%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU606^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 09:35:34 AM UTC 2026
% Result : Theorem 2.56s 1.67s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 2568 ( 705 equ; 0 cnn)
% Maximal formula atoms : 125 ( 64 avg)
% Number of connectives : 1362 ( 71 ~; 34 |; 389 &; 232 @)
% ( 6 <=>; 630 =>; 0 <=; 0 <~>)
% Maximal formula depth : 132 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 247 ( 244 usr; 132 con; 0-4 aty)
% Number of variables : 63 ( 0 ^; 45 !; 18 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_154,type,
sP0: $i > $i > $o ).
thf(func_def_155,type,
sP1: $i > $o ).
thf(func_def_156,type,
sP2: $i > $i > $o ).
thf(func_def_157,type,
sP3: $i > $i > $o ).
thf(func_def_159,type,
sK5: $i > $i ).
thf(func_def_170,type,
sK16: $i > $i > $i ).
thf(func_def_173,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK20: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK21: $i > $o ).
thf(func_def_176,type,
sK22: $i > $o ).
thf(func_def_186,type,
sK32: $o > $i > $i > $i ).
thf(func_def_193,type,
sK39: $i > $o ).
thf(func_def_199,type,
sK45: $i > $o ).
thf(func_def_200,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_202,type,
sK48: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_203,type,
sK49: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_206,type,
sK52: $i > $o ).
thf(func_def_207,type,
sK53: $i > $o ).
thf(func_def_216,type,
sK62: $i > $i ).
thf(func_def_232,type,
sK78: $i > $o ).
thf(func_def_235,type,
sK81: $i > ( $i > $o ) > $i ).
thf(func_def_241,type,
sK87: $i > $i > $i ).
thf(func_def_242,type,
sK88: $i > $o ).
thf(func_def_243,type,
sK89: $i > $i ).
thf(func_def_244,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK98: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK99: $i > $o ).
thf(func_def_256,type,
sK102: $i > ( $i > $o ) > $i ).
thf(func_def_257,type,
sK103: $i > $o ).
thf(func_def_280,type,
sK126: $i > $o ).
thf(func_def_286,type,
sK132: $i > $o ).
thf(func_def_289,type,
sK135: $i > $o ).
thf(func_def_295,type,
sK141: $i > $i > $i ).
thf(func_def_301,type,
sK147: $i > $i > $i ).
thf(func_def_305,type,
sK151: $i > $o ).
thf(func_def_308,type,
sK154: $i > $o ).
thf(func_def_310,type,
sK156: $i > $o ).
thf(func_def_315,type,
sK161: $i > $i > $i ).
thf(func_def_316,type,
sK162: $i > $i > $i ).
thf(func_def_320,type,
sK166: $i > $o ).
thf(func_def_328,type,
sK174: ( $i > $o ) > $i ).
thf(func_def_329,type,
sK175: ( $i > $o ) > $i ).
thf(func_def_330,type,
sK176: $i > $o ).
thf(func_def_333,type,
sK179: $i > $o ).
thf(func_def_335,type,
sK181: ( $i > $o ) > $i > $i ).
thf(func_def_346,type,
sK192: $i > $o ).
thf(func_def_347,type,
sK193: $i > $o ).
thf(func_def_348,type,
sK194: $i > $i > $i ).
thf(func_def_351,type,
sK197: $i > $i > $i ).
thf(func_def_352,type,
sK198: $i > $i > $i ).
thf(func_def_353,type,
sK199: $i > $i > $i ).
thf(func_def_354,type,
sK200: $i > $i > $i ).
thf(func_def_355,type,
sK201: $i > $i > $i > $i ).
thf(func_def_356,type,
sK202: $i > $i ).
thf(func_def_357,type,
sK203: $i > $i ).
thf(func_def_358,type,
sK204: $i > $i ).
thf(func_def_359,type,
sK205: $i > $i ).
thf(func_def_360,type,
sK206: $i > $i > $i ).
thf(func_def_361,type,
sK207: $i > $i > $i > $i ).
thf(func_def_362,type,
sK208: $i > $i > $i > $i ).
thf(func_def_363,type,
sK209: $i > $i > $i ).
thf(func_def_364,type,
sK210: $i > $i > $i ).
thf(func_def_365,type,
sK211: $i > $i ).
thf(func_def_366,type,
sK212: $i > $i > $i ).
thf(func_def_368,type,
sK214: $i > $i ).
thf(func_def_369,type,
sK215: $i > $i ).
thf(func_def_370,type,
sK216: $i > $o ).
thf(func_def_376,type,
sK222: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_377,type,
sK223: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_378,type,
sK224: $i > $o ).
thf(func_def_379,type,
sK225: $i > $o ).
thf(func_def_381,type,
sK227: $i > $o ).
thf(func_def_383,type,
sK229: ( $i > $o ) > $i > $i ).
thf(func_def_387,type,
sK233: $i > $o ).
thf(func_def_389,type,
sK235: $i > ( $i > $o ) > $i ).
thf(func_def_398,type,
sK244: $i > $i > $o ).
thf(func_def_400,type,
sK246: $i > $i ).
thf(func_def_401,type,
sK247: $i > $i ).
thf(func_def_402,type,
sK248: $i > ( $i > $i > $o ) > $i ).
thf(func_def_403,type,
sK249: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_404,type,
sK250: $i > ( $i > $i > $o ) > $i ).
thf(func_def_405,type,
sK251: $i > $i ).
thf(func_def_414,type,
sK260: $i > $i ).
thf(func_def_422,type,
sK268: $i > $o ).
thf(func_def_423,type,
sK269: $i > $i ).
thf(func_def_424,type,
sK270: ( $i > $o ) > $i ).
thf(func_def_438,type,
sK284: $i > ( $i > $o ) > $i ).
thf(func_def_439,type,
sK285: $i > $o ).
thf(func_def_452,type,
sK298: $i > $i > $i ).
thf(func_def_454,type,
sK300: $i > $o ).
thf(func_def_465,type,
sK311: $i > $i > $i ).
thf(func_def_466,type,
sK312: $i > ( $i > $o ) > $i ).
thf(func_def_467,type,
sK313: $i > $o ).
thf(func_def_479,type,
sK325: $i > $i ).
thf(func_def_482,type,
sK328: $i > $i ).
thf(func_def_483,type,
sK329: $i > $i ).
thf(func_def_491,type,
ph337:
!>[X0: $tType] : X0 ).
thf(f1910,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1859,f1891,f1906]) ).
thf(f1906,plain,
~ spl336_4,
inference(avatar_contradiction_clause,[status(thm)],[f1905]) ).
thf(f1905,plain,
( $false
| ~ spl336_4 ),
inference(trivial_inequality_removal,[status(thm)],[f1903]) ).
thf(f1903,plain,
( ( $true != $true )
| ~ spl336_4 ),
inference(superposition,[status(thm)],[f1312,f1855]) ).
thf(f1855,plain,
( ( ( in @ sK130 @ sK128 )
= $true )
| ~ spl336_4 ),
inference(avatar_component_clause,[status(thm)],[f1853]) ).
thf(f1853,definition,
( spl336_4
<=> ( ( in @ sK130 @ sK128 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl336_4])],[avatar_definition]) ).
thf(f1312,plain,
( ( in @ sK130 @ sK128 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f748]) ).
thf(f748,plain,
( ( nonemptyI1 = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( setbeta = $true )
& ( descrp = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( binunionE = $true )
& ( setextsub = $true )
& ( exuE3e = $true )
& ( powersetsubset = $true )
& ( exu__Cong = $true )
& ( omegaSAx = $true )
& ( notinsingleton = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( binintersectSubset5 = $true )
& ( powersetE1 = $true )
& ( exuI1 = $true )
& ( eqimpsubset1 = $true )
& ( notequalI2 = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( subsetE2 = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( eqimpsubset2 = $true )
& ( eqinunit = $true )
& ( dsetconstrEL = $true )
& ( in__Cong = $true )
& ( binunionRsub = $true )
& ( bs114d = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( setadjoinIR = $true )
& ( setunionI = $true )
& ( quantDeMorgan1 = $true )
& ( disjointsetsI1 = $true )
& ( prop2setI = $true )
& ( exuI2 = $true )
& ( singletonsswitch = $true )
& ( upairset2IR = $true )
& ( binintersectSubset1 = $true )
& ( foundationAx = $true )
& ( omega__Cong = $true )
& ( sepInPowerset = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( subPowSU = $true )
& ( powerset__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinIL = $true )
& ( powersetI = $true )
& ( subset2powerset = $true )
& ( setminusSubset2 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( powersetE = $true )
& ( binintersectEL = $true )
& ( binintersectSubset2 = $true )
& ( powersetI1 = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset3 = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ( binunionIL = $true )
& ( binintersectSubset4 = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( sepSubset = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( setminusI = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( uniqinunit = $true )
& ( ( in @ sK130 @ sK129 )
= $true )
& ( ( in @ sK130 @ sK128 )
!= $true )
& ( ( in @ sK130 @ ( setminus @ sK129 @ sK128 ) )
!= $true )
& ( subsetI2 = $true )
& ( notdexE = $true )
& ( setminusERneg = $true )
& ( emptysetsubset = $true )
& ( omegaIndAx = $true )
& ( setunionE = $true )
& ( emptyE1 = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyInPowerset = $true )
& ( nonemptyE1 = $true )
& ( binunionEcases = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( vacuousDall = $true )
& ( setext = $true )
& ( notinemptyset = $true )
& ( binintersectRsub = $true )
& ( notsubsetI = $true )
& ( exuE2 = $true )
& ( upairsetE = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( subsetTrans = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129,sK130])],[f450,f747]) ).
thf(f747,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) )
=> ( ( ( in @ sK130 @ sK129 )
= $true )
& ( ( in @ sK130 @ sK128 )
!= $true )
& ( ( in @ sK130 @ ( setminus @ sK129 @ sK128 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f450,plain,
( ( nonemptyI1 = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( setbeta = $true )
& ( descrp = $true )
& ( setadjoinOr = $true )
& ( emptyinunitempty = $true )
& ( binunionE = $true )
& ( setextsub = $true )
& ( exuE3e = $true )
& ( powersetsubset = $true )
& ( exu__Cong = $true )
& ( omegaSAx = $true )
& ( notinsingleton = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( binintersectSubset5 = $true )
& ( powersetE1 = $true )
& ( exuI1 = $true )
& ( eqimpsubset1 = $true )
& ( notequalI2 = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( subsetE2 = $true )
& ( notdallE = $true )
& ( setminusER = $true )
& ( eqimpsubset2 = $true )
& ( eqinunit = $true )
& ( dsetconstrEL = $true )
& ( in__Cong = $true )
& ( binunionRsub = $true )
& ( bs114d = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( setadjoinIR = $true )
& ( setunionI = $true )
& ( quantDeMorgan1 = $true )
& ( disjointsetsI1 = $true )
& ( prop2setI = $true )
& ( exuI2 = $true )
& ( singletonsswitch = $true )
& ( upairset2IR = $true )
& ( binintersectSubset1 = $true )
& ( foundationAx = $true )
& ( omega__Cong = $true )
& ( sepInPowerset = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( subPowSU = $true )
& ( powerset__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinIL = $true )
& ( powersetI = $true )
& ( subset2powerset = $true )
& ( setminusSubset2 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( powersetE = $true )
& ( binintersectEL = $true )
& ( binintersectSubset2 = $true )
& ( powersetI1 = $true )
& ( wellorderingAx = $true )
& ( upairsetIR = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset3 = $true )
& ( nonemptyI = $true )
& ( emptysetAx = $true )
& ( binunionIL = $true )
& ( binintersectSubset4 = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( sepSubset = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( binunionLsub = $true )
& ( subsetE = $true )
& ( setminusI = $true )
& ( binintersectER = $true )
& ( binintersectLsub = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) )
& ( subsetI2 = $true )
& ( notdexE = $true )
& ( setminusERneg = $true )
& ( emptysetsubset = $true )
& ( omegaIndAx = $true )
& ( setunionE = $true )
& ( emptyE1 = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyInPowerset = $true )
& ( nonemptyE1 = $true )
& ( binunionEcases = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( vacuousDall = $true )
& ( setext = $true )
& ( notinemptyset = $true )
& ( binintersectRsub = $true )
& ( notsubsetI = $true )
& ( exuE2 = $true )
& ( upairsetE = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( dsetconstrI = $true )
& ( subsetTrans = $true ) ),
inference(flattening,[status(thm)],[f449]) ).
