007)Memory used [KB]: 1279
% 6.38/2.24 % (30007)Time elapsed: 0.004 s
% 6.38/2.24 % (30007)Instructions burned: 6 (million)
% 6.38/2.24 % (30007)------------------------------
% 6.38/2.24 % (30007)------------------------------
% 6.38/2.25 % (30008)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_29850 for (2993ds/150Mi)
% 6.38/2.25 % (30006)Instruction limit reached!
% 6.38/2.25 % (30006)------------------------------
% 6.38/2.25 % (30006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.25 % (30006)Termination reason: Unknown
% 6.38/2.25 % (30006)Termination phase: Function definition elimination
% 6.38/2.25
% 6.38/2.25 % (30006)Memory used [KB]: 1663
% 6.38/2.25 % (30006)Time elapsed: 0.019 s
% 6.38/2.25 % (30006)Instructions burned: 41 (million)
% 6.38/2.25 % (30006)------------------------------
% 6.38/2.25 % (30006)------------------------------
% 6.38/2.26 % (29991)Instruction limit reached!
% 6.38/2.26 % (29991)------------------------------
% 6.38/2.26 % (29991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.26 % (29991)Termination reason: Unknown
% 6.38/2.26 % (29991)Termination phase: Saturation
% 6.38/2.26
% 6.38/2.26 % (29991)Memory used [KB]: 7164
% 6.38/2.26 % (29991)Time elapsed: 0.242 s
% 6.38/2.26 % (29991)Instructions burned: 507 (million)
% 6.38/2.26 % (29991)------------------------------
% 6.38/2.26 % (29991)------------------------------
% 6.38/2.27 % (30009)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_29850 for (2993ds/343Mi)
% 6.38/2.27 % (30010)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_29850 for (2993ds/109Mi)
% 6.38/2.28 % (30011)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_29850 for (2993ds/253Mi)
% 6.38/2.29 % (29998)Instruction limit reached!
% 6.38/2.29 % (29998)------------------------------
% 6.38/2.29 % (29998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.29 % (29998)Termination reason: Unknown
% 6.38/2.29 % (29998)Termination phase: Saturation
% 6.38/2.29
% 6.38/2.29 % (29998)Memory used [KB]: 2430
% 6.38/2.29 % (29998)Time elapsed: 0.175 s
% 6.38/2.29 % (29998)Instructions burned: 434 (million)
% 6.38/2.29 % (29998)------------------------------
% 6.38/2.29 % (29998)------------------------------
% 7.08/2.31 % (30012)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_29850 for (2992ds/140Mi)
% 7.08/2.31 % (30010)Instruction limit reached!
% 7.08/2.31 % (30010)------------------------------
% 7.08/2.31 % (30010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.31 % (30010)Termination reason: Unknown
% 7.08/2.31 % (30010)Termination phase: Saturation
% 7.08/2.31
% 7.08/2.31 % (30010)Memory used [KB]: 6652
% 7.08/2.31 % (30010)Time elapsed: 0.050 s
% 7.08/2.31 % (30010)Instructions burned: 109 (million)
% 7.08/2.31 % (30010)------------------------------
% 7.08/2.31 % (30010)------------------------------
% 7.08/2.32 % (30008)Instruction limit reached!
% 7.08/2.32 % (30008)------------------------------
% 7.08/2.32 % (30008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.32 % (30008)Termination reason: Unknown
% 7.08/2.32 % (30008)Termination phase: Saturation
% 7.08/2.32
% 7.08/2.32 % (30008)Memory used [KB]: 7419
% 7.08/2.32 % (30008)Time elapsed: 0.075 s
% 7.08/2.32 % (30008)Instructions burned: 151 (million)
% 7.08/2.32 % (30008)------------------------------
% 7.08/2.32 % (30008)------------------------------
% 7.08/2.33 % (30013)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_29850 for (2992ds/614Mi)
% 7.08/2.34 % (30014)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_29850 for (2992ds/202Mi)
% 7.08/2.35 % (30002)Instruction limit reached!
% 7.08/2.35 % (30002)------------------------------
% 7.08/2.35 % (30002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.35 % (30002)Termination reason: Unknown
% 7.08/2.35 % (30002)Termination phase: Saturation
% 7.08/2.35
% 7.08/2.35 % (30002)Memory used [KB]: 6268
% 7.08/2.35 % (30002)Time elapsed: 0.169 s
% 7.08/2.35 % (30002)Instructions burned: 454 (million)
% 7.08/2.35 % (30002)------------------------------
% 7.08/2.35 % (30002)------------------------------
% 7.08/2.36 % (30015)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_29850 for (2992ds/339Mi)
% 7.08/2.37 % (30012)Instruction limit reached!
% 7.08/2.37 % (30012)------------------------------
% 7.08/2.37 % (30012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.08/2.37 % (30012)Termination reason: Unknown
% 7.08/2.37 % (30012)Termination phase: Saturation
% 7.08/2.37
% 7.08/2.37 % (30012)Memory used [KB]: 6268
% 7.08/2.37 % (30012)Time elapsed: 0.065 s
% 7.08/2.37 % (30012)Instructions burned: 142 (million)
% 7.08/2.37 % (30012)------------------------------
% 7.08/2.37 % (30012)------------------------------
% 7.08/2.39 % (30016)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_29850 for (2991ds/283Mi)
% 7.49/2.40 % (30011)Instruction limit reached!
% 7.49/2.40 % (30011)------------------------------
% 7.49/2.40 % (30011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.40 % (30011)Termination reason: Unknown
% 7.49/2.40 % (30011)Termination phase: Saturation
% 7.49/2.40
% 7.49/2.40 % (30011)Memory used [KB]: 7803
% 7.49/2.40 % (30011)Time elapsed: 0.126 s
% 7.49/2.40 % (30011)Instructions burned: 253 (million)
% 7.49/2.40 % (30011)------------------------------
% 7.49/2.40 % (30011)------------------------------
% 7.49/2.42 % (30017)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_29850 for (2991ds/134Mi)
% 7.49/2.43 % (30009)Instruction limit reached!
% 7.49/2.43 % (30009)------------------------------
% 7.49/2.43 % (30009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.43 % (30009)Termination reason: Unknown
% 7.49/2.43 % (30009)Termination phase: Saturation
% 7.49/2.43
% 7.49/2.43 % (30009)Memory used [KB]: 7291
% 7.49/2.43 % (30009)Time elapsed: 0.192 s
% 7.49/2.43 % (30009)Instructions burned: 343 (million)
% 7.49/2.43 % (30009)------------------------------
% 7.49/2.43 % (30009)------------------------------
% 7.49/2.44 % (30014)Instruction limit reached!
% 7.49/2.44 % (30014)------------------------------
% 7.49/2.44 % (30014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.44 % (30014)Termination reason: Unknown
% 7.49/2.44 % (30014)Termination phase: Saturation
% 7.49/2.44
% 7.49/2.44 % (30014)Memory used [KB]: 7675
% 7.49/2.44 % (30014)Time elapsed: 0.103 s
% 7.49/2.44 % (30014)Instructions burned: 203 (million)
% 7.49/2.44 % (30014)------------------------------
% 7.49/2.44 % (30014)------------------------------
% 7.49/2.45 % (30018)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_29850 for (2991ds/298Mi)
% 7.49/2.46 % (30019)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_29850 for (2991ds/192Mi)
% 7.49/2.48 % (30017)Instruction limit reached!
% 7.49/2.48 % (30017)------------------------------
% 7.49/2.48 % (30017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.48 % (30017)Termination reason: Unknown
% 7.49/2.48 % (30017)Termination phase: Saturation
% 7.49/2.48
% 7.49/2.48 % (30017)Memory used [KB]: 6908
% 7.49/2.48 % (30017)Time elapsed: 0.065 s
% 7.49/2.48 % (30017)Instructions burned: 134 (million)
% 7.49/2.48 % (30017)------------------------------
% 7.49/2.48 % (30017)------------------------------
% 8.01/2.50 % (30020)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_29850 for (2990ds/258Mi)
% 8.01/2.50 % (30016)Instruction limit reached!
% 8.01/2.50 % (30016)------------------------------
% 8.01/2.50 % (30016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.50 % (30016)Termination reason: Unknown
% 8.01/2.50 % (30016)Termination phase: Saturation
% 8.01/2.50
% 8.01/2.50 % (30016)Memory used [KB]: 8315
% 8.01/2.50 % (30016)Time elapsed: 0.116 s
% 8.01/2.50 % (30016)Instructions burned: 285 (million)
% 8.01/2.50 % (30016)------------------------------
% 8.01/2.50 % (30016)------------------------------
% 8.01/2.52 % (30015)Instruction limit reached!
% 8.01/2.52 % (30015)------------------------------
% 8.01/2.52 % (30015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.52 % (30015)Termination reason: Unknown
% 8.01/2.52 % (30015)Termination phase: Saturation
% 8.01/2.52
% 8.01/2.52 % (30015)Memory used [KB]: 7547
% 8.01/2.52 % (30015)Time elapsed: 0.159 s
% 8.01/2.52 % (30015)Instructions burned: 340 (million)
% 8.01/2.52 % (30015)------------------------------
% 8.01/2.52 % (30015)------------------------------
% 8.01/2.52 % (30021)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_29850 for (2990ds/90Mi)
% 8.01/2.54 % (30022)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_29850 for (2990ds/231Mi)
% 8.01/2.55 % (30019)Instruction limit reached!
% 8.01/2.55 % (30019)------------------------------
% 8.01/2.55 % (30019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.55 % (30019)Termination reason: Unknown
% 8.01/2.55 % (30019)Termination phase: Saturation
% 8.01/2.55
% 8.01/2.55 % (30019)Memory used [KB]: 7036
% 8.01/2.55 % (30019)Time elapsed: 0.092 s
% 8.01/2.55 % (30019)Instructions burned: 193 (million)
% 8.01/2.55 % (30019)------------------------------
% 8.01/2.55 % (30019)------------------------------
% 8.01/2.56 % (30021)Instruction limit reached!
% 8.01/2.56 % (30021)------------------------------
% 8.01/2.56 % (30021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.56 % (30021)Termination reason: Unknown
% 8.01/2.56 % (30021)Termination phase: Saturation
% 8.01/2.56
% 8.01/2.56 % (30021)Memory used [KB]: 6524
% 8.01/2.56 % (30021)Time elapsed: 0.043 s
% 8.01/2.56 % (30021)Instructions burned: 91 (million)
% 8.01/2.56 % (30021)------------------------------
% 8.01/2.56 % (30021)------------------------------
% 8.01/2.56 % (30023)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_29850 for (2990ds/458Mi)
% 8.01/2.57 % (30018)Instruction limit reached!
% 8.01/2.57 % (30018)------------------------------
% 8.01/2.57 % (30018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.57 % (30018)Termination reason: Unknown
% 8.01/2.57 % (30018)Termination phase: Saturation
% 8.01/2.57
% 8.01/2.57 % (30018)Memory used [KB]: 6396
% 8.01/2.57 % (30018)Time elapsed: 0.126 s
% 8.01/2.57 % (30018)Instructions burned: 300 (million)
% 8.01/2.57 % (30018)------------------------------
% 8.01/2.57 % (30018)------------------------------
% 8.01/2.58 % (30024)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_29850 for (2990ds/31Mi)
% 8.01/2.59 % (30025)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_29850 for (2990ds/297Mi)
% 8.01/2.59 % (30024)Instruction limit reached!
% 8.01/2.59 % (30024)------------------------------
% 8.01/2.59 % (30024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.01/2.59 % (30024)Termination reason: Unknown
% 8.01/2.59 % (30024)Termination phase: Property scanning
% 8.01/2.59
% 8.01/2.59 % (30024)Memory used [KB]: 1535
% 8.01/2.59 % (30024)Time elapsed: 0.016 s
% 8.01/2.59 % (30024)Instructions burned: 32 (million)
% 8.01/2.59 % (30024)------------------------------
% 8.01/2.59 % (30024)------------------------------
% 8.65/2.60 % (29995)Instruction limit reached!
% 8.65/2.60 % (29995)------------------------------
% 8.65/2.60 % (29995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.60 % (29995)Termination reason: Unknown
% 8.65/2.60 % (29995)Termination phase: Saturation
% 8.65/2.60
% 8.65/2.60 % (29995)Memory used [KB]: 9978
% 8.65/2.60 % (29995)Time elapsed: 0.533 s
% 8.65/2.60 % (29995)Instructions burned: 1087 (million)
% 8.65/2.60 % (29995)------------------------------
% 8.65/2.60 % (29995)------------------------------
% 8.65/2.61 % (30026)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_29850 for (2989ds/987Mi)
% 8.65/2.62 % (30027)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_29850 for (2989ds/182Mi)
% 8.65/2.62 % (30020)Instruction limit reached!