thf(f449,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true ) )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f381]) ).
thf(f381,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f205]) ).
thf(f205,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
!= $true )
=> ( ( ( in @ X2 @ X0 )
!= $true )
=> ( ( in @ X2 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f204]) ).
thf(f204,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ( ~ ( in @ X2 @ X0 )
=> ~ ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f126]) ).
thf(f126,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ! [X4: $i,X3: $i,X1: $i] :
( ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f125]) ).
thf(f125,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ! [X4: $i,X3: $i,X1: $i] :
( ~ ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glf2gEZoRt/DTF2THF_21016.p',setminusELneg) ).
thf(f1891,plain,
spl336_3,
inference(avatar_contradiction_clause,[status(thm)],[f1890]) ).
thf(f1890,plain,
( $false
| spl336_3 ),
inference(trivial_inequality_removal,[status(thm)],[f1880]) ).
thf(f1880,plain,
( ( $true != $true )
| spl336_3 ),
inference(superposition,[status(thm)],[f1851,f1313]) ).
thf(f1313,plain,
( ( in @ sK130 @ sK129 )
= $true ),
inference(cnf_transformation,[status(thm)],[f748]) ).
thf(f1851,plain,
( ( ( in @ sK130 @ sK129 )
!= $true )
| spl336_3 ),
inference(avatar_component_clause,[status(thm)],[f1849]) ).
thf(f1849,definition,
( spl336_3
<=> ( ( in @ sK130 @ sK129 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl336_3])],[avatar_definition]) ).
thf(f1859,plain,
( spl336_4
| ~ spl336_3 ),
inference(avatar_split_clause,[status(thm)],[f1858,f1849,f1853]) ).
thf(f1858,plain,
( ( ( in @ sK130 @ sK128 )
= $true )
| ( ( in @ sK130 @ sK129 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1857]) ).
thf(f1857,plain,
( ( ( in @ sK130 @ sK128 )
= $true )
| ( $true != $true )
| ( ( in @ sK130 @ sK129 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1828,f1317]) ).
thf(f1317,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f748]) ).
thf(f1828,plain,
( ( ( in @ sK130 @ sK129 )
!= $true )
| ( setminusI != $true )
| ( ( in @ sK130 @ sK128 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1819]) ).
thf(f1819,plain,
( ( $true != $true )
| ( setminusI != $true )
| ( ( in @ sK130 @ sK129 )
!= $true )
| ( ( in @ sK130 @ sK128 )
= $true ) ),
inference(superposition,[status(thm)],[f1311,f1112]) ).
thf(f1112,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X5 )
= $true )
| ( setminusI != $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f548]) ).
thf(f548,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK8 @ ( setminus @ sK9 @ sK10 ) )
!= $true )
& ( ( in @ sK8 @ sK9 )
= $true )
& ( ( in @ sK8 @ sK10 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f546,f547]) ).
thf(f547,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) )
=> ( ( ( in @ sK8 @ ( setminus @ sK9 @ sK10 ) )
!= $true )
& ( ( in @ sK8 @ sK9 )
= $true )
& ( ( in @ sK8 @ sK10 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f546,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true )
| ( ( in @ X3 @ X4 )
!= $true )
| ( ( in @ X3 @ X5 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f545]) ).
thf(f545,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ X2 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f515]) ).
thf(f515,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f514]) ).
thf(f514,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f401]) ).
thf(f401,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f359]) ).
thf(f359,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f358]) ).
thf(f358,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f120]) ).
thf(f120,axiom,
( setminusI
= ( ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.glf2gEZoRt/DTF2THF_21016.p',setminusI) ).
thf(f1311,plain,
( ( in @ sK130 @ ( setminus @ sK129 @ sK128 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU606^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:28:08 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU606^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! B:i.! x:i.~(in x (setminus A B)) -> ~(in x B) ->
% 0.29/0.46 % ~(in x A))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC108g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 266 ( 124 unt; 141 typ; 124 def)
% 0.29/0.46 % Number of atoms : 662 ( 180 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 125 ( 5 avg)
% 0.29/0.46 % Number of connectives : 1049 ( 36 ~; 6 |; 28 &; 671 @)
% 0.29/0.46 % ( 14 <=>; 294 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 131 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 144 ( 141 usr; 126 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 360 ( 30 ^; 301 !; 29 ?; 360 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=461
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ( sepSubset
% 0.29/0.46 => ( binunionIL
% 0.29/0.46 => ( upairset2IR
% 0.29/0.46 => ( binunionIR
% 0.29/0.46 => ( binunionEcases
% 0.29/0.46 => ( binunionE
% 0.29/0.46 => ( binunionLsub
% 0.29/0.47 => ( binunionRsub
% 0.29/0.47 => ( binintersectI
% 0.29/0.47 => ( binintersectSubset5
% 0.29/0.47 => ( binintersectEL
% 0.29/0.47 => ( binintersectLsub
% 0.29/0.47 => ( binintersectSubset2
% 0.29/0.47 => ( binintersectSubset3
% 0.29/0.47 => ( binintersectER
% 0.29/0.47 => ( disjointsetsI1
% 0.29/0.47 => ( binintersectRsub
% 0.29/0.47 => ( binintersectSubset4
% 0.29/0.47 => ( binintersectSubset1
% 0.29/0.47 => ( bs114d
% 0.29/0.47 => ( setminusI
% 0.29/0.47 => ( setminusEL
% 0.29/0.47 => ( setminusER
% 0.29/0.47 => ( setminusSubset2
% 0.29/0.47 => ( setminusERneg
% 0.29/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.25/1.49 ---- Embedded in THF ---
% 2.25/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.25/1.49 %%% Generated on Tue Feb 24 12:28:09 EST 2026
% 2.25/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.25/1.49 %%% Logic specification used:
% 2.25/1.49 %%% thf(spec, logic, $$dhol).
% 2.25/1.49
% 2.25/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.glf2gEZoRt/DTF2DTF21016.p
% See solution above
% 2.25/1.49 ------------------------
% 2.54/1.52 ---- Cleaned THF ---
% 2.54/1.52 thf(in_type,type,
% 2.54/1.52 in: $i > $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(exu_type,type,
% 2.54/1.52 exu: ( $i > $o ) > $o ).
% 2.54/1.52
% 2.54/1.52 thf(exu,definition,
% 2.54/1.52 ( exu
% 2.54/1.52 = ( ^ [Xphi: $i > $o] :
% 2.54/1.52 ? [Xx: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 & ! [Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setextAx_type,type,
% 2.54/1.52 setextAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setextAx,definition,
% 2.54/1.52 ( setextAx
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 <=> ( in @ Xx @ B ) )
% 2.54/1.52 => ( A = B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyset_type,type,
% 2.54/1.52 emptyset: $i ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetAx_type,type,
% 2.54/1.52 emptysetAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetAx,definition,
% 2.54/1.52 ( emptysetAx
% 2.54/1.52 = ( ! [Xx: $i] :
% 2.54/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoin_type,type,
% 2.54/1.52 setadjoin: $i > $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinAx_type,type,
% 2.54/1.52 setadjoinAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinAx,definition,
% 2.54/1.52 ( setadjoinAx
% 2.54/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.52 <=> ( ( Xy = Xx )
% 2.54/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powerset_type,type,
% 2.54/1.52 powerset: $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(powersetAx_type,type,
% 2.54/1.52 powersetAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetAx,definition,
% 2.54/1.52 ( powersetAx
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.52 <=> ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setunion_type,type,
% 2.54/1.52 setunion: $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(setunionAx_type,type,
% 2.54/1.52 setunionAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setunionAx,definition,
% 2.54/1.52 ( setunionAx
% 2.54/1.52 = ( ! [A: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.54/1.52 <=> ? [B: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(omega_type,type,
% 2.54/1.52 omega: $i ).
% 2.54/1.52
% 2.54/1.52 thf(omega0Ax_type,type,
% 2.54/1.52 omega0Ax: $o ).
% 2.54/1.52
% 2.54/1.52 thf(omega0Ax,definition,
% 2.54/1.52 ( omega0Ax
% 2.54/1.52 = ( in @ emptyset @ omega ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(omegaSAx_type,type,
% 2.54/1.52 omegaSAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(omegaSAx,definition,
% 2.54/1.52 ( omegaSAx
% 2.54/1.52 = ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ omega )
% 2.54/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(omegaIndAx_type,type,
% 2.54/1.52 omegaIndAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(omegaIndAx,definition,
% 2.54/1.52 ( omegaIndAx
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ( ( in @ emptyset @ A )
% 2.54/1.52 & ! [Xx: $i] :
% 2.54/1.52 ( ( ( in @ Xx @ omega )
% 2.54/1.52 & ( in @ Xx @ A ) )
% 2.54/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.54/1.52 => ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ omega )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(replAx_type,type,
% 2.54/1.52 replAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(replAx,definition,
% 2.54/1.52 ( replAx
% 2.54/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( exu
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.54/1.52 => ? [B: $i] :
% 2.54/1.52 ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 <=> ? [Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ A )
% 2.54/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(foundationAx_type,type,
% 2.54/1.52 foundationAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(foundationAx,definition,
% 2.54/1.52 ( foundationAx
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.54/1.52 => ? [B: $i] :
% 2.54/1.52 ( ( in @ B @ A )
% 2.54/1.52 & ~ ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(wellorderingAx_type,type,
% 2.54/1.52 wellorderingAx: $o ).
% 2.54/1.52
% 2.54/1.52 thf(wellorderingAx,definition,
% 2.54/1.52 ( wellorderingAx
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ? [B: $i] :
% 2.54/1.52 ( ! [C: $i] :
% 2.54/1.52 ( ( in @ C @ B )
% 2.54/1.52 => ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ C )
% 2.54/1.52 => ( in @ Xx @ A ) ) )
% 2.54/1.52 & ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( ( in @ Xx @ A )
% 2.54/1.52 & ( in @ Xy @ A ) )
% 2.54/1.52 => ( ! [C: $i] :
% 2.54/1.52 ( ( in @ C @ B )
% 2.54/1.52 => ( ( in @ Xx @ C )
% 2.54/1.52 <=> ( in @ Xy @ C ) ) )
% 2.54/1.52 => ( Xx = Xy ) ) )
% 2.54/1.52 & ! [C: $i,D: $i] :
% 2.54/1.52 ( ( ( in @ C @ B )
% 2.54/1.52 & ( in @ D @ B ) )
% 2.54/1.52 => ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ C )
% 2.54/1.52 => ( in @ Xx @ D ) )
% 2.54/1.52 | ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ D )
% 2.54/1.52 => ( in @ Xx @ C ) ) ) )
% 2.54/1.52 & ! [C: $i] :
% 2.54/1.52 ( ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ C )
% 2.54/1.52 => ( in @ Xx @ A ) )
% 2.54/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.54/1.52 => ? [D: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ D @ B )
% 2.54/1.52 & ( in @ Xx @ C )
% 2.54/1.52 & ~ ? [Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ D )
% 2.54/1.52 & ( in @ Xy @ C ) )
% 2.54/1.52 & ! [E: $i] :
% 2.54/1.52 ( ( in @ E @ B )
% 2.54/1.52 => ( ! [Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ E )
% 2.54/1.52 => ( in @ Xy @ D ) )
% 2.54/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(descr_type,type,
% 2.54/1.52 descr: ( $i > $o ) > $i ).
% 2.54/1.52
% 2.54/1.52 thf(descrp_type,type,
% 2.54/1.52 descrp: $o ).
% 2.54/1.52
% 2.54/1.52 thf(descrp,definition,
% 2.54/1.52 ( descrp
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ( Xphi
% 2.54/1.52 @ ( descr
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstr_type,type,
% 2.54/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrI_type,type,
% 2.54/1.52 dsetconstrI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrI,definition,
% 2.54/1.52 ( dsetconstrI
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ( Xphi @ Xx )
% 2.54/1.52 => ( in @ Xx
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrEL_type,type,
% 2.54/1.52 dsetconstrEL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrEL,definition,
% 2.54/1.52 ( dsetconstrEL
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrER_type,type,
% 2.54/1.52 dsetconstrER: $o ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstrER,definition,
% 2.54/1.52 ( dsetconstrER
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuE1_type,type,
% 2.54/1.52 exuE1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuE1,definition,
% 2.54/1.52 ( exuE1
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ? [Xx: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 & ! [Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(prop2set_type,type,
% 2.54/1.52 prop2set: $o > $i ).
% 2.54/1.52
% 2.54/1.52 thf(prop2setE_type,type,
% 2.54/1.52 prop2setE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(prop2setE,definition,
% 2.54/1.52 ( prop2setE
% 2.54/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.54/1.52 => Xphi ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetE_type,type,
% 2.54/1.52 emptysetE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetE,definition,
% 2.54/1.52 ( emptysetE
% 2.54/1.52 = ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ emptyset )
% 2.54/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetimpfalse_type,type,
% 2.54/1.52 emptysetimpfalse: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetimpfalse,definition,
% 2.54/1.52 ( emptysetimpfalse
% 2.54/1.52 = ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ emptyset )
% 2.54/1.52 => $false ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notinemptyset_type,type,
% 2.54/1.52 notinemptyset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notinemptyset,definition,
% 2.54/1.52 ( notinemptyset
% 2.54/1.52 = ( ! [Xx: $i] :
% 2.54/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuE3e_type,type,
% 2.54/1.52 exuE3e: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuE3e,definition,
% 2.54/1.52 ( exuE3e
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setext_type,type,
% 2.54/1.52 setext: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setext,definition,
% 2.54/1.52 ( setext
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ B ) )
% 2.54/1.52 => ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ A ) )
% 2.54/1.52 => ( A = B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyI_type,type,
% 2.54/1.52 emptyI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyI,definition,
% 2.54/1.52 ( emptyI
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ~ ( in @ Xx @ A )
% 2.54/1.52 => ( A = emptyset ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(noeltsimpempty_type,type,
% 2.54/1.52 noeltsimpempty: $o ).
% 2.54/1.52
% 2.54/1.52 thf(noeltsimpempty,definition,
% 2.54/1.52 ( noeltsimpempty
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ~ ( in @ Xx @ A )
% 2.54/1.52 => ( A = emptyset ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setbeta_type,type,
% 2.54/1.52 setbeta: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setbeta,definition,
% 2.54/1.52 ( setbeta
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ( in @ Xx
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(nonempty_type,type,
% 2.54/1.52 nonempty: $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(nonempty,definition,
% 2.54/1.52 ( nonempty
% 2.54/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyE1_type,type,
% 2.54/1.52 nonemptyE1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyE1,definition,
% 2.54/1.52 ( nonemptyE1
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ( nonempty @ A )
% 2.54/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyI_type,type,
% 2.54/1.52 nonemptyI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyI,definition,
% 2.54/1.52 ( nonemptyI
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ( Xphi @ Xx )
% 2.54/1.52 => ( nonempty
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyI1_type,type,
% 2.54/1.52 nonemptyI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyI1,definition,
% 2.54/1.52 ( nonemptyI1
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.54/1.52 => ( nonempty @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinIL_type,type,
% 2.54/1.52 setadjoinIL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinIL,definition,
% 2.54/1.52 ( setadjoinIL
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyinunitempty_type,type,
% 2.54/1.52 emptyinunitempty: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyinunitempty,definition,
% 2.54/1.52 ( emptyinunitempty
% 2.54/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinIR_type,type,
% 2.54/1.52 setadjoinIR: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinIR,definition,
% 2.54/1.52 ( setadjoinIR
% 2.54/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ A )
% 2.54/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinE_type,type,
% 2.54/1.52 setadjoinE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinE,definition,
% 2.54/1.52 ( setadjoinE
% 2.54/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.52 => ! [Xphi: $o] :
% 2.54/1.52 ( ( ( Xy = Xx )
% 2.54/1.52 => Xphi )
% 2.54/1.52 => ( ( ( in @ Xy @ A )
% 2.54/1.52 => Xphi )
% 2.54/1.52 => Xphi ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinOr_type,type,
% 2.54/1.52 setadjoinOr: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinOr,definition,
% 2.54/1.52 ( setadjoinOr
% 2.54/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.52 => ( ( Xy = Xx )
% 2.54/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setoftrueEq_type,type,
% 2.54/1.52 setoftrueEq: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setoftrueEq,definition,
% 2.54/1.52 ( setoftrueEq
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xx: $i] : $true )
% 2.54/1.52 = A ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powersetI_type,type,
% 2.54/1.52 powersetI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetI,definition,
% 2.54/1.52 ( powersetI
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ A ) )
% 2.54/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyinPowerset_type,type,
% 2.54/1.52 emptyinPowerset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyinPowerset,definition,
% 2.54/1.52 ( emptyinPowerset
% 2.54/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyInPowerset_type,type,
% 2.54/1.52 emptyInPowerset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyInPowerset,definition,
% 2.54/1.52 ( emptyInPowerset
% 2.54/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powersetE_type,type,
% 2.54/1.52 powersetE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetE,definition,
% 2.54/1.52 ( powersetE
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.52 => ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setunionI_type,type,
% 2.54/1.52 setunionI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setunionI,definition,
% 2.54/1.52 ( setunionI
% 2.54/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( ( in @ B @ A )
% 2.54/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setunionE_type,type,
% 2.54/1.52 setunionE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setunionE,definition,
% 2.54/1.52 ( setunionE
% 2.54/1.52 = ( ! [A: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.54/1.52 => ! [Xphi: $o] :
% 2.54/1.52 ( ! [B: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( ( in @ B @ A )
% 2.54/1.52 => Xphi ) )
% 2.54/1.52 => Xphi ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subPowSU_type,type,
% 2.54/1.52 subPowSU: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subPowSU,definition,
% 2.54/1.52 ( subPowSU
% 2.54/1.52 = ( ! [A: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuE2_type,type,
% 2.54/1.52 exuE2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuE2,definition,
% 2.54/1.52 ( exuE2
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ? [Xx: $i] :
% 2.54/1.52 ! [Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xy )
% 2.54/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyImpWitness_type,type,
% 2.54/1.52 nonemptyImpWitness: $o ).
% 2.54/1.52
% 2.54/1.52 thf(nonemptyImpWitness,definition,
% 2.54/1.52 ( nonemptyImpWitness
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ( nonempty @ A )
% 2.54/1.52 => ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & $true ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(uniqinunit_type,type,
% 2.54/1.52 uniqinunit: $o ).
% 2.54/1.52
% 2.54/1.52 thf(uniqinunit,definition,
% 2.54/1.52 ( uniqinunit
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.54/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notinsingleton_type,type,
% 2.54/1.52 notinsingleton: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notinsingleton,definition,
% 2.54/1.52 ( notinsingleton
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx != Xy )
% 2.54/1.52 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(eqinunit_type,type,
% 2.54/1.52 eqinunit: $o ).
% 2.54/1.52
% 2.54/1.52 thf(eqinunit,definition,
% 2.54/1.52 ( eqinunit
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(singletonsswitch_type,type,
% 2.54/1.52 singletonsswitch: $o ).
% 2.54/1.52
% 2.54/1.52 thf(singletonsswitch,definition,
% 2.54/1.52 ( singletonsswitch
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.54/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetE_type,type,
% 2.54/1.52 upairsetE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetE,definition,
% 2.54/1.52 ( upairsetE
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.54/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.54/1.52 => ( ( Xz = Xx )
% 2.54/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetIL_type,type,
% 2.54/1.52 upairsetIL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetIL,definition,
% 2.54/1.52 ( upairsetIL
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetIR_type,type,
% 2.54/1.52 upairsetIR: $o ).
% 2.54/1.52
% 2.54/1.52 thf(upairsetIR,definition,
% 2.54/1.52 ( upairsetIR
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyE1_type,type,
% 2.54/1.52 emptyE1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyE1,definition,
% 2.54/1.52 ( emptyE1
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ( Xphi @ Xx ) )
% 2.54/1.52 => ( ( ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 = emptyset )
% 2.54/1.52 => $false ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(vacuousDall_type,type,
% 2.54/1.52 vacuousDall: $o ).
% 2.54/1.52
% 2.54/1.52 thf(vacuousDall,definition,
% 2.54/1.52 ( vacuousDall
% 2.54/1.52 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ emptyset )
% 2.54/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan1_type,type,
% 2.54/1.52 quantDeMorgan1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan1,definition,
% 2.54/1.52 ( quantDeMorgan1
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ~ ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( Xphi @ Xx ) )
% 2.54/1.52 => ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan2_type,type,
% 2.54/1.52 quantDeMorgan2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan2,definition,
% 2.54/1.52 ( quantDeMorgan2
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ~ ( Xphi @ Xx ) )
% 2.54/1.52 => ~ ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan3_type,type,
% 2.54/1.52 quantDeMorgan3: $o ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan3,definition,
% 2.54/1.52 ( quantDeMorgan3
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ~ ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ( Xphi @ Xx ) )
% 2.54/1.52 => ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan4_type,type,
% 2.54/1.52 quantDeMorgan4: $o ).
% 2.54/1.52
% 2.54/1.52 thf(quantDeMorgan4,definition,
% 2.54/1.52 ( quantDeMorgan4
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ~ ( Xphi @ Xx ) )
% 2.54/1.52 => ~ ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(prop2setI_type,type,
% 2.54/1.52 prop2setI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(prop2setI,definition,
% 2.54/1.52 ( prop2setI
% 2.54/1.52 = ( ! [Xphi: $o] :
% 2.54/1.52 ( Xphi
% 2.54/1.52 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(set2prop_type,type,
% 2.54/1.52 set2prop: $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(prop2set2propI_type,type,
% 2.54/1.52 prop2set2propI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(prop2set2propI,definition,
% 2.54/1.52 ( prop2set2propI
% 2.54/1.52 = ( ! [Xphi: $o] :
% 2.54/1.52 ( Xphi
% 2.54/1.52 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notdexE_type,type,
% 2.54/1.52 notdexE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notdexE,definition,
% 2.54/1.52 ( notdexE
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ~ ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ( Xphi @ Xx ) )
% 2.54/1.52 => ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notdallE_type,type,
% 2.54/1.52 notdallE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notdallE,definition,
% 2.54/1.52 ( notdallE
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( ~ ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( Xphi @ Xx ) )
% 2.54/1.52 => ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuI1_type,type,
% 2.54/1.52 exuI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuI1,definition,
% 2.54/1.52 ( exuI1
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ? [Xx: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 & ! [Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) )
% 2.54/1.52 => ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuI3_type,type,
% 2.54/1.52 exuI3: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuI3,definition,
% 2.54/1.52 ( exuI3
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.54/1.52 => ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 => ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) )
% 2.54/1.52 => ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuI2_type,type,
% 2.54/1.52 exuI2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuI2,definition,
% 2.54/1.52 ( exuI2
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ? [Xx: $i] :
% 2.54/1.52 ! [Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xy )
% 2.54/1.52 <=> ( Xy = Xx ) )
% 2.54/1.52 => ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(inCongP_type,type,
% 2.54/1.52 inCongP: $o ).