% 8.65/2.62 % (30020)------------------------------
% 8.65/2.62 % (30020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.62 % (30020)Termination reason: Unknown
% 8.65/2.62 % (30020)Termination phase: Saturation
% 8.65/2.62
% 8.65/2.62 % (30020)Memory used [KB]: 7036
% 8.65/2.62 % (30020)Time elapsed: 0.127 s
% 8.65/2.62 % (30020)Instructions burned: 258 (million)
% 8.65/2.62 % (30020)------------------------------
% 8.65/2.62 % (30020)------------------------------
% 8.65/2.63 % (30013)Instruction limit reached!
% 8.65/2.63 % (30013)------------------------------
% 8.65/2.63 % (30013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.63 % (30013)Termination reason: Unknown
% 8.65/2.63 % (30013)Termination phase: Saturation
% 8.65/2.63
% 8.65/2.63 % (30013)Memory used [KB]: 7931
% 8.65/2.63 % (30013)Time elapsed: 0.302 s
% 8.65/2.63 % (30013)Instructions burned: 614 (million)
% 8.65/2.63 % (30013)------------------------------
% 8.65/2.63 % (30013)------------------------------
% 8.65/2.64 % (30028)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_29850 for (2989ds/182Mi)
% 8.65/2.65 % (30022)Instruction limit reached!
% 8.65/2.65 % (30022)------------------------------
% 8.65/2.65 % (30022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.65 % (30022)Termination reason: Unknown
% 8.65/2.65 % (30022)Termination phase: Saturation
% 8.65/2.65
% 8.65/2.65 % (30022)Memory used [KB]: 9722
% 8.65/2.65 % (30022)Time elapsed: 0.112 s
% 8.65/2.65 % (30022)Instructions burned: 232 (million)
% 8.65/2.65 % (30022)------------------------------
% 8.65/2.65 % (30022)------------------------------
% 8.65/2.65 % (30029)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_29850 for (2989ds/154Mi)
% 8.65/2.66 % (30030)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_29850 for (2989ds/79Mi)
% 9.78/2.70 % (30030)Instruction limit reached!
% 9.78/2.70 % (30030)------------------------------
% 9.78/2.70 % (30030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.70 % (30030)Termination reason: Unknown
% 9.78/2.70 % (30030)Termination phase: Saturation
% 9.78/2.70
% 9.78/2.70 % (30030)Memory used [KB]: 6396
% 9.78/2.70 % (30030)Time elapsed: 0.037 s
% 9.78/2.70 % (30030)Instructions burned: 79 (million)
% 9.78/2.70 % (30030)------------------------------
% 9.78/2.70 % (30030)------------------------------
% 9.78/2.70 % (30027)Instruction limit reached!
% 9.78/2.70 % (30027)------------------------------
% 9.78/2.70 % (30027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.70 % (30027)Termination reason: Unknown
% 9.78/2.70 % (30027)Termination phase: Saturation
% 9.78/2.70
% 9.78/2.70 % (30027)Memory used [KB]: 6908
% 9.78/2.70 % (30027)Time elapsed: 0.085 s
% 9.78/2.70 % (30027)Instructions burned: 183 (million)
% 9.78/2.70 % (30027)------------------------------
% 9.78/2.70 % (30027)------------------------------
% 9.78/2.70 % (30025)Instruction limit reached!
% 9.78/2.70 % (30025)------------------------------
% 9.78/2.70 % (30025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.70 % (30025)Termination reason: Unknown
% 9.78/2.70 % (30025)Termination phase: Saturation
% 9.78/2.70
% 9.78/2.70 % (30025)Memory used [KB]: 7547
% 9.78/2.70 % (30025)Time elapsed: 0.116 s
% 9.78/2.70 % (30025)Instructions burned: 297 (million)
% 9.78/2.70 % (30025)------------------------------
% 9.78/2.70 % (30025)------------------------------
% 9.78/2.71 % (30029)Instruction limit reached!
% 9.78/2.71 % (30029)------------------------------
% 9.78/2.71 % (30029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.71 % (30029)Termination reason: Unknown
% 9.78/2.71 % (30029)Termination phase: Saturation
% 9.78/2.71
% 9.78/2.71 % (30029)Memory used [KB]: 6268
% 9.78/2.71 % (30029)Time elapsed: 0.063 s
% 9.78/2.71 % (30029)Instructions burned: 156 (million)
% 9.78/2.71 % (30029)------------------------------
% 9.78/2.71 % (30029)------------------------------
% 9.78/2.71 % (30031)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_29850 for (2988ds/216Mi)
% 9.78/2.72 % (30032)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_29850 for (2988ds/114Mi)
% 9.78/2.72 % (30033)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_29850 for (2988ds/922Mi)
% 9.78/2.73 % (30034)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_29850 for (2988ds/182Mi)
% 9.78/2.73 % (30028)Instruction limit reached!
% 9.78/2.73 % (30028)------------------------------
% 9.78/2.73 % (30028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.73 % (30028)Termination reason: Unknown
% 9.78/2.73 % (30028)Termination phase: Saturation
% 9.78/2.73
% 9.78/2.73 % (30028)Memory used [KB]: 8699
% 9.78/2.73 % (30028)Time elapsed: 0.119 s
% 9.78/2.73 % (30028)Instructions burned: 183 (million)
% 9.78/2.73 % (30028)------------------------------
% 9.78/2.73 % (30028)------------------------------
% 9.78/2.75 % (30035)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_29850 for (2988ds/164Mi)
% 9.78/2.77 % (30032)Instruction limit reached!
% 9.78/2.77 % (30032)------------------------------
% 9.78/2.77 % (30032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.77 % (30032)Termination reason: Unknown
% 9.78/2.77 % (30032)Termination phase: Saturation
% 9.78/2.77
% 9.78/2.77 % (30032)Memory used [KB]: 6652
% 9.78/2.77 % (30032)Time elapsed: 0.052 s
% 9.78/2.77 % (30032)Instructions burned: 115 (million)
% 9.78/2.77 % (30032)------------------------------
% 9.78/2.77 % (30032)------------------------------
% 9.78/2.78 % (30036)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/50Mi)
% 9.78/2.79 % (30023)Instruction limit reached!
% 9.78/2.79 % (30023)------------------------------
% 9.78/2.79 % (30023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.79 % (30023)Termination reason: Unknown
% 9.78/2.79 % (30023)Termination phase: Saturation
% 9.78/2.79
% 9.78/2.79 % (30023)Memory used [KB]: 7291
% 9.78/2.79 % (30023)Time elapsed: 0.229 s
% 9.78/2.79 % (30023)Instructions burned: 459 (million)
% 9.78/2.79 % (30023)------------------------------
% 9.78/2.79 % (30023)------------------------------
% 10.55/2.80 % (30034)Instruction limit reached!
% 10.55/2.80 % (30034)------------------------------
% 10.55/2.80 % (30034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.80 % (30034)Termination reason: Unknown
% 10.55/2.80 % (30034)Termination phase: Saturation
% 10.55/2.80
% 10.55/2.80 % (30034)Memory used [KB]: 6268
% 10.55/2.80 % (30034)Time elapsed: 0.073 s
% 10.55/2.80 % (30034)Instructions burned: 183 (million)
% 10.55/2.80 % (30034)------------------------------
% 10.55/2.80 % (30034)------------------------------
% 10.55/2.80 % (30031)Instruction limit reached!
% 10.55/2.80 % (30031)------------------------------
% 10.55/2.80 % (30031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.80 % (30031)Termination reason: Unknown
% 10.55/2.80 % (30031)Termination phase: Saturation
% 10.55/2.80
% 10.55/2.80 % (30031)Memory used [KB]: 7036
% 10.55/2.80 % (30031)Time elapsed: 0.088 s
% 10.55/2.80 % (30031)Instructions burned: 217 (million)
% 10.55/2.80 % (30031)------------------------------
% 10.55/2.80 % (30031)------------------------------
% 10.55/2.80 % (30036)Instruction limit reached!
% 10.55/2.80 % (30036)------------------------------
% 10.55/2.80 % (30036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.80 % (30036)Termination reason: Unknown
% 10.55/2.80 % (30036)Termination phase: Property scanning
% 10.55/2.80
% 10.55/2.80 % (30036)Memory used [KB]: 1663
% 10.55/2.80 % (30036)Time elapsed: 0.023 s
% 10.55/2.80 % (30036)Instructions burned: 50 (million)
% 10.55/2.80 % (30036)------------------------------
% 10.55/2.80 % (30036)------------------------------
% 10.55/2.81 % (30037)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/368Mi)
% 10.55/2.81 % (30038)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/1021Mi)
% 10.55/2.82 % (30039)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/267Mi)
% 10.55/2.82 % (30040)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/204Mi)
% 10.55/2.82 % (30035)Instruction limit reached!
% 10.55/2.82 % (30035)------------------------------
% 10.55/2.82 % (30035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.82 % (30035)Termination reason: Unknown
% 10.55/2.82 % (30035)Termination phase: Saturation
% 10.55/2.82
% 10.55/2.82 % (30035)Memory used [KB]: 2174
% 10.55/2.82 % (30035)Time elapsed: 0.078 s
% 10.55/2.82 % (30035)Instructions burned: 164 (million)
% 10.55/2.82 % (30035)------------------------------
% 10.55/2.82 % (30035)------------------------------
% 10.55/2.84 % (30041)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/26Mi)
% 10.55/2.85 % (30041)Instruction limit reached!
% 10.55/2.85 % (30041)------------------------------
% 10.55/2.85 % (30041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.85 % (30041)Termination reason: Unknown
% 10.55/2.85 % (30041)Termination phase: Property scanning
% 10.55/2.85
% 10.55/2.85 % (30041)Memory used [KB]: 1535
% 10.55/2.85 % (30041)Time elapsed: 0.013 s
% 10.55/2.85 % (30041)Instructions burned: 28 (million)
% 10.55/2.85 % (30041)------------------------------
% 10.55/2.85 % (30041)------------------------------
% 10.55/2.87 % (30042)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_29850 for (2987ds/53Mi)
% 10.55/2.89 % (30042)Instruction limit reached!
% 10.55/2.89 % (30042)------------------------------
% 10.55/2.89 % (30042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.89 % (30042)Termination reason: Unknown
% 10.55/2.89 % (30042)Termination phase: Property scanning
% 10.55/2.89
% 10.55/2.89 % (30042)Memory used [KB]: 1663
% 10.55/2.89 % (30042)Time elapsed: 0.024 s
% 10.55/2.89 % (30042)Instructions burned: 54 (million)
% 10.55/2.89 % (30042)------------------------------
% 10.55/2.89 % (30042)------------------------------
% 10.94/2.91 % (30043)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_29850 for (2986ds/4436Mi)
% 10.94/2.91 % (30040)Instruction limit reached!
% 10.94/2.91 % (30040)------------------------------
% 10.94/2.91 % (30040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.91 % (30040)Termination reason: Unknown
% 10.94/2.91 % (30040)Termination phase: Saturation
% 10.94/2.91
% 10.94/2.91 % (30040)Memory used [KB]: 6908
% 10.94/2.91 % (30040)Time elapsed: 0.095 s
% 10.94/2.91 % (30040)Instructions burned: 204 (million)
% 10.94/2.91 % (30040)------------------------------
% 10.94/2.91 % (30040)------------------------------
% 10.94/2.92 % (30039)Instruction limit reached!
% 10.94/2.92 % (30039)------------------------------
% 10.94/2.92 % (30039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.92 % (30039)Termination reason: Unknown
% 10.94/2.92 % (30039)Termination phase: Saturation
% 10.94/2.92
% 10.94/2.92 % (30039)Memory used [KB]: 8315
% 10.94/2.92 % (30039)Time elapsed: 0.110 s
% 10.94/2.92 % (30039)Instructions burned: 268 (million)
% 10.94/2.92 % (30039)------------------------------
% 10.94/2.92 % (30039)------------------------------
% 10.94/2.93 % (30044)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_29850 for (2986ds/1539Mi)
% 10.94/2.94 % (30045)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_29850 for (2986ds/408Mi)
% 10.94/2.98 % (30026)Instruction limit reached!