% 2.54/1.52
% 2.54/1.52 thf(inCongP,definition,
% 2.54/1.52 ( inCongP
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(in__Cong_type,type,
% 2.54/1.52 in__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(in__Cong,definition,
% 2.54/1.52 ( in__Cong
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ( ( in @ Xx @ A )
% 2.54/1.52 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuE3u_type,type,
% 2.54/1.52 exuE3u: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuE3u,definition,
% 2.54/1.52 ( exuE3u
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 => ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exu__Cong_type,type,
% 2.54/1.52 exu__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exu__Cong,definition,
% 2.54/1.52 ( exu__Cong
% 2.54/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ( ( Xphi @ Xx )
% 2.54/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.54/1.52 => ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 <=> ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptyset__Cong_type,type,
% 2.54/1.52 emptyset__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptyset__Cong,definition,
% 2.54/1.52 ( emptyset__Cong
% 2.54/1.52 = ( emptyset = emptyset ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoin__Cong_type,type,
% 2.54/1.52 setadjoin__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoin__Cong,definition,
% 2.54/1.52 ( setadjoin__Cong
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ! [Xz: $i,Xu: $i] :
% 2.54/1.52 ( ( Xz = Xu )
% 2.54/1.52 => ( ( setadjoin @ Xx @ Xz )
% 2.54/1.52 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powerset__Cong_type,type,
% 2.54/1.52 powerset__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powerset__Cong,definition,
% 2.54/1.52 ( powerset__Cong
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ( ( powerset @ A )
% 2.54/1.52 = ( powerset @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setunion__Cong_type,type,
% 2.54/1.52 setunion__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setunion__Cong,definition,
% 2.54/1.52 ( setunion__Cong
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ( ( setunion @ A )
% 2.54/1.52 = ( setunion @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(omega__Cong_type,type,
% 2.54/1.52 omega__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(omega__Cong,definition,
% 2.54/1.52 ( omega__Cong
% 2.54/1.52 = ( omega = omega ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(exuEu_type,type,
% 2.54/1.52 exuEu: $o ).
% 2.54/1.52
% 2.54/1.52 thf(exuEu,definition,
% 2.54/1.52 ( exuEu
% 2.54/1.52 = ( ! [Xphi: $i > $o] :
% 2.54/1.52 ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xphi @ Xx )
% 2.54/1.52 => ( ( Xphi @ Xy )
% 2.54/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(descr__Cong_type,type,
% 2.54/1.52 descr__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(descr__Cong,definition,
% 2.54/1.52 ( descr__Cong
% 2.54/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.54/1.52 ( ( Xx = Xy )
% 2.54/1.52 => ( ( Xphi @ Xx )
% 2.54/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.54/1.52 => ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 => ( ( exu
% 2.54/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.54/1.52 => ( ( descr
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 = ( descr
% 2.54/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstr__Cong_type,type,
% 2.54/1.52 dsetconstr__Cong: $o ).
% 2.54/1.52
% 2.54/1.52 thf(dsetconstr__Cong,definition,
% 2.54/1.52 ( dsetconstr__Cong
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ! [Xy: $i] :
% 2.54/1.52 ( ( in @ Xy @ B )
% 2.54/1.52 => ( ( Xx = Xy )
% 2.54/1.52 => ( ( Xphi @ Xx )
% 2.54/1.52 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.54/1.52 => ( ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 = ( dsetconstr @ B
% 2.54/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subset_type,type,
% 2.54/1.52 subset: $i > $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(disjoint_type,type,
% 2.54/1.52 disjoint: $i > $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(setsmeet_type,type,
% 2.54/1.52 setsmeet: $i > $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetI1_type,type,
% 2.54/1.52 subsetI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetI1,definition,
% 2.54/1.52 ( subsetI1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ B ) )
% 2.54/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(eqimpsubset2_type,type,
% 2.54/1.52 eqimpsubset2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(eqimpsubset2,definition,
% 2.54/1.52 ( eqimpsubset2
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(eqimpsubset1_type,type,
% 2.54/1.52 eqimpsubset1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(eqimpsubset1,definition,
% 2.54/1.52 ( eqimpsubset1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( A = B )
% 2.54/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetI2_type,type,
% 2.54/1.52 subsetI2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetI2,definition,
% 2.54/1.52 ( subsetI2
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ! [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ B ) )
% 2.54/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetsubset_type,type,
% 2.54/1.52 emptysetsubset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(emptysetsubset,definition,
% 2.54/1.52 ( emptysetsubset
% 2.54/1.52 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetE_type,type,
% 2.54/1.52 subsetE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetE,definition,
% 2.54/1.52 ( subsetE
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetE2_type,type,
% 2.54/1.52 subsetE2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetE2,definition,
% 2.54/1.52 ( subsetE2
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ~ ( in @ Xx @ B )
% 2.54/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notsubsetI_type,type,
% 2.54/1.52 notsubsetI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notsubsetI,definition,
% 2.54/1.52 ( notsubsetI
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ~ ( in @ Xx @ B )
% 2.54/1.52 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notequalI1_type,type,
% 2.54/1.52 notequalI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notequalI1,definition,
% 2.54/1.52 ( notequalI1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ~ ( subset @ A @ B )
% 2.54/1.52 => ( A != B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(notequalI2_type,type,
% 2.54/1.52 notequalI2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(notequalI2,definition,
% 2.54/1.52 ( notequalI2
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ~ ( in @ Xx @ B )
% 2.54/1.52 => ( A != B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetRefl_type,type,
% 2.54/1.52 subsetRefl: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetRefl,definition,
% 2.54/1.52 ( subsetRefl
% 2.54/1.52 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetTrans_type,type,
% 2.54/1.52 subsetTrans: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetTrans,definition,
% 2.54/1.52 ( subsetTrans
% 2.54/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ( subset @ B @ C )
% 2.54/1.52 => ( subset @ A @ C ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinSub_type,type,
% 2.54/1.52 setadjoinSub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinSub,definition,
% 2.54/1.52 ( setadjoinSub
% 2.54/1.52 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinSub2_type,type,
% 2.54/1.52 setadjoinSub2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setadjoinSub2,definition,
% 2.54/1.52 ( setadjoinSub2
% 2.54/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subset2powerset_type,type,
% 2.54/1.52 subset2powerset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subset2powerset,definition,
% 2.54/1.52 ( subset2powerset
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setextsub_type,type,
% 2.54/1.52 setextsub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setextsub,definition,
% 2.54/1.52 ( setextsub
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ( subset @ B @ A )
% 2.54/1.52 => ( A = B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(subsetemptysetimpeq_type,type,
% 2.54/1.52 subsetemptysetimpeq: $o ).
% 2.54/1.52
% 2.54/1.52 thf(subsetemptysetimpeq,definition,
% 2.54/1.52 ( subsetemptysetimpeq
% 2.54/1.52 = ( ! [A: $i] :
% 2.54/1.52 ( ( subset @ A @ emptyset )
% 2.54/1.52 => ( A = emptyset ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powersetI1_type,type,
% 2.54/1.52 powersetI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetI1,definition,
% 2.54/1.52 ( powersetI1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ B @ A )
% 2.54/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powersetE1_type,type,
% 2.54/1.52 powersetE1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetE1,definition,
% 2.54/1.52 ( powersetE1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(inPowerset_type,type,
% 2.54/1.52 inPowerset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(inPowerset,definition,
% 2.54/1.52 ( inPowerset
% 2.54/1.52 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(powersetsubset_type,type,
% 2.54/1.52 powersetsubset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(powersetsubset,definition,
% 2.54/1.52 ( powersetsubset
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(sepInPowerset_type,type,
% 2.54/1.52 sepInPowerset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(sepInPowerset,definition,
% 2.54/1.52 ( sepInPowerset
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( in
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 @ ( powerset @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(sepSubset_type,type,
% 2.54/1.52 sepSubset: $o ).
% 2.54/1.52
% 2.54/1.52 thf(sepSubset,definition,
% 2.54/1.52 ( sepSubset
% 2.54/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.52 ( subset
% 2.54/1.52 @ ( dsetconstr @ A
% 2.54/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.52 @ A ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunion_type,type,
% 2.54/1.52 binunion: $i > $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(binunionIL_type,type,
% 2.54/1.52 binunionIL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionIL,definition,
% 2.54/1.52 ( binunionIL
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(upairset2IR_type,type,
% 2.54/1.52 upairset2IR: $o ).
% 2.54/1.52
% 2.54/1.52 thf(upairset2IR,definition,
% 2.54/1.52 ( upairset2IR
% 2.54/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunionIR_type,type,
% 2.54/1.52 binunionIR: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionIR,definition,
% 2.54/1.52 ( binunionIR
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunionEcases_type,type,
% 2.54/1.52 binunionEcases: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionEcases,definition,
% 2.54/1.52 ( binunionEcases
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.54/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.54/1.52 => ( ( ( in @ Xx @ A )
% 2.54/1.52 => Xphi )
% 2.54/1.52 => ( ( ( in @ Xx @ B )
% 2.54/1.52 => Xphi )
% 2.54/1.52 => Xphi ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunionE_type,type,
% 2.54/1.52 binunionE: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionE,definition,
% 2.54/1.52 ( binunionE
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.54/1.52 => ( ( in @ Xx @ A )
% 2.54/1.52 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunionLsub_type,type,
% 2.54/1.52 binunionLsub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionLsub,definition,
% 2.54/1.52 ( binunionLsub
% 2.54/1.52 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binunionRsub_type,type,
% 2.54/1.52 binunionRsub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binunionRsub,definition,
% 2.54/1.52 ( binunionRsub
% 2.54/1.52 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersect_type,type,
% 2.54/1.52 binintersect: $i > $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectI_type,type,
% 2.54/1.52 binintersectI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectI,definition,
% 2.54/1.52 ( binintersectI
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset5_type,type,
% 2.54/1.52 binintersectSubset5: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset5,definition,
% 2.54/1.52 ( binintersectSubset5
% 2.54/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.54/1.52 ( ( subset @ C @ A )
% 2.54/1.52 => ( ( subset @ C @ B )
% 2.54/1.52 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectEL_type,type,
% 2.54/1.52 binintersectEL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectEL,definition,
% 2.54/1.52 ( binintersectEL
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectLsub_type,type,
% 2.54/1.52 binintersectLsub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectLsub,definition,
% 2.54/1.52 ( binintersectLsub
% 2.54/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset2_type,type,
% 2.54/1.52 binintersectSubset2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset2,definition,
% 2.54/1.52 ( binintersectSubset2
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ( binintersect @ A @ B )
% 2.54/1.52 = A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset3_type,type,
% 2.54/1.52 binintersectSubset3: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset3,definition,
% 2.54/1.52 ( binintersectSubset3
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( ( binintersect @ A @ B )
% 2.54/1.52 = B )
% 2.54/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectER_type,type,
% 2.54/1.52 binintersectER: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectER,definition,
% 2.54/1.52 ( binintersectER
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.54/1.52 => ( in @ Xx @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(disjointsetsI1_type,type,
% 2.54/1.52 disjointsetsI1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(disjointsetsI1,definition,
% 2.54/1.52 ( disjointsetsI1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ~ ? [Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 & ( in @ Xx @ B ) )
% 2.54/1.52 => ( ( binintersect @ A @ B )
% 2.54/1.52 = emptyset ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectRsub_type,type,
% 2.54/1.52 binintersectRsub: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectRsub,definition,
% 2.54/1.52 ( binintersectRsub
% 2.54/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset4_type,type,
% 2.54/1.52 binintersectSubset4: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset4,definition,
% 2.54/1.52 ( binintersectSubset4
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ B @ A )
% 2.54/1.52 => ( ( binintersect @ A @ B )
% 2.54/1.52 = B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset1_type,type,
% 2.54/1.52 binintersectSubset1: $o ).
% 2.54/1.52
% 2.54/1.52 thf(binintersectSubset1,definition,
% 2.54/1.52 ( binintersectSubset1
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( ( binintersect @ A @ B )
% 2.54/1.52 = A )
% 2.54/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(bs114d_type,type,
% 2.54/1.52 bs114d: $o ).
% 2.54/1.52
% 2.54/1.52 thf(bs114d,definition,
% 2.54/1.52 ( bs114d
% 2.54/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.54/1.52 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.54/1.52 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(regular_type,type,
% 2.54/1.52 regular: $i > $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminus_type,type,
% 2.54/1.52 setminus: $i > $i > $i ).
% 2.54/1.52
% 2.54/1.52 thf(setminusI_type,type,
% 2.54/1.52 setminusI: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminusI,definition,
% 2.54/1.52 ( setminusI
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ A )
% 2.54/1.52 => ( ~ ( in @ Xx @ B )
% 2.54/1.52 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setminusEL_type,type,
% 2.54/1.52 setminusEL: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminusEL,definition,
% 2.54/1.52 ( setminusEL
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.54/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setminusER_type,type,
% 2.54/1.52 setminusER: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminusER,definition,
% 2.54/1.52 ( setminusER
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.54/1.52 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setminusSubset2_type,type,
% 2.54/1.52 setminusSubset2: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminusSubset2,definition,
% 2.54/1.52 ( setminusSubset2
% 2.54/1.52 = ( ! [A: $i,B: $i] :
% 2.54/1.52 ( ( subset @ A @ B )
% 2.54/1.52 => ( ( setminus @ A @ B )
% 2.54/1.52 = emptyset ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setminusERneg_type,type,
% 2.54/1.52 setminusERneg: $o ).
% 2.54/1.52
% 2.54/1.52 thf(setminusERneg,definition,
% 2.54/1.52 ( setminusERneg
% 2.54/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.54/1.52 => ( ( in @ Xx @ A )
% 2.54/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.54/1.52
% 2.54/1.52 thf(setminusELneg,conjecture,
% 2.54/1.52 ( setextAx
% 2.54/1.52 => ( emptysetAx
% 2.54/1.52 => ( setadjoinAx
% 2.54/1.52 => ( powersetAx
% 2.54/1.52 => ( setunionAx
% 2.54/1.52 => ( omega0Ax
% 2.54/1.52 => ( omegaSAx
% 2.54/1.52 => ( omegaIndAx
% 2.54/1.52 => ( replAx
% 2.54/1.52 => ( foundationAx
% 2.54/1.52 => ( wellorderingAx
% 2.54/1.52 => ( descrp
% 2.54/1.52 => ( dsetconstrI
% 2.54/1.52 => ( dsetconstrEL
% 2.54/1.52 => ( dsetconstrER
% 2.54/1.52 => ( exuE1
% 2.54/1.52 => ( prop2setE
% 2.54/1.52 => ( emptysetE
% 2.54/1.52 => ( emptysetimpfalse
% 2.54/1.52 => ( notinemptyset
% 2.54/1.52 => ( exuE3e
% 2.54/1.52 => ( setext
% 2.54/1.52 => ( emptyI
% 2.54/1.52 => ( noeltsimpempty
% 2.54/1.52 => ( setbeta
% 2.54/1.52 => ( nonemptyE1
% 2.54/1.52 => ( nonemptyI
% 2.54/1.52 => ( nonemptyI1
% 2.54/1.52 => ( setadjoinIL
% 2.54/1.52 => ( emptyinunitempty
% 2.54/1.52 => ( setadjoinIR
% 2.54/1.52 => ( setadjoinE
% 2.54/1.52 => ( setadjoinOr
% 2.54/1.52 => ( setoftrueEq
% 2.54/1.52 => ( powersetI
% 2.54/1.52 => ( emptyinPowerset
% 2.54/1.52 => ( emptyInPowerset
% 2.54/1.52 => ( powersetE
% 2.54/1.52 => ( setunionI
% 2.54/1.52 => ( setunionE
% 2.54/1.52 => ( subPowSU
% 2.54/1.52 => ( exuE2
% 2.54/1.52 => ( nonemptyImpWitness
% 2.54/1.52 => ( uniqinunit
% 2.54/1.52 => ( notinsingleton
% 2.54/1.52 => ( eqinunit
% 2.54/1.52 => ( singletonsswitch
% 2.54/1.52 => ( upairsetE
% 2.54/1.52 => ( upairsetIL
% 2.54/1.52 => ( upairsetIR
% 2.54/1.52 => ( emptyE1
% 2.54/1.52 => ( vacuousDall
% 2.54/1.52 => ( quantDeMorgan1
% 2.54/1.52 => ( quantDeMorgan2
% 2.54/1.52 => ( quantDeMorgan3
% 2.54/1.52 => ( quantDeMorgan4
% 2.54/1.52 => ( prop2setI
% 2.54/1.52 => ( prop2set2propI
% 2.54/1.52 => ( notdexE
% 2.54/1.52 => ( notdallE
% 2.54/1.52 => ( exuI1
% 2.54/1.52 => ( exuI3
% 2.54/1.52 => ( exuI2
% 2.54/1.52 => ( inCongP
% 2.54/1.52 => ( in__Cong
% 2.54/1.52 => ( exuE3u
% 2.54/1.52 => ( exu__Cong
% 2.54/1.52 => ( emptyset__Cong
% 2.54/1.52 => ( setadjoin__Cong
% 2.54/1.52 => ( powerset__Cong
% 2.54/1.52 => ( setunion__Cong
% 2.54/1.52 => ( omega__Cong
% 2.54/1.52 => ( exuEu
% 2.54/1.52 => ( descr__Cong
% 2.54/1.52 => ( dsetconstr__Cong
% 2.54/1.52 => ( subsetI1
% 2.54/1.52 => ( eqimpsubset2
% 2.54/1.52 => ( eqimpsubset1
% 2.54/1.52 => ( subsetI2
% 2.54/1.52 => ( emptysetsubset
% 2.54/1.52 => ( subsetE
% 2.54/1.52 => ( subsetE2
% 2.54/1.52 => ( notsubsetI
% 2.54/1.52 => ( notequalI1
% 2.54/1.52 => ( notequalI2
% 2.54/1.52 => ( subsetRefl
% 2.54/1.52 => ( subsetTrans
% 2.54/1.52 => ( setadjoinSub
% 2.54/1.52 => ( setadjoinSub2
% 2.54/1.52 => ( subset2powerset
% 2.54/1.52 => ( setextsub
% 2.54/1.52 => ( subsetemptysetimpeq
% 2.54/1.52 => ( powersetI1
% 2.54/1.52 => ( powersetE1
% 2.54/1.52 => ( inPowerset
% 2.54/1.52 => ( powersetsubset
% 2.54/1.52 => ( sepInPowerset
% 2.54/1.52 => ( sepSubset
% 2.54/1.52 => ( binunionIL
% 2.54/1.52 => ( upairset2IR
% 2.54/1.52 => ( binunionIR
% 2.54/1.52 => ( binunionEcases
% 2.54/1.52 => ( binunionE
% 2.54/1.52 => ( binunionLsub
% 2.54/1.52 => ( binunionRsub
% 2.54/1.52 => ( binintersectI
% 2.54/1.52 => ( binintersectSubset5
% 2.54/1.52 => ( binintersectEL
% 2.54/1.52 => ( binintersectLsub
% 2.54/1.52 => ( binintersectSubset2
% 2.54/1.52 => ( binintersectSubset3
% 2.54/1.52 => ( binintersectER
% 2.54/1.52 => ( disjointsetsI1
% 2.54/1.52 => ( binintersectRsub
% 2.54/1.52 => ( binintersectSubset4
% 2.54/1.52 => ( binintersectSubset1
% 2.54/1.52 => ( bs114d
% 2.54/1.52 => ( setminusI
% 2.54/1.52 => ( setminusEL
% 2.54/1.52 => ( setminusER
% 2.54/1.52 => ( setminusSubset2
% 2.54/1.52 => ( setminusERneg
% 2.54/1.52 => ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.54/1.52 => ( ~ ( in @ Xx @ B )
% 2.54/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.54/1.52 ------------------------
% 2.54/1.54 % (21270)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_21016 for (2999ds/27Mi)
% 2.54/1.54 % (21271)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/2Mi)
% 2.54/1.54 % (21271)Instruction limit reached!
% 2.54/1.54 % (21271)------------------------------
% 2.54/1.54 % (21271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (21271)Termination reason: Unknown
% 2.54/1.54 % (21271)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (21271)Memory used [KB]: 1151
% 2.54/1.54 % (21271)Time elapsed: 0.002 s
% 2.54/1.54 % (21271)Instructions burned: 3 (million)
% 2.54/1.54 % (21271)------------------------------
% 2.54/1.54 % (21271)------------------------------
% 2.54/1.55 % (21269)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_21016 for (2999ds/4Mi)
% 2.54/1.55 % (21268)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/183Mi)
% 2.54/1.55 % (21272)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_21016 for (2999ds/2Mi)
% 2.54/1.55 % (21274)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/18Mi)
% 2.54/1.55 % (21273)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_21016 for (2999ds/275Mi)
% 2.54/1.55 % (21270)Instruction limit reached!
% 2.54/1.55 % (21270)------------------------------
% 2.54/1.55 % (21270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (21270)Termination reason: Unknown
% 2.54/1.55 % (21270)Termination phase: Property scanning
% 2.54/1.55
% 2.54/1.55 % (21270)Memory used [KB]: 1535
% 2.54/1.55 % (21270)Time elapsed: 0.009 s
% 2.54/1.55 % (21270)Instructions burned: 27 (million)
% 2.54/1.55 % (21270)------------------------------
% 2.54/1.55 % (21270)------------------------------
% 2.54/1.55 % (21272)Instruction limit reached!
% 2.54/1.55 % (21272)------------------------------
% 2.54/1.55 % (21272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (21272)Termination reason: Unknown
% 2.54/1.55 % (21272)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (21272)Memory used [KB]: 1151
% 2.54/1.55 % (21272)Time elapsed: 0.004 s
% 2.54/1.55 % (21272)Instructions burned: 3 (million)
% 2.54/1.55 % (21272)------------------------------
% 2.54/1.55 % (21272)------------------------------
% 2.54/1.55 % (21269)Instruction limit reached!
% 2.54/1.55 % (21269)------------------------------
% 2.54/1.55 % (21269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (21269)Termination reason: Unknown
% 2.54/1.55 % (21269)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (21269)Memory used [KB]: 1279
% 2.54/1.55 % (21269)Time elapsed: 0.005 s
% 2.54/1.55 % (21269)Instructions burned: 5 (million)
% 2.54/1.55 % (21269)------------------------------
% 2.54/1.55 % (21269)------------------------------
% 2.54/1.55 % (21275)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/3Mi)
% 2.54/1.55 % (21275)Instruction limit reached!
% 2.54/1.55 % (21275)------------------------------
% 2.54/1.55 % (21275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (21275)Termination reason: Unknown
% 2.54/1.55 % (21275)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (21275)Memory used [KB]: 1279
% 2.54/1.55 % (21275)Time elapsed: 0.003 s
% 2.54/1.55 % (21275)Instructions burned: 4 (million)
% 2.54/1.55 % (21275)------------------------------
% 2.54/1.55 % (21275)------------------------------
% 2.54/1.56 % (21276)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_21016 for (2999ds/37Mi)
% 2.54/1.56 % (21274)Instruction limit reached!
% 2.54/1.56 % (21274)------------------------------
% 2.54/1.56 % (21274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (21274)Termination reason: Unknown
% 2.54/1.56 % (21274)Termination phase: Preprocessing 3
% 2.54/1.56
% 2.54/1.56 % (21274)Memory used [KB]: 1535
% 2.54/1.56 % (21274)Time elapsed: 0.013 s
% 2.54/1.56 % (21274)Instructions burned: 19 (million)
% 2.54/1.56 % (21274)------------------------------
% 2.54/1.56 % (21274)------------------------------
% 2.54/1.56 % (21279)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_21016 for (2999ds/1041Mi)
% 2.54/1.56 % (21277)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_21016 for (2999ds/15Mi)
% 2.54/1.57 % (21278)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_21016 for (2999ds/3Mi)
% 2.54/1.57 % (21276)Instruction limit reached!
% 2.54/1.57 % (21276)------------------------------
% 2.54/1.57 % (21276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (21276)Termination reason: Unknown
% 2.54/1.57 % (21276)Termination phase: Property scanning
% 2.54/1.57
% 2.54/1.57 % (21276)Memory used [KB]: 1663
% 2.54/1.57 % (21276)Time elapsed: 0.012 s
% 2.54/1.57 % (21276)Instructions burned: 37 (million)
% 2.54/1.57 % (21276)------------------------------
% 2.54/1.57 % (21276)------------------------------
% 2.54/1.57 % (21278)Instruction limit reached!