% 10.94/2.98 % (30026)------------------------------
% 10.94/2.98 % (30026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.98 % (30026)Termination reason: Unknown
% 10.94/2.98 % (30026)Termination phase: Saturation
% 10.94/2.98
% 10.94/2.98 % (30026)Memory used [KB]: 8187
% 10.94/2.98 % (30026)Time elapsed: 0.394 s
% 10.94/2.98 % (30026)Instructions burned: 988 (million)
% 10.94/2.98 % (30026)------------------------------
% 10.94/2.98 % (30026)------------------------------
% 10.94/2.99 % (30037)Instruction limit reached!
% 10.94/2.99 % (30037)------------------------------
% 10.94/2.99 % (30037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.94/2.99 % (30037)Termination reason: Unknown
% 10.94/2.99 % (30037)Termination phase: Saturation
% 10.94/2.99
% 10.94/2.99 % (30037)Memory used [KB]: 7291
% 10.94/2.99 % (30037)Time elapsed: 0.183 s
% 10.94/2.99 % (30037)Instructions burned: 369 (million)
% 10.94/2.99 % (30037)------------------------------
% 10.94/2.99 % (30037)------------------------------
% 10.94/3.00 % (30046)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_29850 for (2985ds/5205Mi)
% 10.94/3.01 % (30047)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_29850 for (2985ds/1913Mi)
% 13.38/3.15 % (30045)Instruction limit reached!
% 13.38/3.15 % (30045)------------------------------
% 13.38/3.15 % (30045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.38/3.15 % (30045)Termination reason: Unknown
% 13.38/3.15 % (30045)Termination phase: Saturation
% 13.38/3.15
% 13.38/3.15 % (30045)Memory used [KB]: 9083
% 13.38/3.15 % (30045)Time elapsed: 0.208 s
% 13.38/3.15 % (30045)Instructions burned: 409 (million)
% 13.38/3.15 % (30045)------------------------------
% 13.38/3.15 % (30045)------------------------------
% 13.38/3.16 % (30048)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_29850 for (2984ds/4350Mi)
% 13.38/3.18 % (30033)Instruction limit reached!
% 13.38/3.18 % (30033)------------------------------
% 13.38/3.18 % (30033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.38/3.18 % (30033)Termination reason: Unknown
% 13.38/3.18 % (30033)Termination phase: Saturation
% 13.38/3.18
% 13.38/3.18 % (30033)Memory used [KB]: 9083
% 13.38/3.18 % (30033)Time elapsed: 0.459 s
% 13.38/3.18 % (30033)Instructions burned: 922 (million)
% 13.38/3.18 % (30033)------------------------------
% 13.38/3.18 % (30033)------------------------------
% 13.38/3.19 % (30049)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_29850 for (2983ds/68Mi)
% 13.83/3.22 % (30049)Instruction limit reached!
% 13.83/3.22 % (30049)------------------------------
% 13.83/3.22 % (30049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.83/3.22 % (30049)Termination reason: Unknown
% 13.83/3.22 % (30049)Termination phase: Saturation
% 13.83/3.22
% 13.83/3.22 % (30049)Memory used [KB]: 6268
% 13.83/3.22 % (30049)Time elapsed: 0.032 s
% 13.83/3.22 % (30049)Instructions burned: 69 (million)
% 13.83/3.22 % (30049)------------------------------
% 13.83/3.22 % (30049)------------------------------
% 13.83/3.24 % (30050)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_29850 for (2983ds/358Mi)
% 14.37/3.33 % (30038)Instruction limit reached!
% 14.37/3.33 % (30038)------------------------------
% 14.37/3.33 % (30038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.37/3.33 % (30038)Termination reason: Unknown
% 14.37/3.33 % (30038)Termination phase: Saturation
% 14.37/3.33
% 14.37/3.33 % (30038)Memory used [KB]: 9466
% 14.37/3.33 % (30038)Time elapsed: 0.517 s
% 14.37/3.33 % (30038)Instructions burned: 1021 (million)
% 14.37/3.33 % (30038)------------------------------
% 14.37/3.33 % (30038)------------------------------
% 14.37/3.35 % (30051)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_29850 for (2982ds/31Mi)
% 14.37/3.36 % (30051)Instruction limit reached!
% 14.37/3.36 % (30051)------------------------------
% 14.37/3.36 % (30051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.37/3.36 % (30051)Termination reason: Unknown
% 14.37/3.36 % (30051)Termination phase: Property scanning
% 14.37/3.36
% 14.37/3.36 % (30051)Memory used [KB]: 1535
% 14.37/3.36 % (30051)Time elapsed: 0.016 s
% 14.37/3.36 % (30051)Instructions burned: 31 (million)
% 14.37/3.36 % (30051)------------------------------
% 14.37/3.36 % (30051)------------------------------
% 14.37/3.38 % (30052)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_29850 for (2982ds/279Mi)
% 14.85/3.41 % (30050)Instruction limit reached!
% 14.85/3.41 % (30050)------------------------------
% 14.85/3.41 % (30050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.41 % (30050)Termination reason: Unknown
% 14.85/3.41 % (30050)Termination phase: Saturation
% 14.85/3.41
% 14.85/3.41 % (30050)Memory used [KB]: 7164
% 14.85/3.41 % (30050)Time elapsed: 0.173 s
% 14.85/3.41 % (30050)Instructions burned: 359 (million)
% 14.85/3.41 % (30050)------------------------------
% 14.85/3.41 % (30050)------------------------------
% 14.85/3.43 % (30053)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_29850 for (2981ds/258Mi)
% 14.85/3.48 % (30052)Instruction limit reached!
% 14.85/3.48 % (30052)------------------------------
% 14.85/3.48 % (30052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.48 % (30052)Termination reason: Unknown
% 14.85/3.48 % (30052)Termination phase: Saturation
% 14.85/3.48
% 14.85/3.48 % (30052)Memory used [KB]: 6396
% 14.85/3.48 % (30052)Time elapsed: 0.110 s
% 14.85/3.48 % (30052)Instructions burned: 279 (million)
% 14.85/3.48 % (30052)------------------------------
% 14.85/3.48 % (30052)------------------------------
% 15.56/3.50 % (30054)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_29850 for (2980ds/26Mi)
% 15.56/3.51 % (30054)Instruction limit reached!
% 15.56/3.51 % (30054)------------------------------
% 15.56/3.51 % (30054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.56/3.51 % (30054)Termination reason: Unknown
% 15.56/3.51 % (30054)Termination phase: Property scanning
% 15.56/3.51
% 15.56/3.51 % (30054)Memory used [KB]: 1535
% 15.56/3.51 % (30054)Time elapsed: 0.014 s
% 15.56/3.51 % (30054)Instructions burned: 26 (million)
% 15.56/3.51 % (30054)------------------------------
% 15.56/3.51 % (30054)------------------------------
% 15.56/3.53 % (30055)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_29850 for (2980ds/995Mi)
% 15.56/3.55 % (30053)Instruction limit reached!
% 15.56/3.55 % (30053)------------------------------
% 15.56/3.55 % (30053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.56/3.55 % (30053)Termination reason: Unknown
% 15.56/3.55 % (30053)Termination phase: Saturation
% 15.56/3.55
% 15.56/3.55 % (30053)Memory used [KB]: 7803
% 15.56/3.55 % (30053)Time elapsed: 0.120 s
% 15.56/3.55 % (30053)Instructions burned: 259 (million)
% 15.56/3.55 % (30053)------------------------------
% 15.56/3.55 % (30053)------------------------------
% 15.56/3.56 % (30056)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_29850 for (2980ds/373Mi)
% 16.12/3.69 % (30044)Instruction limit reached!
% 16.12/3.69 % (30044)------------------------------
% 16.12/3.69 % (30044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.12/3.69 % (30044)Termination reason: Unknown
% 16.12/3.69 % (30044)Termination phase: Saturation
% 16.12/3.69
% 16.12/3.69 % (30044)Memory used [KB]: 8827
% 16.12/3.69 % (30044)Time elapsed: 0.758 s
% 16.12/3.69 % (30044)Instructions burned: 1539 (million)
% 16.12/3.69 % (30044)------------------------------
% 16.12/3.69 % (30044)------------------------------
% 16.51/3.70 % (30057)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_29850 for (2978ds/253Mi)
% 16.51/3.75 % (30056)Instruction limit reached!
% 16.51/3.75 % (30056)------------------------------
% 16.51/3.75 % (30056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.51/3.75 % (30056)Termination reason: Unknown
% 16.51/3.75 % (30056)Termination phase: Saturation
% 16.51/3.75
% 16.51/3.75 % (30056)Memory used [KB]: 7164
% 16.51/3.75 % (30056)Time elapsed: 0.185 s
% 16.51/3.75 % (30056)Instructions burned: 373 (million)
% 16.51/3.75 % (30056)------------------------------
% 16.51/3.75 % (30056)------------------------------
% 16.51/3.76 % (30058)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_29850 for (2978ds/832Mi)
% 17.00/3.80 % (30057)Instruction limit reached!
% 17.00/3.80 % (30057)------------------------------
% 17.00/3.80 % (30057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.00/3.80 % (30057)Termination reason: Unknown
% 17.00/3.80 % (30057)Termination phase: Saturation
% 17.00/3.80
% 17.00/3.80 % (30057)Memory used [KB]: 6268
% 17.00/3.80 % (30057)Time elapsed: 0.102 s
% 17.00/3.80 % (30057)Instructions burned: 255 (million)
% 17.00/3.80 % (30057)------------------------------
% 17.00/3.80 % (30057)------------------------------
% 17.00/3.82 % (30059)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_29850 for (2977ds/668Mi)
% 17.41/3.91 % (30055)Instruction limit reached!
% 17.41/3.91 % (30055)------------------------------
% 17.41/3.91 % (30055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.92 % (30055)Termination reason: Unknown
% 17.41/3.92 % (30055)Termination phase: Saturation
% 17.41/3.92
% 17.41/3.92 % (30055)Memory used [KB]: 8059
% 17.41/3.92 % (30055)Time elapsed: 0.387 s
% 17.41/3.92 % (30055)Instructions burned: 995 (million)
% 17.41/3.92 % (30055)------------------------------
% 17.41/3.92 % (30055)------------------------------
% 17.41/3.92 % (30047)Instruction limit reached!
% 17.41/3.92 % (30047)------------------------------
% 17.41/3.92 % (30047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.92 % (30047)Termination reason: Unknown
% 17.41/3.92 % (30047)Termination phase: Saturation
% 17.41/3.92
% 17.41/3.92 % (30047)Memory used [KB]: 3582
% 17.41/3.92 % (30047)Time elapsed: 0.916 s
% 17.41/3.92 % (30047)Instructions burned: 1914 (million)
% 17.41/3.92 % (30047)------------------------------
% 17.41/3.92 % (30047)------------------------------
% 17.41/3.93 % (30060)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_29850 for (2976ds/40Mi)
% 17.41/3.94 % (30061)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_29850 for (2976ds/294Mi)
% 17.41/3.95 % (30060)Instruction limit reached!
% 17.41/3.95 % (30060)------------------------------
% 17.41/3.95 % (30060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.41/3.95 % (30060)Termination reason: Unknown
% 17.41/3.95 % (30060)Termination phase: Function definition elimination
% 17.41/3.95
% 17.41/3.95 % (30060)Memory used [KB]: 1663
% 17.41/3.95 % (30060)Time elapsed: 0.019 s
% 17.41/3.95 % (30060)Instructions burned: 40 (million)
% 17.41/3.95 % (30060)------------------------------
% 17.41/3.95 % (30060)------------------------------
% 17.41/3.97 % (30062)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_29850 for (2976ds/187Mi)
% 19.66/4.06 % (30062)Instruction limit reached!
% 19.66/4.06 % (30062)------------------------------
% 19.66/4.06 % (30062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.66/4.06 % (30062)Termination reason: Unknown
% 19.66/4.06 % (30062)Termination phase: Saturation
% 19.66/4.06
% 19.66/4.06 % (30062)Memory used [KB]: 7036
% 19.66/4.06 % (30062)Time elapsed: 0.114 s
% 19.66/4.06 % (30062)Instructions burned: 187 (million)
% 19.66/4.06 % (30062)------------------------------
% 19.66/4.06 % (30062)------------------------------
% 19.66/4.06 % (30061)Instruction limit reached!
% 19.66/4.06 % (30061)------------------------------
% 19.66/4.06 % (30061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.66/4.06 % (30061)Termination reason: Unknown
% 19.66/4.06 % (30061)Termination phase: Saturation
% 19.66/4.06
% 19.66/4.06 % (30061)Memory used [KB]: 6268
% 19.66/4.06 % (30061)Time elapsed: 0.124 s
% 19.66/4.06 % (30061)Instructions burned: 294 (million)
% 19.66/4.06 % (30061)------------------------------
% 19.66/4.06 % (30061)------------------------------
% 19.66/4.07 % (30059)Instruction limit reached!
% 19.66/4.07 % (30059)------------------------------
% 19.66/4.07 % (30059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.66/4.07 % (30059)Termination reason: Unknown
% 19.66/4.07 % (30059)Termination phase: Saturation
% 19.66/4.07
% 19.66/4.07 % (30059)Memory used [KB]: 12665
% 19.66/4.07 % (30059)Time elapsed: 0.253 s
% 19.66/4.07 % (30059)Instructions burned: 668 (million)
% 19.66/4.07 % (30059)------------------------------
% 19.66/4.07 % (30059)------------------------------
% 19.66/4.07 % (30063)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_29850 for (2975ds/371Mi)
% 19.66/4.07 % (30064)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_29850 for (2975ds/1827Mi)
% 19.66/4.09 % (30065)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_29850 for (2975ds/70Mi)
% 19.66/4.12 % (30065)Instruction limit reached!
% 19.66/4.12 % (30065)------------------------------
% 19.66/4.12 % (30065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.66/4.12 % (30065)Termination reason: Unknown
% 19.66/4.12 % (30065)Termination phase: Saturation
% 19.66/4.12
% 19.66/4.12 % (30065)Memory used [KB]: 1663
% 19.66/4.12 % (30065)Time elapsed: 0.031 s
% 19.66/4.12 % (30065)Instructions burned: 70 (million)
% 19.66/4.12 % (30065)------------------------------
% 19.66/4.12 % (30065)------------------------------
% 20.25/4.13 % (30066)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_29850 for (2974ds/316Mi)
% 20.25/4.17 % (30058)Instruction limit reached!
% 20.25/4.17 % (30058)------------------------------
% 20.25/4.17 % (30058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.25/4.17 % (30058)Termination reason: Unknown
% 20.25/4.17 % (30058)Termination phase: Saturation
% 20.25/4.17
% 20.25/4.17 % (30058)Memory used [KB]: 8699
% 20.25/4.17 % (30058)Time elapsed: 0.408 s
% 20.25/4.17 % (30058)Instructions burned: 832 (million)
% 20.25/4.17 % (30058)------------------------------
% 20.25/4.17 % (30058)------------------------------
% 20.25/4.19 % (30067)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_29850 for (2974ds/932Mi)
% 20.51/4.25 % (30063)Refutation not found, non-redundant clauses discarded% (30063)------------------------------
% 20.51/4.25 % (30063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.51/4.25 % (30063)Termination reason: Refutation not found, non-redundant clauses discarded
% 20.51/4.25
% 20.51/4.25 % (30063)Memory used [KB]: 7291
% 20.51/4.25 % (30063)Time elapsed: 0.201 s
% 20.51/4.25 % (30063)Instructions burned: 361 (million)
% 20.51/4.25 % (30063)------------------------------
% 20.51/4.25 % (30063)------------------------------
% 20.51/4.26 % (30066)Instruction limit reached!
% 20.51/4.26 % (30066)------------------------------
% 20.51/4.26 % (30066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.51/4.26 % (30066)Termination reason: Unknown
% 20.51/4.26 % (30066)Termination phase: Saturation
% 20.51/4.26
% 20.51/4.26 % (30066)Memory used [KB]: 6780
% 20.51/4.26 % (30066)Time elapsed: 0.151 s
% 20.51/4.26 % (30066)Instructions burned: 318 (million)
% 20.51/4.26 % (30066)------------------------------
% 20.51/4.26 % (30066)------------------------------
% 20.51/4.27 % (30068)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_29850 for (2973ds/4714Mi)
% 20.51/4.28 % (30069)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_29850 for (2973ds/8250Mi)
% 21.75/4.56 % (30067)Instruction limit reached!
% 21.75/4.56 % (30067)------------------------------
% 21.75/4.56 % (30067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.75/4.56 % (30067)Termination reason: Unknown
% 21.75/4.56 % (30067)Termination phase: Saturation
% 21.75/4.56
% 21.75/4.56 % (30067)Memory used [KB]: 8571
% 21.75/4.56 % (30067)Time elapsed: 0.400 s
% 21.75/4.56 % (30067)Instructions burned: 933 (million)
% 21.75/4.56 % (30067)------------------------------
% 21.75/4.56 % (30067)------------------------------
% 21.75/4.58 % (30070)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_29850 for (2970ds/770Mi)
% 23.36/4.92 % (30070)Instruction limit reached!
% 23.36/4.92 % (30070)------------------------------
% 23.36/4.92 % (30070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.92 % (30070)Termination reason: Unknown
% 23.36/4.92 % (30070)Termination phase: Saturation
% 23.36/4.92
% 23.36/4.92 % (30070)Memory used [KB]: 6524
% 23.36/4.92 % (30070)Time elapsed: 0.370 s
% 23.36/4.92 % (30070)Instructions burned: 770 (million)
% 23.36/4.92 % (30070)------------------------------
% 23.36/4.92 % (30070)------------------------------
% 23.36/4.94 % (30071)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_29850 for (2966ds/794Mi)
% 23.36/4.97 % (30064)Instruction limit reached!
% 23.36/4.97 % (30064)------------------------------
% 23.36/4.97 % (30064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.97 % (30064)Termination reason: Unknown
% 23.36/4.97 % (30064)Termination phase: Saturation
% 23.36/4.97
% 23.36/4.97 % (30064)Memory used [KB]: 14583
% 23.36/4.97 % (30064)Time elapsed: 0.916 s
% 23.36/4.97 % (30064)Instructions burned: 1828 (million)
% 23.36/4.97 % (30064)------------------------------
% 23.36/4.97 % (30064)------------------------------
% 23.36/4.98 % (30072)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_29850 for (2965ds/464Mi)
% 23.36/5.00 % (30046)Instruction limit reached!
% 23.36/5.00 % (30046)------------------------------
% 23.36/5.00 % (30046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/5.00 % (30046)Termination reason: Unknown
% 23.36/5.00 % (30046)Termination phase: Saturation
% 23.36/5.00
% 23.36/5.00 % (30046)Memory used [KB]: 9466
% 23.36/5.00 % (30046)Time elapsed: 2.010 s
% 23.36/5.00 % (30046)Instructions burned: 5206 (million)
% 23.36/5.00 % (30046)------------------------------
% 23.36/5.00 % (30046)------------------------------
% 23.36/5.02 % (30073)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_29850 for (2965ds/1376Mi)
% 27.26/5.14 % (30043)Instruction limit reached!
% 27.26/5.14 % (30043)------------------------------
% 27.26/5.14 % (30043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.26/5.14 % (30043)Termination reason: Unknown
% 27.26/5.14 % (30043)Termination phase: Saturation
% 27.26/5.14
% 27.26/5.14 % (30043)Memory used [KB]: 14583
% 27.26/5.14 % (30043)Time elapsed: 2.233 s
% 27.26/5.14 % (30043)Instructions burned: 4436 (million)
% 27.26/5.14 % (30043)------------------------------
% 27.26/5.14 % (30043)------------------------------
% 27.26/5.16 % (30074)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_29850 for (2964ds/906Mi)
% 27.62/5.21 % (30072)Instruction limit reached!
% 27.62/5.21 % (30072)------------------------------
% 27.62/5.21 % (30072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.62/5.21 % (30072)Termination reason: Unknown
% 27.62/5.21 % (30072)Termination phase: Saturation
% 27.62/5.21
% 27.62/5.21 % (30072)Memory used [KB]: 7675
% 27.62/5.21 % (30072)Time elapsed: 0.226 s
% 27.62/5.21 % (30072)Instructions burned: 464 (million)
% 27.62/5.21 % (30072)------------------------------
% 27.62/5.21 % (30072)------------------------------
% 27.62/5.23 % (30075)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_29850 for (2963ds/434Mi)
% 28.04/5.32 % (30048)Instruction limit reached!
% 28.04/5.32 % (30048)------------------------------
% 28.04/5.32 % (30048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.04/5.32 % (30048)Termination reason: Unknown
% 28.04/5.32 % (30048)Termination phase: Saturation
% 28.04/5.32
% 28.04/5.32 % (30048)Memory used [KB]: 10746
% 28.04/5.32 % (30048)Time elapsed: 2.154 s
% 28.04/5.32 % (30048)Instructions burned: 4352 (million)
% 28.04/5.32 % (30048)------------------------------
% 28.04/5.32 % (30048)------------------------------
% 28.04/5.33 % (30076)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_29850 for (2962ds/865Mi)
% 28.04/5.34 % (30071)Instruction limit reached!
% 28.04/5.34 % (30071)------------------------------
% 28.04/5.34 % (30071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.04/5.34 % (30071)Termination reason: Unknown
% 28.04/5.34 % (30071)Termination phase: Saturation
% 28.04/5.34
% 28.04/5.34 % (30071)Memory used [KB]: 3709
% 28.04/5.34 % (30071)Time elapsed: 0.393 s
% 28.04/5.34 % (30071)Instructions burned: 795 (million)
% 28.04/5.34 % (30071)------------------------------
% 28.04/5.34 % (30071)------------------------------
% 28.04/5.35 % (30077)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_29850 for (2962ds/593Mi)
% 28.34/5.44 % (30075)Instruction limit reached!
% 28.34/5.44 % (30075)------------------------------
% 28.34/5.44 % (30075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.34/5.44 % (30075)Termination reason: Unknown
% 28.34/5.44 % (30075)Termination phase: Saturation
% 28.34/5.44
% 28.34/5.44 % (30075)Memory used [KB]: 8443
% 28.34/5.44 % (30075)Time elapsed: 0.213 s
% 28.34/5.44 % (30075)Instructions burned: 435 (million)
% 28.34/5.44 % (30075)------------------------------
% 28.34/5.44 % (30075)------------------------------
% 28.34/5.46 % (30078)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_29850 for (2961ds/443Mi)
% 28.77/5.57 % (30077)Instruction limit reached!
% 28.77/5.57 % (30077)------------------------------
% 28.77/5.57 % (30077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.77/5.57 % (30077)Termination reason: Unknown
% 28.77/5.57 % (30077)Termination phase: Saturation
% 28.77/5.57
% 28.77/5.57 % (30077)Memory used [KB]: 6396
% 28.77/5.57 % (30077)Time elapsed: 0.215 s
% 28.77/5.57 % (30077)Instructions burned: 596 (million)
% 28.77/5.57 % (30077)------------------------------
% 28.77/5.57 % (30077)------------------------------
% 28.77/5.58 % (30073)Instruction limit reached!
% 28.77/5.58 % (30073)------------------------------
% 28.77/5.58 % (30073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.77/5.58 % (30073)Termination reason: Unknown
% 28.77/5.58 % (30073)Termination phase: Saturation
% 28.77/5.58
% 28.77/5.58 % (30073)Memory used [KB]: 7675
% 28.77/5.58 % (30073)Time elapsed: 0.557 s
% 28.77/5.58 % (30073)Instructions burned: 1377 (million)
% 28.77/5.58 % (30073)------------------------------
% 28.77/5.58 % (30073)------------------------------
% 28.77/5.58 % (30079)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_29850 for (2959ds/594Mi)
% 28.77/5.59 % (30080)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_29850 for (2959ds/327Mi)
% 29.76/5.62 % (30074)Instruction limit reached!
% 29.76/5.62 % (30074)------------------------------
% 29.76/5.62 % (30074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.76/5.62 % (30074)Termination reason: Unknown
% 29.76/5.62 % (30074)Termination phase: Saturation
% 29.76/5.62
% 29.76/5.62 % (30074)Memory used [KB]: 8187
% 29.76/5.62 % (30074)Time elapsed: 0.467 s
% 29.76/5.62 % (30074)Instructions burned: 907 (million)
% 29.76/5.62 % (30074)------------------------------
% 29.76/5.62 % (30074)------------------------------
% 29.76/5.63 % (30081)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_29850 for (2959ds/5411Mi)
% 30.37/5.70 % (30076)Instruction limit reached!
% 30.37/5.70 % (30076)------------------------------
% 30.37/5.70 % (30076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.37/5.70 % (30076)Termination reason: Unknown
% 30.37/5.70 % (30076)Termination phase: Saturation
% 30.37/5.70
% 30.37/5.70 % (30076)Memory used [KB]: 7547
% 30.37/5.70 % (30076)Time elapsed: 0.370 s
% 30.37/5.70 % (30076)Instructions burned: 866 (million)
% 30.37/5.70 % (30076)------------------------------
% 30.37/5.70 % (30076)------------------------------
% 30.37/5.72 % (30078)Instruction limit reached!