% 2.54/1.57 % (21278)------------------------------
% 2.54/1.57 % (21278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (21278)Termination reason: Unknown
% 2.54/1.57 % (21278)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (21278)Memory used [KB]: 1151
% 2.54/1.57 % (21278)Time elapsed: 0.003 s
% 2.54/1.57 % (21278)Instructions burned: 3 (million)
% 2.54/1.57 % (21278)------------------------------
% 2.54/1.57 % (21278)------------------------------
% 2.54/1.57 % (21277)Instruction limit reached!
% 2.54/1.57 % (21277)------------------------------
% 2.54/1.57 % (21277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (21277)Termination reason: Unknown
% 2.54/1.57 % (21277)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (21277)Memory used [KB]: 1407
% 2.54/1.57 % (21277)Time elapsed: 0.011 s
% 2.54/1.57 % (21277)Instructions burned: 16 (million)
% 2.54/1.57 % (21277)------------------------------
% 2.54/1.57 % (21277)------------------------------
% 2.54/1.57 % (21280)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/7Mi)
% 2.54/1.58 % (21282)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_21016 for (2999ds/3Mi)
% 2.54/1.58 % (21280)Instruction limit reached!
% 2.54/1.58 % (21280)------------------------------
% 2.54/1.58 % (21280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (21280)Termination reason: Unknown
% 2.54/1.58 % (21282)Instruction limit reached!
% 2.54/1.58 % (21282)------------------------------
% 2.54/1.58 % (21282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (21280)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (21282)Termination reason: Unknown
% 2.54/1.58 % (21280)Memory used [KB]: 1279
% 2.54/1.58 % (21282)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (21280)Time elapsed: 0.006 s
% 2.54/1.58 % (21282)Memory used [KB]: 1279
% 2.54/1.58 % (21280)Instructions burned: 8 (million)
% 2.54/1.58 % (21282)Time elapsed: 0.002 s
% 2.54/1.58 % (21282)Instructions burned: 4 (million)
% 2.54/1.58 % (21280)------------------------------
% 2.54/1.58 % (21280)------------------------------
% 2.54/1.58 % (21282)------------------------------
% 2.54/1.58 % (21282)------------------------------
% 2.54/1.58 % (21281)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/16Mi)
% 2.54/1.59 % (21281)Instruction limit reached!
% 2.54/1.59 % (21281)------------------------------
% 2.54/1.59 % (21281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (21281)Termination reason: Unknown
% 2.54/1.59 % (21281)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (21281)Memory used [KB]: 1535
% 2.54/1.59 % (21281)Time elapsed: 0.007 s
% 2.54/1.59 % (21281)Instructions burned: 16 (million)
% 2.54/1.59 % (21281)------------------------------
% 2.54/1.59 % (21281)------------------------------
% 2.54/1.59 % (21284)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/7Mi)
% 2.54/1.59 % (21284)Instruction limit reached!
% 2.54/1.59 % (21284)------------------------------
% 2.54/1.59 % (21284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (21284)Termination reason: Unknown
% 2.54/1.59 % (21284)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (21284)Memory used [KB]: 1279
% 2.54/1.59 % (21284)Time elapsed: 0.004 s
% 2.54/1.59 % (21284)Instructions burned: 8 (million)
% 2.54/1.59 % (21284)------------------------------
% 2.54/1.59 % (21284)------------------------------
% 2.54/1.59 % (21283)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_21016 for (2999ds/3Mi)
% 2.54/1.59 % (21283)Instruction limit reached!
% 2.54/1.59 % (21283)------------------------------
% 2.54/1.59 % (21283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (21283)Termination reason: Unknown
% 2.54/1.59 % (21283)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (21283)Memory used [KB]: 1279
% 2.54/1.59 % (21283)Time elapsed: 0.004 s
% 2.54/1.59 % (21283)Instructions burned: 4 (million)
% 2.54/1.59 % (21283)------------------------------
% 2.54/1.59 % (21283)------------------------------
% 2.54/1.60 % (21285)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/3Mi)
% 2.54/1.60 % (21286)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/4Mi)
% 2.56/1.60 % (21286)Instruction limit reached!
% 2.56/1.60 % (21286)------------------------------
% 2.56/1.60 % (21286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.60 % (21286)Termination reason: Unknown
% 2.56/1.60 % (21286)Termination phase: shuffling
% 2.56/1.60
% 2.56/1.60 % (21286)Memory used [KB]: 1279
% 2.56/1.60 % (21286)Time elapsed: 0.003 s
% 2.56/1.60 % (21286)Instructions burned: 4 (million)
% 2.56/1.60 % (21286)------------------------------
% 2.56/1.60 % (21286)------------------------------
% 2.56/1.60 % (21285)Instruction limit reached!
% 2.56/1.60 % (21285)------------------------------
% 2.56/1.60 % (21285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.60 % (21285)Termination reason: Unknown
% 2.56/1.60 % (21285)Termination phase: shuffling
% 2.56/1.60
% 2.56/1.60 % (21285)Memory used [KB]: 1279
% 2.56/1.60 % (21285)Time elapsed: 0.004 s
% 2.56/1.60 % (21285)Instructions burned: 4 (million)
% 2.56/1.60 % (21285)------------------------------
% 2.56/1.60 % (21285)------------------------------
% 2.56/1.60 % (21287)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/18Mi)
% 2.56/1.61 % (21287)Instruction limit reached!
% 2.56/1.61 % (21287)------------------------------
% 2.56/1.61 % (21287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.61 % (21287)Termination reason: Unknown
% 2.56/1.61 % (21287)Termination phase: shuffling
% 2.56/1.61
% 2.56/1.61 % (21287)Memory used [KB]: 1535
% 2.56/1.61 % (21287)Time elapsed: 0.007 s
% 2.56/1.61 % (21287)Instructions burned: 18 (million)
% 2.56/1.61 % (21287)------------------------------
% 2.56/1.61 % (21287)------------------------------
% 2.56/1.61 % (21288)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/710Mi)
% 2.56/1.61 % (21289)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/6Mi)
% 2.56/1.62 % (21290)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_21016 for (2999ds/902Mi)
% 2.56/1.62 % (21291)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_21016 for (2999ds/21Mi)
% 2.56/1.62 % (21289)Instruction limit reached!
% 2.56/1.62 % (21289)------------------------------
% 2.56/1.62 % (21289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.62 % (21289)Termination reason: Unknown
% 2.56/1.62 % (21289)Termination phase: shuffling
% 2.56/1.62
% 2.56/1.62 % (21289)Memory used [KB]: 1279
% 2.56/1.62 % (21289)Time elapsed: 0.005 s
% 2.56/1.62 % (21289)Instructions burned: 6 (million)
% 2.56/1.62 % (21289)------------------------------
% 2.56/1.62 % (21289)------------------------------
% 2.56/1.62 % (21291)Instruction limit reached!
% 2.56/1.62 % (21291)------------------------------
% 2.56/1.62 % (21291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.62 % (21291)Termination reason: Unknown
% 2.56/1.62 % (21291)Termination phase: Property scanning
% 2.56/1.62
% 2.56/1.62 % (21291)Memory used [KB]: 1535
% 2.56/1.62 % (21291)Time elapsed: 0.008 s
% 2.56/1.62 % (21291)Instructions burned: 21 (million)
% 2.56/1.62 % (21291)------------------------------
% 2.56/1.62 % (21291)------------------------------
% 2.56/1.63 % (21293)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_21016 for (2999ds/6Mi)
% 2.56/1.63 % (21293)Instruction limit reached!
% 2.56/1.63 % (21293)------------------------------
% 2.56/1.63 % (21293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.63 % (21293)Termination reason: Unknown
% 2.56/1.63 % (21293)Termination phase: shuffling
% 2.56/1.63
% 2.56/1.63 % (21293)Memory used [KB]: 1279
% 2.56/1.63 % (21293)Time elapsed: 0.004 s
% 2.56/1.63 % (21293)Instructions burned: 7 (million)
% 2.56/1.63 % (21293)------------------------------
% 2.56/1.63 % (21293)------------------------------
% 2.56/1.63 % (21292)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21016 for (2999ds/5Mi)
% 2.56/1.64 % (21268)Instruction limit reached!
% 2.56/1.64 % (21268)------------------------------
% 2.56/1.64 % (21268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.64 % (21268)Termination reason: Unknown
% 2.56/1.64 % (21268)Termination phase: Saturation
% 2.56/1.64
% 2.56/1.64 % (21268)Memory used [KB]: 7036
% 2.56/1.64 % (21268)Time elapsed: 0.093 s
% 2.56/1.64 % (21268)Instructions burned: 185 (million)
% 2.56/1.64 % (21268)------------------------------
% 2.56/1.64 % (21268)------------------------------
% 2.56/1.64 % (21292)Instruction limit reached!
% 2.56/1.64 % (21292)------------------------------
% 2.56/1.64 % (21292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.64 % (21292)Termination reason: Unknown
% 2.56/1.64 % (21292)Termination phase: shuffling
% 2.56/1.64
% 2.56/1.64 % (21292)Memory used [KB]: 1279
% 2.56/1.64 % (21292)Time elapsed: 0.005 s
% 2.56/1.64 % (21292)Instructions burned: 7 (million)
% 2.56/1.64 % (21292)------------------------------
% 2.56/1.64 % (21292)------------------------------
% 2.56/1.64 % (21294)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21016 for (2998ds/377Mi)
% 2.56/1.65 % (21295)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_21016 for (2998ds/779Mi)
% 2.56/1.65 % (21296)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_21016 for (2998ds/19Mi)
% 2.56/1.65 % (21296)Instruction limit reached!
% 2.56/1.65 % (21296)------------------------------
% 2.56/1.65 % (21296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.65 % (21296)Termination reason: Unknown
% 2.56/1.65 % (21296)Termination phase: Property scanning
% 2.56/1.65
% 2.56/1.65 % (21296)Memory used [KB]: 1535
% 2.56/1.65 % (21296)Time elapsed: 0.007 s
% 2.56/1.65 % (21296)Instructions burned: 19 (million)
% 2.56/1.65 % (21296)------------------------------
% 2.56/1.65 % (21296)------------------------------
% 2.56/1.66 % (21273)Instruction limit reached!
% 2.56/1.66 % (21273)------------------------------
% 2.56/1.66 % (21273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.66 % (21273)Termination reason: Unknown
% 2.56/1.66 % (21273)Termination phase: Saturation
% 2.56/1.66
% 2.56/1.66 % (21273)Memory used [KB]: 7803
% 2.56/1.66 % (21273)Time elapsed: 0.115 s
% 2.56/1.66 % (21273)Instructions burned: 277 (million)
% 2.56/1.66 % (21273)------------------------------
% 2.56/1.66 % (21273)------------------------------
% 2.56/1.66 % (21297)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21016 for (2998ds/879Mi)
% 2.56/1.67 % (21290)First to succeed.
% 2.56/1.67 % (21298)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21016 for (2998ds/17Mi)
% 2.56/1.67 % (21290)Refutation found. Thanks to Tanya!
% 2.56/1.67 % SZS status Theorem for DTF2THF_21016
% 2.56/1.67 % SZS output start Proof for DTF2THF_21016
% 2.56/1.67 thf(func_def_0, type, in: $i > $i > $o).
% 2.56/1.67 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.56/1.67 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.56/1.67 thf(func_def_8, type, powerset: $i > $i).
% 2.56/1.67 thf(func_def_10, type, setunion: $i > $i).
% 2.56/1.67 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_26, type, prop2set: $o > $i).
% 2.56/1.67 thf(func_def_36, type, nonempty: $i > $o).
% 2.56/1.67 thf(func_def_69, type, set2prop: $i > $o).
% 2.56/1.67 thf(func_def_88, type, subset: $i > $i > $o).
% 2.56/1.67 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.56/1.67 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.56/1.67 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.56/1.67 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.56/1.67 thf(func_def_135, type, regular: $i > $o).
% 2.56/1.67 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.56/1.67 thf(func_def_154, type, sP0: $i > $i > $o).