% 30.37/5.72 % (30078)------------------------------
% 30.37/5.72 % (30078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.37/5.72 % (30078)Termination reason: Unknown
% 30.37/5.72 % (30078)Termination phase: Saturation
% 30.37/5.72
% 30.37/5.72 % (30078)Memory used [KB]: 7291
% 30.37/5.72 % (30078)Time elapsed: 0.263 s
% 30.37/5.72 % (30078)Instructions burned: 443 (million)
% 30.37/5.72 % (30078)------------------------------
% 30.37/5.72 % (30078)------------------------------
% 30.37/5.72 % (30082)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_29850 for (2958ds/1762Mi)
% 30.37/5.74 % (30083)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_29850 for (2958ds/96Mi)
% 30.37/5.76 % (30080)Instruction limit reached!
% 30.37/5.76 % (30080)------------------------------
% 30.37/5.76 % (30080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.37/5.76 % (30080)Termination reason: Unknown
% 30.37/5.76 % (30080)Termination phase: Saturation
% 30.37/5.76
% 30.37/5.76 % (30080)Memory used [KB]: 8827
% 30.37/5.76 % (30080)Time elapsed: 0.166 s
% 30.37/5.76 % (30080)Instructions burned: 328 (million)
% 30.37/5.76 % (30080)------------------------------
% 30.37/5.76 % (30080)------------------------------
% 30.37/5.77 % (30084)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_29850 for (2958ds/503Mi)
% 30.37/5.79 % (30083)Instruction limit reached!
% 30.37/5.79 % (30083)------------------------------
% 30.37/5.79 % (30083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.37/5.79 % (30083)Termination reason: Unknown
% 30.37/5.79 % (30083)Termination phase: Saturation
% 30.37/5.79
% 30.37/5.79 % (30083)Memory used [KB]: 6140
% 30.37/5.79 % (30083)Time elapsed: 0.027 s
% 30.37/5.79 % (30083)Instructions burned: 96 (million)
% 30.37/5.79 % (30083)------------------------------
% 30.37/5.79 % (30083)------------------------------
% 31.35/5.80 % (30085)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_29850 for (2957ds/90Mi)
% 31.35/5.81 % (30068)Instruction limit reached!
% 31.35/5.81 % (30068)------------------------------
% 31.35/5.81 % (30068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.35/5.81 % (30068)Termination reason: Unknown
% 31.35/5.81 % (30068)Termination phase: Saturation
% 31.35/5.81
% 31.35/5.81 % (30068)Memory used [KB]: 6780
% 31.35/5.81 % (30068)Time elapsed: 1.571 s
% 31.35/5.81 % (30068)Instructions burned: 4716 (million)
% 31.35/5.81 % (30068)------------------------------
% 31.35/5.81 % (30068)------------------------------
% 31.35/5.84 % (30086)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_29850 for (2957ds/593Mi)
% 31.35/5.85 % (30085)Instruction limit reached!
% 31.35/5.85 % (30085)------------------------------
% 31.35/5.85 % (30085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.35/5.85 % (30085)Termination reason: Unknown
% 31.35/5.85 % (30085)Termination phase: Saturation
% 31.35/5.85
% 31.35/5.85 % (30085)Memory used [KB]: 6524
% 31.35/5.85 % (30085)Time elapsed: 0.043 s
% 31.35/5.85 % (30085)Instructions burned: 92 (million)
% 31.35/5.85 % (30085)------------------------------
% 31.35/5.85 % (30085)------------------------------
% 31.35/5.87 % (30079)Instruction limit reached!
% 31.35/5.87 % (30079)------------------------------
% 31.35/5.87 % (30079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.35/5.87 % (30079)Termination reason: Unknown
% 31.35/5.87 % (30079)Termination phase: Saturation
% 31.35/5.87
% 31.35/5.87 % (30079)Memory used [KB]: 7419
% 31.35/5.87 % (30079)Time elapsed: 0.293 s
% 31.35/5.87 % (30079)Instructions burned: 594 (million)
% 31.35/5.87 % (30079)------------------------------
% 31.35/5.87 % (30079)------------------------------
% 31.35/5.87 % (30087)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_29850 for (2957ds/1512Mi)
% 31.35/5.89 % (30088)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_29850 for (2956ds/569Mi)
% 31.84/6.02 % (30084)Instruction limit reached!
% 31.84/6.02 % (30084)------------------------------
% 31.84/6.02 % (30084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.84/6.02 % (30084)Termination reason: Unknown
% 31.84/6.02 % (30084)Termination phase: Saturation
% 31.84/6.02
% 31.84/6.02 % (30084)Memory used [KB]: 7291
% 31.84/6.02 % (30084)Time elapsed: 0.246 s
% 31.84/6.02 % (30084)Instructions burned: 503 (million)
% 31.84/6.02 % (30084)------------------------------
% 31.84/6.02 % (30084)------------------------------
% 33.40/6.03 % (30089)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_29850 for (2955ds/501Mi)
% 33.40/6.12 % (30088)Instruction limit reached!
% 33.40/6.12 % (30088)------------------------------
% 33.40/6.12 % (30088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.40/6.12 % (30088)Termination reason: Unknown
% 33.40/6.12 % (30088)Termination phase: Saturation
% 33.40/6.12
% 33.40/6.12 % (30088)Memory used [KB]: 7931
% 33.40/6.12 % (30088)Time elapsed: 0.228 s
% 33.40/6.12 % (30088)Instructions burned: 569 (million)
% 33.40/6.12 % (30088)------------------------------
% 33.40/6.12 % (30088)------------------------------
% 33.40/6.13 % (30086)Instruction limit reached!
% 33.40/6.13 % (30086)------------------------------
% 33.40/6.13 % (30086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.40/6.13 % (30086)Termination reason: Unknown
% 33.40/6.13 % (30086)Termination phase: Saturation
% 33.40/6.13
% 33.40/6.13 % (30086)Memory used [KB]: 7547
% 33.40/6.13 % (30086)Time elapsed: 0.313 s
% 33.40/6.13 % (30086)Instructions burned: 593 (million)
% 33.40/6.13 % (30086)------------------------------
% 33.40/6.13 % (30086)------------------------------
% 33.40/6.13 % (30090)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_29850 for (2954ds/562Mi)
% 34.00/6.15 % (30091)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_29850 for (2954ds/406Mi)
% 34.25/6.24 % (30091)Refutation not found, incomplete strategy
% 34.25/6.24 % (30091)------------------------------
% 34.25/6.24 % (30091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.25/6.24 % (30091)Termination reason: Refutation not found, incomplete strategy
% 34.25/6.24
% 34.25/6.24
% 34.25/6.24 % (30091)Memory used [KB]: 6396
% 34.25/6.24 % (30091)Time elapsed: 0.092 s
% 34.25/6.24 % (30091)Instructions burned: 194 (million)
% 34.25/6.24 % (30091)------------------------------
% 34.25/6.24 % (30091)------------------------------
% 34.25/6.27 % (30092)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_29850 for (2953ds/582Mi)
% 34.25/6.28 % (30089)Instruction limit reached!
% 34.25/6.28 % (30089)------------------------------
% 34.25/6.28 % (30089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.25/6.28 % (30089)Termination reason: Unknown
% 34.25/6.28 % (30089)Termination phase: Saturation
% 34.25/6.28
% 34.25/6.28 % (30089)Memory used [KB]: 8443
% 34.25/6.28 % (30089)Time elapsed: 0.249 s
% 34.25/6.28 % (30089)Instructions burned: 501 (million)
% 34.25/6.28 % (30089)------------------------------
% 34.25/6.28 % (30089)------------------------------
% 35.02/6.30 % (30093)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_29850 for (2952ds/456Mi)
% 35.02/6.39 % (30090)Instruction limit reached!
% 35.02/6.39 % (30090)------------------------------
% 35.02/6.39 % (30090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.02/6.39 % (30090)Termination reason: Unknown
% 35.02/6.39 % (30090)Termination phase: Saturation
% 35.02/6.39
% 35.02/6.39 % (30090)Memory used [KB]: 7419
% 35.02/6.39 % (30090)Time elapsed: 0.263 s
% 35.02/6.39 % (30090)Instructions burned: 562 (million)
% 35.02/6.39 % (30090)------------------------------
% 35.02/6.39 % (30090)------------------------------
% 35.69/6.41 % (30094)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_29850 for (2951ds/393Mi)
% 35.69/6.42 % (30082)Instruction limit reached!
% 35.69/6.42 % (30082)------------------------------
% 35.69/6.42 % (30082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.42 % (30082)Termination reason: Unknown
% 35.69/6.42 % (30082)Termination phase: Saturation
% 35.69/6.42
% 35.69/6.42 % (30082)Memory used [KB]: 9466
% 35.69/6.42 % (30082)Time elapsed: 0.698 s
% 35.69/6.42 % (30082)Instructions burned: 1762 (million)
% 35.69/6.42 % (30082)------------------------------
% 35.69/6.42 % (30082)------------------------------
% 35.69/6.43 % (30095)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_29850 for (2951ds/1335Mi)
% 36.03/6.51 % (30092)Instruction limit reached!
% 36.03/6.51 % (30092)------------------------------
% 36.03/6.51 % (30092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.03/6.51 % (30092)Termination reason: Unknown
% 36.03/6.51 % (30092)Termination phase: Saturation
% 36.03/6.51
% 36.03/6.51 % (30092)Memory used [KB]: 8315
% 36.03/6.51 % (30092)Time elapsed: 0.264 s
% 36.03/6.51 % (30092)Instructions burned: 583 (million)
% 36.03/6.51 % (30092)------------------------------
% 36.03/6.51 % (30092)------------------------------
% 36.03/6.52 % (30096)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_29850 for (2950ds/3373Mi)
% 36.03/6.52 % (30093)Instruction limit reached!
% 36.03/6.52 % (30093)------------------------------
% 36.03/6.52 % (30093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.03/6.52 % (30093)Termination reason: Unknown
% 36.03/6.52 % (30093)Termination phase: Saturation
% 36.03/6.52
% 36.03/6.52 % (30093)Memory used [KB]: 7291
% 36.03/6.52 % (30093)Time elapsed: 0.222 s
% 36.03/6.52 % (30093)Instructions burned: 457 (million)
% 36.03/6.52 % (30093)------------------------------
% 36.03/6.52 % (30093)------------------------------
% 36.03/6.54 % (30097)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_29850 for (2950ds/474Mi)
% 36.03/6.60 % (30094)Instruction limit reached!
% 36.03/6.60 % (30094)------------------------------
% 36.03/6.60 % (30094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.03/6.60 % (30094)Termination reason: Unknown
% 36.03/6.60 % (30094)Termination phase: Saturation
% 36.03/6.60
% 36.03/6.60 % (30094)Memory used [KB]: 7803
% 36.03/6.60 % (30094)Time elapsed: 0.186 s
% 36.03/6.60 % (30094)Instructions burned: 393 (million)
% 36.03/6.60 % (30094)------------------------------
% 36.03/6.60 % (30094)------------------------------
% 36.82/6.61 % (30098)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_29850 for (2949ds/157Mi)
% 36.82/6.63 % (30087)Instruction limit reached!
% 36.82/6.63 % (30087)------------------------------
% 36.82/6.63 % (30087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/6.63 % (30087)Termination reason: Unknown
% 36.82/6.63 % (30087)Termination phase: Saturation
% 36.82/6.63
% 36.82/6.63 % (30087)Memory used [KB]: 9850
% 36.82/6.63 % (30087)Time elapsed: 0.777 s
% 36.82/6.63 % (30087)Instructions burned: 1513 (million)
% 36.82/6.63 % (30087)------------------------------
% 36.82/6.63 % (30087)------------------------------
% 36.82/6.65 % (30099)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_29850 for (2949ds/590Mi)
% 36.82/6.68 % (30098)Instruction limit reached!
% 36.82/6.68 % (30098)------------------------------
% 36.82/6.68 % (30098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.82/6.68 % (30098)Termination reason: Unknown
% 36.82/6.68 % (30098)Termination phase: Saturation
% 36.82/6.68
% 36.82/6.68 % (30098)Memory used [KB]: 6268
% 36.82/6.68 % (30098)Time elapsed: 0.065 s
% 36.82/6.68 % (30098)Instructions burned: 157 (million)
% 36.82/6.68 % (30098)------------------------------
% 36.82/6.68 % (30098)------------------------------
% 36.82/6.69 % (30100)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_29850 for (2948ds/104Mi)
% 37.34/6.70 % (30097)Instruction limit reached!
% 37.34/6.70 % (30097)------------------------------
% 37.34/6.70 % (30097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.34/6.70 % (30097)Termination reason: Unknown
% 37.34/6.70 % (30097)Termination phase: Saturation
% 37.34/6.70
% 37.34/6.70 % (30097)Memory used [KB]: 7931
% 37.34/6.70 % (30097)Time elapsed: 0.165 s
% 37.34/6.70 % (30097)Instructions burned: 474 (million)
% 37.34/6.70 % (30097)------------------------------
% 37.34/6.70 % (30097)------------------------------
% 37.34/6.71 % (30101)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_29850 for (2948ds/414Mi)
% 37.34/6.74 % (30100)Instruction limit reached!
% 37.34/6.74 % (30100)------------------------------
% 37.34/6.74 % (30100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.34/6.74 % (30100)Termination reason: Unknown
% 37.34/6.74 % (30100)Termination phase: Saturation
% 37.34/6.74
% 37.34/6.74 % (30100)Memory used [KB]: 6652
% 37.34/6.74 % (30100)Time elapsed: 0.049 s
% 37.34/6.74 % (30100)Instructions burned: 104 (million)
% 37.34/6.74 % (30100)------------------------------
% 37.34/6.74 % (30100)------------------------------
% 37.34/6.76 % (30102)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_29850 for (2948ds/715Mi)
% 37.78/6.81 % (30101)Instruction limit reached!
% 37.78/6.81 % (30101)------------------------------
% 37.78/6.81 % (30101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.78/6.81 % (30101)Termination reason: Unknown
% 37.78/6.81 % (30101)Termination phase: Saturation
% 37.78/6.81
% 37.78/6.81 % (30101)Memory used [KB]: 6268
% 37.78/6.81 % (30101)Time elapsed: 0.100 s
% 37.78/6.81 % (30101)Instructions burned: 415 (million)
% 37.78/6.81 % (30101)------------------------------
% 37.78/6.81 % (30101)------------------------------
% 37.78/6.82 % (30103)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_29850 for (2947ds/961Mi)
% 38.09/6.93 % (30099)Instruction limit reached!
% 38.09/6.93 % (30099)------------------------------
% 38.09/6.93 % (30099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.09/6.93 % (30099)Termination reason: Unknown
% 38.09/6.93 % (30099)Termination phase: Saturation
% 38.09/6.93
% 38.09/6.93 % (30099)Memory used [KB]: 8571
% 38.09/6.93 % (30099)Time elapsed: 0.279 s
% 38.09/6.93 % (30099)Instructions burned: 590 (million)
% 38.09/6.93 % (30099)------------------------------
% 38.09/6.93 % (30099)------------------------------
% 38.09/6.94 % (30104)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_29850 for (2946ds/1213Mi)
% 38.09/6.97 % (30069)First to succeed.
% 38.09/6.97 % (30069)Refutation found. Thanks to Tanya!
% 38.09/6.97 % SZS status Theorem for DTF2THF_29850
% 38.09/6.97 % SZS output start Proof for DTF2THF_29850
% 38.09/6.97 thf(func_def_0, type, in: $i > $i > $o).
% 38.09/6.97 thf(func_def_1, type, exu: ($i > $o) > $o).
% 38.09/6.97 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 38.09/6.97 thf(func_def_8, type, powerset: $i > $i).
% 38.09/6.97 thf(func_def_10, type, setunion: $i > $i).
% 38.09/6.97 thf(func_def_19, type, descr: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_26, type, prop2set: $o > $i).
% 38.09/6.97 thf(func_def_36, type, nonempty: $i > $o).
% 38.09/6.97 thf(func_def_69, type, set2prop: $i > $o).
% 38.09/6.97 thf(func_def_88, type, subset: $i > $i > $o).
% 38.09/6.97 thf(func_def_89, type, disjoint: $i > $i > $o).
% 38.09/6.97 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 38.09/6.97 thf(func_def_114, type, binunion: $i > $i > $i).
% 38.09/6.97 thf(func_def_122, type, binintersect: $i > $i > $i).
% 38.09/6.97 thf(func_def_145, type, sP1: $i > $i > $o).
% 38.09/6.97 thf(func_def_146, type, sP2: $i > $o).
% 38.09/6.97 thf(func_def_147, type, sP3: $i > $i > $o).
% 38.09/6.97 thf(func_def_148, type, sP4: $i > $i > $o).
% 38.09/6.97 thf(func_def_151, type, sK7: $i > $i > $i).
% 38.09/6.97 thf(func_def_154, type, sK10: $i > $i > $i).
% 38.09/6.97 thf(func_def_158, type, sK14: $i > $o).
% 38.09/6.97 thf(func_def_160, type, sK16: ($i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_165, type, sK21: $i > $o).
% 38.09/6.97 thf(func_def_167, type, sK23: ($i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_169, type, sK25: $i > $o).
% 38.09/6.97 thf(func_def_179, type, sK35: $i > $o).
% 38.09/6.97 thf(func_def_182, type, sK38: $i > $o).
% 38.09/6.97 thf(func_def_183, type, sK39: $i > $o).
% 38.09/6.97 thf(func_def_184, type, sK40: ($i > $o) > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_185, type, sK41: ($i > $o) > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_189, type, sK45: $i > $i > $o).
% 38.09/6.97 thf(func_def_190, type, sK46: $i > $i).
% 38.09/6.97 thf(func_def_191, type, sK47: $i > $i).
% 38.09/6.97 thf(func_def_192, type, sK48: ($i > $i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_193, type, sK49: $i > ($i > $i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_194, type, sK50: ($i > $i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_197, type, sK53: $i > $i > $i).
% 38.09/6.97 thf(func_def_198, type, sK54: $i > $i > $i).
% 38.09/6.97 thf(func_def_205, type, sK61: $i > $o).
% 38.09/6.97 thf(func_def_206, type, sK62: $i > $o).
% 38.09/6.97 thf(func_def_207, type, sK63: ($i > $o) > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_208, type, sK64: ($i > $o) > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_217, type, sK73: $i > $o).
% 38.09/6.97 thf(func_def_224, type, sK80: $i > $o).
% 38.09/6.97 thf(func_def_225, type, sK81: $i > $o).
% 38.09/6.97 thf(func_def_228, type, sK84: $i > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_231, type, sK87: $i > $o).
% 38.09/6.97 thf(func_def_234, type, sK90: $i > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_242, type, sK98: $i > $i > $i).
% 38.09/6.97 thf(func_def_248, type, sK104: $i > $i).
% 38.09/6.97 thf(func_def_250, type, sK106: $i > $i).
% 38.09/6.97 thf(func_def_252, type, sK108: $i > $i).
% 38.09/6.97 thf(func_def_258, type, sK114: $i > $o).
% 38.09/6.97 thf(func_def_267, type, sK123: $i > $o).
% 38.09/6.97 thf(func_def_269, type, sK125: $i > $i).
% 38.09/6.97 thf(func_def_274, type, sK130: $i > $o).
% 38.09/6.97 thf(func_def_276, type, sK132: ($i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_280, type, sK136: $i > $i > $i).
% 38.09/6.97 thf(func_def_287, type, sK143: $i > $i > $i).
% 38.09/6.97 thf(func_def_288, type, sK144: $i > $i > $i).
% 38.09/6.97 thf(func_def_289, type, sK145: $i > $i > $i).
% 38.09/6.97 thf(func_def_290, type, sK146: $i > $i > $i).
% 38.09/6.97 thf(func_def_291, type, sK147: $i > $i > $i).
% 38.09/6.97 thf(func_def_292, type, sK148: $i > $i > $i > $i).
% 38.09/6.97 thf(func_def_293, type, sK149: $i > $i).
% 38.09/6.97 thf(func_def_294, type, sK150: $i > $i).
% 38.09/6.97 thf(func_def_295, type, sK151: $i > $i).
% 38.09/6.97 thf(func_def_296, type, sK152: $i > $i).
% 38.09/6.97 thf(func_def_297, type, sK153: $i > $i > $i).
% 38.09/6.97 thf(func_def_298, type, sK154: $i > $i > $i > $i).
% 38.09/6.97 thf(func_def_299, type, sK155: $i > $i > $i > $i).
% 38.09/6.97 thf(func_def_300, type, sK156: $i > $i > $i).
% 38.09/6.97 thf(func_def_301, type, sK157: $i > $i > $i).
% 38.09/6.97 thf(func_def_303, type, sK159: $i > $i).
% 38.09/6.97 thf(func_def_304, type, sK160: $i > $i).
% 38.09/6.97 thf(func_def_305, type, sK161: $i > $i).
% 38.09/6.97 thf(func_def_310, type, sK166: $i > $o).
% 38.09/6.97 thf(func_def_314, type, sK170: $i > $o).
% 38.09/6.97 thf(func_def_318, type, sK174: ($i > $o) > ($i > $o) > $i > $i > $i).
% 38.09/6.97 thf(func_def_319, type, sK175: ($i > $o) > ($i > $o) > $i > $i > $i).
% 38.09/6.97 thf(func_def_322, type, sK178: $i > $o).
% 38.09/6.97 thf(func_def_323, type, sK179: $i > $o).
% 38.09/6.97 thf(func_def_324, type, sK180: $i > $i > $i).
% 38.09/6.97 thf(func_def_330, type, sK186: $i > $o).
% 38.09/6.97 thf(func_def_332, type, sK188: ($i > $o) > $i > $i).
% 38.09/6.97 thf(func_def_352, type, sK208: $i > $o).
% 38.09/6.97 thf(func_def_355, type, sK211: $i > $i).
% 38.09/6.97 thf(func_def_359, type, sK215: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_360, type, sK216: $i > $o).
% 38.09/6.97 thf(func_def_361, type, sK217: $i > $i).
% 38.09/6.97 thf(func_def_368, type, sK224: $i > $i).
% 38.09/6.97 thf(func_def_386, type, sK242: $i > $i > $i).
% 38.09/6.97 thf(func_def_389, type, sK245: $o > $i > $i > $i).
% 38.09/6.97 thf(func_def_394, type, sK250: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_395, type, sK251: $i > $o).
% 38.09/6.97 thf(func_def_396, type, sK252: $i > $o).
% 38.09/6.97 thf(func_def_398, type, sK254: $i > $o).
% 38.09/6.97 thf(func_def_400, type, sK256: $i > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_404, type, sK260: $i > $o).
% 38.09/6.97 thf(func_def_413, type, sK269: $i > $i > $i).
% 38.09/6.97 thf(func_def_417, type, sK273: $i > $o).
% 38.09/6.97 thf(func_def_419, type, sK275: $i > ($i > $o) > $i).
% 38.09/6.97 thf(func_def_431, type, sK287: $i > $i).
% 38.09/6.97 thf(func_def_445, type, sK301: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_446, type, sK302: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_447, type, sK303: $i > $o).
% 38.09/6.97 thf(func_def_452, type, sK308: $i > $o).
% 38.09/6.97 thf(func_def_453, type, sK309: $i > $i).
% 38.09/6.97 thf(func_def_454, type, sK310: ($i > $o) > $i).
% 38.09/6.97 thf(func_def_457, type, sK313: $i > $o).
% 38.09/6.97 thf(func_def_459, type, ph315: !>[X0: $tType]:(X0)).
% 38.09/6.97 thf(f23994,plain,(
% 38.09/6.97 $false),
% 38.09/6.97 inference(avatar_sat_refutation,[status(thm)],[f1757,f1858,f2097,f2778,f2948,f3394,f4050,f4157,f23993])).
% 38.09/6.97 thf(f23993,plain,(
% 38.09/6.97 ~spl314_5 | ~spl314_98 | ~spl314_236 | ~spl314_501),
% 38.09/6.97 inference(avatar_contradiction_clause,[status(thm)],[f23992])).
% 38.09/6.97 thf(f23992,plain,(
% 38.09/6.97 $false | (~spl314_5 | ~spl314_98 | ~spl314_236 | ~spl314_501)),
% 38.09/6.97 inference(subsumption_resolution,[status(thm)],[f23960,f1506])).