% 2.56/1.67 thf(func_def_155, type, sP1: $i > $o).
% 2.56/1.67 thf(func_def_156, type, sP2: $i > $i > $o).
% 2.56/1.67 thf(func_def_157, type, sP3: $i > $i > $o).
% 2.56/1.67 thf(func_def_159, type, sK5: $i > $i).
% 2.56/1.67 thf(func_def_170, type, sK16: $i > $i > $i).
% 2.56/1.67 thf(func_def_173, type, sK19: ($i > $o) > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_174, type, sK20: ($i > $o) > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_175, type, sK21: $i > $o).
% 2.56/1.67 thf(func_def_176, type, sK22: $i > $o).
% 2.56/1.67 thf(func_def_186, type, sK32: $o > $i > $i > $i).
% 2.56/1.67 thf(func_def_193, type, sK39: $i > $o).
% 2.56/1.67 thf(func_def_199, type, sK45: $i > $o).
% 2.56/1.67 thf(func_def_200, type, sK46: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_202, type, sK48: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.56/1.67 thf(func_def_203, type, sK49: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.56/1.67 thf(func_def_206, type, sK52: $i > $o).
% 2.56/1.67 thf(func_def_207, type, sK53: $i > $o).
% 2.56/1.67 thf(func_def_216, type, sK62: $i > $i).
% 2.56/1.67 thf(func_def_232, type, sK78: $i > $o).
% 2.56/1.67 thf(func_def_235, type, sK81: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_241, type, sK87: $i > $i > $i).
% 2.56/1.67 thf(func_def_242, type, sK88: $i > $o).
% 2.56/1.67 thf(func_def_243, type, sK89: $i > $i).
% 2.56/1.67 thf(func_def_244, type, sK90: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_252, type, sK98: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_253, type, sK99: $i > $o).
% 2.56/1.67 thf(func_def_256, type, sK102: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_257, type, sK103: $i > $o).
% 2.56/1.67 thf(func_def_280, type, sK126: $i > $o).
% 2.56/1.67 thf(func_def_286, type, sK132: $i > $o).
% 2.56/1.67 thf(func_def_289, type, sK135: $i > $o).
% 2.56/1.67 thf(func_def_295, type, sK141: $i > $i > $i).
% 2.56/1.67 thf(func_def_301, type, sK147: $i > $i > $i).
% 2.56/1.67 thf(func_def_305, type, sK151: $i > $o).
% 2.56/1.67 thf(func_def_308, type, sK154: $i > $o).
% 2.56/1.67 thf(func_def_310, type, sK156: $i > $o).
% 2.56/1.67 thf(func_def_315, type, sK161: $i > $i > $i).
% 2.56/1.67 thf(func_def_316, type, sK162: $i > $i > $i).
% 2.56/1.67 thf(func_def_320, type, sK166: $i > $o).
% 2.56/1.67 thf(func_def_328, type, sK174: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_329, type, sK175: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_330, type, sK176: $i > $o).
% 2.56/1.67 thf(func_def_333, type, sK179: $i > $o).
% 2.56/1.67 thf(func_def_335, type, sK181: ($i > $o) > $i > $i).
% 2.56/1.67 thf(func_def_346, type, sK192: $i > $o).
% 2.56/1.67 thf(func_def_347, type, sK193: $i > $o).
% 2.56/1.67 thf(func_def_348, type, sK194: $i > $i > $i).
% 2.56/1.67 thf(func_def_351, type, sK197: $i > $i > $i).
% 2.56/1.67 thf(func_def_352, type, sK198: $i > $i > $i).
% 2.56/1.67 thf(func_def_353, type, sK199: $i > $i > $i).
% 2.56/1.67 thf(func_def_354, type, sK200: $i > $i > $i).
% 2.56/1.67 thf(func_def_355, type, sK201: $i > $i > $i > $i).
% 2.56/1.67 thf(func_def_356, type, sK202: $i > $i).
% 2.56/1.67 thf(func_def_357, type, sK203: $i > $i).
% 2.56/1.67 thf(func_def_358, type, sK204: $i > $i).
% 2.56/1.67 thf(func_def_359, type, sK205: $i > $i).
% 2.56/1.67 thf(func_def_360, type, sK206: $i > $i > $i).
% 2.56/1.67 thf(func_def_361, type, sK207: $i > $i > $i > $i).
% 2.56/1.67 thf(func_def_362, type, sK208: $i > $i > $i > $i).
% 2.56/1.67 thf(func_def_363, type, sK209: $i > $i > $i).
% 2.56/1.67 thf(func_def_364, type, sK210: $i > $i > $i).
% 2.56/1.67 thf(func_def_365, type, sK211: $i > $i).
% 2.56/1.67 thf(func_def_366, type, sK212: $i > $i > $i).
% 2.56/1.67 thf(func_def_368, type, sK214: $i > $i).
% 2.56/1.67 thf(func_def_369, type, sK215: $i > $i).
% 2.56/1.67 thf(func_def_370, type, sK216: $i > $o).
% 2.56/1.67 thf(func_def_376, type, sK222: ($i > $o) > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_377, type, sK223: ($i > $o) > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_378, type, sK224: $i > $o).
% 2.56/1.67 thf(func_def_379, type, sK225: $i > $o).
% 2.56/1.67 thf(func_def_381, type, sK227: $i > $o).
% 2.56/1.67 thf(func_def_383, type, sK229: ($i > $o) > $i > $i).
% 2.56/1.67 thf(func_def_387, type, sK233: $i > $o).
% 2.56/1.67 thf(func_def_389, type, sK235: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_398, type, sK244: $i > $i > $o).
% 2.56/1.67 thf(func_def_400, type, sK246: $i > $i).
% 2.56/1.67 thf(func_def_401, type, sK247: $i > $i).
% 2.56/1.67 thf(func_def_402, type, sK248: $i > ($i > $i > $o) > $i).
% 2.56/1.67 thf(func_def_403, type, sK249: $i > $i > ($i > $i > $o) > $i).
% 2.56/1.67 thf(func_def_404, type, sK250: $i > ($i > $i > $o) > $i).
% 2.56/1.67 thf(func_def_405, type, sK251: $i > $i).
% 2.56/1.67 thf(func_def_414, type, sK260: $i > $i).
% 2.56/1.67 thf(func_def_422, type, sK268: $i > $o).
% 2.56/1.67 thf(func_def_423, type, sK269: $i > $i).
% 2.56/1.67 thf(func_def_424, type, sK270: ($i > $o) > $i).
% 2.56/1.67 thf(func_def_438, type, sK284: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_439, type, sK285: $i > $o).
% 2.56/1.67 thf(func_def_452, type, sK298: $i > $i > $i).
% 2.56/1.67 thf(func_def_454, type, sK300: $i > $o).
% 2.56/1.67 thf(func_def_465, type, sK311: $i > $i > $i).
% 2.56/1.67 thf(func_def_466, type, sK312: $i > ($i > $o) > $i).
% 2.56/1.67 thf(func_def_467, type, sK313: $i > $o).
% 2.56/1.67 thf(func_def_479, type, sK325: $i > $i).
% 2.56/1.67 thf(func_def_482, type, sK328: $i > $i).
% 2.56/1.67 thf(func_def_483, type, sK329: $i > $i).
% 2.56/1.67 thf(func_def_491, type, ph337: !>[X0: $tType]:(X0)).
% 2.56/1.67 thf(f1910,plain,(
% 2.56/1.67 $false),
% 2.56/1.67 inference(avatar_sat_refutation,[status(thm)],[f1859,f1891,f1906])).
% 2.56/1.67 thf(f1906,plain,(
% 2.56/1.67 ~spl336_4),
% 2.56/1.67 inference(avatar_contradiction_clause,[status(thm)],[f1905])).
% 2.56/1.67 thf(f1905,plain,(
% 2.56/1.67 $false | ~spl336_4),
% 2.56/1.67 inference(trivial_inequality_removal,[status(thm)],[f1903])).
% 2.56/1.67 thf(f1903,plain,(
% 2.56/1.67 ($true != $true) | ~spl336_4),
% 2.56/1.67 inference(superposition,[status(thm)],[f1312,f1855])).
% 2.56/1.67 thf(f1855,plain,(
% 2.56/1.67 ((in @ sK130 @ sK128) = $true) | ~spl336_4),
% 2.56/1.67 inference(avatar_component_clause,[status(thm)],[f1853])).
% 2.56/1.67 thf(f1853,definition,(
% 2.56/1.67 spl336_4 <=> ((in @ sK130 @ sK128) = $true)),
% 2.56/1.67 introduced(definition,[new_symbols(naming,[spl336_4])],[avatar_definition])).
% 2.56/1.67 thf(f1312,plain,(
% 2.56/1.67 ((in @ sK130 @ sK128) != $true)),
% 2.56/1.67 inference(cnf_transformation,[status(thm)],[f748])).
% 2.56/1.67 thf(f748,plain,(
% 2.56/1.67 (nonemptyI1 = $true) & (setunionAx = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (setbeta = $true) & (descrp = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (binunionE = $true) & (setextsub = $true) & (exuE3e = $true) & (powersetsubset = $true) & (exu__Cong = $true) & (omegaSAx = $true) & (notinsingleton = $true) & (notequalI1 = $true) & (setoftrueEq = $true) & (subsetRefl = $true) & (binintersectSubset5 = $true) & (powersetE1 = $true) & (exuI1 = $true) & (eqimpsubset1 = $true) & (notequalI2 = $true) & (emptysetE = $true) & (prop2setE = $true) & (subsetE2 = $true) & (notdallE = $true) & (setminusER = $true) & (eqimpsubset2 = $true) & (eqinunit = $true) & (dsetconstrEL = $true) & (in__Cong = $true) & (binunionRsub = $true) & (bs114d = $true) & (setadjoin__Cong = $true) & (binintersectI = $true) & (upairsetIL = $true) & (setadjoinSub = $true) & (setadjoinIR = $true) & (setunionI = $true) & (quantDeMorgan1 = $true) & (disjointsetsI1 = $true) & (prop2setI = $true) & (exuI2 = $true) & (singletonsswitch = $true) & (upairset2IR = $true) & (binintersectSubset1 = $true) & (foundationAx = $true) & (omega__Cong = $true) & (sepInPowerset = $true) & (binunionIR = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (subPowSU = $true) & (powerset__Cong = $true) & (exuI3 = $true) & (setadjoinIL = $true) & (powersetI = $true) & (subset2powerset = $true) & (setminusSubset2 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (powersetE = $true) & (binintersectEL = $true) & (binintersectSubset2 = $true) & (powersetI1 = $true) & (wellorderingAx = $true) & (upairsetIR = $true) & (dsetconstr__Cong = $true) & (binintersectSubset3 = $true) & (nonemptyI = $true) & (emptysetAx = $true) & (binunionIL = $true) & (binintersectSubset4 = $true) & (inCongP = $true) & (replAx = $true) & (subsetI1 = $true) & (sepSubset = $true) & (emptyset__Cong = $true) & (exuE3u = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan3 = $true) & (descr__Cong = $true) & (exuE1 = $true) & (inPowerset = $true) & (powersetAx = $true) & (binunionLsub = $true) & (subsetE = $true) & (setminusI = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & (((in @ sK130 @ sK129) = $true) & ((in @ sK130 @ sK128) != $true) & ((in @ sK130 @ (setminus @ sK129 @ sK128)) != $true)) & (subsetI2 = $true) & (notdexE = $true) & (setminusERneg = $true) & (emptysetsubset = $true) & (omegaIndAx = $true) & (setunionE = $true) & (emptyE1 = $true) & (exuEu = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (setadjoinAx = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (emptyInPowerset = $true) & (nonemptyE1 = $true) & (binunionEcases = $true) & (noeltsimpempty = $true) & (setadjoinE = $true) & (vacuousDall = $true) & (setext = $true) & (notinemptyset = $true) & (binintersectRsub = $true) & (notsubsetI = $true) & (exuE2 = $true) & (upairsetE = $true) & (nonemptyImpWitness = $true) & (setadjoinSub2 = $true) & (setextAx = $true) & (dsetconstrI = $true) & (subsetTrans = $true)),
% 2.56/1.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129,sK130])],[f450,f747])).