% 38.09/6.97 thf(f1506,plain,(
% 38.09/6.97 (sK262 != (binintersect @ sK261 @ sK262))),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f943,plain,(
% 38.09/6.97 (replAx = $true) & (exuEu = $true) & (emptyset__Cong = $true) & (setadjoinE = $true) & (powersetE = $true) & (notsubsetI = $true) & (disjointsetsI1 = $true) & (setbeta = $true) & (setunionAx = $true) & (uniqinunit = $true) & (in__Cong = $true) & (eqinunit = $true) & (binunionEcases = $true) & (dsetconstrI = $true) & (powersetI1 = $true) & ((sK262 != (binintersect @ sK261 @ sK262)) & ((subset @ sK262 @ sK261) = $true)) & (emptyInPowerset = $true) & (nonemptyI = $true) & (powersetE1 = $true) & (exuI3 = $true) & (quantDeMorgan4 = $true) & (binintersectSubset5 = $true) & (descr__Cong = $true) & (notdexE = $true) & (exuE1 = $true) & (exu__Cong = $true) & (subsetE = $true) & (omega0Ax = $true) & (vacuousDall = $true) & (emptysetimpfalse = $true) & (singletonsswitch = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (prop2setE = $true) & (setadjoin__Cong = $true) & (notdallE = $true) & (exuI1 = $true) & (subsetI1 = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (binintersectI = $true) & (emptyE1 = $true) & (powerset__Cong = $true) & (binunionRsub = $true) & (omegaIndAx = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (binunionIR = $true) & (quantDeMorgan1 = $true) & (emptysetsubset = $true) & (nonemptyImpWitness = $true) & (setadjoinOr = $true) & (prop2setI = $true) & (subsetE2 = $true) & (powersetAx = $true) & (inCongP = $true) & (setextAx = $true) & (sepSubset = $true) & (setadjoinIL = $true) & (notequalI1 = $true) & (setadjoinSub2 = $true) & (upairset2IR = $true) & (powersetI = $true) & (setunion__Cong = $true) & (inPowerset = $true) & (powersetsubset = $true) & (subsetI2 = $true) & (upairsetIR = $true) & (exuE3u = $true) & (nonemptyE1 = $true) & (subPowSU = $true) & (setunionE = $true) & (binintersectEL = $true) & (nonemptyI1 = $true) & (subsetemptysetimpeq = $true) & (binintersectRsub = $true) & (setext = $true) & (binunionE = $true) & (dsetconstrEL = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (emptyI = $true) & (subsetTrans = $true) & (noeltsimpempty = $true) & (prop2set2propI = $true) & (setextsub = $true) & (notequalI2 = $true) & (exuE2 = $true) & (notinsingleton = $true) & (omega__Cong = $true) & (descrp = $true) & (subset2powerset = $true) & (binunionIL = $true) & (exuE3e = $true) & (binunionLsub = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (emptysetAx = $true) & (quantDeMorgan2 = $true) & (setadjoinIR = $true) & (binintersectER = $true) & (dsetconstr__Cong = $true) & (setunionI = $true) & (emptysetE = $true) & (exuI2 = $true) & (binintersectSubset3 = $true) & (setoftrueEq = $true) & (subsetRefl = $true) & (notinemptyset = $true) & (dsetconstrER = $true)),
% 38.09/6.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK261,sK262])],[f469,f942])).
% 38.09/6.97 thf(f942,plain,(
% 38.09/6.97 ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ($true = (subset @ X1 @ X0))) => ((sK262 != (binintersect @ sK261 @ sK262)) & ((subset @ sK262 @ sK261) = $true))),
% 38.09/6.97 introduced(definition,[],[choice_axiom])).
% 38.09/6.97 thf(f469,plain,(
% 38.09/6.97 (replAx = $true) & (exuEu = $true) & (emptyset__Cong = $true) & (setadjoinE = $true) & (powersetE = $true) & (notsubsetI = $true) & (disjointsetsI1 = $true) & (setbeta = $true) & (setunionAx = $true) & (uniqinunit = $true) & (in__Cong = $true) & (eqinunit = $true) & (binunionEcases = $true) & (dsetconstrI = $true) & (powersetI1 = $true) & ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ($true = (subset @ X1 @ X0))) & (emptyInPowerset = $true) & (nonemptyI = $true) & (powersetE1 = $true) & (exuI3 = $true) & (quantDeMorgan4 = $true) & (binintersectSubset5 = $true) & (descr__Cong = $true) & (notdexE = $true) & (exuE1 = $true) & (exu__Cong = $true) & (subsetE = $true) & (omega0Ax = $true) & (vacuousDall = $true) & (emptysetimpfalse = $true) & (singletonsswitch = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (prop2setE = $true) & (setadjoin__Cong = $true) & (notdallE = $true) & (exuI1 = $true) & (subsetI1 = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (eqimpsubset2 = $true) & (eqimpsubset1 = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (binintersectI = $true) & (emptyE1 = $true) & (powerset__Cong = $true) & (binunionRsub = $true) & (omegaIndAx = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (binunionIR = $true) & (quantDeMorgan1 = $true) & (emptysetsubset = $true) & (nonemptyImpWitness = $true) & (setadjoinOr = $true) & (prop2setI = $true) & (subsetE2 = $true) & (powersetAx = $true) & (inCongP = $true) & (setextAx = $true) & (sepSubset = $true) & (setadjoinIL = $true) & (notequalI1 = $true) & (setadjoinSub2 = $true) & (upairset2IR = $true) & (powersetI = $true) & (setunion__Cong = $true) & (inPowerset = $true) & (powersetsubset = $true) & (subsetI2 = $true) & (upairsetIR = $true) & (exuE3u = $true) & (nonemptyE1 = $true) & (subPowSU = $true) & (setunionE = $true) & (binintersectEL = $true) & (nonemptyI1 = $true) & (subsetemptysetimpeq = $true) & (binintersectRsub = $true) & (setext = $true) & (binunionE = $true) & (dsetconstrEL = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (emptyI = $true) & (subsetTrans = $true) & (noeltsimpempty = $true) & (prop2set2propI = $true) & (setextsub = $true) & (notequalI2 = $true) & (exuE2 = $true) & (notinsingleton = $true) & (omega__Cong = $true) & (descrp = $true) & (subset2powerset = $true) & (binunionIL = $true) & (exuE3e = $true) & (binunionLsub = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (emptysetAx = $true) & (quantDeMorgan2 = $true) & (setadjoinIR = $true) & (binintersectER = $true) & (dsetconstr__Cong = $true) & (setunionI = $true) & (emptysetE = $true) & (exuI2 = $true) & (binintersectSubset3 = $true) & (setoftrueEq = $true) & (subsetRefl = $true) & (notinemptyset = $true) & (dsetconstrER = $true)),
% 38.09/6.97 inference(flattening,[status(thm)],[f468])).
% 38.09/6.97 thf(f468,plain,(
% 38.09/6.97 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ($true = (subset @ X1 @ X0))) & (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)),
% 38.09/6.97 inference(ennf_transformation,[status(thm)],[f311])).
% 38.09/6.97 thf(f311,plain,(
% 38.09/6.97 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => ((binintersect @ X0 @ X1) = X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 38.09/6.97 inference(fool_elimination,[status(thm)],[f310])).
% 38.09/6.97 thf(f310,plain,(
% 38.09/6.97 ~(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 => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 38.09/6.97 inference(rectify,[status(thm)],[f118])).
% 38.09/6.97 thf(f118,negated_conjecture,(
% 38.09/6.97 ~(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 => ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 38.09/6.97 inference(negated_conjecture,[status(cth)],[f117])).
% 38.09/6.97 thf(f117,conjecture,(
% 38.09/6.97 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 => ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 38.09/6.97 file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectSubset4)).
% 38.09/6.97 thf(f23960,plain,(
% 38.09/6.97 (sK262 = (binintersect @ sK261 @ sK262)) | (~spl314_5 | ~spl314_98 | ~spl314_236 | ~spl314_501)),
% 38.09/6.97 inference(trivial_inequality_removal,[status(thm)],[f23936])).
% 38.09/6.97 thf(f23936,plain,(
% 38.09/6.97 ($true != $true) | (sK262 = (binintersect @ sK261 @ sK262)) | (~spl314_5 | ~spl314_98 | ~spl314_236 | ~spl314_501)),
% 38.09/6.97 inference(superposition,[status(thm)],[f4425,f23918])).
% 38.09/6.97 thf(f23918,plain,(
% 38.09/6.97 ((subset @ sK262 @ (binintersect @ sK261 @ sK262)) = $true) | (~spl314_5 | ~spl314_98)),
% 38.09/6.97 inference(trivial_inequality_removal,[status(thm)],[f23882])).
% 38.09/6.97 thf(f23882,plain,(
% 38.09/6.97 ((subset @ sK262 @ (binintersect @ sK261 @ sK262)) = $true) | ($true != $true) | (~spl314_5 | ~spl314_98)),
% 38.09/6.97 inference(superposition,[status(thm)],[f6852,f1505])).
% 38.09/6.97 thf(f1505,plain,(
% 38.09/6.97 ((subset @ sK262 @ sK261) = $true)),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f6852,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X0)) = $true)) ) | (~spl314_5 | ~spl314_98)),
% 38.09/6.97 inference(trivial_inequality_removal,[status(thm)],[f6834])).
% 38.09/6.97 thf(f6834,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X1 @ X0)) = $true) | ($true != (subset @ X0 @ X1)) | ($true != $true)) ) | (~spl314_5 | ~spl314_98)),
% 38.09/6.97 inference(superposition,[status(thm)],[f1752,f2158])).
% 38.09/6.97 thf(f2158,plain,(
% 38.09/6.97 ( ! [X1 : $i] : (((subset @ X1 @ X1) = $true)) ) | ~spl314_98),
% 38.09/6.97 inference(avatar_component_clause,[status(thm)],[f2157])).
% 38.09/6.97 thf(f2157,definition,(
% 38.09/6.97 spl314_98 <=> ! [X1 : $i] : ((subset @ X1 @ X1) = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_98])],[avatar_definition])).
% 38.09/6.97 thf(f1752,plain,(
% 38.09/6.97 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) != $true) | ((subset @ X4 @ (binintersect @ X3 @ X5)) = $true) | ((subset @ X4 @ X3) != $true)) ) | ~spl314_5),
% 38.09/6.97 inference(avatar_component_clause,[status(thm)],[f1751])).
% 38.09/6.97 thf(f1751,definition,(
% 38.09/6.97 spl314_5 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) != $true) | ((subset @ X4 @ (binintersect @ X3 @ X5)) = $true))),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_5])],[avatar_definition])).
% 38.09/6.97 thf(f4425,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binintersect @ X0 @ X1)) != $true) | ((binintersect @ X0 @ X1) = X1)) ) | (~spl314_236 | ~spl314_501)),
% 38.09/6.97 inference(trivial_inequality_removal,[status(thm)],[f4411])).
% 38.09/6.97 thf(f4411,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((binintersect @ X0 @ X1) = X1) | ((subset @ X1 @ (binintersect @ X0 @ X1)) != $true)) ) | (~spl314_236 | ~spl314_501)),
% 38.09/6.97 inference(superposition,[status(thm)],[f2777,f4049])).
% 38.09/6.97 thf(f4049,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X0) = $true)) ) | ~spl314_501),
% 38.09/6.97 inference(avatar_component_clause,[status(thm)],[f4048])).
% 38.09/6.97 thf(f4048,definition,(
% 38.09/6.97 spl314_501 <=> ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_501])],[avatar_definition])).
% 38.09/6.97 thf(f2777,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ($true != (subset @ X0 @ X1)) | (X0 = X1)) ) | ~spl314_236),
% 38.09/6.97 inference(avatar_component_clause,[status(thm)],[f2776])).
% 38.09/6.97 thf(f2776,definition,(
% 38.09/6.97 spl314_236 <=> ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1))),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_236])],[avatar_definition])).
% 38.09/6.97 thf(f4157,plain,(
% 38.09/6.97 spl314_381),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1440,f3468])).
% 38.09/6.97 thf(f3468,definition,(
% 38.09/6.97 spl314_381 <=> (binintersectRsub = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_381])],[avatar_definition])).
% 38.09/6.97 thf(f1440,plain,(
% 38.09/6.97 (binintersectRsub = $true)),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f4050,plain,(
% 38.09/6.97 ~spl314_381 | spl314_501),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1175,f4048,f3468])).
% 38.09/6.97 thf(f1175,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : ((binintersectRsub != $true) | ((subset @ (binintersect @ X1 @ X0) @ X0) = $true)) )),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f674])).
% 38.09/6.97 thf(f674,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ((subset @ (binintersect @ sK110 @ sK109) @ sK109) != $true))),
% 38.09/6.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110])],[f672,f673])).
% 38.09/6.97 thf(f673,plain,(
% 38.09/6.97 ? [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X2) != $true) => ((subset @ (binintersect @ sK110 @ sK109) @ sK109) != $true)),
% 38.09/6.97 introduced(definition,[],[choice_axiom])).
% 38.09/6.97 thf(f672,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X2) != $true))),
% 38.09/6.97 inference(rectify,[status(thm)],[f671])).
% 38.09/6.97 thf(f671,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) != $true))),
% 38.09/6.97 inference(nnf_transformation,[status(thm)],[f157])).
% 38.09/6.97 thf(f157,plain,(
% 38.09/6.97 ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X0) = $true) <=> (binintersectRsub = $true)),
% 38.09/6.97 inference(fool_elimination,[status(thm)],[f156])).
% 38.09/6.97 thf(f156,plain,(
% 38.09/6.97 (binintersectRsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X0))),
% 38.09/6.97 inference(rectify,[status(thm)],[f116])).
% 38.09/6.97 thf(f116,axiom,(
% 38.09/6.97 (binintersectRsub = ! [X4 : $i,X3 : $i] : (subset @ (binintersect @ X3 @ X4) @ X4))),
% 38.09/6.97 file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectRsub)).
% 38.09/6.97 thf(f3394,plain,(
% 38.09/6.97 spl314_98 | ~spl314_260),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1633,f2891,f2157])).
% 38.09/6.97 thf(f2891,definition,(
% 38.09/6.97 spl314_260 <=> (notequalI1 = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_260])],[avatar_definition])).
% 38.09/6.97 thf(f1633,plain,(
% 38.09/6.97 ( ! [X3 : $i] : ((notequalI1 != $true) | ((subset @ X3 @ X3) = $true)) )),
% 38.09/6.97 inference(equality_resolution,[status(thm)],[f1589])).
% 38.09/6.97 thf(f1589,plain,(
% 38.09/6.97 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | (X2 != X3) | (notequalI1 != $true)) )),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f1020])).
% 38.09/6.97 thf(f1020,plain,(
% 38.09/6.97 ((notequalI1 = $true) | (((subset @ sK306 @ sK305) != $true) & (sK306 = sK305))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | (X2 != X3)) | (notequalI1 != $true))),
% 38.09/6.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK305,sK306])],[f1018,f1019])).
% 38.09/6.97 thf(f1019,plain,(
% 38.09/6.97 ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & (X0 = X1)) => (((subset @ sK306 @ sK305) != $true) & (sK306 = sK305))),
% 38.09/6.97 introduced(definition,[],[choice_axiom])).
% 38.09/6.97 thf(f1018,plain,(
% 38.09/6.97 ((notequalI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & (X0 = X1))) & (! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) = $true) | (X2 != X3)) | (notequalI1 != $true))),
% 38.09/6.97 inference(rectify,[status(thm)],[f1017])).
% 38.09/6.97 thf(f1017,plain,(
% 38.09/6.97 ((notequalI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & (X0 = X1))) & (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | (X0 != X1)) | (notequalI1 != $true))),
% 38.09/6.97 inference(nnf_transformation,[status(thm)],[f449])).
% 38.09/6.97 thf(f449,plain,(
% 38.09/6.97 (notequalI1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | (X0 != X1))),
% 38.09/6.97 inference(ennf_transformation,[status(thm)],[f367])).
% 38.09/6.97 thf(f367,plain,(
% 38.09/6.97 ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) => (X0 != X1)) <=> (notequalI1 = $true)),
% 38.09/6.97 inference(flattening,[status(thm)],[f317])).
% 38.09/6.97 thf(f317,plain,(
% 38.09/6.97 ! [X0 : $i,X1 : $i] : (~($true = (subset @ X1 @ X0)) => (X0 != X1)) <=> (notequalI1 = $true)),
% 38.09/6.97 inference(fool_elimination,[status(thm)],[f316])).
% 38.09/6.97 thf(f316,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)) = notequalI1)),
% 38.09/6.97 inference(rectify,[status(thm)],[f86])).
% 38.09/6.97 thf(f86,axiom,(
% 38.09/6.97 (! [X4 : $i,X3 : $i] : (~(subset @ X3 @ X4) => (X3 != X4)) = notequalI1)),
% 38.09/6.97 file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',notequalI1)).
% 38.09/6.97 thf(f2948,plain,(
% 38.09/6.97 spl314_260),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1456,f2891])).
% 38.09/6.97 thf(f1456,plain,(
% 38.09/6.97 (notequalI1 = $true)),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f2778,plain,(
% 38.09/6.97 ~spl314_16 | spl314_236),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1567,f2776,f1797])).
% 38.09/6.97 thf(f1797,definition,(
% 38.09/6.97 spl314_16 <=> (setextsub = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_16])],[avatar_definition])).
% 38.09/6.97 thf(f1567,plain,(
% 38.09/6.97 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | (setextsub != $true) | ($true != (subset @ X1 @ X0))) )),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f997])).
% 38.09/6.97 thf(f997,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ($true != (subset @ X1 @ X0))) | (setextsub != $true)) & ((setextsub = $true) | (((subset @ sK290 @ sK291) = $true) & (sK290 != sK291) & ($true = (subset @ sK291 @ sK290))))),
% 38.09/6.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK290,sK291])],[f995,f996])).
% 38.09/6.97 thf(f996,plain,(
% 38.09/6.97 ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & (X2 != X3) & ((subset @ X3 @ X2) = $true)) => (((subset @ sK290 @ sK291) = $true) & (sK290 != sK291) & ($true = (subset @ sK291 @ sK290)))),
% 38.09/6.97 introduced(definition,[],[choice_axiom])).
% 38.09/6.97 thf(f995,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ($true != (subset @ X1 @ X0))) | (setextsub != $true)) & ((setextsub = $true) | ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & (X2 != X3) & ((subset @ X3 @ X2) = $true)))),
% 38.09/6.97 inference(rectify,[status(thm)],[f994])).
% 38.09/6.97 thf(f994,plain,(
% 38.09/6.97 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ($true != (subset @ X1 @ X0))) | (setextsub != $true)) & ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & (X0 != X1) & ($true = (subset @ X1 @ X0))))),
% 38.09/6.97 inference(nnf_transformation,[status(thm)],[f436])).
% 38.09/6.97 thf(f436,plain,(
% 38.09/6.97 ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ($true != (subset @ X1 @ X0))) <=> (setextsub = $true)),
% 38.09/6.97 inference(flattening,[status(thm)],[f435])).
% 38.09/6.97 thf(f435,plain,(
% 38.09/6.97 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ($true != (subset @ X0 @ X1))) | ($true != (subset @ X1 @ X0)))),
% 38.09/6.97 inference(ennf_transformation,[status(thm)],[f147])).
% 38.09/6.97 thf(f147,plain,(
% 38.09/6.97 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => (($true = (subset @ X0 @ X1)) => (X0 = X1)))),
% 38.09/6.97 inference(fool_elimination,[status(thm)],[f146])).
% 38.09/6.97 thf(f146,plain,(
% 38.09/6.97 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))))),
% 38.09/6.97 inference(rectify,[status(thm)],[f93])).
% 38.09/6.97 thf(f93,axiom,(
% 38.09/6.97 (setextsub = ! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))),
% 38.09/6.97 file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',setextsub)).
% 38.09/6.97 thf(f2097,plain,(
% 38.09/6.97 spl314_6),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1499,f1754])).
% 38.09/6.97 thf(f1754,definition,(
% 38.09/6.97 spl314_6 <=> (binintersectSubset5 = $true)),
% 38.09/6.97 introduced(definition,[new_symbols(naming,[spl314_6])],[avatar_definition])).
% 38.09/6.97 thf(f1499,plain,(
% 38.09/6.97 (binintersectSubset5 = $true)),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f1858,plain,(
% 38.09/6.97 spl314_16),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1430,f1797])).
% 38.09/6.97 thf(f1430,plain,(
% 38.09/6.97 (setextsub = $true)),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f943])).
% 38.09/6.97 thf(f1757,plain,(
% 38.09/6.97 spl314_5 | ~spl314_6),
% 38.09/6.97 inference(avatar_split_clause,[status(thm)],[f1309,f1754,f1751])).
% 38.09/6.97 thf(f1309,plain,(
% 38.09/6.97 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((subset @ X4 @ (binintersect @ X3 @ X5)) = $true) | (binintersectSubset5 != $true) | ((subset @ X4 @ X5) != $true)) )),
% 38.09/6.97 inference(cnf_transformation,[status(thm)],[f821])).
% 38.09/6.97 thf(f821,plain,(
% 38.09/6.97 ((binintersectSubset5 = $true) | (((subset @ sK199 @ sK200) = $true) & ($true != (subset @ sK199 @ (binintersect @ sK198 @ sK200))) & ($true = (subset @ sK199 @ sK198)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) != $true) | ((subset @ X4 @ (binintersect @ X3 @ X5)) = $true) | ((subset @ X4 @ X3) != $true)) | (binintersectSubset5 != $true))),
% 38.09/6.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199,sK200])],[f819,f820])).
% 38.09/6.97 thf(f820,plain,(
% 38.09/6.97 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) & ((subset @ X1 @ (binintersect @ X0 @ X2)) != $true) & ($true = (subset @ X1 @ X0))) => (((subset @ sK199 @ sK200) = $true) & ($true != (subset @ sK199 @ (binintersect @ sK198 @ sK200))) & ($true = (subset @ sK199 @ sK198)))),
% 38.09/6.98 introduced(definition,[],[choice_axiom])).
% 38.09/6.98 thf(f819,plain,(
% 38.09/6.98 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) & ((subset @ X1 @ (binintersect @ X0 @ X2)) != $true) & ($true = (subset @ X1 @ X0)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) != $true) | ((subset @ X4 @ (binintersect @ X3 @ X5)) = $true) | ((subset @ X4 @ X3) != $true)) | (binintersectSubset5 != $true))),
% 38.09/6.98 inference(rectify,[status(thm)],[f818])).
% 38.09/6.98 thf(f818,plain,(
% 38.09/6.98 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) & ((subset @ X1 @ (binintersect @ X0 @ X2)) != $true) & ($true = (subset @ X1 @ X0)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ((subset @ X1 @ (binintersect @ X0 @ X2)) = $true) | ($true != (subset @ X1 @ X0))) | (binintersectSubset5 != $true))),
% 38.09/6.98 inference(nnf_transformation,[status(thm)],[f423])).
% 38.09/6.98 thf(f423,plain,(
% 38.09/6.98 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ((subset @ X1 @ (binintersect @ X0 @ X2)) = $true) | ($true != (subset @ X1 @ X0)))),
% 38.09/6.98 inference(flattening,[status(thm)],[f422])).
% 38.09/6.98 thf(f422,plain,(
% 38.09/6.98 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X1 @ (binintersect @ X0 @ X2)) = $true) | ((subset @ X1 @ X2) != $true)) | ($true != (subset @ X1 @ X0)))),
% 38.09/6.98 inference(ennf_transformation,[status(thm)],[f171])).
% 38.09/6.98 thf(f171,plain,(
% 38.09/6.98 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X0)) => (((subset @ X1 @ X2) = $true) => ((subset @ X1 @ (binintersect @ X0 @ X2)) = $true)))),
% 38.09/6.98 inference(fool_elimination,[status(thm)],[f170])).
% 38.09/6.98 thf(f170,plain,(
% 38.09/6.98 (binintersectSubset5 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((subset @ X1 @ X2) => (subset @ X1 @ (binintersect @ X0 @ X2)))))),
% 38.09/6.98 inference(rectify,[status(thm)],[f109])).
% 38.09/6.98 thf(f109,axiom,(
% 38.09/6.98 (binintersectSubset5 = ! [X3 : $i,X5 : $i,X4 : $i] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))))),
% 38.09/6.98 file('/export/starexec/sandbox/tmp/tmp.k1V0VHujP1/DTF2THF_29850.p',binintersectSubset5)).
% 38.09/6.98 % SZS output end Proof for DTF2THF_29850
% 38.09/6.98 % (30069)------------------------------
% 38.09/6.98 % (30069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.09/6.98 % (30069)Termination reason: Refutation
% 38.09/6.98
% 38.09/6.98 % (30069)Memory used [KB]: 19701
% 38.09/6.98 % (30069)Time elapsed: 2.718 s
% 38.09/6.98 % (30069)Instructions burned: 5242 (million)
% 38.09/6.98 % (30069)------------------------------
% 38.09/6.98 % (30069)------------------------------
% 38.09/6.98 % (29947)Success in time 5.398 s
%------------------------------------------------------------------------------