% 2.56/1.67 thf(f747,plain,(
% 2.56/1.67 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ((in @ X2 @ (setminus @ X1 @ X0)) != $true)) => (((in @ sK130 @ sK129) = $true) & ((in @ sK130 @ sK128) != $true) & ((in @ sK130 @ (setminus @ sK129 @ sK128)) != $true))),
% 2.56/1.67 introduced(definition,[],[choice_axiom])).
% 2.56/1.67 thf(f450,plain,(
% 2.56/1.67 (nonemptyI1 = $true) & (setunionAx = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (setbeta = $true) & (descrp = $true) & (setadjoinOr = $true) & (emptyinunitempty = $true) & (binunionE = $true) & (setextsub = $true) & (exuE3e = $true) & (powersetsubset = $true) & (exu__Cong = $true) & (omegaSAx = $true) & (notinsingleton = $true) & (notequalI1 = $true) & (setoftrueEq = $true) & (subsetRefl = $true) & (binintersectSubset5 = $true) & (powersetE1 = $true) & (exuI1 = $true) & (eqimpsubset1 = $true) & (notequalI2 = $true) & (emptysetE = $true) & (prop2setE = $true) & (subsetE2 = $true) & (notdallE = $true) & (setminusER = $true) & (eqimpsubset2 = $true) & (eqinunit = $true) & (dsetconstrEL = $true) & (in__Cong = $true) & (binunionRsub = $true) & (bs114d = $true) & (setadjoin__Cong = $true) & (binintersectI = $true) & (upairsetIL = $true) & (setadjoinSub = $true) & (setadjoinIR = $true) & (setunionI = $true) & (quantDeMorgan1 = $true) & (disjointsetsI1 = $true) & (prop2setI = $true) & (exuI2 = $true) & (singletonsswitch = $true) & (upairset2IR = $true) & (binintersectSubset1 = $true) & (foundationAx = $true) & (omega__Cong = $true) & (sepInPowerset = $true) & (binunionIR = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (subPowSU = $true) & (powerset__Cong = $true) & (exuI3 = $true) & (setadjoinIL = $true) & (powersetI = $true) & (subset2powerset = $true) & (setminusSubset2 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (powersetE = $true) & (binintersectEL = $true) & (binintersectSubset2 = $true) & (powersetI1 = $true) & (wellorderingAx = $true) & (upairsetIR = $true) & (dsetconstr__Cong = $true) & (binintersectSubset3 = $true) & (nonemptyI = $true) & (emptysetAx = $true) & (binunionIL = $true) & (binintersectSubset4 = $true) & (inCongP = $true) & (replAx = $true) & (subsetI1 = $true) & (sepSubset = $true) & (emptyset__Cong = $true) & (exuE3u = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan3 = $true) & (descr__Cong = $true) & (exuE1 = $true) & (inPowerset = $true) & (powersetAx = $true) & (binunionLsub = $true) & (subsetE = $true) & (setminusI = $true) & (binintersectER = $true) & (binintersectLsub = $true) & (uniqinunit = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ((in @ X2 @ (setminus @ X1 @ X0)) != $true)) & (subsetI2 = $true) & (notdexE = $true) & (setminusERneg = $true) & (emptysetsubset = $true) & (omegaIndAx = $true) & (setunionE = $true) & (emptyE1 = $true) & (exuEu = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (setadjoinAx = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (emptyInPowerset = $true) & (nonemptyE1 = $true) & (binunionEcases = $true) & (noeltsimpempty = $true) & (setadjoinE = $true) & (vacuousDall = $true) & (setext = $true) & (notinemptyset = $true) & (binintersectRsub = $true) & (notsubsetI = $true) & (exuE2 = $true) & (upairsetE = $true) & (nonemptyImpWitness = $true) & (setadjoinSub2 = $true) & (setextAx = $true) & (dsetconstrI = $true) & (subsetTrans = $true)),
% 2.56/1.67 inference(flattening,[status(thm)],[f449])).
% 2.56/1.67 thf(f449,plain,(
% 2.56/1.67 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) & ((in @ X2 @ (setminus @ X1 @ X0)) != $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.56/1.67 inference(ennf_transformation,[status(thm)],[f381])).
% 2.56/1.67 thf(f381,plain,(
% 2.56/1.67 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setminus @ X1 @ X0)) != $true) => (((in @ X2 @ X0) != $true) => ((in @ X2 @ X1) != $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.56/1.67 inference(flattening,[status(thm)],[f205])).
% 2.56/1.67 thf(f205,plain,(
% 2.56/1.67 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (~((in @ X2 @ (setminus @ X1 @ X0)) = $true) => (~((in @ X2 @ X0) = $true) => ~((in @ X2 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.56/1.67 inference(fool_elimination,[status(thm)],[f204])).
% 2.56/1.67 thf(f204,plain,(
% 2.56/1.67 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X2 @ (setminus @ X1 @ X0)) => (~(in @ X2 @ X0) => ~(in @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.56/1.67 inference(rectify,[status(thm)],[f126])).
% 2.56/1.67 thf(f126,negated_conjecture,(
% 2.56/1.67 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => ! [X4 : $i,X3 : $i,X1 : $i] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.56/1.67 inference(negated_conjecture,[status(cth)],[f125])).
% 2.56/1.67 thf(f125,conjecture,(
% 2.56/1.67 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => ! [X4 : $i,X3 : $i,X1 : $i] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.56/1.67 file('/export/starexec/sandbox2/tmp/tmp.glf2gEZoRt/DTF2THF_21016.p',setminusELneg)).
% 2.56/1.67 thf(f1891,plain,(
% 2.56/1.67 spl336_3),
% 2.56/1.67 inference(avatar_contradiction_clause,[status(thm)],[f1890])).
% 2.56/1.67 thf(f1890,plain,(
% 2.56/1.67 $false | spl336_3),
% 2.56/1.67 inference(trivial_inequality_removal,[status(thm)],[f1880])).
% 2.56/1.67 thf(f1880,plain,(
% 2.56/1.67 ($true != $true) | spl336_3),
% 2.56/1.67 inference(superposition,[status(thm)],[f1851,f1313])).
% 2.56/1.67 thf(f1313,plain,(
% 2.56/1.67 ((in @ sK130 @ sK129) = $true)),
% 2.56/1.67 inference(cnf_transformation,[status(thm)],[f748])).
% 2.56/1.67 thf(f1851,plain,(
% 2.56/1.67 ((in @ sK130 @ sK129) != $true) | spl336_3),
% 2.56/1.67 inference(avatar_component_clause,[status(thm)],[f1849])).
% 2.56/1.67 thf(f1849,definition,(
% 2.56/1.67 spl336_3 <=> ((in @ sK130 @ sK129) = $true)),
% 2.56/1.67 introduced(definition,[new_symbols(naming,[spl336_3])],[avatar_definition])).
% 2.56/1.67 thf(f1859,plain,(
% 2.56/1.67 spl336_4 | ~spl336_3),
% 2.56/1.67 inference(avatar_split_clause,[status(thm)],[f1858,f1849,f1853])).
% 2.56/1.67 thf(f1858,plain,(
% 2.56/1.67 ((in @ sK130 @ sK128) = $true) | ((in @ sK130 @ sK129) != $true)),
% 2.56/1.67 inference(trivial_inequality_removal,[status(thm)],[f1857])).
% 2.56/1.67 thf(f1857,plain,(
% 2.56/1.67 ((in @ sK130 @ sK128) = $true) | ($true != $true) | ((in @ sK130 @ sK129) != $true)),
% 2.56/1.67 inference(forward_demodulation,[status(thm)],[f1828,f1317])).
% 2.56/1.67 thf(f1317,plain,(
% 2.56/1.67 (setminusI = $true)),
% 2.56/1.67 inference(cnf_transformation,[status(thm)],[f748])).
% 2.56/1.67 thf(f1828,plain,(
% 2.56/1.67 ((in @ sK130 @ sK129) != $true) | (setminusI != $true) | ((in @ sK130 @ sK128) = $true)),
% 2.56/1.67 inference(trivial_inequality_removal,[status(thm)],[f1819])).
% 2.56/1.67 thf(f1819,plain,(
% 2.56/1.67 ($true != $true) | (setminusI != $true) | ((in @ sK130 @ sK129) != $true) | ((in @ sK130 @ sK128) = $true)),
% 2.56/1.67 inference(superposition,[status(thm)],[f1311,f1112])).
% 2.56/1.67 thf(f1112,plain,(
% 2.56/1.67 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | (setminusI != $true) | ((in @ X3 @ X4) != $true)) )),
% 2.56/1.67 inference(cnf_transformation,[status(thm)],[f548])).
% 2.56/1.67 thf(f548,plain,(
% 2.56/1.67 ((setminusI = $true) | (((in @ sK8 @ (setminus @ sK9 @ sK10)) != $true) & ((in @ sK8 @ sK9) = $true) & ((in @ sK8 @ sK10) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ X5) = $true)) | (setminusI != $true))),
% 2.56/1.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f546,f547])).
% 2.56/1.67 thf(f547,plain,(
% 2.56/1.67 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true)) => (((in @ sK8 @ (setminus @ sK9 @ sK10)) != $true) & ((in @ sK8 @ sK9) = $true) & ((in @ sK8 @ sK10) != $true))),
% 2.56/1.67 introduced(definition,[],[choice_axiom])).
% 2.56/1.67 thf(f546,plain,(
% 2.56/1.67 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ X5) = $true)) | (setminusI != $true))),
% 2.56/1.67 inference(rectify,[status(thm)],[f545])).
% 2.56/1.67 thf(f545,plain,(
% 2.56/1.67 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true)) | (setminusI != $true))),
% 2.56/1.67 inference(nnf_transformation,[status(thm)],[f515])).
% 2.56/1.67 thf(f515,plain,(
% 2.56/1.67 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X1) != $true) | ((in @ X0 @ X2) = $true))),
% 2.56/1.67 inference(flattening,[status(thm)],[f514])).
% 2.56/1.67 thf(f514,plain,(
% 2.56/1.67 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X2) = $true)) | ((in @ X0 @ X1) != $true)) <=> (setminusI = $true)),
% 2.56/1.67 inference(ennf_transformation,[status(thm)],[f401])).
% 2.56/1.67 thf(f401,plain,(
% 2.56/1.67 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true))) <=> (setminusI = $true)),
% 2.56/1.67 inference(flattening,[status(thm)],[f359])).
% 2.56/1.67 thf(f359,plain,(
% 2.56/1.67 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true)))),
% 2.56/1.67 inference(fool_elimination,[status(thm)],[f358])).
% 2.56/1.67 thf(f358,plain,(
% 2.56/1.67 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))))),
% 2.56/1.67 inference(rectify,[status(thm)],[f120])).
% 2.56/1.67 thf(f120,axiom,(
% 2.56/1.67 (setminusI = ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))))),
% 2.56/1.67 file('/export/starexec/sandbox2/tmp/tmp.glf2gEZoRt/DTF2THF_21016.p',setminusI)).
% 2.56/1.67 thf(f1311,plain,(
% 2.56/1.67 ((in @ sK130 @ (setminus @ sK129 @ sK128)) != $true)),
% 2.56/1.67 inference(cnf_transformation,[status(thm)],[f748])).
% 2.56/1.67 % SZS output end Proof for DTF2THF_21016
% 2.56/1.67 % (21290)------------------------------
% 2.56/1.67 % (21290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.67 % (21290)Termination reason: Refutation
% 2.56/1.67
% 2.56/1.67 % (21290)Memory used [KB]: 7419
% 2.56/1.67 % (21290)Time elapsed: 0.055 s
% 2.56/1.67 % (21290)Instructions burned: 125 (million)
% 2.56/1.67 % (21290)------------------------------
% 2.56/1.67 % (21290)------------------------------
% 2.56/1.67 % (21267)Success in time 0.135 s
%------------------------------------------------------------------------------